Program Details : University Catalogs : University of Minnesota

MATH 1371 - CSE Calculus I (MATH)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 1271/Math 1281/Math 1371/
Typically offered:	Every Fall & Spring

Differentiation of single-variable functions, basics of integration of single-variable functions. Applications: max-min, related rates, area, curve-sketching. Use of calculator, cooperative learning. prereq: CSE or pre-bioprod concurrent registration is required (or allowed) in biosys engn (PRE), background in [precalculus, geometry, visualization of functions/graphs], instr consent; familiarity with graphing calculators recommended

MATH 1271 - Calculus I (MATH)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 1271/Math 1281/Math 1371/
Typically offered:	Every Fall, Spring & Summer

Differential calculus of functions of a single variable, including polynomial, rational, exponential, and trig functions. Applications, including optimization and related rates problems. Single variable integral calculus, using anti-derivatives and simple substitution. Applications may include area, volume, work problems. prereq: 4 yrs high school math including trig or satisfactory score on placement test or grade of at least C- in [1151 or 1155]

MATH 1571H - Honors Calculus I (MATH)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 1271/Math 1281/Math 1371/
Grading Basis:	A-F only
Typically offered:	Every Fall

Differential/integral calculus of functions of a single variable. Emphasizes hard problem-solving rather than theory. prereq: Honors student and permission of University Honors Program

MATH 1372 - CSE Calculus II

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 1272/Math 1282/Math 1372/
Typically offered:	Every Spring

Techniques of integration. Calculus involving transcendental functions, polar coordinates, Taylor polynomials, vectors/curves in space, cylindrical/spherical coordinates. Use of calculators, cooperative learning. prereq: Grade of at least C- in [1371 or equiv], CSE or pre-Bioprod/Biosys Engr

MATH 1272 - Calculus II

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 1272/Math 1282/Math 1372/
Typically offered:	Every Fall, Spring & Summer

Techniques of integration. Calculus involving transcendental functions, polar coordinates. Taylor polynomials, vectors/curves in space, cylindrical/spherical coordinates. prereq: [1271 or equiv] with grade of at least C-

MATH 1572H - Honors Calculus II

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 1272/Math 1282/Math 1372/
Grading Basis:	A-F only
Typically offered:	Every Fall & Spring

Continuation of 1571. Infinite series, differential calculus of several variables, introduction to linear algebra. prereq: 1571H (or equivalent) honors student

MATH 2243 - Linear Algebra and Differential Equations

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2243/Math 2373/Math 2574H
Typically offered:	Every Fall, Spring & Summer

Linear algebra: basis, dimension, matrices, eigenvalues/eigenvectors. Differential equations: first-order linear, separable; second-order linear with constant coefficients; linear systems with constant coefficients. prereq: [1272 or 1282 or 1372 or 1572] w/grade of at least C-

MATH 2373 - CSE Linear Algebra and Differential Equations

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2243/Math 2373/Math 2574H
Typically offered:	Every Fall & Spring

Linear algebra: basis, dimension, eigenvalues/eigenvectors. Differential equations: linear equations/systems, phase space, forcing/resonance, qualitative/numerical analysis of nonlinear systems, Laplace transforms. Use of computer technology. prereq: [1272 or 1282 or 1372 or 1572] w/grade of at least C-, CSE or pre-Bio Prod/Biosys Engr

MATH 2574H - Honors Calculus IV

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2243/Math 2373/Math 2574H
Grading Basis:	A-F only
Typically offered:	Every Spring

Advanced linear algebra, differential equations. Additional topics as time permits. prereq: Math 1572H or Math 2573H, honors student and permission of University Honors Program

MATH 3592H - Honors Mathematics I

Credits:	5.0 [max 5.0]
Grading Basis:	A-F only
Typically offered:	Every Fall

First semester of two-semester sequence. Focuses on multivariable calculus at deeper level than regular calculus offerings. Rigorous introduction to sequences/series. Theoretical treatment of multivariable calculus. Strong introduction to linear algebra.

MATH 2263 - Multivariable Calculus

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2263/Math 2374/Math 2573H
Typically offered:	Every Fall, Spring & Summer

Derivative as linear map. Differential/integral calculus of functions of several variables, including change of coordinates using Jacobians. Line/surface integrals. Gauss, Green, Stokes Theorems. prereq: [1272 or 1372 or 1572] w/grade of at least C-

MATH 2374 - CSE Multivariable Calculus and Vector Analysis

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2263/Math 2374/Math 2573H
Typically offered:	Every Fall & Spring

Derivative as linear map. Differential/integral calculus of functions of several variables, including change of coordinates using Jacobians. Line/surface integrals. Gauss, Green, Stokes theorems. Use of computer technology. prereq: [1272 or 1282 or 1372 or 1572] w/grade of at least C-, CSE or pre-Bioprod/Biosys Engr

MATH 2573H - Honors Calculus III

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2263/Math 2374/Math 2573H
Grading Basis:	A-F only
Typically offered:	Every Fall

Integral calculus of several variables. Vector analysis, including theorems of Gauss, Green, Stokes. prereq: Math 1572H (or equivalent), honors student

MATH 3593H - Honors Mathematics II

Credits:	5.0 [max 5.0]
Grading Basis:	A-F or Aud
Typically offered:	Every Spring

Second semester of three-semester sequence. Focuses on multivariable calculus at deeper level than regular calculus offerings. Rigorous introduction to sequences/series. Theoretical treatment of multivariable calculus. Strong introduction to linear algebra. prereq: 3592H or instr consent

PHYS 1301W - Introductory Physics for Science and Engineering I (PHYS, WI)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Phys 1201W/1301W/1401V/1501V
Typically offered:	Every Fall, Spring & Summer

Use of fundamental principles to solve quantitative problems. Motion, forces, conservation principles, structure of matter. Applications to mechanical systems. Prereq or Concurrent: MATH 1271/1371/1371H or equivalent

PHYS 1401V - Honors Physics I (PHYS, WI)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Phys 1201W/1301W/1401V/1501V
Grading Basis:	A-F only
Typically offered:	Every Fall

Comprehensive, calculus-level general physics. Emphasizes use of fundamental principles to solve quantitative problems. Description of motion, forces, conservation principles. Structure of matter, with applications to mechanical systems. Prereq: Honors program or with permission, Prereq or Concurrent: MATH 1271/1371/1571H or equivalent

PHYS 1302W - Introductory Physics for Science and Engineering II (PHYS, WI)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Phys 1202W/1302W/1402V/1502V
Typically offered:	Every Fall & Spring

Use of fundamental principles to solve quantitative problems. Motion, forces, conservation principles, fields, structure of matter. Applications to electromagnetic phenomena. Prereq: PHYS 1301 or equivalent, Prereq or Concurrent: MATH 1272/1372/1572H or equivalent

PHYS 1402V - Honors Physics II (PHYS, WI)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Phys 1202W/1302W/1402V/1502V
Grading Basis:	A-F only
Typically offered:	Every Spring

Fundamental principles to solve quantitative problems. Description of motion, forces, conservation principles, fields. Structure of matter, with applications to electro-magnetic phenomena. Honors program or with permission, PHYS 1401V or equivalent, Prereq or CC: MATH 1272/1372/1572H or equivalent

MATH 2243 - Linear Algebra and Differential Equations

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2243/Math 2373/Math 2574H
Typically offered:	Every Fall, Spring & Summer

Linear algebra: basis, dimension, matrices, eigenvalues/eigenvectors. Differential equations: first-order linear, separable; second-order linear with constant coefficients; linear systems with constant coefficients. prereq: [1272 or 1282 or 1372 or 1572] w/grade of at least C-

MATH 2373 - CSE Linear Algebra and Differential Equations

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2243/Math 2373/Math 2574H
Typically offered:	Every Fall & Spring

Linear algebra: basis, dimension, eigenvalues/eigenvectors. Differential equations: linear equations/systems, phase space, forcing/resonance, qualitative/numerical analysis of nonlinear systems, Laplace transforms. Use of computer technology. prereq: [1272 or 1282 or 1372 or 1572] w/grade of at least C-, CSE or pre-Bio Prod/Biosys Engr

MATH 2574H - Honors Calculus IV

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2243/Math 2373/Math 2574H
Grading Basis:	A-F only
Typically offered:	Every Spring

Advanced linear algebra, differential equations. Additional topics as time permits. prereq: Math 1572H or Math 2573H, honors student and permission of University Honors Program

MATH 3592H - Honors Mathematics I

Credits:	5.0 [max 5.0]
Grading Basis:	A-F only
Typically offered:	Every Fall

First semester of two-semester sequence. Focuses on multivariable calculus at deeper level than regular calculus offerings. Rigorous introduction to sequences/series. Theoretical treatment of multivariable calculus. Strong introduction to linear algebra.

MATH 2263 - Multivariable Calculus

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2263/Math 2374/Math 2573H
Typically offered:	Every Fall, Spring & Summer

Derivative as linear map. Differential/integral calculus of functions of several variables, including change of coordinates using Jacobians. Line/surface integrals. Gauss, Green, Stokes Theorems. prereq: [1272 or 1372 or 1572] w/grade of at least C-

MATH 2374 - CSE Multivariable Calculus and Vector Analysis

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2263/Math 2374/Math 2573H
Typically offered:	Every Fall & Spring

Derivative as linear map. Differential/integral calculus of functions of several variables, including change of coordinates using Jacobians. Line/surface integrals. Gauss, Green, Stokes theorems. Use of computer technology. prereq: [1272 or 1282 or 1372 or 1572] w/grade of at least C-, CSE or pre-Bioprod/Biosys Engr

MATH 2573H - Honors Calculus III

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2263/Math 2374/Math 2573H
Grading Basis:	A-F only
Typically offered:	Every Fall

Integral calculus of several variables. Vector analysis, including theorems of Gauss, Green, Stokes. prereq: Math 1572H (or equivalent), honors student

MATH 3593H - Honors Mathematics II

Credits:	5.0 [max 5.0]
Grading Basis:	A-F or Aud
Typically offered:	Every Spring

Second semester of three-semester sequence. Focuses on multivariable calculus at deeper level than regular calculus offerings. Rigorous introduction to sequences/series. Theoretical treatment of multivariable calculus. Strong introduction to linear algebra. prereq: 3592H or instr consent

MATH 3283W - Sequences, Series, and Foundations: Writing Intensive (WI)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2283/3283W
Typically offered:	Every Fall & Spring

Introduction to reasoning used in advanced mathematics courses. Logic, mathematical induction, real number system, general/monotone/recursively defined sequences, convergence of infinite series/sequences, Taylor's series, power series with applications to differential equations, Newton's method. Writing-intensive component. prereq: [concurrent registration is required (or allowed) in 2243 or concurrent registration is required (or allowed) in 2263 or concurrent registration is required (or allowed) in 2373 or concurrent registration is required (or allowed) in 2374] w/grade of at least C-

MATH 3283W - Sequences, Series, and Foundations: Writing Intensive (WI)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 2283/3283W
Typically offered:	Every Fall & Spring

Introduction to reasoning used in advanced mathematics courses. Logic, mathematical induction, real number system, general/monotone/recursively defined sequences, convergence of infinite series/sequences, Taylor's series, power series with applications to differential equations, Newton's method. Writing-intensive component. prereq: [concurrent registration is required (or allowed) in 2243 or concurrent registration is required (or allowed) in 2263 or concurrent registration is required (or allowed) in 2373 or concurrent registration is required (or allowed) in 2374] w/grade of at least C-

MATH 4067W - Actuarial Mathematics in Practice (WI)

Credits:	3.0 [max 3.0]
Grading Basis:	A-F only
Typically offered:	Every Spring

Real world actuarial problems that require integration of mathematical skills with knowledge from other disciplines such as economics, statistics, and finance. Communication and interpersonal skills are enhanced by teamwork/presentations to the practitioner actuaries who co-instruct. prereq: 4065, ACCT 2050, ECON 1101, ECON 1102

MATH 4997W - Senior project (Writing Intensive) (WI)

Credits:	1.0 [max 2.0]
Prerequisites:	2 sem upper div math, %
Grading Basis:	A-F or Aud
Typically offered:	Every Fall, Spring & Summer

Directed study. A 10-15 page paper on a specialized area, including some math that is new to student. At least two drafts of paper given to instructor for feedback before final version. Student keeps journal of preliminary work on project. Scope/topic vary with instructor. prereq: 2 sem upper div math, dept consent

MATH 4281 - Introduction to Modern Algebra

Credits:	4.0 [max 4.0]
Typically offered:	Periodic Fall

Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent

MATH 5248 - Cryptology and Number Theory

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math

MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math

MATH 5285H - Honors: Fundamental Structures of Algebra I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 5286H - Honors: Fundamental Structures of Algebra II

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285

MATH 5385 - Introduction to Computational Algebraic Geometry

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]

MATH 4242 - Applied Linear Algebra

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4242/Math 4457
Typically offered:	Every Fall, Spring & Summer

Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. prereq: 2243 or 2373 or 2573

MATH 5165 - Mathematical Logic I

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4152/5165
Typically offered:	Every Fall

Theory of computability: notion of algorithm, Turing machines, primitive recursive functions, recursive functions, Kleene normal form, recursion theorem. Propositional logic. prereq: 2283 or 3283 or Phil 5201 or CSci course in theory of algorithms or instr consent

MATH 5335 - Geometry I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Advanced two-dimensional Euclidean geometry from a vector viewpoint. Theorems/problems about triangles/circles, isometries, connections with Euclid's axioms. Hyperbolic geometry, how it compares with Euclidean geometry. prereq: [2243 or 2373 or 2573], [concurrent registration is required (or allowed) in 2263 or concurrent registration is required (or allowed) in 2374 or concurrent registration is required (or allowed) in 2574]

MATH 5345H - Honors: Introduction to Topology

Credits:	4.0 [max 4.0]
Grading Basis:	A-F only
Typically offered:	Every Fall

Rigorous introduction to general topology. Set theory, Euclidean/metric spaces, compactness/connectedness. May include Urysohn metrization, Tychonoff theorem or fundamental group/covering spaces. prereq: [2263 or 2374 or 2573], [concurrent registration is required (or allowed) in 2283 or concurrent registration is required (or allowed) in 2574 or concurrent registration is required (or allowed) in 3283]

MATH 5485 - Introduction to Numerical Methods I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Solution of nonlinear equations in one variable. Interpolation, polynomial approximation. Methods for solving linear systems, eigenvalue problems, systems of nonlinear equations. prereq: [2243 or 2373 or 2573], familiarity with some programming language

MATH 5705 - Enumerative Combinatorics

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Basic enumeration, bijections, inclusion-exclusion, recurrence relations, ordinary/exponential generating functions, partitions, Polya theory. Optional topics include trees, asymptotics, listing algorithms, rook theory, involutions, tableaux, permutation statistics. prereq: [2243 or 2373 or 2573], [2263 or 2283 or 2374 or 2574 or 3283]

MATH 5707 - Graph Theory and Non-enumerative Combinatorics

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Basic topics in graph theory: connectedness, Eulerian/Hamiltonian properties, trees, colorings, planar graphs, matchings, flows in networks. Optional topics include graph algorithms, Latin squares, block designs, Ramsey theory. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]; [2283 or 3283 or experience in writing proofs] highly recommended; Credit will not be granted if credit has been received for: 4707

MATH 5711 - Linear Programming and Combinatorial Optimization

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Simplex method, connections to geometry, duality theory, sensitivity analysis. Applications to cutting stock, allocation of resources, scheduling problems. Flows, matching/transportation problems, spanning trees, distance in graphs, integer programs, branch/bound, cutting planes, heuristics. Applications to traveling salesman, knapsack problems. prereq: 2 sems soph math [including 2243 or 2373 or 2573]

MATH 4567 - Applied Fourier Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Fourier series, integral/transform. Convergence. Fourier series, transform in complex form. Solution of wave, heat, Laplace equations by separation of variables. Sturm-Liouville systems, finite Fourier, fast Fourier transform. Applications. Other topics as time permits. prereq: 2243 or 2373 or 2573

MATH 4603 - Advanced Calculus I

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4606/Math 5615/Math 5616
Typically offered:	Every Fall, Spring & Summer

Axioms for the real numbers. Techniques of proof for limits, continuity, uniform convergence. Rigorous treatment of differential/integral calculus for single-variable functions. prereq: [[2243 or 2373], [2263 or 2374]] or 2574 or instr consent

MATH 4604 - Advanced Calculus II

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4604/Math 5616
Typically offered:	Every Spring

Sequel to MATH 4603. Topology of n-dimensional Euclidean space. Rigorous treatment of multivariable differentiation and integration, including chain rule, Taylor's Theorem, implicit function theorem, Fubini's Theorem, change of variables, Stokes' Theorem. prereq: 4603 or 5615 or instr consent

MATH 5378 - Differential Geometry

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Basic geometry of curves in plane and in space, including Frenet formula, theory of surfaces, differential forms, Riemannian geometry. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]; [2283 or 3283] recommended]

MATH 5445 - Mathematical Analysis of Biological Networks

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Development/analysis of models for complex biological networks. Examples taken from signal transduction networks, metabolic networks, gene control networks, and ecological networks. prereq: Linear algebra, differential equations

MATH 5447 - Theoretical Neuroscience

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Nonlinear dynamical system models of neurons and neuronal networks. Computation by excitatory/inhibitory networks. Neural oscillations, adaptation, bursting, synchrony. Memory systems. prereq: 2243 or 2373 or 2574

MATH 5467 - Introduction to the Mathematics of Image and Data Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Background theory/experience in wavelets. Inner product spaces, operator theory, Fourier transforms applied to Gabor transforms, multi-scale analysis, discrete wavelets, self-similarity. Computing techniques. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283 or instr consent]; [[2263 or 2374], 4567] recommended

MATH 5486 - Introduction To Numerical Methods II

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Numerical integration/differentiation. Numerical solution of initial-value problems, boundary value problems for ordinary differential equations, partial differential equations. prereq: 5485

MATH 5525 - Introduction to Ordinary Differential Equations

Credits:	4.0 [max 4.0]
Typically offered:	Periodic Fall & Spring

Ordinary differential equations, solution of linear systems, qualitative/numerical methods for nonlinear systems. Linear algebra background, fundamental matrix solutions, variation of parameters, existence/uniqueness theorems, phase space. Rest points, their stability. Periodic orbits, Poincare-Bendixson theory, strange attractors. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 5535 - Dynamical Systems and Chaos

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]

MATH 5583 - Complex Analysis

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 3574/Math 5583
Typically offered:	Every Fall, Spring & Summer

Algebra, geometry of complex numbers. Linear fractional transformations. Conformal mappings. Holomorphic functions. Theorems of Abel/Cauchy, power series. Schwarz' lemma. Complex exponential, trig functions. Entire functions, theorems of Liouville/Morera. Reflection principle. Singularities, Laurent series. Residues. prereq: 2 sems soph math [including [2263 or 2374 or 2573], [2283 or 3283]] recommended

MATH 5587 - Elementary Partial Differential Equations I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Emphasizes partial differential equations w/physical applications, including heat, wave, Laplace's equations. Interpretations of boundary conditions. Characteristics, Fourier series, transforms, Green's functions, images, computational methods. Applications include wave propagation, diffusions, electrostatics, shocks. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]

MATH 5588 - Elementary Partial Differential Equations II

Credits:	4.0 [max 4.0]
Grading Basis:	A-F or Aud
Typically offered:	Every Spring

Heat, wave, Laplace's equations in higher dimensions. Green's functions, Fourier series, transforms. Asymptotic methods, boundary layer theory, bifurcation theory for linear/nonlinear PDEs. Variational methods. Free boundary problems. Additional topics as time permits. prereq: [[2243 or 2373 or 2573], [2263 or 2374 or 2574], 5587] or instr consent

MATH 5615H - Honors: Introduction to Analysis I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Axiomatic treatment of real/complex number systems. Introduction to metric spaces: convergence, connectedness, compactness. Convergence of sequences/series of real/complex numbers, Cauchy criterion, root/ratio tests. Continuity in metric spaces. Rigorous treatment of differentiation of single-variable functions, Taylor's Theorem. prereq: [[2243 or 2373], [2263 or 2374], [2283 or 3283]] or 2574

MATH 5616H - Honors: Introduction to Analysis II

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Rigorous treatment of Riemann-Stieltjes integration. Sequences/series of functions, uniform convergence, equicontinuous families, Stone-Weierstrass Theorem, power series. Rigorous treatment of differentiation/integration of multivariable functions, Implicit Function Theorem, Stokes' Theorem. Additional topics as time permits. prereq: 5615

MATH 5651 - Basic Theory of Probability and Statistics

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 5651/Stat 5101
Typically offered:	Every Fall & Spring

Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.

MATH 5652 - Introduction to Stochastic Processes

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Random walks, Markov chains, branching processes, martingales, queuing theory, Brownian motion. prereq: 5651 or Stat 5101

MATH 5654 - Prediction and Filtering

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Markov chains, Wiener process, stationary sequences, Ornstein-Uhlenbeck process. Partially observable Markov processes (hidden Markov models), stationary processes. Equations for general filters, Kalman filter. Prediction of future values of partially observable processes. prereq: 5651 or Stat 5101

STAT 5101 - Theory of Statistics I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: (MATH 2263 or MATH 2374 or MATH 2573H), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)

MATH 4065 - Theory of Interest

Credits:	4.0 [max 4.0]
Grading Basis:	A-F only
Typically offered:	Every Fall & Spring

Time value of money, compound interest and general annuities, loans, bonds, general cash flows, basic financial derivatives and their valuation. Primarily for students who are interested in actuarial mathematics. prereq: 1272 or 1372 or 1572

MATH 4152 - Elementary Mathematical Logic

Credits:	3.0 [max 3.0]
Course Equivalencies:	Math 4152/5165
Typically offered:	Every Spring

Propositional logic. Predicate logic: notion of a first order language, a deductive system for first order logic, first order structures, Godel's completeness theorem, axiom systems, models of formal theories. prereq: one soph math course or instr consent

MATH 4242 - Applied Linear Algebra

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4242/Math 4457
Typically offered:	Every Fall, Spring & Summer

Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. prereq: 2243 or 2373 or 2573

MATH 4281 - Introduction to Modern Algebra

Credits:	4.0 [max 4.0]
Typically offered:	Periodic Fall

Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent

MATH 4428 - Mathematical Modeling

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Modeling techniques for analysis/decision-making in industry. Optimization (sensitivity analysis, Lagrange multipliers, linear programming). Dynamical modeling (steady-states, stability analysis, eigenvalue methods, phase portraits, simulation). Probabilistic methods (probability/statistical models, Markov chains, linear regression, simulation). prereq: 2243 or 2373 or 2573

MATH 4512 - Differential Equations with Applications

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall & Spring

Laplace transforms, series solutions, systems, numerical methods, plane autonomous systems, stability. prereq: 2243 or 2373 or 2573

MATH 4567 - Applied Fourier Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Fourier series, integral/transform. Convergence. Fourier series, transform in complex form. Solution of wave, heat, Laplace equations by separation of variables. Sturm-Liouville systems, finite Fourier, fast Fourier transform. Applications. Other topics as time permits. prereq: 2243 or 2373 or 2573

MATH 4603 - Advanced Calculus I

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4606/Math 5615/Math 5616
Typically offered:	Every Fall, Spring & Summer

Axioms for the real numbers. Techniques of proof for limits, continuity, uniform convergence. Rigorous treatment of differential/integral calculus for single-variable functions. prereq: [[2243 or 2373], [2263 or 2374]] or 2574 or instr consent

MATH 4604 - Advanced Calculus II

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4604/Math 5616
Typically offered:	Every Spring

Sequel to MATH 4603. Topology of n-dimensional Euclidean space. Rigorous treatment of multivariable differentiation and integration, including chain rule, Taylor's Theorem, implicit function theorem, Fubini's Theorem, change of variables, Stokes' Theorem. prereq: 4603 or 5615 or instr consent

MATH 4653 - Elementary Probability

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Probability spaces, distributions of discrete/continuous random variables, conditioning. Basic theorems, calculational methodology. Examples of random sequences. Emphasizes problem-solving. prereq: [2263 or 2374 or 2573]; [2283 or 2574 or 3283] recommended

MATH 4707 - Introduction to Combinatorics and Graph Theory

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Existence, enumeration, construction, algorithms, optimization. Pigeonhole principle, bijective combinatorics, inclusion-exclusion, recursions, graph modeling, isomorphism. Degree sequences and edge counting. Connectivity, Eulerian graphs, trees, Euler's formula, network flows, matching theory. Mathematical induction as proof technique. prereq: 2243, [2283 or 3283]

MATH 5067 - Actuarial Mathematics I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Future lifetime random variable, survival function. Insurance, life annuity, future loss random variables. Net single premium, actuarial present value, net premium, net reserves. prereq: 4065, [one sem [4xxx or 5xxx] [probability or statistics] course]

MATH 5068 - Actuarial Mathematics II

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Multiple decrement insurance, pension valuation. Expense analysis, gross premium, reserves. Problem of withdrawals. Regulatory reserving systems. Minimum cash values. Additional topics at instructor's discretion. prereq: 5067

MATH 5075 - Mathematics of Options, Futures, and Derivative Securities I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Mathematical background (e.g., partial differential equations, Fourier series, computational methods, Black-Scholes theory, numerical methods--including Monte Carlo simulation). Interest-rate derivative securities, exotic options, risk theory. First course of two-course sequence. prereq: Two yrs calculus, basic computer skills

MATH 5076 - Mathematics of Options, Futures, and Derivative Securities II

Credits:	4.0 [max 4.0]
Grading Basis:	A-F or Aud
Typically offered:	Every Spring

Mathematical background such as partial differential equations, Fourier series, computational methods, Black-Scholes theory, numerical methods (including Monte Carlo simulation), interest-rate derivative securities, exotic options, risk theory. prereq: 5075

MATH 5165 - Mathematical Logic I

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4152/5165
Typically offered:	Every Fall

Theory of computability: notion of algorithm, Turing machines, primitive recursive functions, recursive functions, Kleene normal form, recursion theorem. Propositional logic. prereq: 2283 or 3283 or Phil 5201 or CSci course in theory of algorithms or instr consent

MATH 5248 - Cryptology and Number Theory

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math

MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math

MATH 5285H - Honors: Fundamental Structures of Algebra I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 5286H - Honors: Fundamental Structures of Algebra II

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285

MATH 5335 - Geometry I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Advanced two-dimensional Euclidean geometry from a vector viewpoint. Theorems/problems about triangles/circles, isometries, connections with Euclid's axioms. Hyperbolic geometry, how it compares with Euclidean geometry. prereq: [2243 or 2373 or 2573], [concurrent registration is required (or allowed) in 2263 or concurrent registration is required (or allowed) in 2374 or concurrent registration is required (or allowed) in 2574]

MATH 5345H - Honors: Introduction to Topology

Credits:	4.0 [max 4.0]
Grading Basis:	A-F only
Typically offered:	Every Fall

Rigorous introduction to general topology. Set theory, Euclidean/metric spaces, compactness/connectedness. May include Urysohn metrization, Tychonoff theorem or fundamental group/covering spaces. prereq: [2263 or 2374 or 2573], [concurrent registration is required (or allowed) in 2283 or concurrent registration is required (or allowed) in 2574 or concurrent registration is required (or allowed) in 3283]

MATH 5378 - Differential Geometry

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Basic geometry of curves in plane and in space, including Frenet formula, theory of surfaces, differential forms, Riemannian geometry. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]; [2283 or 3283] recommended]

MATH 5385 - Introduction to Computational Algebraic Geometry

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]

MATH 5445 - Mathematical Analysis of Biological Networks

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Development/analysis of models for complex biological networks. Examples taken from signal transduction networks, metabolic networks, gene control networks, and ecological networks. prereq: Linear algebra, differential equations

MATH 5447 - Theoretical Neuroscience

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Nonlinear dynamical system models of neurons and neuronal networks. Computation by excitatory/inhibitory networks. Neural oscillations, adaptation, bursting, synchrony. Memory systems. prereq: 2243 or 2373 or 2574

MATH 5467 - Introduction to the Mathematics of Image and Data Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Background theory/experience in wavelets. Inner product spaces, operator theory, Fourier transforms applied to Gabor transforms, multi-scale analysis, discrete wavelets, self-similarity. Computing techniques. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283 or instr consent]; [[2263 or 2374], 4567] recommended

MATH 5485 - Introduction to Numerical Methods I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Solution of nonlinear equations in one variable. Interpolation, polynomial approximation. Methods for solving linear systems, eigenvalue problems, systems of nonlinear equations. prereq: [2243 or 2373 or 2573], familiarity with some programming language

MATH 5486 - Introduction To Numerical Methods II

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Numerical integration/differentiation. Numerical solution of initial-value problems, boundary value problems for ordinary differential equations, partial differential equations. prereq: 5485

MATH 5525 - Introduction to Ordinary Differential Equations

Credits:	4.0 [max 4.0]
Typically offered:	Periodic Fall & Spring

Ordinary differential equations, solution of linear systems, qualitative/numerical methods for nonlinear systems. Linear algebra background, fundamental matrix solutions, variation of parameters, existence/uniqueness theorems, phase space. Rest points, their stability. Periodic orbits, Poincare-Bendixson theory, strange attractors. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 5535 - Dynamical Systems and Chaos

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]

MATH 5583 - Complex Analysis

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 3574/Math 5583
Typically offered:	Every Fall, Spring & Summer

Algebra, geometry of complex numbers. Linear fractional transformations. Conformal mappings. Holomorphic functions. Theorems of Abel/Cauchy, power series. Schwarz' lemma. Complex exponential, trig functions. Entire functions, theorems of Liouville/Morera. Reflection principle. Singularities, Laurent series. Residues. prereq: 2 sems soph math [including [2263 or 2374 or 2573], [2283 or 3283]] recommended

MATH 5587 - Elementary Partial Differential Equations I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Emphasizes partial differential equations w/physical applications, including heat, wave, Laplace's equations. Interpretations of boundary conditions. Characteristics, Fourier series, transforms, Green's functions, images, computational methods. Applications include wave propagation, diffusions, electrostatics, shocks. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]

MATH 5588 - Elementary Partial Differential Equations II

Credits:	4.0 [max 4.0]
Grading Basis:	A-F or Aud
Typically offered:	Every Spring

Heat, wave, Laplace's equations in higher dimensions. Green's functions, Fourier series, transforms. Asymptotic methods, boundary layer theory, bifurcation theory for linear/nonlinear PDEs. Variational methods. Free boundary problems. Additional topics as time permits. prereq: [[2243 or 2373 or 2573], [2263 or 2374 or 2574], 5587] or instr consent

MATH 5615H - Honors: Introduction to Analysis I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Axiomatic treatment of real/complex number systems. Introduction to metric spaces: convergence, connectedness, compactness. Convergence of sequences/series of real/complex numbers, Cauchy criterion, root/ratio tests. Continuity in metric spaces. Rigorous treatment of differentiation of single-variable functions, Taylor's Theorem. prereq: [[2243 or 2373], [2263 or 2374], [2283 or 3283]] or 2574

MATH 5616H - Honors: Introduction to Analysis II

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Rigorous treatment of Riemann-Stieltjes integration. Sequences/series of functions, uniform convergence, equicontinuous families, Stone-Weierstrass Theorem, power series. Rigorous treatment of differentiation/integration of multivariable functions, Implicit Function Theorem, Stokes' Theorem. Additional topics as time permits. prereq: 5615

MATH 5651 - Basic Theory of Probability and Statistics

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 5651/Stat 5101
Typically offered:	Every Fall & Spring

Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.

MATH 5652 - Introduction to Stochastic Processes

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Random walks, Markov chains, branching processes, martingales, queuing theory, Brownian motion. prereq: 5651 or Stat 5101

MATH 5654 - Prediction and Filtering

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Markov chains, Wiener process, stationary sequences, Ornstein-Uhlenbeck process. Partially observable Markov processes (hidden Markov models), stationary processes. Equations for general filters, Kalman filter. Prediction of future values of partially observable processes. prereq: 5651 or Stat 5101

MATH 5705 - Enumerative Combinatorics

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Basic enumeration, bijections, inclusion-exclusion, recurrence relations, ordinary/exponential generating functions, partitions, Polya theory. Optional topics include trees, asymptotics, listing algorithms, rook theory, involutions, tableaux, permutation statistics. prereq: [2243 or 2373 or 2573], [2263 or 2283 or 2374 or 2574 or 3283]

MATH 5707 - Graph Theory and Non-enumerative Combinatorics

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Basic topics in graph theory: connectedness, Eulerian/Hamiltonian properties, trees, colorings, planar graphs, matchings, flows in networks. Optional topics include graph algorithms, Latin squares, block designs, Ramsey theory. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]; [2283 or 3283 or experience in writing proofs] highly recommended; Credit will not be granted if credit has been received for: 4707

MATH 5711 - Linear Programming and Combinatorial Optimization

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Simplex method, connections to geometry, duality theory, sensitivity analysis. Applications to cutting stock, allocation of resources, scheduling problems. Flows, matching/transportation problems, spanning trees, distance in graphs, integer programs, branch/bound, cutting planes, heuristics. Applications to traveling salesman, knapsack problems. prereq: 2 sems soph math [including 2243 or 2373 or 2573]

STAT 5101 - Theory of Statistics I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: (MATH 2263 or MATH 2374 or MATH 2573H), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)

STAT 5102 - Theory of Statistics II

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Sampling, sufficiency, estimation, test of hypotheses, size/power. Categorical data. Contingency tables. Linear models. Decision theory. prereq: [5101 or Math 5651 or instr consent]

CSCI 1103 - Introduction to Computer Programming in Java

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Fundamental programming concepts/software development using Java language. Problem solving skills. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Substantial programming projects. Weekly lab.

CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall, Spring & Summer

Programming for scientists/engineers. C/C++ programming constructs, object-oriented programming, software development, fundamental numerical techniques. Exercises/examples from various scientific fields. The online modality for CSci 1113 will only be offered during the summer session. prereq: Math 1271 or Math 1371 or Math 1571H or instr consent.

CSCI 1133 - Introduction to Computing and Programming Concepts

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 1133/CSci 1133H
Typically offered:	Every Fall, Spring & Summer

Fundamental programming concepts using Python language. Problem solving skills, recursion, object-oriented programming. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Develop programs to solve real-world problems. prereq: concurrent registration is required (or allowed) in MATH 1271 or concurrent registration is required (or allowed) in MATH 1371 or concurrent registration is required (or allowed) in MATH 1571H or instr consent

PHYS 2303 - Physics III: Physics of Matter

Credits:	4.0 [max 4.0]
Course Equivalencies:	Phys 2303/2403H/2503/2503H
Typically offered:	Every Spring

Thermodynamics, mechanical/electromagnetic waves, optics, quantum theory. Applications of quantum nature of solids. prereq: 1302, [MATH 1272 or MATH 1372 or MATH 1572H], [MatSci or EE] student

PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity

Credits:	4.0 [max 4.0]
Course Equivalencies:	Phys 2303/2403H/2503/2503H
Typically offered:	Every Fall

Third semester of introductory physics. Mechanical/electromagnetic waves, optics, special relativity. prereq: 1302W or equivalent

CHEM 4501 - Introduction to Thermodynamics, Kinetics, and Statistical Mechanics

Credits:	3.0 [max 3.0]
Course Equivalencies:	Chem 3501/4501
Grading Basis:	A-F or Aud
Typically offered:	Every Fall & Spring

Physical chemistry as it relates to macroscopic descriptions of chemical systems. Chemical thermodynamics, phase equilibria, chemical equilibria. Statistical mechanics. Phenomenological reaction kinetics. Kinetic theory of gases. Collision, statistical theories of reaction rates. prereq: [1062/1066 or 1071H/1075H], [MATH 2263 or concurrent registration is required (or allowed) in MATH 2263 or MATH 2374 or concurrent registration is required (or allowed) in MATH 2374], [PHYS 1302 or PHYS 1402V or PHYS 1502V]

CHEM 4502 - Introduction to Quantum Mechanics and Spectroscopy

Credits:	3.0 [max 3.0]
Course Equivalencies:	Chem 3502/4502
Grading Basis:	A-F or Aud
Typically offered:	Every Fall & Spring

Microscopic descriptions of chemical systems. Quantum theory. Applications to atomic/molecular structure. Molecular spectroscopy. Quantum statistical mechanics. Discussion of solutions to several differential equations. prereq: [1062/1066 or 1072H/1076H of 1082/1086], [MATH 2263 or concurrent registration is required (or allowed) in MATH 2263 or MATH 2374 or concurrent registration is required (or allowed) in MATH 2374 or MATH 2243 or concurrent registration is required (or allowed) in MATH 2243 or MATH 2373 or concurrent registration is required (or allowed) in MATH 2373], [PHYS 1302 or PHYS 1402V or PHYS 1502V]

CHEN 3101 - Chemical Engineering Thermodynamics

Credits:	4.0 [max 4.0]
Grading Basis:	A-F only
Typically offered:	Every Spring

Applications of thermodynamics/chemical equilibrium to problems in chemical engineering. prereq: ChEn 2001, Chem 1062/1066 Math 2374 or equivalent, & Math 2373 or equivalent

CHEN 3102 - Reaction Kinetics and Reactor Engineering

Credits:	4.0 [max 4.0]
Grading Basis:	A-F only
Typically offered:	Every Fall

Chemical equilibrium/chemical kinetics applied to chemical engineering systems. Behavior/design of chemical reactors, interaction between chemical/physical rate processes. Mathematical modeling, design of reactors. prereq: [2001 or 4001], [3101 or 4101], [upper div ChEn major or dept consent], C- or better in all pre-reqs

CSCI 4011 - Formal Languages and Automata Theory

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Logical/mathematical foundations of computer science. Formal languages, their correspondence to machine models. Lexical analysis, string matching, parsing. Decidability, undecidability, limits of computability. Computational complexity. prereq: 2041 or instr consent

CSCI 4041 - Algorithms and Data Structures

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 4041/CSci 4041H
Typically offered:	Every Fall & Spring

Rigorous analysis of algorithms/implementation. Algorithm analysis, sorting algorithms, binary trees, heaps, priority queues, heapsort, balanced binary search trees, AVL trees, hash tables and hashing, graphs, graph traversal, single source shortest path, minimum cost spanning trees. prereq: [(1913 or 1933) and 2011] or instr consent; cannot be taken for grad CSci cr

CSCI 4061 - Introduction to Operating Systems

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 4061/INet 4001
Typically offered:	Every Fall & Spring

Processes/threads, process coordination, interprocess communication, asynchronous events, memory management/file systems. Systems programming projects using operating system interfaces and program development tools. prereq: 2021 or EE 2361; CS upper div, CompE upper div., EE upper div., EE grad, ITI upper div., Univ. honors student, or dept. permission; no cr for grads in CSci.

CSCI 4611 - Programming Interactive Computer Graphics and Games

Credits:	3.0 [max 3.0]
Typically offered:	Every Spring

Tools/techniques for programming games/interactive computer graphics. Event loops, rendering/animation, polygonal models, texturing, physical simulation. Modern graphics toolkits. History/future of computer games technology. Social impact of interactive computer graphics. prereq: 2021 or instr consent

CSCI 5106 - Programming Languages

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall

Design and implementation of high-level languages. Course has two parts: (1) language design principles, concepts, constructs; (2) language paradigms, applications. Note: course does not teach how to program in specific languages. prereq: 4011 or instr consent

CSCI 5304 - Computational Aspects of Matrix Theory

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall

Perturbation theory for linear systems and eigenvalue problems. Direct/iterative solution of large linear systems. Matrix factorizations. Computation of eigenvalues/eigenvectors. Singular value decomposition. LAPACK/other software packages. Introduction to sparse matrix methods. prereq: 2031 or 2033 or instr consent

CSCI 5421 - Advanced Algorithms and Data Structures

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall & Spring

Fundamental paradigms of algorithm and data structure design. Divide-and-conquer, dynamic programming, greedy method, graph algorithms, amortization, priority queues and variants, search structures, disjoint-set structures. Theoretical underpinnings. Examples from various problem domains. prereq: 4041 or instr consent

CSCI 5451 - Introduction to Parallel Computing: Architectures, Algorithms, and Programming

Credits:	3.0 [max 3.0]
Typically offered:	Every Spring

Parallel architectures design, embeddings, routing. Examples of parallel computers. Fundamental communication operations. Performance metrics. Parallel algorithms for sorting. Matrix problems, graph problems, dynamic load balancing, types of parallelisms. Parallel programming paradigms. Message passing programming in MPI. Shared-address space programming in openMP or threads. prereq: 4041 or instr consent

CSCI 5471 - Modern Cryptography

Credits:	3.0 [max 3.0]
Typically offered:	Periodic Fall & Spring

Introduction to cryptography. Theoretical foundations, practical applications. Threats, attacks, and countermeasures, including cryptosystems and cryptographic protocols. Secure systems/networks. History of cryptography, encryption (conventional, public key), digital signatures, hash functions, message authentication codes, identification, authentication, applications. prereq: [2011, 4041, [familiarity with number theory or finite fields]] or instr consent

CSCI 5511 - Artificial Intelligence I

Credits:	3.0 [max 3.0]
Course Equivalencies:	CSci 4511W/CSci 5511
Prerequisites:	[2041 or #], grad student
Typically offered:	Every Fall

Introduction to AI. Problem solving, search, inference techniques. Logic/theorem proving. Knowledge representation, rules, frames, semantic networks. Planning/scheduling. Lisp programming language. prereq: [2041 or instr consent], grad student

CSCI 5512 - Artificial Intelligence II

Credits:	3.0 [max 3.0]
Course Equivalencies:	CSci 5512W/CSci 5512
Typically offered:	Every Spring

Uncertainty in artificial intelligence. Probability as a model of uncertainty, methods for reasoning/learning under uncertainty, utility theory, decision-theoretic methods. prereq: [STAT 3021, 4041] or instr consent

CSCI 5521 - Machine Learning Fundamentals

Credits:	3.0 [max 3.0]
Typically offered:	Periodic Fall

Problems of pattern recognition, feature selection, measurement techniques. Statistical decision theory, nonstatistical techniques. Automatic feature selection/data clustering. Syntactic pattern recognition. Mathematical pattern recognition/artificial intelligence. Prereq: [2031 or 2033], STAT 3021, and knowledge of partial derivatives

CSCI 5523 - Introduction to Data Mining

Credits:	3.0 [max 3.0]
Typically offered:	Periodic Fall & Spring

Data pre-processing techniques, data types, similarity measures, data visualization/exploration. Predictive models (e.g., decision trees, SVM, Bayes, K-nearest neighbors, bagging, boosting). Model evaluation techniques, Clustering (hierarchical, partitional, density-based), association analysis, anomaly detection. Case studies from areas such as earth science, the Web, network intrusion, and genomics. Hands-on projects. prereq: 4041 or equiv or instr consent

CSCI 5607 - Fundamentals of Computer Graphics 1

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall

Fundamental algorithms in computer graphics. Emphasizes programming projects in C/C++. Scan conversion, hidden surface removal, geometrical transformations, projection, illumination/shading, parametric cubic curves, texture mapping, antialising, ray tracing. Developing graphics software, graphics research. prereq: concurrent registration is required (or allowed) in 2033, concurrent registration is required (or allowed) in 3081

CSCI 5608 - Fundamentals of Computer Graphics II

Credits:	3.0 [max 3.0]
Typically offered:	Periodic Spring

Advanced topics in image synthesis, modeling, rendering. Image processing, image warping, global illumination, non-photorealistic rendering, texture synthesis. Parametric cubic surfaces, subdivision surfaces, acceleration techniques, advanced texture mapping. Programming in C/C++. prereq: 5607 or instr consent

PHYS 4001 - Analytical Mechanics

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Analytic Newtonian mechanics. Mathematics beyond prerequisites developed as required. Prereq: PHYS 2503/2503H or equivalent, PHYS 3041

PHYS 4002 - Electricity and Magnetism

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Classical theory of electromagnetic fields using vector algebra and vector calculus. prereq: PHYS 3041, PHYS 2503/2503H or equivalent

PHYS 4051 - Methods of Experimental Physics I

Credits:	5.0 [max 5.0]
Typically offered:	Every Fall

Contemporary experimental techniques. Introduction to modern analog and digital electronics from an experimental viewpoint. Use of computers for data acquisition and experimental control. Statistics of data analysis. Prereq or Concurrent PHYS 3605W, PHYS 3041

PHYS 4101 - Quantum Mechanics

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Mathematical techniques of quantum mechanics. Schrodinger Equation and simple applications. General structure of wave mechanics. Operator methods, perturbation theory, radiation from atoms. Prereq: PHYS 3041, PHYS 2601

PHYS 4201 - Statistical and Thermal Physics

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall

Principles of thermodynamics and statistical mechanics. Selected applications such as kinetic theory, transport theory, and phase transitions. Prereq: PHYS 3041, PHYS 2201, PHYS 2601

PHYS 4511 - Introduction to Nuclear and Particle Physics

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall

Fundamental particles and Standard Model. Symmetries/quarks, models of nuclei, interactions between particles/nuclei, tests of conservation laws, fission/fusion. prereq: 4101

PHYS 5001 - Quantum Mechanics I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Schrodinger equation: bound state and scattering problems in one dimension. Spherically symmetric problems in three dimensions, angular momentum, and the hydrogen atom. Approximation methods for stationary states. Time-dependent perturbation theory. Operators and state vectors: general formalism of quantum theory. prereq: 4101 or equiv or instr consent

ECON 3101 - Intermediate Microeconomics

Credits:	4.0 [max 4.0]
Course Equivalencies:	Econ 3101/Econ 3101H/ApEc 3001
Grading Basis:	A-F or Aud
Typically offered:	Every Fall, Spring & Summer

Behavior of households, firms, and industries under competitive/monopolistic conditions. Factors influencing production, price, and other decisions. Applications of theory. Economic efficiency. Distribution of well-being. Students cannot take this course if they have taken ApEc 3001, as ApEc 3001 does not contain all material in Econ 3101. prereq: ECON 1101, 1102, and MATH 1271 or equivalent courses approved by the Economics Department.

ECON 3102 - Intermediate Macroeconomics

Credits:	4.0 [max 4.0]
Course Equivalencies:	Econ 3102/ApEc 3006
Grading Basis:	A-F or Aud
Typically offered:	Every Fall, Spring & Summer

Determinants of national income, employment, and price level; effects of monetary and fiscal policies; emphasis on a general equilibrium approach. Applications of the theory, especially to current modern macroeconomic policy issues. ApEc 3006 cannot be substituted for ECON 3102. prereqs: ECON 1101 (or ECON 1165, APEC 1101), ECON 1102 (or APEC1102), ECON 3101, MATH 1271 or equivalent courses approved by the Economics Department.

ECON 4261 - Introduction to Econometrics

Credits:	4.0 [max 4.0]
Grading Basis:	A-F or Aud
Typically offered:	Every Fall, Spring & Summer

For Econ B.S. majors only. Review of basic linear regression model, its variants. Time series/simultaneous equation models. Material may include panel data, censored/truncated regressions, discrete choice models. prereq: (ECON 1101 or ECON 1165, APEC 1101), ECON 1102 (or APEC 1102), ECON 3101, MATH 1271, MATH 1272, MATH 2243, MATH 2263, STAT 4101 (or 5101), STAT 4102 (or 5102) or equivalent courses approved by the Economics Department.

ECON 4751 - Financial Economics

Credits:	3.0 [max 3.0]
Course Equivalencies:	Econ 4751/Econ 4751H/Econ 4758
Grading Basis:	A-F or Aud
Typically offered:	Every Fall, Spring & Summer

Financial decisions of firms/investors. Determination of interest rates and asset prices. Role of risk/uncertainty. Emphasizes economic models. prereqs: (ECON 1101 or ECON 1165, APEC 1101), (ECON 1102 or APEC 1102), ECON 3101, MATH 1271, STAT 3011 or equivalent courses approved by the Economics Department.

STAT 3021 - Introduction to Probability and Statistics

Credits:	3.0 [max 3.0]
Course Equivalencies:	STAT 3021/STAT 3021H
Typically offered:	Every Fall, Spring & Summer

This is an introductory course in statistics whose primary objectives are to teach students the theory of elementary probability theory and an introduction to the elements of statistical inference, including testing, estimation, and confidence statements. prereq: Math 1272

STAT 3022 - Data Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Practical survey of applied statistical inference/computing covering widely used statistical tools. Multiple regression, variance analysis, experiment design, nonparametric methods, model checking/selection, variable transformation, categorical data analysis, logistic regression. prereq: 3011 or 3021 or SOC 3811

STAT 3701 - Introduction to Statistical Computing

Credits:	4.0 [max 3.0]
Grading Basis:	A-F only
Typically offered:	Every Fall & Spring

Elementary Monte Carlo, simulation studies, elementary optimization, programming in R, and graphics in R. Prerequisites: (MATH 1272 or 1372 or 1572H), CSCI 1113, and STAT 3032

STAT 5021 - Statistical Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Intensive introduction to statistical methods for graduate students needing statistics as a research technique. prereq: college algebra or instr consent; credit will not be granted if credit has been received for STAT 3011

STAT 5302 - Applied Regression Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall, Spring & Summer

Simple, multiple, and polynomial regression. Estimation, testing, prediction. Use of graphics in regression. Stepwise and other numerical methods. Weighted least squares, nonlinear models, response surfaces. Experimental research/applications. prereq: 3032 or 3022 or 4102 or 5021 or 5102 or instr consent Please note this course generally does not count in the Statistical Practice BA or Statistical Science BS degrees. Please consult with a department advisor with questions.

STAT 5303 - Designing Experiments

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall, Spring & Summer

Analysis of variance. Multiple comparisons. Variance-stabilizing transformations. Contrasts. Construction/analysis of complete/incomplete block designs. Fractional factorial designs. Confounding split plots. Response surface design. prereq: 3022 or 3032 or 3301 or 4102 or 5021 or 5102 or instr consent

STAT 5421 - Analysis of Categorical Data

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall & Spring

Varieties of categorical data, cross-classifications, contingency tables. Tests for independence. Combining 2x2 tables. Multidimensional tables/loglinear models. Maximum-likelihood estimation. Tests for goodness of fit. Logistic regression. Generalized linear/multinomial-response models. prereq: STAT 3022 or 3032 or 3301 or 5302 or 4051 or 8051 or 5102 or 4102

STAT 5101 - Theory of Statistics I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: (MATH 2263 or MATH 2374 or MATH 2573H), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)

STAT 5102 - Theory of Statistics II

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Sampling, sufficiency, estimation, test of hypotheses, size/power. Categorical data. Contingency tables. Linear models. Decision theory. prereq: [5101 or Math 5651 or instr consent]

MATH 4281 - Introduction to Modern Algebra

Credits:	4.0 [max 4.0]
Typically offered:	Periodic Fall

Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent

MATH 5248 - Cryptology and Number Theory

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math

MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math

MATH 5285H - Honors: Fundamental Structures of Algebra I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 5286H - Honors: Fundamental Structures of Algebra II

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285

MATH 5385 - Introduction to Computational Algebraic Geometry

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]

MATH 4242 - Applied Linear Algebra

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4242/Math 4457
Typically offered:	Every Fall, Spring & Summer

Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. prereq: 2243 or 2373 or 2573

MATH 5651 - Basic Theory of Probability and Statistics

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 5651/Stat 5101
Typically offered:	Every Fall & Spring

Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.

STAT 5101 - Theory of Statistics I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: (MATH 2263 or MATH 2374 or MATH 2573H), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)

MATH 5652 - Introduction to Stochastic Processes

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Random walks, Markov chains, branching processes, martingales, queuing theory, Brownian motion. prereq: 5651 or Stat 5101

MATH 4065 - Theory of Interest

Credits:	4.0 [max 4.0]
Grading Basis:	A-F only
Typically offered:	Every Fall & Spring

Time value of money, compound interest and general annuities, loans, bonds, general cash flows, basic financial derivatives and their valuation. Primarily for students who are interested in actuarial mathematics. prereq: 1272 or 1372 or 1572

MATH 5067 - Actuarial Mathematics I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Future lifetime random variable, survival function. Insurance, life annuity, future loss random variables. Net single premium, actuarial present value, net premium, net reserves. prereq: 4065, [one sem [4xxx or 5xxx] [probability or statistics] course]

MATH 5068 - Actuarial Mathematics II

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Multiple decrement insurance, pension valuation. Expense analysis, gross premium, reserves. Problem of withdrawals. Regulatory reserving systems. Minimum cash values. Additional topics at instructor's discretion. prereq: 5067

MATH 5075 - Mathematics of Options, Futures, and Derivative Securities I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Mathematical background (e.g., partial differential equations, Fourier series, computational methods, Black-Scholes theory, numerical methods--including Monte Carlo simulation). Interest-rate derivative securities, exotic options, risk theory. First course of two-course sequence. prereq: Two yrs calculus, basic computer skills

MATH 5485 - Introduction to Numerical Methods I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Solution of nonlinear equations in one variable. Interpolation, polynomial approximation. Methods for solving linear systems, eigenvalue problems, systems of nonlinear equations. prereq: [2243 or 2373 or 2573], familiarity with some programming language

MATH 4428 - Mathematical Modeling

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Modeling techniques for analysis/decision-making in industry. Optimization (sensitivity analysis, Lagrange multipliers, linear programming). Dynamical modeling (steady-states, stability analysis, eigenvalue methods, phase portraits, simulation). Probabilistic methods (probability/statistical models, Markov chains, linear regression, simulation). prereq: 2243 or 2373 or 2573

CSCI 1103 - Introduction to Computer Programming in Java

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Fundamental programming concepts/software development using Java language. Problem solving skills. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Substantial programming projects. Weekly lab.

CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall, Spring & Summer

Programming for scientists/engineers. C/C++ programming constructs, object-oriented programming, software development, fundamental numerical techniques. Exercises/examples from various scientific fields. The online modality for CSci 1113 will only be offered during the summer session. prereq: Math 1271 or Math 1371 or Math 1571H or instr consent.

CSCI 1133 - Introduction to Computing and Programming Concepts

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 1133/CSci 1133H
Typically offered:	Every Fall, Spring & Summer

Fundamental programming concepts using Python language. Problem solving skills, recursion, object-oriented programming. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Develop programs to solve real-world problems. prereq: concurrent registration is required (or allowed) in MATH 1271 or concurrent registration is required (or allowed) in MATH 1371 or concurrent registration is required (or allowed) in MATH 1571H or instr consent

ECON 1101 - Principles of Microeconomics (SOCS, GP)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Econ 1101/1165 ApEc 1101/1101H
Typically offered:	Every Fall, Spring & Summer

Microeconomic behavior of consumers, firms, and markets in domestic and world economy. Demand and supply. Competition and monopoly. Distribution of income. Economic interdependencies in the global economy. Effects of global linkages on individual decisions. prereq: knowledge of plane geometry and advanced algebra

ECON 1102 - Principles of Macroeconomics

Credits:	4.0 [max 4.0]
Course Equivalencies:	ApEc 1102/Econ 1102/1105/1112
Typically offered:	Every Fall, Spring & Summer

Aggregate consumption, saving, investment, and national income. Role of money, banking, and business cycles in domestic and world economy. International trade, growth, and development. U.S. economy and its role in the world economy. International interdependencies among nations. prereq: [1101 or equiv], knowledge of plane geometry and advanced algebra

ACCT 2051 - Introduction to Financial Reporting

Credits:	4.0 [max 4.0]
Course Equivalencies:	Acct 2050/ApEc 1251/Dbln 2051
Grading Basis:	A-F or Aud
Typically offered:	Every Fall, Spring & Summer

This course introduces the topics of financial reporting and accounting. The purpose of financial accounting is to provide information to the entity owners and external parties to serve as the basis for making decisions about that entity. A student who successfully completes this class should be able to 1) understand the concepts and principles of accounting, 2) analyze, record and report the accounting treatment of business transactions, and 3) prepare, interpret, and analyze financial statements.

FINA 3001 - Finance Fundamentals

Credits:	3.0 [max 3.0]
Course Equivalencies:	ApEc 3501/Fina 3001/Fina 3001H
Grading Basis:	A-F or Aud
Typically offered:	Every Fall & Spring

How competition for capital in Capital Markets establishes metrics and measures used to understand financial performance of the firm. The course introduces the finance view of the firm and the application of value creation principles to firm decision making. Course presents the centrality of cash flows, the theoretical foundations for Time Value of Money, decision tools for investment of capital, basic valuation of stocks and bonds, and the theoretical foundations for the impact of risk on the required return on investor capital. prereq: ACCT 2050 or ACCT 2051, SCO 2550 or BA 2551 or equivalent statistics course

STAT 3021 - Introduction to Probability and Statistics

Credits:	3.0 [max 3.0]
Course Equivalencies:	STAT 3021/STAT 3021H
Typically offered:	Every Fall, Spring & Summer

This is an introductory course in statistics whose primary objectives are to teach students the theory of elementary probability theory and an introduction to the elements of statistical inference, including testing, estimation, and confidence statements. prereq: Math 1272

STAT 3032 - Regression and Correlated Data

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

This is a second course in statistics with a focus on linear regression and correlated data. The intent of this course is to prepare statistics, economics and actuarial science students for statistical modeling needed in their discipline. The course covers the basic concepts of linear algebra and computing in R, simple linear regression, multiple linear regression, statistical inference, model diagnostics, transformations, model selection, model validation, and basics of time series and mixed models. Numerous datasets will be analyzed and interpreted using the open-source statistical software R. prereq: STAT 3011 or STAT 3021

STAT 5102 - Theory of Statistics II

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Sampling, sufficiency, estimation, test of hypotheses, size/power. Categorical data. Contingency tables. Linear models. Decision theory. prereq: [5101 or Math 5651 or instr consent]

INS 4105 - Corporate Risk Management

Credits:	2.0 [max 2.0]
Course Equivalencies:	Ins 6105/ Ins 4105
Typically offered:	Every Fall & Spring

Theory applied to corporate risk management and insurance practices. Identification, measurement, and treatment of an organization.s financial risks integrated with its property, liability, workers compensation, and human resource risks. Selection and application of risk control and risk financing tools: risk retention, reduction and transfer, including insurance.

INS 4205 - Insurance Theory and Practice

Credits:	2.0 [max 2.0]
Typically offered:	Every Spring

Risk theory is applied to practices in health, liability, life, property, and workers compensation insurance. Insurance marketing, pricing, underwriting, and claims administration, with adverse selection and moral hazard effects. Policy issues of tort versus no-fault compensation systems. Self-insurance and integrated risk financing methods.

MATH 4281 - Introduction to Modern Algebra

Credits:	4.0 [max 4.0]
Typically offered:	Periodic Fall

Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent

MATH 5248 - Cryptology and Number Theory

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math

MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math

MATH 5285H - Honors: Fundamental Structures of Algebra I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 5286H - Honors: Fundamental Structures of Algebra II

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285

MATH 5385 - Introduction to Computational Algebraic Geometry

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]

MATH 5485 - Introduction to Numerical Methods I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Solution of nonlinear equations in one variable. Interpolation, polynomial approximation. Methods for solving linear systems, eigenvalue problems, systems of nonlinear equations. prereq: [2243 or 2373 or 2573], familiarity with some programming language

MATH 5486 - Introduction To Numerical Methods II

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Numerical integration/differentiation. Numerical solution of initial-value problems, boundary value problems for ordinary differential equations, partial differential equations. prereq: 5485

MATH 4567 - Applied Fourier Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Fourier series, integral/transform. Convergence. Fourier series, transform in complex form. Solution of wave, heat, Laplace equations by separation of variables. Sturm-Liouville systems, finite Fourier, fast Fourier transform. Applications. Other topics as time permits. prereq: 2243 or 2373 or 2573

MATH 4603 - Advanced Calculus I

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4606/Math 5615/Math 5616
Typically offered:	Every Fall, Spring & Summer

Axioms for the real numbers. Techniques of proof for limits, continuity, uniform convergence. Rigorous treatment of differential/integral calculus for single-variable functions. prereq: [[2243 or 2373], [2263 or 2374]] or 2574 or instr consent

MATH 4604 - Advanced Calculus II

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4604/Math 5616
Typically offered:	Every Spring

Sequel to MATH 4603. Topology of n-dimensional Euclidean space. Rigorous treatment of multivariable differentiation and integration, including chain rule, Taylor's Theorem, implicit function theorem, Fubini's Theorem, change of variables, Stokes' Theorem. prereq: 4603 or 5615 or instr consent

MATH 5378 - Differential Geometry

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Basic geometry of curves in plane and in space, including Frenet formula, theory of surfaces, differential forms, Riemannian geometry. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]; [2283 or 3283] recommended]

MATH 5445 - Mathematical Analysis of Biological Networks

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Development/analysis of models for complex biological networks. Examples taken from signal transduction networks, metabolic networks, gene control networks, and ecological networks. prereq: Linear algebra, differential equations

MATH 5447 - Theoretical Neuroscience

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Nonlinear dynamical system models of neurons and neuronal networks. Computation by excitatory/inhibitory networks. Neural oscillations, adaptation, bursting, synchrony. Memory systems. prereq: 2243 or 2373 or 2574

MATH 5467 - Introduction to the Mathematics of Image and Data Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Background theory/experience in wavelets. Inner product spaces, operator theory, Fourier transforms applied to Gabor transforms, multi-scale analysis, discrete wavelets, self-similarity. Computing techniques. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283 or instr consent]; [[2263 or 2374], 4567] recommended

MATH 5525 - Introduction to Ordinary Differential Equations

Credits:	4.0 [max 4.0]
Typically offered:	Periodic Fall & Spring

Ordinary differential equations, solution of linear systems, qualitative/numerical methods for nonlinear systems. Linear algebra background, fundamental matrix solutions, variation of parameters, existence/uniqueness theorems, phase space. Rest points, their stability. Periodic orbits, Poincare-Bendixson theory, strange attractors. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 5535 - Dynamical Systems and Chaos

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]

MATH 5583 - Complex Analysis

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 3574/Math 5583
Typically offered:	Every Fall, Spring & Summer

Algebra, geometry of complex numbers. Linear fractional transformations. Conformal mappings. Holomorphic functions. Theorems of Abel/Cauchy, power series. Schwarz' lemma. Complex exponential, trig functions. Entire functions, theorems of Liouville/Morera. Reflection principle. Singularities, Laurent series. Residues. prereq: 2 sems soph math [including [2263 or 2374 or 2573], [2283 or 3283]] recommended

MATH 5587 - Elementary Partial Differential Equations I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Emphasizes partial differential equations w/physical applications, including heat, wave, Laplace's equations. Interpretations of boundary conditions. Characteristics, Fourier series, transforms, Green's functions, images, computational methods. Applications include wave propagation, diffusions, electrostatics, shocks. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]

MATH 5588 - Elementary Partial Differential Equations II

Credits:	4.0 [max 4.0]
Grading Basis:	A-F or Aud
Typically offered:	Every Spring

Heat, wave, Laplace's equations in higher dimensions. Green's functions, Fourier series, transforms. Asymptotic methods, boundary layer theory, bifurcation theory for linear/nonlinear PDEs. Variational methods. Free boundary problems. Additional topics as time permits. prereq: [[2243 or 2373 or 2573], [2263 or 2374 or 2574], 5587] or instr consent

MATH 5615H - Honors: Introduction to Analysis I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Axiomatic treatment of real/complex number systems. Introduction to metric spaces: convergence, connectedness, compactness. Convergence of sequences/series of real/complex numbers, Cauchy criterion, root/ratio tests. Continuity in metric spaces. Rigorous treatment of differentiation of single-variable functions, Taylor's Theorem. prereq: [[2243 or 2373], [2263 or 2374], [2283 or 3283]] or 2574

MATH 5616H - Honors: Introduction to Analysis II

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Rigorous treatment of Riemann-Stieltjes integration. Sequences/series of functions, uniform convergence, equicontinuous families, Stone-Weierstrass Theorem, power series. Rigorous treatment of differentiation/integration of multivariable functions, Implicit Function Theorem, Stokes' Theorem. Additional topics as time permits. prereq: 5615

MATH 5651 - Basic Theory of Probability and Statistics

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 5651/Stat 5101
Typically offered:	Every Fall & Spring

Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.

MATH 5652 - Introduction to Stochastic Processes

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Random walks, Markov chains, branching processes, martingales, queuing theory, Brownian motion. prereq: 5651 or Stat 5101

MATH 5654 - Prediction and Filtering

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Markov chains, Wiener process, stationary sequences, Ornstein-Uhlenbeck process. Partially observable Markov processes (hidden Markov models), stationary processes. Equations for general filters, Kalman filter. Prediction of future values of partially observable processes. prereq: 5651 or Stat 5101

STAT 5101 - Theory of Statistics I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: (MATH 2263 or MATH 2374 or MATH 2573H), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)

MATH 5165 - Mathematical Logic I

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4152/5165
Typically offered:	Every Fall

Theory of computability: notion of algorithm, Turing machines, primitive recursive functions, recursive functions, Kleene normal form, recursion theorem. Propositional logic. prereq: 2283 or 3283 or Phil 5201 or CSci course in theory of algorithms or instr consent

MATH 4242 - Applied Linear Algebra

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4242/Math 4457
Typically offered:	Every Fall, Spring & Summer

Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. prereq: 2243 or 2373 or 2573

MATH 5248 - Cryptology and Number Theory

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math

MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math

MATH 5285H - Honors: Fundamental Structures of Algebra I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 5286H - Honors: Fundamental Structures of Algebra II

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285

MATH 5385 - Introduction to Computational Algebraic Geometry

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]

MATH 5705 - Enumerative Combinatorics

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Basic enumeration, bijections, inclusion-exclusion, recurrence relations, ordinary/exponential generating functions, partitions, Polya theory. Optional topics include trees, asymptotics, listing algorithms, rook theory, involutions, tableaux, permutation statistics. prereq: [2243 or 2373 or 2573], [2263 or 2283 or 2374 or 2574 or 3283]

MATH 5707 - Graph Theory and Non-enumerative Combinatorics

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Basic topics in graph theory: connectedness, Eulerian/Hamiltonian properties, trees, colorings, planar graphs, matchings, flows in networks. Optional topics include graph algorithms, Latin squares, block designs, Ramsey theory. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]; [2283 or 3283 or experience in writing proofs] highly recommended; Credit will not be granted if credit has been received for: 4707

MATH 5711 - Linear Programming and Combinatorial Optimization

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Simplex method, connections to geometry, duality theory, sensitivity analysis. Applications to cutting stock, allocation of resources, scheduling problems. Flows, matching/transportation problems, spanning trees, distance in graphs, integer programs, branch/bound, cutting planes, heuristics. Applications to traveling salesman, knapsack problems. prereq: 2 sems soph math [including 2243 or 2373 or 2573]

CSCI 1133 - Introduction to Computing and Programming Concepts

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 1133/CSci 1133H
Typically offered:	Every Fall, Spring & Summer

Fundamental programming concepts using Python language. Problem solving skills, recursion, object-oriented programming. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Develop programs to solve real-world problems. prereq: concurrent registration is required (or allowed) in MATH 1271 or concurrent registration is required (or allowed) in MATH 1371 or concurrent registration is required (or allowed) in MATH 1571H or instr consent

CSCI 1133H - Honors Introduction to Computing and Programming Concepts

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 1133/CSci 1133H
Grading Basis:	A-F only
Typically offered:	Every Fall

Programming concepts using Python language. Real world problem solving, recursion, object-oriented programming. Algorithm development techniques. Abstractions/modularity. Optional honors topics: programming robots, programming paradigms, artificial intelligence. prereq: [concurrent registration is required (or allowed) in MATH 1271 or concurrent registration is required (or allowed) in MATH 1371 or concurrent registration is required (or allowed) in MATH 1571H], CSci majors, pre-majors in CSE/CLA, honors student

CSCI 1933 - Introduction to Algorithms and Data Structures

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 1902/CSci 1933/CSci 1933H
Typically offered:	Every Fall, Spring & Summer

Advanced object oriented programming to implement abstract data types (stacks, queues, linked lists, hash tables, binary trees) using Java language. Inheritance. Searching/sorting algorithms. Basic algorithmic analysis. Use of software development tools. Weekly lab. prereq: 1133 or instr consent

CSCI 1933H - Honors Introduction to Algorithms and Data Structures

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 1902/CSci 1933/CSci 1933H
Grading Basis:	A-F only
Typically offered:	Every Spring

Advanced object oriented programming to implement abstract data types (stacks, queues, linked lists, hash tables, binary trees) using Java language. Inheritance. Searching/sorting algorithms. Basic algorithmic analysis. Use of software development tools. Weekly lab. Optional honors topics: Advanced Java topics, GUI programming, CS research examples. prereq: [1133 or 1133H] and honors student, or inst consent

CSCI 1103 - Introduction to Computer Programming in Java

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Fundamental programming concepts/software development using Java language. Problem solving skills. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Substantial programming projects. Weekly lab.

CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall, Spring & Summer

Programming for scientists/engineers. C/C++ programming constructs, object-oriented programming, software development, fundamental numerical techniques. Exercises/examples from various scientific fields. The online modality for CSci 1113 will only be offered during the summer session. prereq: Math 1271 or Math 1371 or Math 1571H or instr consent.

CSCI 1913 - Introduction to Algorithms, Data Structures, and Program Development

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall, Spring & Summer

Advanced object oriented programming to implement abstract data types(stacks, queues, linked lists, hash tables, binary trees) using Java language. Searching/sorting algorithms. Basic algorithmic analysis. Scripting languages using Python language. Substantial programming projects. Weekly lab. prereq: (EE major and EE 1301) or (CmpE major and EE 1301) or 1103 or 1113 or instr consent

CSCI 2011 - Discrete Structures of Computer Science

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 2011/CSci 2011H
Typically offered:	Every Fall & Spring

Foundations of discrete mathematics. Sets, sequences, functions, big-O, propositional/predicate logic, proof methods, counting methods, recursion/recurrences, relations, trees/graph fundamentals. prereq: MATH 1271 or MATH 1371 or instr consent

CSCI 4011 - Formal Languages and Automata Theory

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Logical/mathematical foundations of computer science. Formal languages, their correspondence to machine models. Lexical analysis, string matching, parsing. Decidability, undecidability, limits of computability. Computational complexity. prereq: 2041 or instr consent

CSCI 4041 - Algorithms and Data Structures

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 4041/CSci 4041H
Typically offered:	Every Fall & Spring

Rigorous analysis of algorithms/implementation. Algorithm analysis, sorting algorithms, binary trees, heaps, priority queues, heapsort, balanced binary search trees, AVL trees, hash tables and hashing, graphs, graph traversal, single source shortest path, minimum cost spanning trees. prereq: [(1913 or 1933) and 2011] or instr consent; cannot be taken for grad CSci cr

CSCI 4511W - Introduction to Artificial Intelligence (WI)

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 4511W/CSci 5511
Typically offered:	Every Fall & Spring

Problem solving, search, inference techniques. Knowledge representation. Planning. Machine learning. Robotics. Lisp programming language. Cannot be taken for grad CSci credit. prereq: 2041 or instr consent

CSCI 5421 - Advanced Algorithms and Data Structures

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall & Spring

Fundamental paradigms of algorithm and data structure design. Divide-and-conquer, dynamic programming, greedy method, graph algorithms, amortization, priority queues and variants, search structures, disjoint-set structures. Theoretical underpinnings. Examples from various problem domains. prereq: 4041 or instr consent

CSCI 5451 - Introduction to Parallel Computing: Architectures, Algorithms, and Programming

Credits:	3.0 [max 3.0]
Typically offered:	Every Spring

Parallel architectures design, embeddings, routing. Examples of parallel computers. Fundamental communication operations. Performance metrics. Parallel algorithms for sorting. Matrix problems, graph problems, dynamic load balancing, types of parallelisms. Parallel programming paradigms. Message passing programming in MPI. Shared-address space programming in openMP or threads. prereq: 4041 or instr consent

CSCI 5511 - Artificial Intelligence I

Credits:	3.0 [max 3.0]
Course Equivalencies:	CSci 4511W/CSci 5511
Prerequisites:	[2041 or #], grad student
Typically offered:	Every Fall

Introduction to AI. Problem solving, search, inference techniques. Logic/theorem proving. Knowledge representation, rules, frames, semantic networks. Planning/scheduling. Lisp programming language. prereq: [2041 or instr consent], grad student

CSCI 5512 - Artificial Intelligence II

Credits:	3.0 [max 3.0]
Course Equivalencies:	CSci 5512W/CSci 5512
Typically offered:	Every Spring

Uncertainty in artificial intelligence. Probability as a model of uncertainty, methods for reasoning/learning under uncertainty, utility theory, decision-theoretic methods. prereq: [STAT 3021, 4041] or instr consent

CSCI 5521 - Machine Learning Fundamentals

Credits:	3.0 [max 3.0]
Typically offered:	Periodic Fall

Problems of pattern recognition, feature selection, measurement techniques. Statistical decision theory, nonstatistical techniques. Automatic feature selection/data clustering. Syntactic pattern recognition. Mathematical pattern recognition/artificial intelligence. Prereq: [2031 or 2033], STAT 3021, and knowledge of partial derivatives

CSCI 5607 - Fundamentals of Computer Graphics 1

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall

Fundamental algorithms in computer graphics. Emphasizes programming projects in C/C++. Scan conversion, hidden surface removal, geometrical transformations, projection, illumination/shading, parametric cubic curves, texture mapping, antialising, ray tracing. Developing graphics software, graphics research. prereq: concurrent registration is required (or allowed) in 2033, concurrent registration is required (or allowed) in 3081

CSCI 5608 - Fundamentals of Computer Graphics II

Credits:	3.0 [max 3.0]
Typically offered:	Periodic Spring

Advanced topics in image synthesis, modeling, rendering. Image processing, image warping, global illumination, non-photorealistic rendering, texture synthesis. Parametric cubic surfaces, subdivision surfaces, acceleration techniques, advanced texture mapping. Programming in C/C++. prereq: 5607 or instr consent

PHYS 2303 - Physics III: Physics of Matter

Credits:	4.0 [max 4.0]
Course Equivalencies:	Phys 2303/2403H/2503/2503H
Typically offered:	Every Spring

Thermodynamics, mechanical/electromagnetic waves, optics, quantum theory. Applications of quantum nature of solids. prereq: 1302, [MATH 1272 or MATH 1372 or MATH 1572H], [MatSci or EE] student

PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity

Credits:	4.0 [max 4.0]
Course Equivalencies:	Phys 2303/2403H/2503/2503H
Typically offered:	Every Fall

Third semester of introductory physics. Mechanical/electromagnetic waves, optics, special relativity. prereq: 1302W or equivalent

MATH 4281 - Introduction to Modern Algebra

Credits:	4.0 [max 4.0]
Typically offered:	Periodic Fall

Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent

MATH 5248 - Cryptology and Number Theory

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math

MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math

MATH 5285H - Honors: Fundamental Structures of Algebra I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 4707 - Introduction to Combinatorics and Graph Theory

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Existence, enumeration, construction, algorithms, optimization. Pigeonhole principle, bijective combinatorics, inclusion-exclusion, recursions, graph modeling, isomorphism. Degree sequences and edge counting. Connectivity, Eulerian graphs, trees, Euler's formula, network flows, matching theory. Mathematical induction as proof technique. prereq: 2243, [2283 or 3283]

MATH 5705 - Enumerative Combinatorics

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Basic enumeration, bijections, inclusion-exclusion, recurrence relations, ordinary/exponential generating functions, partitions, Polya theory. Optional topics include trees, asymptotics, listing algorithms, rook theory, involutions, tableaux, permutation statistics. prereq: [2243 or 2373 or 2573], [2263 or 2283 or 2374 or 2574 or 3283]

MATH 5707 - Graph Theory and Non-enumerative Combinatorics

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Basic topics in graph theory: connectedness, Eulerian/Hamiltonian properties, trees, colorings, planar graphs, matchings, flows in networks. Optional topics include graph algorithms, Latin squares, block designs, Ramsey theory. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]; [2283 or 3283 or experience in writing proofs] highly recommended; Credit will not be granted if credit has been received for: 4707

MATH 5335 - Geometry I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Advanced two-dimensional Euclidean geometry from a vector viewpoint. Theorems/problems about triangles/circles, isometries, connections with Euclid's axioms. Hyperbolic geometry, how it compares with Euclidean geometry. prereq: [2243 or 2373 or 2573], [concurrent registration is required (or allowed) in 2263 or concurrent registration is required (or allowed) in 2374 or concurrent registration is required (or allowed) in 2574]

MATH 4653 - Elementary Probability

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Probability spaces, distributions of discrete/continuous random variables, conditioning. Basic theorems, calculational methodology. Examples of random sequences. Emphasizes problem-solving. prereq: [2263 or 2374 or 2573]; [2283 or 2574 or 3283] recommended

MATH 5651 - Basic Theory of Probability and Statistics

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 5651/Stat 5101
Typically offered:	Every Fall & Spring

Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.

STAT 5101 - Theory of Statistics I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: (MATH 2263 or MATH 2374 or MATH 2573H), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)

MATH 4567 - Applied Fourier Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Fourier series, integral/transform. Convergence. Fourier series, transform in complex form. Solution of wave, heat, Laplace equations by separation of variables. Sturm-Liouville systems, finite Fourier, fast Fourier transform. Applications. Other topics as time permits. prereq: 2243 or 2373 or 2573

MATH 4603 - Advanced Calculus I

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4606/Math 5615/Math 5616
Typically offered:	Every Fall, Spring & Summer

Axioms for the real numbers. Techniques of proof for limits, continuity, uniform convergence. Rigorous treatment of differential/integral calculus for single-variable functions. prereq: [[2243 or 2373], [2263 or 2374]] or 2574 or instr consent

MATH 4604 - Advanced Calculus II

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4604/Math 5616
Typically offered:	Every Spring

Sequel to MATH 4603. Topology of n-dimensional Euclidean space. Rigorous treatment of multivariable differentiation and integration, including chain rule, Taylor's Theorem, implicit function theorem, Fubini's Theorem, change of variables, Stokes' Theorem. prereq: 4603 or 5615 or instr consent

MATH 5378 - Differential Geometry

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Basic geometry of curves in plane and in space, including Frenet formula, theory of surfaces, differential forms, Riemannian geometry. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]; [2283 or 3283] recommended]

MATH 5445 - Mathematical Analysis of Biological Networks

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Development/analysis of models for complex biological networks. Examples taken from signal transduction networks, metabolic networks, gene control networks, and ecological networks. prereq: Linear algebra, differential equations

MATH 5447 - Theoretical Neuroscience

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Nonlinear dynamical system models of neurons and neuronal networks. Computation by excitatory/inhibitory networks. Neural oscillations, adaptation, bursting, synchrony. Memory systems. prereq: 2243 or 2373 or 2574

MATH 5467 - Introduction to the Mathematics of Image and Data Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Background theory/experience in wavelets. Inner product spaces, operator theory, Fourier transforms applied to Gabor transforms, multi-scale analysis, discrete wavelets, self-similarity. Computing techniques. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283 or instr consent]; [[2263 or 2374], 4567] recommended

MATH 5486 - Introduction To Numerical Methods II

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Numerical integration/differentiation. Numerical solution of initial-value problems, boundary value problems for ordinary differential equations, partial differential equations. prereq: 5485

MATH 5525 - Introduction to Ordinary Differential Equations

Credits:	4.0 [max 4.0]
Typically offered:	Periodic Fall & Spring

Ordinary differential equations, solution of linear systems, qualitative/numerical methods for nonlinear systems. Linear algebra background, fundamental matrix solutions, variation of parameters, existence/uniqueness theorems, phase space. Rest points, their stability. Periodic orbits, Poincare-Bendixson theory, strange attractors. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 5535 - Dynamical Systems and Chaos

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]

MATH 5583 - Complex Analysis

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 3574/Math 5583
Typically offered:	Every Fall, Spring & Summer

Algebra, geometry of complex numbers. Linear fractional transformations. Conformal mappings. Holomorphic functions. Theorems of Abel/Cauchy, power series. Schwarz' lemma. Complex exponential, trig functions. Entire functions, theorems of Liouville/Morera. Reflection principle. Singularities, Laurent series. Residues. prereq: 2 sems soph math [including [2263 or 2374 or 2573], [2283 or 3283]] recommended

MATH 5587 - Elementary Partial Differential Equations I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Emphasizes partial differential equations w/physical applications, including heat, wave, Laplace's equations. Interpretations of boundary conditions. Characteristics, Fourier series, transforms, Green's functions, images, computational methods. Applications include wave propagation, diffusions, electrostatics, shocks. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]

MATH 5588 - Elementary Partial Differential Equations II

Credits:	4.0 [max 4.0]
Grading Basis:	A-F or Aud
Typically offered:	Every Spring

Heat, wave, Laplace's equations in higher dimensions. Green's functions, Fourier series, transforms. Asymptotic methods, boundary layer theory, bifurcation theory for linear/nonlinear PDEs. Variational methods. Free boundary problems. Additional topics as time permits. prereq: [[2243 or 2373 or 2573], [2263 or 2374 or 2574], 5587] or instr consent

MATH 5615H - Honors: Introduction to Analysis I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Axiomatic treatment of real/complex number systems. Introduction to metric spaces: convergence, connectedness, compactness. Convergence of sequences/series of real/complex numbers, Cauchy criterion, root/ratio tests. Continuity in metric spaces. Rigorous treatment of differentiation of single-variable functions, Taylor's Theorem. prereq: [[2243 or 2373], [2263 or 2374], [2283 or 3283]] or 2574

MATH 5616H - Honors: Introduction to Analysis II

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Rigorous treatment of Riemann-Stieltjes integration. Sequences/series of functions, uniform convergence, equicontinuous families, Stone-Weierstrass Theorem, power series. Rigorous treatment of differentiation/integration of multivariable functions, Implicit Function Theorem, Stokes' Theorem. Additional topics as time permits. prereq: 5615

MATH 5651 - Basic Theory of Probability and Statistics

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 5651/Stat 5101
Typically offered:	Every Fall & Spring

Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.

MATH 5652 - Introduction to Stochastic Processes

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Random walks, Markov chains, branching processes, martingales, queuing theory, Brownian motion. prereq: 5651 or Stat 5101

MATH 5654 - Prediction and Filtering

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Markov chains, Wiener process, stationary sequences, Ornstein-Uhlenbeck process. Partially observable Markov processes (hidden Markov models), stationary processes. Equations for general filters, Kalman filter. Prediction of future values of partially observable processes. prereq: 5651 or Stat 5101

STAT 5101 - Theory of Statistics I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: (MATH 2263 or MATH 2374 or MATH 2573H), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)

STAT 5102 - Theory of Statistics II

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Sampling, sufficiency, estimation, test of hypotheses, size/power. Categorical data. Contingency tables. Linear models. Decision theory. prereq: [5101 or Math 5651 or instr consent]

MATH 5652 - Introduction to Stochastic Processes

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Random walks, Markov chains, branching processes, martingales, queuing theory, Brownian motion. prereq: 5651 or Stat 5101

CSCI 1103 - Introduction to Computer Programming in Java

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Fundamental programming concepts/software development using Java language. Problem solving skills. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Substantial programming projects. Weekly lab.

CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall, Spring & Summer

Programming for scientists/engineers. C/C++ programming constructs, object-oriented programming, software development, fundamental numerical techniques. Exercises/examples from various scientific fields. The online modality for CSci 1113 will only be offered during the summer session. prereq: Math 1271 or Math 1371 or Math 1571H or instr consent.

CSCI 1133 - Introduction to Computing and Programming Concepts

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 1133/CSci 1133H
Typically offered:	Every Fall, Spring & Summer

Fundamental programming concepts using Python language. Problem solving skills, recursion, object-oriented programming. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Develop programs to solve real-world problems. prereq: concurrent registration is required (or allowed) in MATH 1271 or concurrent registration is required (or allowed) in MATH 1371 or concurrent registration is required (or allowed) in MATH 1571H or instr consent

PHYS 2303 - Physics III: Physics of Matter

Credits:	4.0 [max 4.0]
Course Equivalencies:	Phys 2303/2403H/2503/2503H
Typically offered:	Every Spring

Thermodynamics, mechanical/electromagnetic waves, optics, quantum theory. Applications of quantum nature of solids. prereq: 1302, [MATH 1272 or MATH 1372 or MATH 1572H], [MatSci or EE] student

PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity

Credits:	4.0 [max 4.0]
Course Equivalencies:	Phys 2303/2403H/2503/2503H
Typically offered:	Every Fall

Third semester of introductory physics. Mechanical/electromagnetic waves, optics, special relativity. prereq: 1302W or equivalent

CHEM 4501 - Introduction to Thermodynamics, Kinetics, and Statistical Mechanics

Credits:	3.0 [max 3.0]
Course Equivalencies:	Chem 3501/4501
Grading Basis:	A-F or Aud
Typically offered:	Every Fall & Spring

Physical chemistry as it relates to macroscopic descriptions of chemical systems. Chemical thermodynamics, phase equilibria, chemical equilibria. Statistical mechanics. Phenomenological reaction kinetics. Kinetic theory of gases. Collision, statistical theories of reaction rates. prereq: [1062/1066 or 1071H/1075H], [MATH 2263 or concurrent registration is required (or allowed) in MATH 2263 or MATH 2374 or concurrent registration is required (or allowed) in MATH 2374], [PHYS 1302 or PHYS 1402V or PHYS 1502V]

CHEM 4502 - Introduction to Quantum Mechanics and Spectroscopy

Credits:	3.0 [max 3.0]
Course Equivalencies:	Chem 3502/4502
Grading Basis:	A-F or Aud
Typically offered:	Every Fall & Spring

Microscopic descriptions of chemical systems. Quantum theory. Applications to atomic/molecular structure. Molecular spectroscopy. Quantum statistical mechanics. Discussion of solutions to several differential equations. prereq: [1062/1066 or 1072H/1076H of 1082/1086], [MATH 2263 or concurrent registration is required (or allowed) in MATH 2263 or MATH 2374 or concurrent registration is required (or allowed) in MATH 2374 or MATH 2243 or concurrent registration is required (or allowed) in MATH 2243 or MATH 2373 or concurrent registration is required (or allowed) in MATH 2373], [PHYS 1302 or PHYS 1402V or PHYS 1502V]

CHEN 3101 - Chemical Engineering Thermodynamics

Credits:	4.0 [max 4.0]
Grading Basis:	A-F only
Typically offered:	Every Spring

Applications of thermodynamics/chemical equilibrium to problems in chemical engineering. prereq: ChEn 2001, Chem 1062/1066 Math 2374 or equivalent, & Math 2373 or equivalent

CHEN 3102 - Reaction Kinetics and Reactor Engineering

Credits:	4.0 [max 4.0]
Grading Basis:	A-F only
Typically offered:	Every Fall

Chemical equilibrium/chemical kinetics applied to chemical engineering systems. Behavior/design of chemical reactors, interaction between chemical/physical rate processes. Mathematical modeling, design of reactors. prereq: [2001 or 4001], [3101 or 4101], [upper div ChEn major or dept consent], C- or better in all pre-reqs

CSCI 4011 - Formal Languages and Automata Theory

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Logical/mathematical foundations of computer science. Formal languages, their correspondence to machine models. Lexical analysis, string matching, parsing. Decidability, undecidability, limits of computability. Computational complexity. prereq: 2041 or instr consent

CSCI 4041 - Algorithms and Data Structures

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 4041/CSci 4041H
Typically offered:	Every Fall & Spring

Rigorous analysis of algorithms/implementation. Algorithm analysis, sorting algorithms, binary trees, heaps, priority queues, heapsort, balanced binary search trees, AVL trees, hash tables and hashing, graphs, graph traversal, single source shortest path, minimum cost spanning trees. prereq: [(1913 or 1933) and 2011] or instr consent; cannot be taken for grad CSci cr

CSCI 4061 - Introduction to Operating Systems

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 4061/INet 4001
Typically offered:	Every Fall & Spring

Processes/threads, process coordination, interprocess communication, asynchronous events, memory management/file systems. Systems programming projects using operating system interfaces and program development tools. prereq: 2021 or EE 2361; CS upper div, CompE upper div., EE upper div., EE grad, ITI upper div., Univ. honors student, or dept. permission; no cr for grads in CSci.

CSCI 4611 - Programming Interactive Computer Graphics and Games

Credits:	3.0 [max 3.0]
Typically offered:	Every Spring

Tools/techniques for programming games/interactive computer graphics. Event loops, rendering/animation, polygonal models, texturing, physical simulation. Modern graphics toolkits. History/future of computer games technology. Social impact of interactive computer graphics. prereq: 2021 or instr consent

CSCI 5106 - Programming Languages

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall

Design and implementation of high-level languages. Course has two parts: (1) language design principles, concepts, constructs; (2) language paradigms, applications. Note: course does not teach how to program in specific languages. prereq: 4011 or instr consent

CSCI 5304 - Computational Aspects of Matrix Theory

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall

Perturbation theory for linear systems and eigenvalue problems. Direct/iterative solution of large linear systems. Matrix factorizations. Computation of eigenvalues/eigenvectors. Singular value decomposition. LAPACK/other software packages. Introduction to sparse matrix methods. prereq: 2031 or 2033 or instr consent

CSCI 5421 - Advanced Algorithms and Data Structures

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall & Spring

Fundamental paradigms of algorithm and data structure design. Divide-and-conquer, dynamic programming, greedy method, graph algorithms, amortization, priority queues and variants, search structures, disjoint-set structures. Theoretical underpinnings. Examples from various problem domains. prereq: 4041 or instr consent

CSCI 5451 - Introduction to Parallel Computing: Architectures, Algorithms, and Programming

Credits:	3.0 [max 3.0]
Typically offered:	Every Spring

Parallel architectures design, embeddings, routing. Examples of parallel computers. Fundamental communication operations. Performance metrics. Parallel algorithms for sorting. Matrix problems, graph problems, dynamic load balancing, types of parallelisms. Parallel programming paradigms. Message passing programming in MPI. Shared-address space programming in openMP or threads. prereq: 4041 or instr consent

CSCI 5511 - Artificial Intelligence I

Credits:	3.0 [max 3.0]
Course Equivalencies:	CSci 4511W/CSci 5511
Prerequisites:	[2041 or #], grad student
Typically offered:	Every Fall

Introduction to AI. Problem solving, search, inference techniques. Logic/theorem proving. Knowledge representation, rules, frames, semantic networks. Planning/scheduling. Lisp programming language. prereq: [2041 or instr consent], grad student

CSCI 5512 - Artificial Intelligence II

Credits:	3.0 [max 3.0]
Course Equivalencies:	CSci 5512W/CSci 5512
Typically offered:	Every Spring

Uncertainty in artificial intelligence. Probability as a model of uncertainty, methods for reasoning/learning under uncertainty, utility theory, decision-theoretic methods. prereq: [STAT 3021, 4041] or instr consent

CSCI 5521 - Machine Learning Fundamentals

Credits:	3.0 [max 3.0]
Typically offered:	Periodic Fall

Problems of pattern recognition, feature selection, measurement techniques. Statistical decision theory, nonstatistical techniques. Automatic feature selection/data clustering. Syntactic pattern recognition. Mathematical pattern recognition/artificial intelligence. Prereq: [2031 or 2033], STAT 3021, and knowledge of partial derivatives

CSCI 5523 - Introduction to Data Mining

Credits:	3.0 [max 3.0]
Typically offered:	Periodic Fall & Spring

Data pre-processing techniques, data types, similarity measures, data visualization/exploration. Predictive models (e.g., decision trees, SVM, Bayes, K-nearest neighbors, bagging, boosting). Model evaluation techniques, Clustering (hierarchical, partitional, density-based), association analysis, anomaly detection. Case studies from areas such as earth science, the Web, network intrusion, and genomics. Hands-on projects. prereq: 4041 or equiv or instr consent

CSCI 5607 - Fundamentals of Computer Graphics 1

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall

Fundamental algorithms in computer graphics. Emphasizes programming projects in C/C++. Scan conversion, hidden surface removal, geometrical transformations, projection, illumination/shading, parametric cubic curves, texture mapping, antialising, ray tracing. Developing graphics software, graphics research. prereq: concurrent registration is required (or allowed) in 2033, concurrent registration is required (or allowed) in 3081

CSCI 5608 - Fundamentals of Computer Graphics II

Credits:	3.0 [max 3.0]
Typically offered:	Periodic Spring

Advanced topics in image synthesis, modeling, rendering. Image processing, image warping, global illumination, non-photorealistic rendering, texture synthesis. Parametric cubic surfaces, subdivision surfaces, acceleration techniques, advanced texture mapping. Programming in C/C++. prereq: 5607 or instr consent

PHYS 4001 - Analytical Mechanics

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Analytic Newtonian mechanics. Mathematics beyond prerequisites developed as required. Prereq: PHYS 2503/2503H or equivalent, PHYS 3041

PHYS 4002 - Electricity and Magnetism

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Classical theory of electromagnetic fields using vector algebra and vector calculus. prereq: PHYS 3041, PHYS 2503/2503H or equivalent

PHYS 4051 - Methods of Experimental Physics I

Credits:	5.0 [max 5.0]
Typically offered:	Every Fall

Contemporary experimental techniques. Introduction to modern analog and digital electronics from an experimental viewpoint. Use of computers for data acquisition and experimental control. Statistics of data analysis. Prereq or Concurrent PHYS 3605W, PHYS 3041

PHYS 4101 - Quantum Mechanics

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Mathematical techniques of quantum mechanics. Schrodinger Equation and simple applications. General structure of wave mechanics. Operator methods, perturbation theory, radiation from atoms. Prereq: PHYS 3041, PHYS 2601

PHYS 4201 - Statistical and Thermal Physics

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall

Principles of thermodynamics and statistical mechanics. Selected applications such as kinetic theory, transport theory, and phase transitions. Prereq: PHYS 3041, PHYS 2201, PHYS 2601

PHYS 4511 - Introduction to Nuclear and Particle Physics

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall

Fundamental particles and Standard Model. Symmetries/quarks, models of nuclei, interactions between particles/nuclei, tests of conservation laws, fission/fusion. prereq: 4101

PHYS 5001 - Quantum Mechanics I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Schrodinger equation: bound state and scattering problems in one dimension. Spherically symmetric problems in three dimensions, angular momentum, and the hydrogen atom. Approximation methods for stationary states. Time-dependent perturbation theory. Operators and state vectors: general formalism of quantum theory. prereq: 4101 or equiv or instr consent

ECON 3101 - Intermediate Microeconomics

Credits:	4.0 [max 4.0]
Course Equivalencies:	Econ 3101/Econ 3101H/ApEc 3001
Grading Basis:	A-F or Aud
Typically offered:	Every Fall, Spring & Summer

Behavior of households, firms, and industries under competitive/monopolistic conditions. Factors influencing production, price, and other decisions. Applications of theory. Economic efficiency. Distribution of well-being. Students cannot take this course if they have taken ApEc 3001, as ApEc 3001 does not contain all material in Econ 3101. prereq: ECON 1101, 1102, and MATH 1271 or equivalent courses approved by the Economics Department.

ECON 3102 - Intermediate Macroeconomics

Credits:	4.0 [max 4.0]
Course Equivalencies:	Econ 3102/ApEc 3006
Grading Basis:	A-F or Aud
Typically offered:	Every Fall, Spring & Summer

Determinants of national income, employment, and price level; effects of monetary and fiscal policies; emphasis on a general equilibrium approach. Applications of the theory, especially to current modern macroeconomic policy issues. ApEc 3006 cannot be substituted for ECON 3102. prereqs: ECON 1101 (or ECON 1165, APEC 1101), ECON 1102 (or APEC1102), ECON 3101, MATH 1271 or equivalent courses approved by the Economics Department.

ECON 4261 - Introduction to Econometrics

Credits:	4.0 [max 4.0]
Grading Basis:	A-F or Aud
Typically offered:	Every Fall, Spring & Summer

For Econ B.S. majors only. Review of basic linear regression model, its variants. Time series/simultaneous equation models. Material may include panel data, censored/truncated regressions, discrete choice models. prereq: (ECON 1101 or ECON 1165, APEC 1101), ECON 1102 (or APEC 1102), ECON 3101, MATH 1271, MATH 1272, MATH 2243, MATH 2263, STAT 4101 (or 5101), STAT 4102 (or 5102) or equivalent courses approved by the Economics Department.

ECON 4751 - Financial Economics

Credits:	3.0 [max 3.0]
Course Equivalencies:	Econ 4751/Econ 4751H/Econ 4758
Grading Basis:	A-F or Aud
Typically offered:	Every Fall, Spring & Summer

Financial decisions of firms/investors. Determination of interest rates and asset prices. Role of risk/uncertainty. Emphasizes economic models. prereqs: (ECON 1101 or ECON 1165, APEC 1101), (ECON 1102 or APEC 1102), ECON 3101, MATH 1271, STAT 3011 or equivalent courses approved by the Economics Department.

STAT 3021 - Introduction to Probability and Statistics

Credits:	3.0 [max 3.0]
Course Equivalencies:	STAT 3021/STAT 3021H
Typically offered:	Every Fall, Spring & Summer

This is an introductory course in statistics whose primary objectives are to teach students the theory of elementary probability theory and an introduction to the elements of statistical inference, including testing, estimation, and confidence statements. prereq: Math 1272

STAT 3022 - Data Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Practical survey of applied statistical inference/computing covering widely used statistical tools. Multiple regression, variance analysis, experiment design, nonparametric methods, model checking/selection, variable transformation, categorical data analysis, logistic regression. prereq: 3011 or 3021 or SOC 3811

STAT 3701 - Introduction to Statistical Computing

Credits:	4.0 [max 3.0]
Grading Basis:	A-F only
Typically offered:	Every Fall & Spring

Elementary Monte Carlo, simulation studies, elementary optimization, programming in R, and graphics in R. Prerequisites: (MATH 1272 or 1372 or 1572H), CSCI 1113, and STAT 3032

STAT 5021 - Statistical Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Intensive introduction to statistical methods for graduate students needing statistics as a research technique. prereq: college algebra or instr consent; credit will not be granted if credit has been received for STAT 3011

STAT 5302 - Applied Regression Analysis

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall, Spring & Summer

Simple, multiple, and polynomial regression. Estimation, testing, prediction. Use of graphics in regression. Stepwise and other numerical methods. Weighted least squares, nonlinear models, response surfaces. Experimental research/applications. prereq: 3032 or 3022 or 4102 or 5021 or 5102 or instr consent Please note this course generally does not count in the Statistical Practice BA or Statistical Science BS degrees. Please consult with a department advisor with questions.

STAT 5303 - Designing Experiments

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall, Spring & Summer

Analysis of variance. Multiple comparisons. Variance-stabilizing transformations. Contrasts. Construction/analysis of complete/incomplete block designs. Fractional factorial designs. Confounding split plots. Response surface design. prereq: 3022 or 3032 or 3301 or 4102 or 5021 or 5102 or instr consent

STAT 5421 - Analysis of Categorical Data

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall & Spring

Varieties of categorical data, cross-classifications, contingency tables. Tests for independence. Combining 2x2 tables. Multidimensional tables/loglinear models. Maximum-likelihood estimation. Tests for goodness of fit. Logistic regression. Generalized linear/multinomial-response models. prereq: STAT 3022 or 3032 or 3301 or 5302 or 4051 or 8051 or 5102 or 4102

MATH 4428 - Mathematical Modeling

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Modeling techniques for analysis/decision-making in industry. Optimization (sensitivity analysis, Lagrange multipliers, linear programming). Dynamical modeling (steady-states, stability analysis, eigenvalue methods, phase portraits, simulation). Probabilistic methods (probability/statistical models, Markov chains, linear regression, simulation). prereq: 2243 or 2373 or 2573

MATH 4281 - Introduction to Modern Algebra

Credits:	4.0 [max 4.0]
Typically offered:	Periodic Fall

Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent

MATH 5248 - Cryptology and Number Theory

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math

MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math

MATH 5285H - Honors: Fundamental Structures of Algebra I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 5286H - Honors: Fundamental Structures of Algebra II

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285

MATH 5385 - Introduction to Computational Algebraic Geometry

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]

MATH 4242 - Applied Linear Algebra

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4242/Math 4457
Typically offered:	Every Fall, Spring & Summer

Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. prereq: 2243 or 2373 or 2573

MATH 5525 - Introduction to Ordinary Differential Equations

Credits:	4.0 [max 4.0]
Typically offered:	Periodic Fall & Spring

Ordinary differential equations, solution of linear systems, qualitative/numerical methods for nonlinear systems. Linear algebra background, fundamental matrix solutions, variation of parameters, existence/uniqueness theorems, phase space. Rest points, their stability. Periodic orbits, Poincare-Bendixson theory, strange attractors. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 5535 - Dynamical Systems and Chaos

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]

MATH 5651 - Basic Theory of Probability and Statistics

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 5651/Stat 5101
Typically offered:	Every Fall & Spring

Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.

STAT 5101 - Theory of Statistics I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: (MATH 2263 or MATH 2374 or MATH 2573H), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)

CSCI 1103 - Introduction to Computer Programming in Java

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Fundamental programming concepts/software development using Java language. Problem solving skills. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Substantial programming projects. Weekly lab.

CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall, Spring & Summer

Programming for scientists/engineers. C/C++ programming constructs, object-oriented programming, software development, fundamental numerical techniques. Exercises/examples from various scientific fields. The online modality for CSci 1113 will only be offered during the summer session. prereq: Math 1271 or Math 1371 or Math 1571H or instr consent.

CSCI 1133 - Introduction to Computing and Programming Concepts

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 1133/CSci 1133H
Typically offered:	Every Fall, Spring & Summer

Fundamental programming concepts using Python language. Problem solving skills, recursion, object-oriented programming. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Develop programs to solve real-world problems. prereq: concurrent registration is required (or allowed) in MATH 1271 or concurrent registration is required (or allowed) in MATH 1371 or concurrent registration is required (or allowed) in MATH 1571H or instr consent

CSCI 5461 - Functional Genomics, Systems Biology, and Bioinformatics

Credits:	3.0 [max 3.0]
Typically offered:	Every Spring

Computational methods for analyzing, integrating, and deriving predictions from genomic/proteomic data. Analyzing gene expression, proteomic data, and protein-protein interaction networks. Protein/gene function prediction, Integrating diverse data, visualizing genomic datasets. prereq: 3003 or 4041 or instr consent

CSCI 5481 - Computational Techniques for Genomics

Credits:	3.0 [max 3.0]
Typically offered:	Every Fall

Techniques to analyze biological data generated by genome sequencing, proteomics, cell-wide measurements of gene expression changes. Algorithms for single/multiple sequence alignments/assembly. Search algorithms for sequence databases, phylogenetic tree construction algorithms. Algorithms for gene/promoter and protein structure prediction. Data mining for micro array expression analysis. Reverse engineering of regulatory networks. prereq: 4041 or instr consent

BIOL 1009 - General Biology (BIOL)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Biol 1009/Biol 1009H
Typically offered:	Every Fall, Spring & Summer

A comprehensive introduction to biology - includes molecular structure of living things, cell processes, energy utilization, genetic information and inheritance, mechanisms of evolution, biological diversity, and ecology. Includes lab. This comprehensive course serves as a prerequisite and requirement in many majors.

BIOL 1009H - Honors: General Biology (BIOL)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Biol 1009/Biol 1009H
Grading Basis:	A-F only
Typically offered:	Every Spring

A comprehensive introduction to biology - includes molecular structure of living things, cell processes, energy utilization, genetic information and inheritance, mechanisms of evolution, biological diversity, and ecology. Includes lab. This comprehensive course serves as a prerequisite and requirement in many majors.

GCD 3022 - Genetics

Credits:	3.0 [max 3.0]
Course Equivalencies:	Biol 4003/GCD 3022
Typically offered:	Every Fall, Spring & Summer

Mechanisms of heredity, implications for biological populations. Applications to practical problems. prereq: Introductory biology course such as Biol 1009

EEB 5042 - Quantitative Genetics

Credits:	3.0 [max 3.0]
Grading Basis:	A-F only
Typically offered:	Every Fall

Fundamentals of quantitative genetics. Genetic/environmental influences on expression of quantitative traits. Approaches to characterizing genetic basis of trait variation. Processes that lead to change in quantitative traits. Applied/evolutionary aspects of quantitative genetic variation. prereq: [BIOL 4003 or GCD 3022] or instr consent; a course in statistics is recommended

GCD 4143 - Human Genetics and Genomics

Credits:	3.0 [max 3.0]
Typically offered:	Every Spring

Human Genetics ? the science of how our genomes function, vary, and shape our unique, individual characteristics ? is a rapidly expanding field with major implications for medical and fundamental research, clinical practice, and many other areas. In this course, students will learn about the principles of human genetics & genomics at the levels of molecules, cells, individuals, and populations. Topics include patterns of inheritance; the molecular causes and biochemical basis of genetic disorders; disease gene identification; the origin and distribution of human genetic variation; genetic influences on common, complex diseases; epigenetics and regulation of gene expression; genomic technologies for understanding human genomes; cancer genetics; behavioral genetics; human ancestry and evolution; applications such as genetic screening, genetic counseling, and gene therapy; and ethical questions raised by emerging abilities to edit the human genome, modify the human germline, and many more. prereq: BIOL 4003 or instructor consent

GCD 4151 - Molecular Biology of Cancer

Credits:	3.0 [max 3.0]
Grading Basis:	A-F or Aud
Typically offered:	Every Fall

Regulatory pathways involved in directing normal development of complex eukaryotic organisms, how disruptions of these pathways can lead to abnormal cell growth/cancer. Causes, detection, treatment, prevention of cancer. prereq: Biol 4003

MATH 5445 - Mathematical Analysis of Biological Networks

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Development/analysis of models for complex biological networks. Examples taken from signal transduction networks, metabolic networks, gene control networks, and ecological networks. prereq: Linear algebra, differential equations

MATH 4428 - Mathematical Modeling

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Modeling techniques for analysis/decision-making in industry. Optimization (sensitivity analysis, Lagrange multipliers, linear programming). Dynamical modeling (steady-states, stability analysis, eigenvalue methods, phase portraits, simulation). Probabilistic methods (probability/statistical models, Markov chains, linear regression, simulation). prereq: 2243 or 2373 or 2573

MATH 4281 - Introduction to Modern Algebra

Credits:	4.0 [max 4.0]
Typically offered:	Periodic Fall

Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent

MATH 5248 - Cryptology and Number Theory

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math

MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math

MATH 5285H - Honors: Fundamental Structures of Algebra I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 5286H - Honors: Fundamental Structures of Algebra II

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285

MATH 5385 - Introduction to Computational Algebraic Geometry

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]

MATH 4242 - Applied Linear Algebra

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 4242/Math 4457
Typically offered:	Every Fall, Spring & Summer

Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. prereq: 2243 or 2373 or 2573

MATH 5525 - Introduction to Ordinary Differential Equations

Credits:	4.0 [max 4.0]
Typically offered:	Periodic Fall & Spring

Ordinary differential equations, solution of linear systems, qualitative/numerical methods for nonlinear systems. Linear algebra background, fundamental matrix solutions, variation of parameters, existence/uniqueness theorems, phase space. Rest points, their stability. Periodic orbits, Poincare-Bendixson theory, strange attractors. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]

MATH 5535 - Dynamical Systems and Chaos

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall & Spring

Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]

MATH 5651 - Basic Theory of Probability and Statistics

Credits:	4.0 [max 4.0]
Course Equivalencies:	Math 5651/Stat 5101
Typically offered:	Every Fall & Spring

Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.

STAT 5101 - Theory of Statistics I

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: (MATH 2263 or MATH 2374 or MATH 2573H), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)

MATH 5445 - Mathematical Analysis of Biological Networks

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Development/analysis of models for complex biological networks. Examples taken from signal transduction networks, metabolic networks, gene control networks, and ecological networks. prereq: Linear algebra, differential equations

MATH 5447 - Theoretical Neuroscience

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Nonlinear dynamical system models of neurons and neuronal networks. Computation by excitatory/inhibitory networks. Neural oscillations, adaptation, bursting, synchrony. Memory systems. prereq: 2243 or 2373 or 2574

CSCI 1103 - Introduction to Computer Programming in Java

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Fundamental programming concepts/software development using Java language. Problem solving skills. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Substantial programming projects. Weekly lab.

CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall, Spring & Summer

Programming for scientists/engineers. C/C++ programming constructs, object-oriented programming, software development, fundamental numerical techniques. Exercises/examples from various scientific fields. The online modality for CSci 1113 will only be offered during the summer session. prereq: Math 1271 or Math 1371 or Math 1571H or instr consent.

CSCI 1133 - Introduction to Computing and Programming Concepts

Credits:	4.0 [max 4.0]
Course Equivalencies:	CSci 1133/CSci 1133H
Typically offered:	Every Fall, Spring & Summer

Fundamental programming concepts using Python language. Problem solving skills, recursion, object-oriented programming. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Develop programs to solve real-world problems. prereq: concurrent registration is required (or allowed) in MATH 1271 or concurrent registration is required (or allowed) in MATH 1371 or concurrent registration is required (or allowed) in MATH 1571H or instr consent

BIOL 1009 - General Biology (BIOL)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Biol 1009/Biol 1009H
Typically offered:	Every Fall, Spring & Summer

A comprehensive introduction to biology - includes molecular structure of living things, cell processes, energy utilization, genetic information and inheritance, mechanisms of evolution, biological diversity, and ecology. Includes lab. This comprehensive course serves as a prerequisite and requirement in many majors.

BIOL 1009H - Honors: General Biology (BIOL)

Credits:	4.0 [max 4.0]
Course Equivalencies:	Biol 1009/Biol 1009H
Grading Basis:	A-F only
Typically offered:	Every Spring

A comprehensive introduction to biology - includes molecular structure of living things, cell processes, energy utilization, genetic information and inheritance, mechanisms of evolution, biological diversity, and ecology. Includes lab. This comprehensive course serves as a prerequisite and requirement in many majors.

CHEM 1061 - Chemical Principles I (PHYS)

Credits:	3.0 [max 3.0]
Course Equivalencies:	Chem 1061/Chem 1071H/Chem 1081
Typically offered:	Every Fall, Spring & Summer

Atomic theory, periodic properties of elements. Thermochemistry, reaction stoichiometry. Behavior of gases, liquids, and solids. Molecular/ionic structure/bonding. Organic chemistry and polymers. energy sources, environmental issues related to energy use. Prereq-Grade of at least C- in [1011 or 1015] or [passing placement exam, concurrent registration is required (or allowed) in 1065]; intended for science or engineering majors; concurrent registration is required (or allowed) in 1065; registration for 1065 must precede registration for 1061

CHEM 1065 - Chemical Principles I Laboratory (PHYS)

Credits:	1.0 [max 1.0]
Course Equivalencies:	Chem 1065/Chem 1075H
Grading Basis:	A-F only
Typically offered:	Every Fall, Spring & Summer

Basic laboratory skills while investigating physical and chemical phenomena closely linked to lecture material. Experimental design, data collection and treatment, discussion of errors, and proper treatment of hazardous wastes. prereq: concurrent registration is required (or allowed) in 1061

CHEM 1071H - Honors Chemistry I (PHYS)

Credits:	3.0 [max 3.0]
Course Equivalencies:	Chem 1061/Chem 1071H/Chem 1081
Grading Basis:	A-F only
Typically offered:	Every Fall

Advanced introduction to atomic theory. Periodic properties of elements. Behavior of gases, liquids, and solids. Molecular/ionic structure, bonding. Aspects of organic chemistry, spectroscopy, and polymers. Mathematically demanding quantitative problems. Writing for scientific journals. prereq: Honors student, permission of University Honors Program, concurrent registration is required (or allowed) in 1075H; registration for 1075H must precede registration for 1071H

CHEM 1075H - Honors Chemistry I Laboratory (PHYS)

Credits:	1.0 [max 1.0]
Course Equivalencies:	Chem 1065/Chem 1075H
Grading Basis:	A-F only
Typically offered:	Every Fall

Develop laboratory skills while investigating physical and chemical phenomena closely linked to lecture material. Experimental design, data collection and treatment, discussion of errors, and the proper treatment of hazardous wastes. prereq: prereq or coreq 1071H; honors student or permission of University Honors Program

CHEM 1062 - Chemical Principles II (PHYS)

Credits:	3.0 [max 3.0]
Course Equivalencies:	Chem 1062/1072H/1082
Typically offered:	Every Fall, Spring & Summer

Chemical kinetics. Radioactive decay. Chemical equilibrium. Solutions. Acids/bases. Solubility. Second law of thermodynamics. Electrochemistry/corrosion. Descriptive chemistry of elements. Coordination chemistry. Biochemistry. prereq: Grade of at least C- in 1061 or equiv, concurrent registration is required (or allowed) in 1066; registration for 1066 must precede registration for 1062

CHEM 1066 - Chemical Principles II Laboratory (PHYS)

Credits:	1.0 [max 1.0]
Course Equivalencies:	Chem 1066/Chem 1076H
Grading Basis:	A-F only
Typically offered:	Every Fall, Spring & Summer

Basic laboratory skills while investigating physical and chemical phenomena closely linked to lecture material. Experimental design, data collection and treatment, discussion of errors, and proper treatment of hazardous wastes. prereq: concurrent registration is required (or allowed) in 1062

CHEM 1072H - Honors Chemistry II (PHYS)

Credits:	3.0 [max 3.0]
Course Equivalencies:	Chem 1062/1072H/1082
Grading Basis:	A-F only
Typically offered:	Every Spring

Advanced introduction. Chemical kinetics/reaction mechanisms, chemical/physical equilibria, acids/bases, entropy/second law of thermodynamics, electrochemistry/corrosion; descriptive chemistry of elements; coordination chemistry; biochemistry. prereq: 1071H, concurrent registration is required (or allowed) in 1076H, honors student, registration for 1076H must precede registration for 1072H

CHEM 1076H - Honors Chemistry II Laboratory (PHYS)

Credits:	1.0 [max 1.0]
Course Equivalencies:	Chem 1066/Chem 1076H
Grading Basis:	A-F only
Typically offered:	Every Spring

Develop laboratory skills as experiments become increasingly complex. Data collection/treatment, discussion of errors, proper treatment of hazardous wastes, experiment design. prereq: concurrent registration is required (or allowed) in 1072H

PHSL 3061 - Principles of Physiology

Credits:	4.0 [max 4.0]
Course Equivalencies:	Phsl 3063/Phsl 3071
Typically offered:	Every Fall

Human physiology with emphasis on quantitative aspects. Organ systems (circulation, respiration, gastrointestinal, renal, endocrine, muscle, peripheral and central nervous systems), cellular transport processes, and scaling in biology. prereq: 1 year college chem and physics and math through integral calculus

PHSL 4702 - Cell Physiology

Credits:	3.0 [max 3.0]
Course Equivalencies:	AnSc 5702/Phsl 4702/Phsl 5702
Grading Basis:	A-F or Aud
Typically offered:	Every Fall

Cell Physiology involves the study of control mechanisms involved in maintaining homeostasis with respect to a variety of parameters including regulation of pH, volume, nutrient content, intracellular electrolyte composition, membrane potential, receptor signaling and aspects of intercellular communication. The first half of this team-taught course is organized in a partially on-line format where students learn from on-line materials and then take an on-line quiz each week before meeting with the instructor to review key concepts in class. The second half of the course is presented in lecture format. Student evaluation is based on quiz scores, in-class exams and graded problem sets. prereq: [3051 or 3061 or BIOL 3211], [CHEM 1022 or equiv], [MATH 1272 or equiv]

PHSL 5444 - Muscle

Credits:	3.0 [max 3.0]
Course Equivalencies:	BioC 5444/ Phsl 5444
Typically offered:	Every Spring

Muscle molecular structure/function and disease. Muscle regulation, ion transport, and force generation. Muscular dystrophy and heart disease. prereq: PHSL 3061 or PHSL 5061 or BioC 3021, BIOL 3021 or BIOL 4331 or instr consent

NSC 5202 - Theoretical Neuroscience: Systems and Information Processing

Credits:	3.0 [max 3.0]
Course Equivalencies:	NSc 5202/Phsl 5202
Typically offered:	Every Spring

Concepts of computational/theoretical neuroscience. Distributed representations and information theory. Methods for single-cell modeling, including compartmental/integrate-and-fire models. Learning rules, including supervised, unsupervised, and reinforcement learning models. Specific systems models from current theoretical neuroscience literature. Lecture/discussion. Readings from current scientific literature. prereq: [3101, 3102W] recommended

MATH 5445 - Mathematical Analysis of Biological Networks

Credits:	4.0 [max 4.0]
Typically offered:	Every Spring

Development/analysis of models for complex biological networks. Examples taken from signal transduction networks, metabolic networks, gene control networks, and ecological networks. prereq: Linear algebra, differential equations

MATH 5447 - Theoretical Neuroscience

Credits:	4.0 [max 4.0]
Typically offered:	Every Fall

Nonlinear dynamical system models of neurons and neuronal networks. Computation by excitatory/inhibitory networks. Neural oscillations, adaptation, bursting, synchrony. Memory systems. prereq: 2243 or 2373 or 2574

University Catalogs

Mathematics B.S.Math.