Twin Cities campus
 
Twin Cities Campus

Mathematics Minor

CLA Dean's Office
College of Liberal Arts
  • Program Type: Undergraduate minor related to major
  • Requirements for this program are current for Spring 2019
  • Required credits in this minor: 25 to 30
Students complete all the lower division requirements in the mathematics major, plus two upper division electives.
Program Delivery
This program is available:
  • via classroom (the majority of instruction is face-to-face)
Admission Requirements
For information about University of Minnesota admission requirements, visit the Office of Admissions website.
Required prerequisites
Calculus I & II
Take exactly 2 course(s) totaling exactly 8 credit(s) from the following:
Calculus I
· MATH 1271 - Calculus I [MATH] (4.0 cr)
or MATH 1371 - CSE Calculus I [MATH] (4.0 cr)
or MATH 1571H - Honors Calculus I [MATH] (4.0 cr)
· Calculus II
· MATH 1272 - Calculus II (4.0 cr)
or MATH 1372 - CSE Calculus II (4.0 cr)
or MATH 1572H - Honors Calculus II (4.0 cr)
Required prerequisites
2xxx/3xxxH-Level Calculus Course
Take exactly 1 course(s) totaling 4 - 5 credit(s) from the following:
Linear Algebra & Differential Equations
· MATH 2243 - Linear Algebra and Differential Equations (4.0 cr)
or MATH 2373 - CSE Linear Algebra and Differential Equations (4.0 cr)
or MATH 2574H - Honors Calculus IV (4.0 cr)
· Multivariable Calculus
· MATH 2263 - Multivariable Calculus (4.0 cr)
or MATH 2374 - CSE Multivariable Calculus and Vector Analysis (4.0 cr)
or MATH 2573H - Honors Calculus III (4.0 cr)
· Honors Mathematics
· MATH 3592H - Honors Mathematics I (5.0 cr)
or MATH 3593H - Honors Mathematics II (5.0 cr)
Minor Requirements
Students may earn no more than one undergraduate degree in mathematics: a BA, a BS, or a minor.
Remaining 2xxx/3xxxH-Level Calculus Course
Courses that counted towards the Admissions requirement for the mathematics BA may not also count towards this requirement.
Take exactly 1 course(s) totaling 4 - 5 credit(s) from the following:
Linear Algebra & Differential Equations
MATH 2243 - Linear Algebra and Differential Equations (4.0 cr)
or MATH 2373 - CSE Linear Algebra and Differential Equations (4.0 cr)
or MATH 2574H - Honors Calculus IV (4.0 cr)
or Multivariable Calculus
MATH 2263 - Multivariable Calculus (4.0 cr)
or MATH 2374 - CSE Multivariable Calculus and Vector Analysis (4.0 cr)
or MATH 2573H - Honors Calculus III (4.0 cr)
or Honors Mathematics
MATH 3593H - Honors Mathematics II (5.0 cr)
Sequences, Series, and Foundations
This course requirement will be waived for students who take MATH 3592H and 3593H.
Take exactly 1 course(s) totaling 3 - 4 credit(s) from the following:
· MATH 2283 - Sequences, Series, and Foundations (3.0 cr)
or MATH 3283W - Sequences, Series, and Foundations: Writing Intensive [WI] (4.0 cr)
Electives
Selection of MATH course electives for the minor requires department advisor approval. As many as 1 STAT course (Theory of Statistics I or II) listed below may count towards the Electives requirement.
Take exactly 2 course(s) totaling 6 - 8 credit(s) from the following:
· MATH 4065 - Theory of Interest (4.0 cr)
· MATH 4151 - Elementary Set Theory (3.0 cr)
· MATH 4152 - Elementary Mathematical Logic (3.0 cr)
· MATH 4242 - Applied Linear Algebra (4.0 cr)
· MATH 4281 - Introduction to Modern Algebra (4.0 cr)
· MATH 4428 - Mathematical Modeling (4.0 cr)
· MATH 4512 - Differential Equations with Applications (3.0 cr)
· MATH 4567 - Applied Fourier Analysis (4.0 cr)
· MATH 4603 - Advanced Calculus I (4.0 cr)
· MATH 4604 - Advanced Calculus II (4.0 cr)
· MATH 4653 - Elementary Probability (4.0 cr)
· MATH 4707 - Introduction to Combinatorics and Graph Theory (4.0 cr)
· MATH 5067 - Actuarial Mathematics I (4.0 cr)
· MATH 5068 - Actuarial Mathematics II (4.0 cr)
· MATH 5075 - Mathematics of Options, Futures, and Derivative Securities I (4.0 cr)
· MATH 5076 - Mathematics of Options, Futures, and Derivative Securities II (4.0 cr)
· MATH 5165 - Mathematical Logic I (4.0 cr)
· MATH 5166 - Mathematical Logic II (4.0 cr)
· MATH 5248 - Cryptology and Number Theory (4.0 cr)
· MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
· MATH 5285H - Honors: Fundamental Structures of Algebra I (4.0 cr)
· MATH 5286H - Honors: Fundamental Structures of Algebra II (4.0 cr)
· MATH 5335 - Geometry I (4.0 cr)
· MATH 5336 - Geometry II (4.0 cr)
· MATH 5345H - Honors: Introduction to Topology (4.0 cr)
· MATH 5378 - Differential Geometry (4.0 cr)
· MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
· MATH 5445 - Mathematical Analysis of Biological Networks (4.0 cr)
· MATH 5447 - Theoretical Neuroscience (4.0 cr)
· MATH 5467 - Introduction to the Mathematics of Image and Data Analysis (4.0 cr)
· MATH 5485 - Introduction to Numerical Methods I (4.0 cr)
· MATH 5486 - Introduction To Numerical Methods II (4.0 cr)
· MATH 5525 - Introduction to Ordinary Differential Equations (4.0 cr)
· MATH 5535 - Dynamical Systems and Chaos (4.0 cr)
· MATH 5583 - Complex Analysis (4.0 cr)
· MATH 5587 - Elementary Partial Differential Equations I (4.0 cr)
· MATH 5588 - Elementary Partial Differential Equations II (4.0 cr)
· MATH 5615H - Honors: Introduction to Analysis I (4.0 cr)
· MATH 5616H - Honors: Introduction to Analysis II (4.0 cr)
· MATH 5652 - Introduction to Stochastic Processes (4.0 cr)
· MATH 5654 - Prediction and Filtering (4.0 cr)
· MATH 5705 - Enumerative Combinatorics (4.0 cr)
· MATH 5707 - Graph Theory and Non-enumerative Combinatorics (4.0 cr)
· MATH 5711 - Linear Programming and Combinatorial Optimization (4.0 cr)
· MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
or STAT 5101 - Theory of Statistics I (4.0 cr)
· STAT 5102 - Theory of Statistics II (4.0 cr)
 
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MATH 1271 - Calculus I (MATH)
Credits: 4.0 [max 4.0]
Course Equivalencies: 00067 - 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 1142/1271/1281/1371/1571H
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: 00067 - Math 1142/1271/1281/1371/1571H
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 1272/1282/1252/1372/1572
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 1272/1282/1252/1372/1572
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: 00068 - Math 1272/1282/1252/1372/1572
Grading Basis: A-F only
Typically offered: Every Spring
Continuation of 1571. Infinite series, differential calculus of several variables, introduction to linear algebra. prereq: 1571H, honors student, permission of University Honors Program
MATH 2243 - Linear Algebra and Differential Equations
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2243/2373/2573
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 2243/2373/2573
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: 00561 - Math 2243/Math 2373/Math 2573H
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 2263/2373/2573H/3251
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 2263/2373/2573H/3251
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: 00069 - Math 2263/2374/3251
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 Math 2574H, 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 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: dept consent; for students with mathematical talent
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 2243/2373/2573
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 2243/2373/2573
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: 00561 - Math 2243/Math 2373/Math 2573H
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 2263/2373/2573H/3251
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 2263/2373/2573H/3251
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: 00069 - Math 2263/2374/3251
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 Math 2574H, honors student and permission of University Honors Program
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 2283 - Sequences, Series, and Foundations
Credits: 3.0 [max 3.0]
Course Equivalencies: Math 2283/3283W
Typically offered: Every Fall & Spring
Mathematical reasoning. Elements of 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. 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 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 4151 - Elementary Set Theory
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Basic properties of operations on sets, cardinal numbers, simply and well-ordered sets, ordinal numbers, axiom of choice, axiomatics. prereq: One soph math course or instr consent
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: 01212 - 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: 01072 - 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: 01776
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 5166 - Mathematical Logic II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
First-order logic: provability/truth in formal systems, models of axiom systems, Godel's completeness theorem. Godel's incompleteness theorem: decidable theories, representability of recursive functions in formal theories, undecidable theories, models of arithmetic. prereq: 5165
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 5336 - Geometry II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Projective geometry, including: relation to Euclidean geometry, finite geometries, fundamental theorem of projective geometry. N-dimensional Euclidean geometry from a vector viewpoint. Emphasizes N=3, including: polyhedra, spheres, isometries. prereq: 5335
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 3574/5583
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: 00259 - MATH 4653/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]
Course Equivalencies: 00259 - Math 5651/Stat 5101
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], [CSCI 2033 or Math 2373 or Math 2243]
STAT 5102 - Theory of Statistics II
Credits: 4.0 [max 4.0]
Course Equivalencies: Stat 4102/5102
Typically offered: Every Spring
Sampling, sufficiency, estimation, test of hypotheses, size/power. Categorical data. Contingency tables. Linear models. Decision theory. prereq: 5101 or Math 5651