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Mathematics (MATH) Courses

Academic Unit: Mathematics, Sch of

MATH 1001 - Excursions in Mathematics [MATH]
(3 cr; Prereq-3 yrs high school math or placement exam or [grade of at least C- in PSTL 731 or 732]; Student Option; offered Every Fall & Spring)
Introduction to the breadth and nature of mathematics and the power of abstract reasoning, with applications to topics that are relevant to the modern world, such as voting, fair division of assets, patterns of growth, and opinion polls.
MATH 1008 - Trigonometry
(2.67 cr; A-F or Audit; offered Every Fall, Spring & Summer)
Analytic trigonometry, identities, equations, properties of trigometric functions, right/oblique triangles.
MATH 1031 - College Algebra and Probability [MATH]
(3 cr; Prereq-3 yrs high school math or satisfactory score on placement exam or grade of at least C- in [PSTL 731 or PSTL 732 or CI 0832]; Student Option; offered Every Fall, Spring & Summer)
Equivalent courses: CI 1806 (starting 20-JAN-15, was PSTL 1006 until 06-SEP-16)
Graphs of equations and functions, transformations of graphs; linear, quadratic, polynomial, and rational functions, with applications; inverses and compositions of functions; exponential and logarithmic functions with applications; basic probability rules, conditional probabilities, binomial probabilities.
MATH 1038 - College Algebra and Probability Submodule
(1 cr; Prereq-1051 or 1151 or 1155; A-F or Audit; offered Every Fall, Spring & Summer)
For students who need probability/permutations/combinations portion of 1031. Meets with 1031, has same grade/work requirements.
MATH 1040 - Topics in Mathematics (Topics course)
(1 cr; S-N only; offered Every Fall & Spring)
See Specific Topic Titles
MATH 1042 - Mathematics of Design [MATH]
(4 cr; Prereq-Satisfactory score on placement test or grade of at least C- in [1031 or 1051]; Student Option; offered Every Fall)
A tour of mathematics relevant to principles of design that support the "making" of things: from objects to buildings. Project-based problem solving. Systems of equations, trigonometry, vectors, analytic geometry, conic sections, transformations, approximation of length, area, and volume.
MATH 1049 - Intermediate Algebra Skills
(1 cr; S-N only; offered Every Fall & Spring)
This course serves as a co-requisite course to MATH 1031 and MATH 1051. It is designed to reinforce the skills in Intermediate Algebra and Trigonometry that are necessary for success in College Algebra. Students should enroll in this course if their placement exam score indicates that their preparedness for College Algebra is borderline. Other students with sufficiently high placement exam scores can enroll in MATH 1031/1051 without registering for MATH 1049. Students enrolled in this course should be concurrently enrolled in MATH 1031 or MATH 1051. This course is designed to build computational skills in material that is important for success in MATH 1031/1051. Skills include signed expressions, simplifying rational numbers and radicals, evaluating expressions, functions and function notation, and simplifying monomial expressions.
MATH 1051 - Precalculus I [MATH]
(3 cr; Prereq-3 yrs of high school math or satisfactory score on placement test or grade of at least C- in [PSTL 731 or PSTL 732 or CI 0832]; Student Option; offered Every Fall, Spring & Summer)
Graphs of equations and functions, transformations of graphs; linear, quadratic, polynomial, and rational functions with applications; zeroes of polynomials; inverses and compositions of functions; exponential and logarithmic functions with applications; coverage beyond that found in the usual 3 years of high school math.
MATH 1139 - College Algebra Skills
(1 cr; S-N only; offered Every Fall & Spring)
This course serves as a co-requisite course to MATH 1142. It is designed to reinforce the skills in College Algebra that are necessary for success in Short Calculus. Students should enroll in this course if their placement exam score indicates that their preparedness for Short Calculus is borderline. Other students with sufficiently high placement exam scores can enroll in MATH 1142 without registering for MATH 1139. Students enrolled in this course should be concurrently enrolled in MATH 1142. This course is designed to review computational skills in material that is important for success in MATH 1142. Skills include simplifying rational expressions, rationalizing the denominator, functions and function notation, factoring polynomials, the distance formula, equations of lines, exponential and logarithmic functions, and systems of equations.
MATH 1142 - Short Calculus [MATH]
(4 cr; Prereq-Satisfactory score on placement test or grade of at least C- in [1031 or 1051]; Student Option; offered Every Fall, Spring & Summer)
A streamlined one-semester tour of differential and integral calculus in one variable, and differential calculus in two variables. No trigonometry/does not have the same depth as MATH 1271-1272. Formulas and their interpretation and use in applications.
MATH 1143 - Introduction to Advanced Mathematics
(4 cr; A-F or Audit; offered Periodic Fall)
Topics that are covered in more depth in 2243 and 2263, plus probability theory. Matrices, eigenvectors, conditional probability, independence, distributions, basic statistical tools, linear regression. Linear differential equations and systems of differential equations. Multivariable differentiability and linearization.
MATH 1149 - College Algebra Skills
(1 cr; S-N only; offered Every Fall & Spring)
This course serves as a co-requisite course to MATH 1151. It is designed to reinforce the skills in College Algebra that are necessary for success in Trigonometry. Students should enroll in this course if their placement exam score indicates that their preparedness for Trigonometry is borderline. Other students with sufficiently high placement exam scores can enroll in MATH 1151 without registering for MATH 1149. Students enrolled in this course should be concurrently enrolled in MATH 1151. This course is designed to review computational skills in material that is important for success in MATH 1151. Skills include simplifying rational expressions, rationalizing the denominator, functions and function notation, factoring polynomials, congruent and similar triangles, distance formula, equations of lines, exponential functions, and sequences.
MATH 1151 - Precalculus II [MATH]
(3 cr; Prereq-Satisfactory score on placement exam or grade of at least C- in [1031 or 1051]; Student Option; offered Every Fall, Spring & Summer)
Equivalent courses: MATH 1155 (starting 02-SEP-08, ending 07-SEP-99), MATH 1031 (ending 04-SEP-01)
Properties of trigonometric functions and their inverses, including graphs and identities, with applications; polar coordinates, equations, graphs; complex numbers, complex plane, DeMoivre's Theorem; conic sections; systems of linear equations and inequalities, with applications; arithmetic and geometric sequences and series.
MATH 1155 - Intensive Precalculus [MATH]
(5 cr; Prereq-3 yrs high school math or satisfactory score on placement exam or grade of at least C- in [PSTL 731 or PSTL 732]; Student Option; offered Every Fall)
Equivalent courses: MATH 1151 (starting 02-SEP-08), MATH 1031 (ending 04-SEP-01)
Graphs of equations and functions; polynomial and rational functions; inverses and composition of functions; exponentials and logarithms; trig functions, graphs, identities; polar coordinates; complex numbers; systems of linear equations; arithmetic, geometric sequences, series; applications.
MATH 1241 - Calculus and Dynamical Systems in Biology [MATH]
(4 cr; Prereq-[4 yrs high school math including trig or satisfactory score on placement test or grade of at least C- in [1151 or 1155]], CBS student; Student Option; offered Every Fall & Spring)
Differential/integral calculus with biological applications. Discrete/continuous dynamical systems. Models from fields such as ecology/evolution, epidemiology, physiology, genetic networks, neuroscience, and biochemistry.
MATH 1269 - Precalculus Skills
(1 cr; S-N only; offered Every Fall & Spring)
This course serves as a co-requisite course to MATH 1241, MATH 1271, and MATH 1371. It is designed to reinforce the skills in College Algebra and Trigonometry that are necessary for success in Calculus. Students should enroll in this course if their placement exam score indicates that their preparedness for Calculus is borderline. Other students with sufficiently high placement exam scores can enroll in MATH 1241/1271/1371 without registering for MATH 1269. Students enrolled in this course should be concurrently enrolled in MATH 1241, MATH 1271, or MATH 1371. This course is designed to review computational skills in material that is important for success in an introductory Differential Calculus. Skills include simplifying rational expressions, factoring, binomial theorem, finding roots, quadratic formula, rationalizing denominators, equations of lines, laws of exponents and logarithms, graphs of common functions, the unit circle, trig identities, inverse trig functions, isolating variables, similar triangles, geometric formulas, inequalities, functions and function notation, domain and range of functions, inverse functions, composition of functions, symmetry, recursion and sequences, and solving systems of equations.
MATH 1271 - Calculus I [MATH]
(4 cr; Prereq-4 yrs high school math including trig or satisfactory score on placement test or grade of at least C- in [1151 or 1155]; Student Option; offered Every Fall, Spring & Summer)
Equivalent courses: MATH 1571H, MATH 1142 (ending 07-SEP-10), MATH 1371, ESPM 1145 (inactive, ending 16-JAN-07), MATH 1281 (inactive), MATH 1471 (starting 02-SEP-08, was MATH 1471H until 02-SEP-08)
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.
MATH 1272 - Calculus II
(4 cr; Prereq-[1271 or equiv] with grade of at least C-; Student Option; offered Every Fall, Spring & Summer)
Equivalent courses: MATH 1282 (inactive), MATH 1372, MATH 1252 (inactive), MATH 1472 (starting 02-SEP-08, was MATH 1472H until 02-SEP-08), MATH 1572H
Techniques of integration. Calculus involving transcendental functions, polar coordinates. Taylor polynomials, vectors/curves in space, cylindrical/spherical coordinates.
MATH 1281 - Calculus with Biological Emphasis I [MATH]
(4 cr; Student Option; offered Every Fall)
Equivalent courses: MATH 1571H, MATH 1142 (ending 07-SEP-10), MATH 1371, ESPM 1145 (inactive, ending 16-JAN-07), MATH 1471 (starting 02-SEP-08, was MATH 1471H until 02-SEP-08), MATH 1271
Differential calculus of single-variable functions, basics of integral calculus. Applications emphasizing biological sciences.
MATH 1282 - Calculus With Biological Emphasis II
(4 cr; Student Option; offered Every Spring)
Equivalent courses: MATH 1372, MATH 1252 (inactive), MATH 1272, MATH 1472 (starting 02-SEP-08, was MATH 1472H until 02-SEP-08), MATH 1572H
Techniques/applications of integration, differential equations/systems, matrix algebra, basics of multivariable calculus. Applications emphasizing biology.
MATH 1371 - CSE Calculus I [MATH]
(4 cr; 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; Student Option; offered Every Fall & Spring)
Equivalent courses: MATH 1571H, MATH 1142 (ending 07-SEP-10), ESPM 1145 (inactive, ending 16-JAN-07), MATH 1281 (inactive), MATH 1471 (starting 02-SEP-08, was MATH 1471H until 02-SEP-08), MATH 1271
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.
MATH 1372 - CSE Calculus II
(4 cr; Prereq-Grade of at least C- in [1371 or equiv], CSE or pre-Bioprod/Biosys Engr; Student Option; offered Every Spring)
Equivalent courses: MATH 1282 (inactive), MATH 1252 (inactive), MATH 1272, MATH 1472 (starting 02-SEP-08, was MATH 1472H until 02-SEP-08), MATH 1572H
Techniques of integration. Calculus involving transcendental functions, polar coordinates, Taylor polynomials, vectors/curves in space, cylindrical/spherical coordinates. Use of calculators, cooperative learning.
MATH 1473 - Honors Calculus IIA for Secondary Students
(2 cr; Student Option; offered Every Fall)
Equivalent courses: was MATH 1473H until 02-SEP-08
Accelerated honors sequence. Differential equations, sequence/series. Linear algebra.
MATH 1474 - Honors Calculus IIB for Secondary Students
(3 cr; Prereq-1473H; Student Option; offered Every Spring)
Equivalent courses: was MATH 1474H until 02-SEP-08
Accelerated honors sequence. Linear Algebra from geometric viewpoint. First-order systems of differential equations.
MATH 1571H - Honors Calculus I [MATH]
(4 cr; Prereq-Honors student and permission of University Honors Program; A-F only; offered Every Fall)
Equivalent courses: was MATH 1571 until 05-SEP-00, MATH 1142 (ending 07-SEP-10), MATH 1371, ESPM 1145 (inactive, ending 16-JAN-07), MATH 1281 (inactive), MATH 1471 (starting 02-SEP-08, was MATH 1471H until 02-SEP-08), MATH 1271
Differential/integral calculus of functions of a single variable. Emphasizes hard problem-solving rather than theory.
MATH 1572H - Honors Calculus II
(4 cr; Prereq-1571H (or equivalent) honors student; A-F only; offered Every Fall & Spring)
Equivalent courses: was MATH 1572 until 05-SEP-00, MATH 1282 (inactive), MATH 1372, MATH 1252 (inactive), MATH 1272, MATH 1472 (starting 02-SEP-08, was MATH 1472H until 02-SEP-08)
Continuation of 1571. Infinite series, differential calculus of several variables, introduction to linear algebra.
MATH 2142 - Elementary Linear Algebra
(4 cr; Student Option; offered Every Fall & Spring)
This course has three primary objectives. (1) To present the basic theory of linear algebra, including: solving systems of linear equations; determinants; the theory of Euclidean vector spaces and general vector spaces; eigenvalues and eigenvectors of matrices; inner products; diagonalization of quadratic forms; and linear transformations between vector spaces. (2) To introduce certain aspects of numerical linear algebra and computation. (3) To introduce applications of linear algebra to other domains such as data science. Objectives (2) and (3) will be taught with hands-on computer projects in a high-level programming language. Prerequisites: MATH 1272 or equivalent
MATH 2241 - Mathematical Modeling of Biological Systems
(3 cr; Prereq-[1241 or 1271 or 1371] w/grade of at least C-; Student Option; offered Every Fall & Spring; may be repeated for 4 credits)
Development, analysis and simulation of models for the dynamics of biological systems. Mathematical topics include discrete and continuous dynamical systems, linear algebra, and probability. Models from fields such as ecology, epidemiology, physiology, genetics, neuroscience, and biochemistry.
MATH 2243 - Linear Algebra and Differential Equations
(4 cr; Prereq-[1272 or 1282 or 1372 or 1572] w/grade of at least C-; Student Option; offered Every Fall, Spring & Summer)
Equivalent courses: MATH 2574H (starting 07-SEP-04, was MATH 3574 until 05-SEP-00), MATH 2471, MATH 2573H (ending 07-SEP-04, starting 05-SEP-00, was MATH 2573 until 05-SEP-00), MATH 2373 (starting 07-SEP-99)
Linear algebra: basis, dimension, matrices, eigenvalues/eigenvectors. Differential equations: first-order linear, separable; second-order linear with constant coefficients; linear systems with constant coefficients.
MATH 2263 - Multivariable Calculus
(4 cr; Prereq-[1272 or 1372 or 1572] w/grade of at least C-; Student Option; offered Every Fall, Spring & Summer)
Equivalent courses: MATH 3251 (inactive), MATH 2374, MATH 2573H (starting 07-SEP-04, ending 05-SEP-00, was MATH 2573 until 05-SEP-00), MATH 2373 (ending 07-SEP-99), MATH 2473 (starting 02-SEP-08, was MATH 2473H until 02-SEP-08)
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.
MATH 2373 - CSE Linear Algebra and Differential Equations
(4 cr; Prereq-[1272 or 1282 or 1372 or 1572] w/grade of at least C-, CSE or pre-Bio Prod/Biosys Engr; Student Option; offered Every Fall & Spring)
Equivalent courses: MATH 2574H (starting 07-SEP-04, was MATH 3574 until 05-SEP-00), MATH 2471, MATH 2243 (starting 12-JUN-00), MATH 2573H (ending 07-SEP-04, starting 05-SEP-00, was MATH 2573 until 05-SEP-00)
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.
MATH 2374 - CSE Multivariable Calculus and Vector Analysis
(4 cr; Prereq-[1272 or 1282 or 1372 or 1572] w/grade of at least C-, CSE or pre-Bioprod/Biosys Engr; Student Option; offered Every Fall & Spring)
Equivalent courses: MATH 2263, MATH 3251 (inactive), MATH 2573H (starting 07-SEP-04, ending 05-SEP-00, was MATH 2573 until 05-SEP-00), MATH 2373 (ending 07-SEP-99), MATH 2473 (starting 02-SEP-08, was MATH 2473H until 02-SEP-08)
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.
MATH 2472 - Honors Calculus IIIA for Secondary Students
(3 cr; Student Option; offered Every Fall)
Equivalent courses: was MATH 2472H until 02-SEP-08
Accelerated honors sequence for selected mathematically talented high school students. The geometry of IR^2 and IR^3. Vectors and vector functions. Multivariable calculus through differentiation using linear algebra.
MATH 2473 - Honors Calculus IIIB for Secondary Students
(3 cr; Student Option; offered Every Spring)
Equivalent courses: was MATH 2473H until 02-SEP-08
Accelerated honors sequence. Integration in multivariable calculus using linear algebra. Vector Analysis. Topics from differential equations.
MATH 2474 - Advanced Topics for Secondary Students
(3 cr; Prereq-2473H; Student Option; offered Every Spring)
Equivalent courses: was MATH 2474H until 02-SEP-08
Topics may include linear algebra, combinatorics, advanced differential equations, probability/statistics, numerical analysis, dynamical systems, topology/geometry. Emphasizes concepts/explorations.
MATH 2573H - Honors Calculus III
(4 cr; Prereq-Math 1572H (or equivalent), honors student; A-F only; offered Every Fall)
Equivalent courses: was MATH 2573 until 05-SEP-00, MATH 2263, MATH 3251 (inactive), MATH 2374, MATH 2373 (ending 07-SEP-99), MATH 2473 (starting 02-SEP-08, was MATH 2473H until 02-SEP-08)
Integral calculus of several variables. Vector analysis, including theorems of Gauss, Green, Stokes.
MATH 2574H - Honors Calculus IV
(4 cr; Prereq-Math 1572H or Math 2573H, honors student and permission of University Honors Program; A-F only; offered Every Spring)
Equivalent courses: was MATH 3574 until 05-SEP-00, MATH 2471, MATH 2243 (starting 12-JUN-00), MATH 2573H (ending 07-SEP-04, starting 05-SEP-00, was MATH 2573 until 05-SEP-00), MATH 2373 (starting 07-SEP-99)
Advanced linear algebra, differential equations. Additional topics as time permits.
MATH 2999 - Special Exam
(5 cr; Student Option; offered Periodic Summer)
TBD
MATH 3283W - Sequences, Series, and Foundations: Writing Intensive [WI]
(4 cr; 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-; Student Option; offered Every Fall & Spring)
Equivalent courses: was MATH 3283 until 05-SEP-00, MATH 2283 (inactive)
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.
MATH 3592H - Honors Mathematics I
(5 cr; Prereq-dept consent; for students with mathematical talent; A-F only; 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
(5 cr; Prereq-3592H or instr consent; A-F or Audit; 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.
MATH 4005 - Calculus Refresher
(4 cr; A-F or Audit)
Review of first-year calculus. Functions of one variable. Limits. Differentiation/integration of functions of one variable. Some applications, including max-min, related rates. Volume and surface area of solids of revolution. Vectors/curves in the plane and in space.
MATH 4065 - Theory of Interest
(4 cr; Prereq-1272 or 1372 or 1572; A-F only; 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.
MATH 4067W - Actuarial Mathematics in Practice [WI]
(3 cr; Prereq-4065, ACCT 2050, ECON 1101, ECON 1102; A-F only; 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.
MATH 4152 - Elementary Mathematical Logic
(3 cr; Prereq-one soph math course or instr consent; Student Option; offered Every Spring)
Equivalent courses: MATH 5165
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.
MATH 4242 - Applied Linear Algebra
(4 cr; Prereq-2243 or 2373 or 2573; Student Option; offered Every Fall, Spring & Summer)
Equivalent courses: MATH 4457 (inactive, starting 16-JAN-01)
Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications.
MATH 4281 - Introduction to Modern Algebra
(4 cr; Prereq-2283 or 3283 or instr consent; Student Option; 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.
MATH 4428 - Mathematical Modeling
(4 cr; Prereq-2243 or 2373 or 2573; Student Option; 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).
MATH 4471W - Mathematics for Social Justice [WI]
(4 cr; Prereq-Math 1272 or instructor consent ; A-F only; 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.
MATH 4512 - Differential Equations with Applications
(3 cr; Prereq-2243 or 2373 or 2573; Student Option; offered Every Fall & Spring)
Laplace transforms, series solutions, systems, numerical methods, plane autonomous systems, stability.
MATH 4567 - Applied Fourier Analysis
(4 cr; Prereq-2243 or 2373 or 2573; Student Option; 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.
MATH 4603 - Advanced Calculus I
(4 cr; Prereq-[[2243 or 2373], [2263 or 2374]] or 2574 or instr consent; Student Option; offered Every Fall, Spring & Summer)
Equivalent courses: MATH 4606 (inactive, ending 23-MAY-05, starting 16-JAN-01)
Axioms for the real numbers. Techniques of proof for limits, continuity, uniform convergence. Rigorous treatment of differential/integral calculus for single-variable functions.
MATH 4604 - Advanced Calculus II
(4 cr; Prereq-4603 or 5615 or instr consent; Student Option; 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.
MATH 4653 - Elementary Probability
(4 cr; Prereq-[2263 or 2374 or 2573]; [2283 or 2574 or 3283] recommended; Student Option; offered Every Fall & Spring)
Probability spaces, distributions of discrete/continuous random variables, conditioning. Basic theorems, calculational methodology. Examples of random sequences. Emphasizes problem-solving.
MATH 4707 - Introduction to Combinatorics and Graph Theory
(4 cr; Prereq-2243, [2283 or 3283]; Student Option; 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.
MATH 4990 - Topics in Mathematics (Topics course)
(1 cr [max 4]; Student Option; offered Every Fall, Spring & Summer; may be repeated for 12 credits; may be repeated 12 times)
MATH 4991 - Independent Study
(1 cr [max 4]; Student Option; offered Every Fall, Spring & Summer; may be repeated for 12 credits; may be repeated 12 times)
MATH 4992 - Directed Reading
(1 cr [max 4]; Student Option; offered Every Fall, Spring & Summer; may be repeated for 12 credits; may be repeated 12 times)
TBD
MATH 4993 - Directed Study
(1 cr [max 4]; Student Option; offered Every Fall, Spring & Summer; may be repeated for 12 credits; may be repeated 12 times)
TBD
MATH 4995 - Senior Project for CLA
(1 cr; Prereq-2 sem of upper div math, dept consent; A-F or Audit; offered Every Fall, Spring & Summer)
Directed study. May consist of paper on specialized area of math or original computer program or other approved project. Covers some math that is new to student. Scope/topic vary with instructor.
MATH 4997W - Senior project (Writing Intensive) [WI]
(1 cr; Prereq-2 sem upper div math, dept consent; A-F or Audit; offered Every Fall, Spring & Summer; may be repeated for 2 credits; may be repeated 2 times)
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.
MATH 5067 - Actuarial Mathematics I
(4 cr; Prereq-4065, [one sem [4xxx or 5xxx] [probability or statistics] course]; Student Option; 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.
MATH 5068 - Actuarial Mathematics II
(4 cr; Prereq-5067; Student Option; 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.
MATH 5075 - Mathematics of Options, Futures, and Derivative Securities I
(4 cr; Prereq-Two yrs calculus, basic computer skills; Student Option; 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.
MATH 5076 - Mathematics of Options, Futures, and Derivative Securities II
(4 cr; Prereq-5075; A-F or Audit; 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.
MATH 5165 - Mathematical Logic I
(4 cr; Prereq-2283 or 3283 or Phil 5201 or CSci course in theory of algorithms or instr consent; Student Option; offered Every Fall)
Equivalent courses: MATH 4152
Theory of computability: notion of algorithm, Turing machines, primitive recursive functions, recursive functions, Kleene normal form, recursion theorem. Propositional logic.
MATH 5248 - Cryptology and Number Theory
(4 cr; Prereq-2 sems soph math; Student Option; 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.
MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves
(4 cr; Prereq-2 sems soph math; Student Option; 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.
MATH 5285H - Honors: Fundamental Structures of Algebra I
(4 cr; Prereq-[2243 or 2373 or 2573], [2283 or 2574 or 3283]; Student Option; offered Every Fall)
Equivalent courses: was MATH 5285 until 05-SEP-00
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.
MATH 5286H - Honors: Fundamental Structures of Algebra II
(4 cr; Prereq-5285; Student Option; offered Every Fall & Spring)
Equivalent courses: was MATH 5286 until 05-SEP-00
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.
MATH 5335 - Geometry I
(4 cr; 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]; Student Option; 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.
MATH 5345H - Honors: Introduction to Topology
(4 cr; 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]; A-F only; offered Every Fall)
Equivalent courses: was MATH 5345 until 04-SEP-12
Rigorous introduction to general topology. Set theory, Euclidean/metric spaces, compactness/connectedness. May include Urysohn metrization, Tychonoff theorem or fundamental group/covering spaces.
MATH 5378 - Differential Geometry
(4 cr; Prereq-[2263 or 2374 or 2573], [2243 or 2373 or 2574]; [2283 or 3283] recommended]; Student Option; offered Every Spring)
Basic geometry of curves in plane and in space, including Frenet formula, theory of surfaces, differential forms, Riemannian geometry.
MATH 5385 - Introduction to Computational Algebraic Geometry
(4 cr; Prereq-[2263 or 2374 or 2573], [2243 or 2373 or 2574]; Student Option; 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.
MATH 5445 - Mathematical Analysis of Biological Networks
(4 cr; Prereq-Linear algebra, differential equations; Student Option; 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.
MATH 5447 - Theoretical Neuroscience
(4 cr; Prereq-2243 or 2373 or 2574; Student Option; offered Every Fall)
Nonlinear dynamical system models of neurons and neuronal networks. Computation by excitatory/inhibitory networks. Neural oscillations, adaptation, bursting, synchrony. Memory systems.
MATH 5465 - Mathematics of Machine Learning and Data Analysis I
(4 cr; Student Option; offered Every Fall)
This course gives a basic overview of the mathematical foundations for some commonly used techniques in machine learning and data science. The course will cover basic topics in fully supervised learning (support vector machines, k-nearest neighbor classification), unsupervised learning techniques (principal component analysis, k-means clustering, multi-dimensional scaling), modern methods in deep learning with applications to image classification, an introduction to graph-based learning (spectral clustering, label propagation, PageRank, the discrete Fourier transform, and applications to image processing), and a basic introduction to the convergence theory for gradient-based optimization. Prerequisites: Linear algebra (for example MATH 2142, 2243 or 2373) and multivariable calculus (for example MATH 2263 or 2374), or consent of the instructor.
MATH 5466 - Mathematics of Machine Learning and Data Analysis II
(4 cr; Student Option; offered Every Spring)
This course gives an overview of the mathematical foundations for some commonly used techniques in machine learning and data science. The course will cover unsupervised learning techniques (Johnson-Lindenstrauss randomized embeddings, spectral embeddings and diffusion maps, the t-distributed stochastic neighbor embedding, low-rank approximations), neural networks and deep learning (auto-differentiation, universal approximation, graph-neural networks), advanced techniques in graph-based learning (graph-cuts and graph total variation, active learning, semi-supervised learning at low label rates), and optimization for machine learning (iteratively reweighted least squares (IRLS), momentum descent, stochastic optimization, proximal gradient descent, Newton's method, matrix optimization and matrix calculus, matrix completion, and the continuum perspective on optimization). Prerequisites: Math 5465. Linear algebra (for example MATH 2142, 2243 or 2373) and multivariable calculus (for example MATH 2263 or 2374), or consent of the instructor.
MATH 5485 - Introduction to Numerical Methods I
(4 cr; Prereq-[2243 or 2373 or 2573], familiarity with some programming language; Student Option; offered Every Fall)
Solution of nonlinear equations in one variable. Interpolation, polynomial approximation. Methods for solving linear systems, eigenvalue problems, systems of nonlinear equations.
MATH 5486 - Introduction To Numerical Methods II
(4 cr; Prereq-5485; Student Option; offered Every Spring)
Numerical integration/differentiation. Numerical solution of initial-value problems, boundary value problems for ordinary differential equations, partial differential equations.
MATH 5490 - Topics in Applied Mathematics (Topics course)
(4 cr; Student Option; offered Periodic Fall & Spring; may be repeated for 12 credits; may be repeated 3 times)
Topics vary by instructor. See class schedule.
MATH 5525 - Introduction to Ordinary Differential Equations
(4 cr; Prereq-[2243 or 2373 or 2573], [2283 or 2574 or 3283]; Student Option; 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.
MATH 5535 - Dynamical Systems and Chaos
(4 cr; Prereq-[2243 or 2373 or 2573], [2263 or 2374 or 2574]; Student Option; 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.
MATH 5583 - Complex Analysis
(4 cr; Prereq-2 sems soph math [including [2263 or 2374 or 2573], [2283 or 3283]] recommended; Student Option; offered Every Fall, Spring & Summer)
Equivalent courses: MATH 2574H (ending 07-SEP-99, was MATH 3574 until 05-SEP-00)
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.
MATH 5587 - Elementary Partial Differential Equations I
(4 cr; Prereq-[2243 or 2373 or 2573], [2263 or 2374 or 2574]; Student Option; 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.
MATH 5588 - Elementary Partial Differential Equations II
(4 cr; Prereq-[[2243 or 2373 or 2573], [2263 or 2374 or 2574], 5587] or instr consent; A-F or Audit; 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.
MATH 5615H - Honors: Introduction to Analysis I
(4 cr; Prereq-[[2243 or 2373], [2263 or 2374], [2283 or 3283]] or 2574; Student Option; offered Every Fall)
Equivalent courses: was MATH 5615 until 05-SEP-00
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.
MATH 5616H - Honors: Introduction to Analysis II
(4 cr; Prereq-5615; Student Option; offered Every Spring)
Equivalent courses: was MATH 5616 until 05-SEP-00
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.
MATH 5651 - Basic Theory of Probability and Statistics
(4 cr; Prereq-[2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.; Student Option; offered Every Fall & Spring)
Equivalent courses: STAT 5101, STAT 4101 (ending 20-JAN-15), MATH 4653 (ending 06-SEP-05)
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.
MATH 5652 - Introduction to Stochastic Processes
(4 cr; Prereq-5651 or Stat 5101; Student Option; offered Every Fall & Spring)
Random walks, Markov chains, branching processes, martingales, queuing theory, Brownian motion.
MATH 5705 - Enumerative Combinatorics
(4 cr; Prereq-[2243 or 2373 or 2573], [2263 or 2283 or 2374 or 2574 or 3283]; Student Option; 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.
MATH 5707 - Graph Theory and Non-enumerative Combinatorics
(4 cr; 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; Student Option; 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.
MATH 5711 - Linear Programming and Combinatorial Optimization
(4 cr; Prereq-2 sems soph math [including 2243 or 2373 or 2573]; Student Option; 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.
MATH 5900 - Tutorial in Advanced Mathematics
(1 cr [max 6]; A-F or Audit; offered Every Fall, Spring & Summer; may be repeated for 120 credits; may be repeated 20 times)
Individually directed study.
MATH 5990 - Topics in Mathematics (Topics course)
(3 cr [max 4]; Student Option; offered Periodic Fall & Spring; may be repeated for 12 credits; may be repeated 3 times)
Topics vary by instructor. See class schedule.
MATH 8001 - Preparation for College Teaching
(1 cr; Prereq-Math grad student in good standing or instr consent; S-N or Audit; offered Every Fall & Spring)
Equivalent courses: was MATH 8000 until 12-JUN-00
New approaches to teaching/learning, issues in mathematics education, components/expectations of a college mathematics professor.
MATH 8002 - Preparation for Graduate Research
(1 cr; S-N only; offered Every Spring)
Further development of professional skills for success in mathematics graduate programs and subsequent career choices, with greater emphasis on the skills needed to do mathematical research. Topics include identifying research questions and advisers, surveying literature, research ethics, and practical research skills.
MATH 8141 - Applied Logic
(3 cr; A-F or Audit; offered Periodic Fall & Spring)
Applying techniques of mathematical logic to other areas of mathematics and computer science. Sample topics: complexity of computation, computable analysis, unsolvability of diophantine problems, program verification, database theory.
MATH 8142 - Applied Logic
(3 cr; A-F or Audit; offered Periodic Spring)
Applying techniques of mathematical logic to other areas of mathematics, computer science. Complexity of computation, computable analysis, unsolvability of diophantine problems, program verification, database theory.
MATH 8151 - Axiomatic Set Theory
(3 cr; Prereq-5166 or instr consent; A-F or Audit; offered Periodic Fall)
Axiomatic development of basic properties of ordinal/cardinal numbers, infinitary combinatorics, well founded sets, consistency of axiom of foundation, constructible sets, consistency of axiom of choice and of generalized continuum hypothesis.
MATH 8152 - Axiomatic Set Theory
(3 cr; Prereq-8151 or instr consent; A-F or Audit; offered Periodic Fall)
Notion of forcing, generic extensions, forcing with finite partial functions, independence of continuum hypothesis, forcing with partial functions of infinite cardinalities, relationship between partial orderings and Boolean algebras, Boolean-valued models, independence of axiom of choice.
MATH 8166 - Recursion Theory
(3 cr; Prereq-Math grad student or instr consent; A-F or Audit; offered Periodic Fall)
Analysis of concept of computability, including various equivalent definitions. Primitive recursive, recursive, partial recursive functions. Oracle Turing machines. Kleene Normal Form Theorem. Recursive, recursively enumerable sets. Degrees of unsolvability. Arithmetic hierarchy.
MATH 8167 - Recursion Theory
(3 cr; Prereq-8166; A-F or Audit; offered Periodic Spring)
Sample topics: complexity theory, recursive analysis, generalized recursion theory, analytical hierarchy, constructive ordinals.
MATH 8172 - Model Theory
(3 cr; Prereq-Math grad student or instr consent; A-F or Audit; offered Periodic Fall)
Interplay of formal theories, their models. Elementary equivalence, elementary extensions, partial isomorphisms. Lowenheim-Skolem theorems, compactness theorems, preservation theorems. Ultraproducts.
MATH 8173 - Model Theory
(3 cr; Prereq-8172 or instr consent; A-F or Audit; offered Periodic Fall)
Types of elements. Prime models, homogeneity, saturation, categoricity in power. Forking.
MATH 8190 - Topics in Logic (Topics course)
(1 cr [max 3]; A-F or Audit; offered Periodic Fall & Spring; may be repeated for 12 credits; may be repeated 12 times)
Offered for one year or one semester as circumstances warrant.
MATH 8201 - General Algebra
(3 cr; A-F or Audit; offered Every Fall; may be repeated 2 times)
Groups through Sylow, Jordan-H[o]lder theorems, structure of finitely generated Abelian groups. Rings and algebras, including Gauss theory of factorization. Modules, including projective and injective modules, chain conditions, Hilbert basis theorem, and structure of modules over principal ideal domains.
MATH 8202 - General Algebra
(3 cr; Prereq-8201 or instr consent; A-F or Audit; offered Every Spring; may be repeated 2 times)
Classical field theory through Galois theory, including solvable equations. Symmetric, Hermitian, orthogonal, and unitary form. Tensor and exterior algebras. Basic Wedderburn theory of rings; basic representation theory of groups.
MATH 8207 - Theory of Modular Forms and L-Functions
(3 cr; A-F or Audit)
Zeta and L-functions, prime number theorem, Dirichlet's theorem on primes in arithmetic progressions, class number formulas; Riemann hypothesis; modular forms and associated L-function; Eisenstein series; Hecke operators, Poincar[e] series, Euler products; Ramanujan conjectures; Theta series and quadratic forms; waveforms and L-functions.
MATH 8208 - Theory of Modular Forms and L-Functions
(3 cr; Prereq-8207 or instr consent; A-F or Audit; offered Periodic Fall)
Applications of Eisenstein series: special values and analytic continuation and functional equations of L-functions. Trace formulas. Applications of representation theory. Computations.
MATH 8211 - Commutative and Homological Algebra
(3 cr; Prereq-8202 or instr consent; A-F or Audit; offered Periodic Fall)
Selected topics.
MATH 8212 - Commutative and Homological Algebra
(3 cr; Prereq-8211 or instr consent; A-F or Audit; may be repeated 2 times)
Selected topics.
MATH 8245 - Group Theory
(3 cr; Prereq-8202 or instr consent; A-F or Audit; offered Every Fall)
Permutations, Sylow's theorems, representations of groups on groups, semi-direct products, solvable and nilpotent groups, generalized Fitting subgroups, p-groups, co-prime action on p-groups.
MATH 8246 - Group Theory
(3 cr; Prereq-8245 or instr consent; A-F or Audit; offered Periodic Fall & Spring)
Representation and character theory, simple groups, free groups and products, presentations, extensions, Schur multipliers.
MATH 8251 - Algebraic Number Theory
(3 cr; Prereq-8202 or instr consent; A-F or Audit; offered Periodic Fall)
Algebraic number fields and algebraic curves. Basic commutative algebra. Completions: p-adic fields, formal power series, Puiseux series. Ramification, discriminant, different. Finiteness of class number and units theorem.
MATH 8252 - Algebraic Number Theory
(3 cr; Prereq-8251 or instr consent; A-F or Audit; offered Periodic Fall)
Zeta and L-functions of global fields. Artin L-functions. Hasse-Weil L-functions. Tchebotarev density. Local and global class field theory. Reciprocity laws. Finer theory of cyclotomic fields.
MATH 8253 - Algebraic Geometry
(3 cr; A-F or Audit; offered Periodic Fall)
Curves, surfaces, projective space, affine and projective varieties. Rational maps. Blowing-up points. Zariski topology. Irreducible varieties, divisors.
MATH 8254 - Algebraic Geometry
(3 cr; Prereq-8253 or instr consent; A-F or Audit; offered Periodic Spring)
Sheaves, ringed spaces, and schemes. Morphisms. Derived functors and cohomology, Serre duality. Riemann-Roch theorem for curves, Hurwitz's theorem. Surfaces: monoidal transformations, birational transformations.
MATH 8270 - Topics in Algebraic Geometry (Topics course)
(1 cr [max 3]; Prereq-Math 8201, Math 8202; offered for one year or one semester as circumstances warrant; A-F or Audit; offered Every Fall & Spring; may be repeated for 12 credits; may be repeated 12 times)
N/A
MATH 8271 - Lie Groups and Lie Algebras
(3 cr; Prereq-8302 or instr consent; A-F or Audit; offered Periodic Fall; may be repeated 2 times)
Definitions and basic properties of Lie groups and Lie algebras; classical matrix Lie groups; Lie subgroups and their corresponding Lie subalgebras; covering groups; Maurer-Cartan forms; exponential map; correspondence between Lie algebras and simply connected Lie groups; Baker-Campbell-Hausdorff formula; homogeneous spaces.
MATH 8272 - Lie Groups and Lie Algebras
(3 cr; Prereq-8271 or instr consent; A-F or Audit; offered Periodic Spring)
Solvable and nilpotent Lie algebras and Lie groups; Lie's and Engels's theorems; semisimple Lie algebras; cohomology of Lie algebras; Whitehead's lemmas and Levi's theorem; classification of complex semisimple Lie algebras and compact Lie groups; representation theory.
MATH 8280 - Topics in Number Theory (Topics course)
(1 cr [max 3]; A-F or Audit; offered Periodic Fall & Spring; may be repeated for 12 credits; may be repeated 12 times)
Various topics in Number Theory.
MATH 8300 - Topics in Algebra (Topics course)
(1 cr [max 3]; Prereq-Grad math major or instr consent; offered as one yr or one sem crse as circumstances warrant; A-F or Audit; offered Every Fall & Spring; may be repeated for 12 credits; may be repeated 12 times)
Selected topics.
MATH 8301 - Algebraic Topology
(3 cr; Prereq-[Some point-set topology, algebra] or instr consent; A-F or Audit; offered Every Fall)
Classification of compact surfaces, fundamental group/covering spaces. Homology group, basic cohomology. Application to degree of a map, invariance of domain/dimension.
MATH 8302 - Manifolds and Topology
(3 cr; Prereq-8301 or instr consent; A-F or Audit; offered Every Spring)
Smooth manifolds, tangent spaces, embedding/immersion, Sard's theorem, Frobenius theorem. Differential forms, integration. Curvature, Gauss-Bonnet theorem. Time permitting: de Rham, duality in manifolds.
MATH 8306 - Algebraic Topology II
(3 cr; Prereq-8301 or instr consent; A-F or Audit; offered Periodic Fall)
Singular homology, cohomology theory with coefficients. Eilenberg-Stenrod axioms, Mayer-Vietoris theorem.
MATH 8307 - Algebraic Topology
(3 cr; Prereq-8306 or instr consent; A-F or Audit)
Basic homotopy theory, cohomology rings with applications. Time permitting: fibre spaces, cohomology operations, extra-ordinary cohomology theories.
MATH 8333 - FTE: Master's
(1 cr; Prereq-Master's student, adviser and DGS consent; No Grade Associated; offered Every Fall, Spring & Summer; 6 academic progress units; 6 financial aid progress units)
(No description)
MATH 8360 - Topics in Topology (Topics course)
(1 cr [max 3]; Prereq-8301 or instr consent; offered as one yr or one sem crse as circumstances warrant; A-F or Audit; offered Periodic Fall & Spring; may be repeated for 12 credits; may be repeated 12 times)
Selected topics.
MATH 8365 - Riemannian Geometry
(3 cr; Prereq-8301 or basic point-set topology or instr consent; A-F or Audit; offered Every Fall)
Riemannian metrics, curvature. Bianchi identities, Gauss-Bonnet theorem, Meyers's theorem, Cartan-Hadamard theorem.
MATH 8366 - Riemannian Geometry
(3 cr; Prereq-8365 or instr consent; A-F or Audit; offered Every Spring)
Gauss, Codazzi equations. Tensor calculus, Hodge theory, spinors, global differential geometry, applications.
MATH 8370 - Topics in Differential Geometry (Topics course)
(1 cr [max 3]; Prereq-8301 or 8365; offered for one yr or one sem as circumstances warrant; A-F or Audit; offered Every Fall & Spring; may be repeated for 12 credits; may be repeated 12 times)
Current research in Differential Geometry.
MATH 8380 - Topics in Advanced Geometry (Topics course)
(1 cr [max 3]; Prereq-8301, 8365; A-F or Audit; offered Periodic Fall & Spring; may be repeated for 12 credits; may be repeated 12 times)
Current research.
MATH 8385 - Calculus of Variations and Minimal Surfaces
(3 cr; Prereq-4xxx partial differential equations or instr consent; A-F or Audit; offered Periodic Fall)
Comprehensive exposition of calculus of variations and its applications. Theory for one-dimensional problems. Survey of typical problems. Necessary conditions. Sufficient conditions. Second variation, accessory eigenvalue problem. Variational problems with subsidiary conditions. Direct methods.
MATH 8386 - Calculus of Variations and Minimal Surfaces
(3 cr; Prereq-8595 or instr consent; A-F or Audit; offered Periodic Fall)
Theory of multiple integrals. Geometrical differential equations, i.e., theory of minimal surfaces and related structures (surfaces of constant or prescribed mean curvature, solutions to variational integrals involving surface curvatures), all extremals for variational problems of current interest as models for interfaces in real materials.
MATH 8387 - Mathematical Modeling of Industrial Problems
(3 cr; Prereq-[5xxx numerical analysis, some computer experience] or instr consent; A-F or Audit; offered Every Fall)
Mathematical models from physical, biological, social systems. Emphasizes industrial applications. Modeling of deterministic/probabilistic, discrete/continuous processes; methods for analysis/computation.
MATH 8388 - Mathematical Modeling of Industrial Problems
(3 cr; Prereq-8597 or instr consent; A-F or Audit; offered Periodic Fall)
Techniques for analysis of mathematical models. Asymptotic methods; design of simulation and visualization techniques. Specific computation for models arising in industrial problems.
MATH 8390 - Topics in Mathematical Physics (Topics course)
(1 cr [max 3]; Prereq-8601; offered for one yr or one sem as circumstances warrant; A-F or Audit; offered Periodic Fall; may be repeated for 12 credits; may be repeated 12 times)
Current research.
MATH 8401 - Mathematical Modeling and Methods of Applied Mathematics
(3 cr; Prereq-4xxx numerical analysis and applied linear algebra or instr consent; A-F or Audit; offered Every Fall; may be repeated 2 times)
Dimension analysis, similarity solutions, linearization, stability theory, well-posedness, and characterization of type. Fourier series and integrals, wavelets, Green's functions, weak solutions and distributions.
MATH 8402 - Mathematical Modeling and Methods of Applied Mathematics
(3 cr; Prereq-8401 or instr consent; A-F or Audit; offered Every Spring)
Calculus of variations, integral equations, eigenvalue problems, spectral theory. Perturbation, asymptotic methods. Artificial boundary conditions, conformal mapping, coordinate transformations. Applications to specific modeling problems.
MATH 8431 - Mathematical Fluid Mechanics
(3 cr; Prereq-5xxx numerical analysis of partial differential equations or instr consent; A-F or Audit; offered Periodic Fall)
Equations of continuity/motion. Kinematics. Bernoulli's theorem, stream function, velocity potential. Applications of conformal mapping.
MATH 8432 - Mathematical Fluid Mechanics
(3 cr; Prereq-8431 or instr consent; Student Option; offered Periodic Fall)
Plane flow of gas, characteristic method, hodograph method. Singular surfaces, shock waves, shock layers. Viscous flow, Navier-Stokes equations, exact solutions. Uniqueness, stability, existence theorems.
MATH 8441 - Numerical Analysis and Scientific Computing
(3 cr; Student Option; offered Every Fall; may be repeated 2 times)
Approximation of functions, numerical integration. Numerical methods for elliptic partial differential equations, including finite element methods, finite difference methods, and spectral methods. Grid generation.
MATH 8442 - Numerical Analysis and Scientific Computing
(3 cr; Prereq-8441 or instr consent; 5477-5478 recommended for engineering and science grad students; Student Option; offered Every Spring; may be repeated 2 times)
Numerical methods for integral equations, parabolic partial differential equations, hyperbolic partial differential equations. Monte Carlo methods.
MATH 8444 - FTE: Doctoral
(1 cr; Prereq-Doctoral student, adviser and DGS consent; No Grade Associated; offered Every Fall, Spring & Summer; 6 academic progress units; 6 financial aid progress units)
(No description)
MATH 8445 - Numerical Analysis of Differential Equations
(3 cr; Prereq-4xxx numerical analysis, 4xxx partial differential equations or instr consent; A-F or Audit; offered Every Fall)
Finite element and finite difference methods for elliptic boundary value problems (e.g., Laplace's equation) and solution of resulting linear systems by direct and iterative methods.
MATH 8446 - Numerical Analysis of Differential Equations
(3 cr; Prereq-8445 or instr consent; A-F or Audit; offered Every Spring)
Numerical methods for parabolic equations (e.g., heat equations). Methods for elasticity, fluid mechanics, electromagnetics. Applications to specific computations.
MATH 8450 - Topics in Numerical Analysis (Topics course)
(1 cr [max 3]; Prereq-Grad math major or instr consent; offered as one year or one semester course as circumstances warrant; A-F or Audit; offered Every Fall & Spring; may be repeated for 12 credits; may be repeated 12 times)
Selected topics.
MATH 8470 - Topics in Mathematical Theory of Continuum Mechanics (Topics course)
(1 cr [max 3]; A-F or Audit; offered Periodic Fall & Spring; may be repeated for 12 credits; may be repeated 12 times)
Offered for one year or one semester as circumstances warrant.
MATH 8501 - Differential Equations and Dynamical Systems I
(3 cr; Prereq-4xxx ODE or instr consent; A-F or Audit; offered Every Fall)
Existence, uniqueness, continuity, and differentiability of solutions. Linear theory and hyperbolicity. Basics of dynamical systems. Local behavior near a fixed point, a periodic orbit, and a homoclinic or heteroclinic orbit. Perturbation theory.
MATH 8502 - Differential Equations and Dynamical Systems II
(3 cr; Prereq-8501 or instr consent; A-F or Audit; offered Every Spring)
Stable, unstable, and center manifolds. Normal hyperbolicity. Nonautonomous dynamics and skew product flows. Invariant manifolds and quasiperiodicity. Transversality and Melnikov method. Approximation dynamics. Morse-Smale systems. Coupled oscillators and network dynamics.
MATH 8503 - Bifurcation Theory in Ordinary Differential Equations
(3 cr; Prereq-8501 or instr consent; A-F or Audit; offered Periodic Fall)
Basic bifurcation theory, Hopf bifurcation, and method averaging. Silnikov bifurcations. Singular perturbations. Higher order bifurcations. Applications.
MATH 8505 - Applied Dynamical Systems and Bifurcation Theory I
(3 cr; Prereq-5525 or 8502 or instr consent; A-F or Audit; offered Periodic Fall)
Static/Hopf bifurcations, invariant manifold theory, normal forms, averaging, Hopf bifurcation in maps, forced oscillations, coupled oscillators, chaotic dynamics, co-dimension 2 bifurcations. Emphasizes computational aspects/applications from biology, chemistry, engineering, physics.
MATH 8506 - Applied Dynamical Systems and Bifurcation Theory II
(3 cr; Prereq-5587 or instr consent; A-F or Audit; offered Periodic Fall)
Background on analysis in Banach spaces, linear operator theory. Lyapunov-Schmidt reduction, static bifurcation, stability at a simple eigenvalue, Hopf bifurcation in infinite dimensions invariant manifold theory. Applications to hydrodynamic stability problems, reaction-diffusion equations, pattern formation, and elasticity.
MATH 8520 - Topics in Dynamical Systems (Topics course)
(1 cr [max 3]; Prereq-8502; A-F or Audit; offered Periodic Fall & Spring; may be repeated for 12 credits; may be repeated 12 times)
Current research.
MATH 8530 - Topics in Ordinary Differential Equations (Topics course)
(1 cr [max 3]; Prereq-8502; A-F or Audit; offered Periodic Fall & Spring; may be repeated for 3 credits)
Offered for one year or one semester as circumstances warrant.
MATH 8540 - Topics in Mathematical Biology (Topics course)
(1 cr [max 3]; A-F or Audit; offered Every Fall & Spring; 3 academic progress units; 3 financial aid progress units; may be repeated for 12 credits; may be repeated 4 times)
Offered for one year or one semester as circumstances warrant.
MATH 8571 - Theory of Evolutionary Equations
(3 cr; Prereq-8502 or instr consent; A-F or Audit; offered Every Fall)
Infinite dimensional dynamical systems, global attractors, existence and robustness. Linear semigroups, analytic semigroups. Linear and nonlinear reaction diffusion equations, strong and weak solutions, well-posedness of solutions.
MATH 8572 - Theory of Evolutionary Equations
(3 cr; Prereq-8571 or instr consent; A-F or Audit; offered Periodic Spring)
Dynamics of Navier-Stokes equations, strong/weak solutions, global attractors. Chemically reacting fluid flows. Dynamics in infinite dimensions, unstable manifolds, center manifolds perturbation theory. Inertial manifolds, finite dimensional structures. Dynamical theories of turbulence.
MATH 8580 - Topics in Evolutionary Equations (Topics course)
(1 cr [max 3]; Prereq-8572 or instr consent; offered for one yr or one semester as circumstances warrant; A-F or Audit; offered Periodic Fall; may be repeated for 12 credits; may be repeated 12 times)
N/A
MATH 8581 - Applications of Linear Operator Theory
(3 cr; Prereq-4xxx applied mathematics or instr consent; A-F or Audit; offered Periodic Fall)
Metric spaces, continuity, completeness, contraction mappings, compactness. Normed linear spaces, continuous linear transformations. Hilbert spaces, orthogonality, projections.
MATH 8582 - Applications of Linear Operator Theory
(3 cr; Prereq-8581 or instr consent; A-F or Audit; offered Periodic Fall)
Fourier theory. Self-adjoint, compact, unbounded linear operators. Spectral analysis, eigenvalue-eigenvector problem, spectral theorem, operational calculus.
MATH 8583 - Theory of Partial Differential Equations
(3 cr; Prereq-[Some 5xxx PDE, 8601] or instr consent; A-F or Audit; offered Every Fall; may be repeated 2 times)
Classification of partial differential equations/characteristics. Laplace, wave, heat equations. Some mixed problems.
MATH 8584 - Theory of Partial Differential Equations
(3 cr; Prereq-8583 or instr consent; A-F or Audit; offered Every Spring; may be repeated 2 times)
Fundamental solutions/distributions, Sobolev spaces, regularity. Advanced elliptic theory (Schauder estimates, Garding's inequality). Hyperbolic systems.
MATH 8590 - Topics in Partial Differential Equations (Topics course)
(1 cr [max 3]; Prereq-8602; offered for one yr or one sem as circumstances warrant; A-F or Audit; offered Every Fall & Spring; may be repeated for 3 credits; may be repeated 2 times)
Research topics.
MATH 8600 - Topics in Advanced Applied Mathematics (Topics course)
(1 cr [max 3]; Student Option; offered Every Fall & Spring; may be repeated for 12 credits; may be repeated 12 times)
Offered for one yr or one semester as circumstances warrant. Topics vary. For details, contact instructor.
MATH 8601 - Real Analysis
(3 cr; A-F or Audit; offered Every Fall)
Set theory/fundamentals. Axiom of choice, measures, measure spaces, Borel/Lebesgue measure, integration, fundamental convergence theorems, Riesz representation.
MATH 8602 - Real Analysis
(3 cr; Prereq-8601 or instr consent; A-F or Audit; offered Every Spring)
Radon-Nikodym, Fubini theorems. C(X). Lp spaces (introduction to metric, Banach, Hilbert spaces). Stone-Weierstrass theorem. Basic Fourier analysis. Theory of differentiation.
MATH 8640 - Topics in Real Analysis (Topics course)
(3 cr; Prereq-8602 or instr consent; offered for one year or one semester as circumstances warrant; A-F or Audit; offered Periodic Fall; may be repeated for 12 credits; may be repeated 4 times)
Current research.
MATH 8641 - Spatial Ecology
(3 cr; Prereq-Two semesters calculus, theoretical population ecology or four semesters more robust calculus, course in statistics or probability or instr consent; S-N or Audit; offered Periodic Fall)
Introduction: role of space in population dynamics and interspecific interaction; includes single species and multispecies models, deterministic and stochastic theory, different modeling approaches, effects of implicit/explicit space on competition, pattern formation, stability diversity and invasion. Recent literature. Computer lab.
MATH 8651 - Theory of Probability Including Measure Theory
(3 cr; Student Option; offered Every Fall)
Probability spaces. Distributions/expectations of random variables. Basic theorems of Lebesque theory. Stochastic independence, sums of independent random variables, random walks, filtrations. Probability, moment generating functions, characteristic functions. Laws of large numbers.
MATH 8652 - Theory of Probability Including Measure Theory
(3 cr; Prereq-8651 or instr consent; Student Option; offered Every Spring)
Conditional distributions and expectations, convergence of sequences of distributions on real line and on Polish spaces, central limit theorem and related limit theorems, Brownian motion, martingales and introduction to other stochastic sequences.
MATH 8654 - Fundamentals of Probability Theory and Stochastic Processes
(3 cr; Prereq-8651 or 8602 or instr consent; Student Option; offered Periodic Spring)
Review of basic theorems of probability for independent random variables; introductions to Brownian motion process, Poisson process, conditioning, Markov processes, stationary processes, martingales, super- and sub-martingales, Doob-Meyer decomposition.
MATH 8655 - Stochastic Calculus with Applications
(3 cr; Prereq-8654 or 8659 or instr consent; Student Option; offered Every Fall)
Stochastic integration with respect to martingales, Ito's formula, applications to business models, filtering, and stochastic control theory.
MATH 8659 - Stochastic Processes
(3 cr; Prereq-8652 or instr consent; Student Option; offered Every Fall)
In-depth coverage of various stochastic processes and related concepts, such as Markov sequences and processes, renewal sequences, exchangeable sequences, stationary sequences, Poisson point processes, Levy processes, interacting particle systems, diffusions, and stochastic integrals.
MATH 8660 - Topics in Probability (Topics course)
(1 cr [max 3]; Student Option; offered Every Fall & Spring; may be repeated for 12 credits; may be repeated 12 times)
Offered for one year or one semester as circumstances warrant.
MATH 8666 - Doctoral Pre-Thesis Credits
(1 cr [max 6]; Prereq-Doctoral student who has not passed prelim oral; no required consent for 1st/2nd registrations, up to 12 combined cr; dept consent for 3rd/4th registrations, up to 24 combined cr; doctoral student admitted before summer 2007 may register up to four times, up to 60 combined cr; No Grade Associated; offered Every Fall, Spring & Summer; may be repeated for 12 credits; may be repeated 2 times)
TBD
MATH 8668 - Combinatorial Theory
(3 cr; A-F or Audit; offered Periodic Fall)
Basic enumeration, including sets and multisets, permutation statistics, inclusion-exclusion, integer/set partitions, involutions and Polya theory. Partially ordered sets, including lattices, incidence algebras, and Mobius inversion. Generating functions.
MATH 8669 - Combinatorial Theory
(3 cr; Prereq-8668 or instr consent; A-F or Audit; offered Spring Even Year)
Further topics in enumeration, including symmetric functions, Schensted correspondence, and standard tableaux; non-enumerative combinatorics, including graph theory and coloring, matching theory, connectivity, flows in networks, codes, and extremal set theory.
MATH 8680 - Topics in Combinatorics (Topics course)
(1 cr [max 3]; Prereq-Grad math major or instr consent; offered as one yr or one sem crse as circumstances warrant; A-F or Audit; offered Every Fall & Spring; may be repeated for 12 credits; may be repeated 12 times)
Selected topics.
MATH 8701 - Complex Analysis
(3 cr; A-F or Audit; offered Every Fall)
Foundations of holomorphic functions of one variable; relation to potential theory, complex manifolds, algebraic geometry, number theory. Cauchy's theorems, Poisson integral. Singularities, series, product representations. Hyperbolic geometry, isometries. Covering surfaces, Riemann-Hurwitz formula. Schwarz-Christoffel polygonal functions. Residues.
MATH 8702 - Complex Analysis
(3 cr; Prereq-8701 or instr consent; A-F or Audit; offered Every Spring)
Riemann mapping, uniformization, Dirichlet problem. Dirichlet principle, Green's functions, harmonic measures. Approximation theory. Complex analysis on tori (elliptic functions, modular functions, conformal moduli). Complex dynamical systems (Julia sets, Mandelbrot set).
MATH 8777 - Thesis Credits: Master's
(1 cr [max 18]; Prereq-Max 18 cr per semester or summer; 10 cr total required [Plan A only]; No Grade Associated; offered Every Fall, Spring & Summer; may be repeated for 50 credits; may be repeated 10 times)
(No description)
MATH 8790 - Topics in Complex Analysis (Topics course)
(1 cr [max 3]; Prereq-8702 or instr consent; offered for one yr or one sem as circumstances warrant; A-F or Audit; offered Periodic Fall; may be repeated for 12 credits; may be repeated 12 times)
Current research.
MATH 8801 - Functional Analysis
(3 cr; Prereq-8602 or instr consent; A-F or Audit; offered Every Fall)
Motivation in terms of specific problems (e.g., Fourier series, eigenfunctions). Theory of compact operators. Basic theory of Banach spaces (Hahn-Banach, open mapping, closed graph theorems). Frechet spaces.
MATH 8802 - Functional Analysis
(3 cr; Prereq-8801 or instr consent; A-F or Audit; offered Periodic Spring)
Spectral theory of operators, theory of distributions (generalized functions), Fourier transformations and applications. Sobolev spaces and pseudo-differential operators. C-star algebras (Gelfand-Naimark theory) and introduction to von Neumann algebras.
MATH 8888 - Thesis Credit: Doctoral
(1 cr [max 24]; Prereq-Max 18 cr per semester or summer; 24 cr required; No Grade Associated; offered Every Fall & Spring; may be repeated for 100 credits; may be repeated 10 times)
(No description)
MATH 8990 - Topics in Mathematics
(1 cr [max 6]; Prereq-instr consent; S-N or Audit; offered Every Fall & Spring; may be repeated for 24 credits; may be repeated 4 times)
Readings, research.
MATH 8991 - Independent Study
(1 cr [max 6]; Prereq-instr consent; Student Option; offered Every Fall, Spring & Summer; may be repeated for 24 credits; may be repeated 4 times)
Individually directed study.
MATH 8992 - Directed Reading
(1 cr [max 6]; Prereq-instr consent; S-N or Audit; offered Every Fall & Spring; may be repeated for 24 credits; may be repeated 6 times)
Individually directed reading.
MATH 8993 - Directed Study
(1 cr [max 6]; Prereq-instr consent; S-N or Audit; offered Every Spring; may be repeated for 24 credits; may be repeated 6 times)
Individually directed study.
MATH 8994 - Topics at the IMA (Topics course)
(1 cr [max 3]; Student Option; offered Every Fall & Spring; may be repeated for 6 credits; may be repeated 2 times)
Current research at IMA.

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