Program Details : University Catalogs : University of Minnesota

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 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 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 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 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 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 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 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 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 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 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 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 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 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 4471W - Mathematics for Social Justice (WI)

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

This course will introduce you to quantitative literacy, critical thinking, and problem solving skills in socially relevant contexts. While students may be accustomed to thinking about mathematics as an abstract set of principles and proofs, this course will encourage thinking about mathematics in concrete contexts as a way to improve our communities and the world. Students will develop the ability and inclination to understand and develop realistic solutions to issues of social, political, and economic justice. Examples of specific topics include: the Flint water crisis, sea level change in an island community, gerrymandering, and racial bias in policing. The mathematical tools used will include basic statistics, modeling, and data analysis, among others. While most students in this class will be ''good at math,'' this class explores using math to do good. Prereq: Math 1272 or instructor consent

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 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]

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)

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]

University Catalogs

Mathematics Minor