Course Descriptions

The Course Descriptions catalog describes all undergraduate and graduate courses offered by Michigan State University. The searches below only return course versions Fall 2000 and forward. Please refer to the Archived Course Descriptions for additional information.

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MTH 101 Quantitative Literacy I

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3
Description:
Quantitative literacy including applications to health and risk, science, and the environment.
Effective Dates:
US18 - Open

MTH 102 Quantitative Literacy II

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3
Description:
Quantitative literacy including applications to finance, economics, and politics.
Effective Dates:
US18 - Open

MTH 103 College Algebra

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
Designated score on Mathematics Placement test
Not open to students with credit in:
MTH 103B, MTH 116
Description:
Number systems; functions and relations; exponents and logarithms; elementary theory of equations; inequalities; and systems of equations.
Effective Dates:
SS22 - Open

MTH 103A College Algebra I

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Not open to students with credit in:
MTH 103 or MTH 116
Description:
Functions, graphing, and modeling, with a focus on linear functions and models.
Effective Dates:
FS18 - Open

MTH 103B College Algebra II

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 103A
Not open to students with credit in:
MTH 103, MTH 116
Description:
Continuation of MTH 103A. Topics focus on exponential, logarithmic, polynomial, and rational functions.
Effective Dates:
SS19 - Open

MTH 114 Trigonometry

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 103
Not open to students with credit in:
MTH 116, MTH 104
Description:
Radian and degree measure of angles. Definitions and graphs of trigonometric functions and their inverses. Solving trigonometric equations. Applications including identities, indirect measurement and trigonometric modeling.
Effective Dates:
FS13 - Open

MTH 116 College Algebra and Trigonometry

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 5   Lecture/Recitation/Discussion Hours:5
Prerequisite:
Designated score on Mathematics Placement test
Not open to students with credit in:
LB 117, MTH 103, MTH 103B
Description:
Functions and graphs. Equations and inequalities. Exponential and logarithmic functions. Trigonometric functions. Systems of equations. Binomial theorem.
Effective Dates:
FS24 - Open

MTH 124 Survey of Calculus I

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 103 or MTH 116) or designated score on Mathematics Placement test
Not open to students with credit in:
LB 118 or MTH 132 or MTH 152H
Description:
Study of limits, continuous functions, derivatives, integrals and their applications.
Effective Dates:
FS13 - Open

MTH 126 Survey of Calculus II

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 124
Not open to students with credit in:
MTH 133 or MTH 153H
Description:
Application of partial derivatives, integrals, optimization of functions of several variables and differential equations.
Effective Dates:
FS23 - Open

MTH 132 Calculus I

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 116 OR (MTH 103 and MTH 114) OR (MTH 103B and MTH 114) OR LB 117
Not open to students with credit in:
LB 118, MTH 152H
Description:
Limits, continuous functions, derivatives and their applications. Integrals and the fundamental theorem of calculus.
Effective Dates:
FS19 - Open

MTH 133 Calculus II

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 4   Lecture/Recitation/Discussion Hours:4
Prerequisite:
MTH 132 or MTH 152H or LB 118
Not open to students with credit in:
LB 119, MTH 153H
Description:
Applications of the integral and methods of integration. Improper integrals. Polar coordinates and parametric curves. Sequences and series. Power series.
Effective Dates:
FS13 - Open

MTH 152H Honors Calculus I

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Restrictions:
Open to students in the Honors College or approval of department.
Not open to students with credit in:
LB 118, MTH 132
Description:
Limits, continuous functions, derivatives, integrals, fundamental theorem of calculus. Special emphasis on concepts and theory.
Effective Dates:
FS13 - Open

MTH 153H Honors Calculus II

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 4   Lecture/Recitation/Discussion Hours:5
Prerequisite:
(MTH 152H or MTH 132 or LB 118)
Restrictions:
Open to students in the Honors College or approval of department.
Not open to students with credit in:
MTH 133, LB 119
Description:
The integral. Improper integrals. Polar coordinates and parametric curves. Sequences and series. Power and Taylor series. Special emphasis on concepts and theory.
Effective Dates:
FS13 - Open

MTH 201 Elementary Mathematics for Teachers I

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 103 or MTH 116 or MTH 124 or MTH 132 or MTH 152H or LB 118 or MTH 101 or MTH 102 or MTH 103B) or designated score on Mathematics Placement test
Restrictions:
Open to students in the Child Development major or in the Education Major or in the Special Education-Learning Disabilities Major or in the Teacher Certification Internship Year Studies Program.
Description:
Mathematics needed for teaching grades PreK - 6. Place value, algorithms for whole numbers, decimals, and fractions with an emphasis on children’s mathematical thinking.
Effective Dates:
FS19 - Open

MTH 234 Multivariable Calculus

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 4   Lecture/Recitation/Discussion Hours:4
Prerequisite:
MTH 133 or MTH 153H or LB 119
Not open to students with credit in:
MTH 254H or LB 220
Description:
Vectors in space. Functions of several variables and partial differentiation. Multiple integrals. Line and surface integrals. Green's and Stokes's theorems.
Effective Dates:
FS13 - Open

MTH 235 Differential Equations

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:4
Prerequisite:
MTH 234 or MTH 254H or LB 220
Restrictions:
Not open to students in the Bachelor of Science in Mathematics or in the Bachelor of Arts in Mathematics or in the Lyman Briggs Mathematics Coordinate Major.
Not open to students with credit in:
MTH 347H or MTH 340
Description:
Separable and exact equations. Linear equations and variation of parameters. Higher order linear equations. Laplace transforms. Systems of first-order linear equations. Introduction to partial differential equations and Fourier series.
Effective Dates:
FS24 - Open

MTH 254H Honors Multivariable Calculus

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 4   Lecture/Recitation/Discussion Hours:5
Prerequisite:
MTH 153H or MTH 133 or LB 119
Restrictions:
Open to students in the Honors College or approval of department.
Not open to students with credit in:
MTH 234 or LB 220
Description:
Vectors in space. Functions of several variables and partial differentiation. Multiple integrals. Line and surface integrals. Green's and Stokes's Theorems.
Effective Dates:
FS13 - Open

MTH 290 Directed Study

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Variable from 1 to 4
Reenrollment Information:
A student may earn a maximum of 6 credits in all enrollments for this course.
Description:
Faculty directed study of selected mathematical topics.
Effective Dates:
FS13 - Open

MTH 299 Transitions

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 4
Prerequisite:
MTH 132 or MTH 152H or LB 118
Recommended Background:
(MTH 133 or concurrently) or (LB 119 or concurrently)
Description:
Introduction to mathematical reasoning, basic logic, set theory, integers, natural numbers and induction, basic number theory, real numbers, limits, sequences, series.
Effective Dates:
FS13 - Open

MTH 304 Algebra and Calculus for Secondary Educators

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3
Prerequisite:
(MTH 132 and MTH 299) and completion of Tier I writing requirement
Restrictions:
Open to students in the Mathematics-Secondary Education Major.
Description:
Algebra, functions and calculus needed for understanding connections between topics of collegiate math and the mathematics taught in grades 7-12.
Effective Dates:
FS23 - Open

MTH 305 Discrete and Computational Mathematics for Secondary Educators

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 304) and completion of Tier I writing requirement
Restrictions:
Open to students in the Mathematics-Secondary Education Major.
Description:
Discrete and Computational mathematics needed for understanding connections between topics of collegiate math and the mathematics taught in grades 7-12.
Effective Dates:
SS24 - Open

MTH 309 Linear Algebra I

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 133 or MTH 153H or LB 119) and completion of Tier I writing requirement
Not open to students with credit in:
MTH 317H
Description:
Matrices, systems of linear equations, vector spaces, linear transformations, inner products and orthogonal spaces, eigenvalues and eigenvectors, and applications to geometry. A writing course with emphasis on proofs.
Effective Dates:
FS23 - Open

MTH 310 Abstract Algebra I and Number Theory

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
((MTH 299 or MTH 317H) or approval of department) and completion of Tier I writing requirement
Not open to students with credit in:
MTH 418H
Description:
Structure of the integers, congruences, rings, ring homomorphisms, ideals, quotient rings. A writing course with an emphasis on proofs.
Effective Dates:
US17 - Open

MTH 314 Matrix Algebra with Computational Applications

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 133 or MTH 153H or LB 119) and (CMSE 201 or CSE 231)
Restrictions:
Not open to students in the Actuarial Science Major or in the Bachelor of Arts in Computational Mathematics or in the Bachelor of Science in Computational Mathematics or in the Bachelor of Science in Mathematics or in the Bachelor of Arts in Mathematics or in the Bachelor of Science in Mathematics, Advanced or in the Bachelor of Arts in Mathematics, Advanced or in the Mathematics Minor or in the Mathematics-Elementary Disciplinary Teaching Minor or in Mathematics-Secondary Disciplinary Teaching Minor.
Description:
Numerical methods in linear algebra with applications to systems of equations and eigenvalue problems, and geometry.
Interdepartmental With:
Computational Mathematics, Science, & Engineering
Administered By:
Mathematics
Effective Dates:
US19 - Open

MTH 317H Honors Linear Algebra

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 4   Lecture/Recitation/Discussion Hours:5
Prerequisite:
MTH 133 or MTH 153H or LB 119
Restrictions:
Open to students in the Honors College or approval of department.
Description:
Systems of equations, matrix algebra, vector spaces, linear transformations, geometry of R^n, eigenvalues, eigenvectors, diagonalization, inner products. Emphasis on mathematical reasoning, proofs, and concepts.
Effective Dates:
FS23 - Open

MTH 320 Analysis I

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 133 or MTH 153H or LB 119) and (MTH 299 or MTH 317H or approval of department)
Not open to students with credit in:
MTH 327H
Description:
Convergence of sequences and series. Upper and lower limits, completeness, limits and continuity. Derivatives. Uniform convergence.
Effective Dates:
US15 - Open

MTH 327H Honors Introduction to Analysis

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 317H
Restrictions:
Approval of department.
Description:
Emphasis on foundations and metric topology. Convergence of sequence and series, continuity of functions. Differentiation and integration in one dimension.
Effective Dates:
FS23 - Open

MTH 330 Higher Geometry

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 299 or MTH 317H
Description:
Topics in transformations: isometries, similarities, inversion. Advanced Euclidean geometry: theorems of Menelaus, Ceva, and Desargues. Cross ratio, harmonic points, analytic, metric, and vector methods, and convexity.
Effective Dates:
US26 - Open

MTH 340 Ordinary Differential Equations I

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 309 or MTH 317H) and (MTH 133 or MTH 153H or LB 119)
Not open to students with credit in:
MTH 347H
Description:
Techniques for solving differential equations, existence and uniqueness theorems, qualitative theory, Fourier series and applications.
Effective Dates:
FS23 - US26

MTH 347H Honors Ordinary Differential Equations

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 309 or MTH 317H) and (MTH 133 or MTH 153H or LB 119)
Restrictions:
Approval of department.
Description:
Separable and exact equations, linear equations and variation of parameters, higher order linear equations, Laplace Transforms, first-order linear systems, classification of singularities, nonlinear systems, partial differential equations and Fourier Series, existence and uniqueness theorems. Emphasis on theory.
Effective Dates:
US15 - Open

MTH 360 Theory of Mathematical Interest

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 133 or concurrently) or (MTH 153H or concurrently) or (LB 119 or concurrently) or approval of department
Description:
Measurement of interest rates, basic problems in interest theory, basic annuities, continuous and varying annuities, yield rates, amortization, bonds and other securities, practical applications, and stochastic approaches to interest.
Effective Dates:
FS13 - Open

MTH 361 Financial Mathematics for Actuaries I

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 360
Corequisite:
STT 441 concurrently
Description:
Introduction to the mathematics of financial derivatives. Options, forwards, futures, swaps, investment and hedging strategies.
Effective Dates:
FS15 - Open

MTH 362 Mathematics of Contract Pricing in Sports Analytics

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 360
Recommended Background:
MTH 361
Description:
Employ tools from mathematics finance to value sports contracts in sports analytics. Connections with utility theory and constrained optimality. Analysis of sports organizations and the leagues they play in.
Effective Dates:
SS25 - Open

MTH 396 Capstone in Mathematics for Secondary Education (W)

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 309 or MTH 317H or approval of department) and (MTH 310 or MTH 418H or approval of department) and (MTH 320 or MTH 327H) and Completion of Tier I Writing Requirement
Restrictions:
Open to students in the Mathematics-Secondary Education Major.
Not open to students with credit in:
MTH 496
Description:
A capstone course for secondary education math majors. High school mathematics from an advanced viewpoint.
Effective Dates:
FS24 - Open

MTH 411 Abstract Algebra II

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 310
Not open to students with credit in:
MTH 419H
Description:
Continuation of MTH 310. Permutation groups, groups of transformations, normal subgroups, homomorphism theorems, modules. Principal ideal rings, unique factorization domains, noncommutative rings, rings of fractions, ideals.
Effective Dates:
US17 - Open

MTH 414 Linear Algebra II

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 309 or MTH 317H
Not open to students with credit in:
MTH 415
Description:
Linear transformations on finite dimensional vector spaces. Invariant subspaces, rank, eigenvalues and eigenvectors. Canonical forms. Bilinear and multilinear forms.
Effective Dates:
FS13 - Open

MTH 415 Applied Linear Algebra

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 234 or MTH 254H or LB 220) and (MTH 309 or MTH 314 or MTH 317H) and (CMSE 201 or CSE 231)
Not open to students with credit in:
MTH 414
Description:
Linear algebra in normed vector spaces. Orthogonal structure and least squares theory. Matrix decompositions. Spectral theory. Singular value decompositions and applications. Discrete convolutions and Fourier transforms.
Effective Dates:
US26 - Open

MTH 416 Introduction to Algebraic Coding

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 309 or MTH 317H
Recommended Background:
MTH 310
Description:
Concepts and techniques of abstract algebra applied to the design of communication systems for use in imperfect circumstances. Theory of codes designed by algebraic means.
Effective Dates:
FS13 - US26

MTH 417 Topics in Number Theory

Semester:
Spring of even years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 310 or MTH 418H) and ((MTH 411 or concurrently) or (MTH 419H or concurrently))
Description:
Congruences of higher degree, primitive roots and quadratic reciprocity. Number-theoretic functions, algebraic numbers. Dirichlet Series, p-order expansion, continued fractions.
Effective Dates:
FS13 - US26

MTH 418H Honors Algebra I

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 317H or MTH 299
Recommended Background:
Linear Algebra
Restrictions:
Approval of department.
Description:
Theory of groups, Sylow theory, the structure of finite Abelian groups, ring theory, ideals, homomorphisms, and polynomial rings.
Effective Dates:
US15 - Open

MTH 419H Honors Algebra II

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 418H
Restrictions:
Approval of department.
Description:
Algebraic field extensions, Galois theory. Classification of finite fields. Fundamental Theorem of Algebra.
Effective Dates:
FS13 - Open

MTH 421 Analysis II

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 320 or MTH 327H) and (MTH 234 or MTH 254H or LB 220)
Not open to students with credit in:
MTH 429H
Description:
Continuation of MTH 320. Riemann integral. Metric spaces. Differentiation in higher dimensions. Inverse and implicit function theorems.
Effective Dates:
US15 - Open

MTH 425 Complex Analysis

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 320
Not open to students with credit in:
MTH 428h
Description:
Analytic functions of a complex variable, Cauchy integral theorem, conformal maps, bilinear transformation, harmonic functions. Classification of singularities, residues, conformal mappings.
Effective Dates:
FS23 - FS26

MTH 428H Honors Complex Analysis

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 327H
Restrictions:
Approval of department.
Description:
Analytic functions of a complex variable, line integrals and harmonic functions, Cauchy's theorem and integral formula, power series, Laurent series, isolated singularities, residue calculus, Rouche's theorem, automorphisms of the disk, the Riemann mapping theorem.
Effective Dates:
US15 - FS26

MTH 429H Honors Real Analysis

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 327H and (MTH 234 or MTH 254H or LB 220)
Restrictions:
Approval of department.
Description:
Continuation of MTH 327H. Convergence of sequences and series of functions, differentiation and integration in higher dimensional settings. Inverse and implicit function theorems.
Effective Dates:
US15 - Open

MTH 432 Axiomatic Geometry

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 299 or MTH 317H
Description:
Axiomatic systems and finite geometries: axioms of Euclidean and hyperbolic geometry, the Poincare model, independence of the parallel postulate. Classical constructions and the impossibility of angle trisection.
Effective Dates:
FS13 - Open

MTH 441 Ordinary Differential Equations II

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 235 or MTH 340 or MTH 347H) and (MTH 309 or MTH 317H or MTH 314 or MTH 415)
Description:
Existence and uniqueness theorems; Linearization; Local and global stability; Saddle-node, Hopf and heteroclinic bifurcations; Hamiltonian and gradient system; The Poincare map; The Poincare-Bendixson theorem and limit cycles; Selected applications.
Effective Dates:
FS15 - Open

MTH 442 Partial Differential Equations

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 235 or MTH 340 or MTH 347H
Description:
Classification of second order partial differential equations. Boundary and initial value problems for heat, Laplace, and wave equations in dimensions 1, 2 and 3. Variational methods and maximum principles. Separation of variables, Fourier series, Sturm-Liouville theory. Greens functions.
Effective Dates:
FS15 - Open

MTH 451 Numerical Analysis I

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(CSE 231 or CMSE 201) and (MTH 235 or MTH 340 or MTH 347H)
Not open to students with credit in:
MTH 351
Description:
Numerical solution of linear and nonlinear algebraic equations and eigenvalue problems. Curve fitting. Interpolation theory. Numerical integration, differentiation, and solution of differential equations. Algorithms implementation with a programming language like Fortran, C/C++ or MATLAB.
Effective Dates:
FS19 - Open

MTH 452 Numerical Analysis II

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 451
Description:
Iterative methods for solving linear systems, approximation theory, approximating eigenvalues, solutions of systems of nonlinear equations, boundary-value problems for ordinary differential equations, numerical methods for partial differential equations.
Effective Dates:
SS16 - Open

MTH 455 Actuarial Models I

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
STT 441 and MTH 360
Description:
Stochastic models used in insurance. Survival distributions, life insurance, life annuities, benefit premiums, benefit reserves, and analysis of benefit reserves.
Interdepartmental With:
Statistics and Probability
Administered By:
Statistics and Probability
Effective Dates:
FS14 - Open

MTH 456 Actuarial Models II

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
STT 455
Description:
Continuation of STT 455. Benefit reserves. Multiple life functions. Multiple decrement models and their applications. Elements of stochastic processes for actuaries including Markov chains and Poisson processes
Interdepartmental With:
Statistics and Probability
Administered By:
Statistics and Probability
Effective Dates:
FS14 - Open

MTH 457 Introduction to Financial Mathematics

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 309) and (MTH 235 or MTH 340 or MTH 347H) and (STT 441 or STT 351)
Description:
Mathematical overview of basic financial instruments. A unified partial differential equation approach to model derivative securities. Partial differential equations in financial mathematics, Black-Scholes equation. Numerical methods for valuing derivatives.
Effective Dates:
FS15 - Open

MTH 458 Computational Methods in Mathematical Finance and Insurance

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 361 and STT 441
Recommended Background:
MTH 235 or MTH 340 or MTH 347H
Description:
Utilize modern computational methods to price contracts in insurance and mathematical finance. Rational valuation of derivative securities using put-call parity and calculation of European and American options. Introduce hybrid contracts and features, such as equity-indexed annuities.
Interdepartmental With:
Statistics and Probability
Administered By:
Mathematics
Effective Dates:
FS23 - Open

MTH 459 Construction and Evaluation of Actuarial Models

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
STT 442
Description:
Severity, frequency, and aggregate models. Construction of empirical models. Parametric statistical methods. Credibility analysis. Simulation methods.
Interdepartmental With:
Statistics and Probability
Administered By:
Statistics and Probability
Effective Dates:
FS14 - Open

MTH 461 Metric and Topological Spaces

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 320 or MTH 327H
Description:
Set theory, metric spaces, topological spaces, maps, product and quotient topologies. Connected and compact spaces, separation axioms, pointwise and uniform convergence.
Effective Dates:
FS13 - Open

MTH 467 Insurance Operations

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(ACC 230 and FI 321 and MTH 360) and completion of Tier I writing requirement
Recommended Background:
STT 441
Description:
Regulation, marketing and distribution, underwriting, risk control, premium auditing, the claim function, actuarial operations, and reinsurance.
Interdepartmental With:
Statistics and Probability
Administered By:
Statistics and Probability
Effective Dates:
SS26 - Open

MTH 468 Predictive Analytics

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(CSE 231) and (MTH 235 or MTH 340) and MTH 360 and STT 442
Description:
Predictive analytics for insurance business and risk management with an emphasis on the use of machine learning tools.
Interdepartmental With:
Statistics and Probability
Administered By:
Mathematics
Effective Dates:
FS19 - Open

MTH 481 Discrete Mathematics I

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 309 or MTH 317H) or (MTH 299 and MTH 314)
Description:
Binomial and multinomial theorems. Graphs and digraphs, graph coloring. Generating functions, asymptotic analysis, trees. Representing graphs in computers.
Effective Dates:
US26 - Open

MTH 482 Discrete Mathematics II

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 481
Recommended Background:
MTH 310
Description:
Recurrence and generating functions, Ramsey theory. Block designs, Latin squares, Eulerian and Hamiltonian paths. Minimum spanning trees, network flows.
Effective Dates:
FS13 - Open

MTH 483 Mathematical Machine Learning

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 309 or MTH 314 or MTH 317H) and (CSE 231 or CMSE 201)
Description:
Regression, clustering, dimension reduction, density estimation, anomaly detection, classification, and related methods (e.g., k-nearest neighbors, support vector machines, neural networks, decision trees, random forests), autoencoders, generative adversarial networks, and existing machine learning tools, training methods, and software.
Effective Dates:
FS24 - Open

MTH 490 Directed Studies

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Variable from 1 to 4
Reenrollment Information:
A student may earn a maximum of 9 credits in all enrollments for this course.
Restrictions:
Approval of department.
Description:
Faculty directed study in a selected mathematical topic.
Effective Dates:
FS13 - Open

MTH 491A Actuarial Internship

Semester:
Summer of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
Completion of Tier I Writing Requirement
Recommended Background:
STT 441 and FI 311 and MTH 360
Restrictions:
Approval of department.
Description:
Survey of typical actuarial type projects at an actuarial firm such as data analysis, risk analysis, interest rate models, life insurance, benefit programming, analysis of benefit reserves.
Effective Dates:
FS13 - Open

MTH 491B Teamwork Experience

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 1   Lecture/Recitation/Discussion Hours:1
Restrictions:
Approval of department.
Description:
A field type experience to develop communication skills working in a group setting on multi-faceted projects.
Effective Dates:
FS13 - Open

MTH 492H Undergraduate Thesis (W)

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: Credits: 3
Reenrollment Information:
A student may earn a maximum of 12 credits in all enrollments for this course.
Prerequisite:
Completion of Tier I Writing Requirement
Restrictions:
Approval of department; application required.
Description:
Undergraduate thesis on an advanced-level topic in mathematics.
Effective Dates:
FS14 - Open

MTH 496 Capstone in Mathematics (W)

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
(MTH 309 or MTH 317H or approval of department) and (MTH 310 or MTH 418H or approval of department) and (MTH 320 or MTH 327H or approval of department) and Completion of Tier I Writing Requirement
Restrictions:
Approval of department.
Description:
A capstone course integrating several areas of mathematics.
Effective Dates:
US15 - Open

MTH 800 Quantitative Foundations for Machine Learning

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 132 and MTH 133 or approval of department
Description:
Advanced calculus and linear algebra tools for machine learning algorithms.
Interdepartmental With:
Statistics and Probability
Administered By:
Mathematics
Effective Dates:
US20 - Open

MTH 801 Machine Learning Algorithms: Mathematical Analysis

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Description:
Introduction to the mathematical basis of machine learning and predictive analytics. Linear and ridge regression, principal component analysis, classification methods, and neural networks. Convergence of algorithms.
Effective Dates:
FS22 - Open

MTH 803 Sports Decision Analytics

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 801
Description:
Theories of sports decisions are developed and assessed through quantitative and stochastic techniques.
Effective Dates:
FS22 - Open

MTH 810 Error-Correcting Codes

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 411 or MTH 414 or MTH 415
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Block codes, maximum likelihood decoding, Shannon's theorem. Generalized Reed-Solomon codes, modification of codes, subfield codes. Alterant and Goppa codes, cyclic codes and BCH codes.
Effective Dates:
FS24 - Open

MTH 818 Algebra I

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 411
Description:
Group theory: Sylow theory, permutation groups, Jordon-Hoelder theory, Abelian groups, free groups. Ring theory: algebra of ideals, unique factorization, polynomial rings, finitely generated modules over PIDs.
Effective Dates:
FS95 - Open

MTH 819 Algebra II

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 818
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Modules and vector spaces, projectives modules, tensor algebra. Fields and Galois groups, algebraic and transcendental numbers, non-commutative rings. The Jacobson radical, the structure of semisimple rings with the descending chain condition.
Effective Dates:
FS24 - Open

MTH 828 Real Analysis I

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 421 and MTH 461
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Lebesgue measure on real line, general measure theory. Convergence theorems, Lusin's theorem, Egorov's theorem, Lp-spaces, Fubini's theorem. Functions of bounded variation, absolutely continuous functions, Lebesgue differentiation theorem.
Effective Dates:
FS24 - Open

MTH 829 Complex Analysis I

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 421 and MTH 425
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Cauchy theorem, identity principle, Liouville's theorem, maximum modulus theorem. Cauchy formula, residue theorem, Rouche's theorem. Casorati-Weierstrass theorem, Arzela-Ascoli theorem. Conformal mapping, Schwarz lemma, Riemann mapping theorem.
Effective Dates:
FS24 - Open

MTH 841 Boundary Value Problems I

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 414 and MTH 421
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Methods for solving boundary and initial value problems for ordinary and partial differential equations.
Effective Dates:
FS24 - Open

MTH 842 Boundary Value Problems II

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 841
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Continuation of MTH 841.
Effective Dates:
FS24 - Open

MTH 843 Survey of Industrial Mathematics

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
(MTH 414 or MTH 415) and ((MTH 421 and MTH 442) or Some familiarity with mathematical software such as Mathematica, Matlab, etc.)
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Fundamentals of mathematical modeling in government and industry, including modes of industrial communication.
Effective Dates:
FS24 - Open

MTH 844 Projects in Industrial Mathematics

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
(MTH 414 or MTH 415) and ((MTH 421 and MTH 442 and MTH 843) or some familiarity with mathematical software such as Mathematica or Matlab.)
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Participation as a member of a 3-4 person team on a significant industrial problem, with participation of an industrial liaison, including project report generation and reporting.
Effective Dates:
FS24 - Open

MTH 847 Partial Differential Equations I

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
Equivalent of MTH 414
Restrictions:
Open to doctoral students in the College of Natural Science.
Description:
Basic theory and techniques for general first-order equations, Laplace's equation, the heat equation and wave equations, with certain generalizations to the second-order linear equations of elliptic, parabolic and hyperbolic types.
Effective Dates:
FS15 - Open

MTH 849 Partial Differential Equations

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 847 or approval of department
Recommended Background:
MTH 828
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Sobolev spaces and embedding theorems, weak solutions of second order elliptic equations in divergence form (existence, uniqueness, and regularity), Fredholm alternative, maximum principle, calculus of variations, Euler-Lagrange equations.
Effective Dates:
FS24 - Open

MTH 850 Numerical Analysis I

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 414 and MTH 421
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Convergence and error analysis of numerical methods in applied mathematics.
Effective Dates:
FS24 - Open

MTH 852 Numerical Methods for Ordinary Differential Equations

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 850
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Linear multi-step methods and single step nonlinear methods for initial value problems. Consistency, stability and convergence. Finite difference, finite element, shooting methods for boundary value problems.
Effective Dates:
FS24 - Open

MTH 868 Geometry and Topology I

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 411 and MTH 421
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Fundamental group and covering spaces, van Kampen's theorem. Homology theory, Differentiable manifolds, vector bundles, transversality, calculus on manifolds. Differential forms, tensor bundles, deRham theorem, Frobenius theorem.
Effective Dates:
FS24 - Open

MTH 869 Geometry and Topology II

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 868
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Continuation of MTH 868.
Effective Dates:
FS24 - Open

MTH 879 Teaching College Mathematics

Semester:
Fall of even years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Reenrollment Information:
A student may earn a maximum of 6 credits in all enrollments for this course.
Recommended Background:
Past or concurrent mathematics teaching experience.
Not open to students with credit in:
SME 879
Description:
Curriculum materials, case studies, approaches to teaching and student learning of particular mathematics topics.
Interdepartmental With:
Counseling, Educational Psy & Special Education, Mathematics Education, Teacher Education
Administered By:
Mathematics Education
Effective Dates:
US13 - Open

MTH 880 Combinatorics I

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 411 or MTH 482
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Enumerative combinatorics, recurrence relations, generating functions, asymptotics, applications to graphs, partially ordered sets, generalized Moebius inversions, combinatorial algorithms.
Effective Dates:
FS24 - Open

MTH 881 Graph Theory

Semester:
Spring of even years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 880
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Basic concepts in graph theory, connectivity, algebraic and topological methods. Networks, graph algorithms, Hamiltonian and Eulerian graphs, extremal graph theory, random graphs.
Effective Dates:
FS24 - Open

MTH 882 Combinatorics II

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 880
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Algebraic combinatorics including symmetric functions, group actions, and cluster algebra, geometric combinatorics including shellability, discrete Morse functions, and polytopes. Extremal combinatorics including Ramsey Theory and Sperner Theory.
Effective Dates:
FS24 - Open

MTH 890 Readings in Mathematics

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Variable from 1 to 6
Reenrollment Information:
A student may earn a maximum of 24 credits in all enrollments for this course.
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Individualized study for Master's level students.
Effective Dates:
FS24 - Open

MTH 910 Commutative Algebra

Semester:
Fall of odd years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 819
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Noetherian rings and modules, localization and tensor products, primary decomposition, Krull dimensions, graded rings and modules, Hilbert's Nullstellensatz, integral extensions, discrete valuation rings, Dedekind domains.
Effective Dates:
FS24 - Open

MTH 912 Group Theory I

Semester:
Fall of even years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 819
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Permutation groups, solvable and nilpotent groups, simple groups. Representation and character theory. Extension theory and cohomology groups.
Effective Dates:
FS24 - Open

MTH 913 Group Theory II

Semester:
Spring of odd years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 912
Description:
Groups of Lie type, linear groups, locally finite groups, free groups and free products, the subgroup theorems.
Effective Dates:
SS25 - Open

MTH 914 Lie Groups and Algebras

Semester:
Fall of odd years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 819
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Nilpotent and semisimple algebras, the ad joint representation, root spaces, Weyl groups, Dynkin diagrams, classification of simple algebras.
Effective Dates:
FS24 - Open

MTH 916 Introduction to Algebraic Geometry I

Semester:
Fall of even years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 818 and MTH 819
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Affine and projective algebraic varieties and their properties. Morphisms and singularities. Schemes and coherent sheaves. Sheaf cohomology and other related topics.
Effective Dates:
FS24 - Open

MTH 917 Introduction to Algebraic Geometry II

Semester:
Spring of odd years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 916
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Continuation of MTH 916.
Effective Dates:
FS24 - Open

MTH 918 Number Theory I

Semester:
Fall of even years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 819 or approval of department
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Number fields and algebraic integers, prime ideals and factorization, cyclotomic fields, the class group, the Dirichlet unit theorem, different, discriminant, decomposition and inertia groups, local fields.
Effective Dates:
FS24 - Open

MTH 919 Number Theory II

Semester:
Spring of odd years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 918 or approval of department
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Topics from: class field theory, zeta and L-functions, modular forms, theory of elliptic curves, diophantine approximation, diophantine geometry.
Effective Dates:
FS24 - Open

MTH 920 Functional Analysis

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 828
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Hilbert spaces, Banach spaces and locally convex vector spaces. Topics include Riesz representation theorem, Parseval's identity, Riesz-Fisher theorem, Fourier series operators, Hahn-Banach theorem, open mapping and closed graph theorems, Banach-Steinhaus theorem, duality theory for locally convex spaces, convexity, Krein-Milman theorem, theory of distributions, compact operators.
Effective Dates:
FS24 - Open

MTH 921 Operator Theory

Semester:
Fall of even years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 829 and MTH 920
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Introduction to operator and spectral theory. Topics include Banach algebras, bounded and unbounded operators on Banach spaces, spectral theory for normal operators on a Hilbert space, C*-algebras, Schatten - von Neumann classes, the theory of Fredholm operators, semigroup theory.
Effective Dates:
FS24 - Open

MTH 922 Harmonic Analysis

Semester:
Fall of odd years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 829 and MTH 920
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Fourier series, mean and pointwise convergence, conjugate functions, Fourier transform, Plancherel theorem, Paley-Wiener theorem, interpolation of operators, Hausdorff-Young thoerem.
Effective Dates:
FS24 - Open

MTH 925 Random Variables and Stochastic Processes

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Introduction to measure-theoretic probability theory. Topics include infinite product spaces, Kolomogorov extension theorem, Borel Cantelli Lemma, law of large numbers, central limit theorem, conditioning, filtrations, martingales, Markov chains, Wiener process.
Effective Dates:
FS24 - Open

MTH 928 Real Analysis II

Semester:
Spring of odd years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 828
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Continuation of MTH 828. Topics include Borel measures on locally compact spaces, complex measures, differentiable transformations and changes of variables in Rn.
Effective Dates:
FS24 - Open

MTH 929 Complex Analysis II

Semester:
Spring of even years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 828 and MTH 829
Restrictions:
Open to doctoral students in the College of Natural Science or approval of department.
Description:
Continuation of MTH 829. Topics include Phragmen-Lindelof method, Analytic continuation and Riemann surfaces, Hadamard's theorem, Runge's theorem, Weierstrass factorization theorem, Mittag-Leffler theorem, Picard's theorem, Hp-spaces, Blaschke products.
Effective Dates:
SS24 - Open

MTH 930 Riemannian Geometry I

Semester:
Fall of even years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 869
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Riemannian metrics, connections, curvature, geodesics. First and second variation, Jacobi fields, conjugate points. Rauch comparison theorems, Hodge theorem, Bochner technique, spinors. Further topics on curvature or submanifold theory.
Effective Dates:
FS24 - Open

MTH 931 Riemannian Geometry II

Semester:
Spring of odd years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 930
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Continuation of MTH 930.
Effective Dates:
FS24 - Open

MTH 935 Complex Manifolds I

Semester:
Spring of even years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 829 and MTH 869
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Riemann surfaces, Serre duality, Riemann-Roch theorem. Weierstrass points, Abel's theorem, Plucker formulas. Hermitian metrics, connections, curvature, Hodge theorem. Kaehler metrics, Kodaira vanishing theorem, Chern classes.
Effective Dates:
FS24 - Open

MTH 940 Topics in Partial Differential Equations for Applied Math

Semester:
Fall of odd years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 828
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Partial differential equation techniques for applied mathematics, including, bifurcation theory, partial differential equations as dynamical systems, boundary layers, asymptotic analysis, matched asymptotic and singular perturbations, and homogenization.
Effective Dates:
FS24 - Open

MTH 941 Linear and Nonlinear Parabolic Equations

Semester:
Spring of even years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 940
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Evolution equations with a comparison principle, including parabolic equations and Hamilton-Jacobi-Bellman equations, with an emphasis on existence and uniqueness of both classical and weak solutions. Linear and nonlinear cases, including quasi-linear parabolic equations related to geometric flows.
Effective Dates:
FS24 - Open

MTH 942 Regularity for Second Order Elliptic Equations

Semester:
Fall of even years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 848 and MTH 849
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Review of classical regularity results, such as Schauder theory and L-p theory. Elliptic equations with coefficients of low regularity (bounded and measurable) and nonlinear elliptic equations. The Harnack inequality and Holder regularity in the context of both weak solutions of divergence form equations and viscosity solutions of equations in non-divergence form. Higher regularity and applications to minimization problems.
Effective Dates:
FS24 - Open

MTH 943 Hyperbolic and Dispersive Equations

Semester:
Spring of odd years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 942
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Classical and modern techniques for higher dimensional hyperbolic and dispersive partial differential equations. Space-time integral estimates, including the classical Strichartz estimate for Schrodinger, Klein-Gordon, and Wave equations, and modern (multi)linear estimates using Fourier, physical-space, and microlocal techniques.
Effective Dates:
FS24 - Open

MTH 950 Numerical Methods for Partial Differential Equations I

Semester:
Spring of odd years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 852
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Finite difference methods for ordinary and partial differential equations.
Effective Dates:
FS24 - Open

MTH 951 Numerical Methods for Partial Differential Equations II

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Finite element methods for ordinary and partial differential equations.
Effective Dates:
FS24 - Open

MTH 960 Algebraic Topology I

Semester:
Fall of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 869
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Cohomology, products, duality, basic homotopy theory, bundles, obstruction theory, spectral sequences, characteristic classes, and other related topics.
Effective Dates:
FS24 - Open

MTH 961 Algebraic Topology II

Semester:
Spring of every year
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Recommended Background:
MTH 960
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Continuation of MTH 960.
Effective Dates:
FS24 - Open

MTH 988 Representation Theory I

Semester:
Fall of odd years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 819 or approval of department
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Representations of finite groups, unitary representations, tensor products and character tables, further theory (Frobenius-Schur indicator, Burnside's theorem, Mackey formula, Frobenius reciprocity), representations of GL(2; Fq), representations of symmetric groups (Young diagrams, Schur-Weyl duality), fundamental theorem of invariant theory, introduction to representations of compact groups
Effective Dates:
FS24 - Open

MTH 989 Representation Theory II

Semester:
Spring of even years
Credits:
Total Credits: Credits: 3   Lecture/Recitation/Discussion Hours:3
Prerequisite:
MTH 988 or approval of department
Description:
Basic objects and notions of representation theory: associative algebras, algebras defined by generators and relations, group algebras, quivers and path algebras, basic general results of representation theory, representations of finite dimensional algebras and semi simple algebras, extensions of representations, representations of quivers.
Effective Dates:
SS24 - Open

MTH 990 Reading in Mathematics

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Variable from 1 to 3
Reenrollment Information:
A student may earn a maximum of 9 credits in all enrollments for this course.
Restrictions:
Open to doctoral students in the Mathematics Major or approval of department.
Description:
Individualized study for doctoral level students.
Effective Dates:
FS24 - Open

MTH 991 Special Topics in Algebra

Semester:
Fall of every year, Spring of every year
Credits:
Variable from 3 to 6
Reenrollment Information:
A student may earn a maximum of 18 credits in all enrollments for this course.
Restrictions:
Open to doctoral students in the Mathematics Major or approval of department.
Description:
Advanced topics in algebra.
Effective Dates:
FS24 - Open

MTH 992 Special Topics in Analysis

Semester:
Fall of every year, Spring of every year
Credits:
Variable from 3 to 6
Reenrollment Information:
A student may earn a maximum of 18 credits in all enrollments for this course.
Restrictions:
Open to doctoral students in the Mathematics Major or approval of department.
Description:
Advanced topics in analysis.
Effective Dates:
FS24 - Open

MTH 993 Special Topics in Geometry

Semester:
Fall of every year, Spring of every year
Credits:
Variable from 3 to 6
Reenrollment Information:
A student may earn a maximum of 18 credits in all enrollments for this course.
Restrictions:
Open to doctoral students in the Mathematics Major or approval of department.
Description:
Advanced topics in geometry.
Effective Dates:
FS24 - Open

MTH 994 Special Topics in Applied Mathematics

Semester:
Fall of every year, Spring of every year
Credits:
Variable from 3 to 6
Reenrollment Information:
A student may earn a maximum of 24 credits in all enrollments for this course.
Restrictions:
Open to doctoral students in the Mathematics Major or approval of department.
Description:
Advanced topics in applied mathematics.
Effective Dates:
FS24 - Open

MTH 996 Special Topics in Topology

Semester:
Fall of every year, Spring of every year
Credits:
Variable from 3 to 6
Reenrollment Information:
A student may earn a maximum of 18 credits in all enrollments for this course.
Restrictions:
Open to doctoral students in the Mathematics Major or approval of department.
Description:
Advanced topics in topology.
Effective Dates:
FS24 - Open

MTH 999 Doctoral Dissertation Research

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Variable from 1 to 24
Reenrollment Information:
A student may earn a maximum of 36 credits in all enrollments for this course.
Restrictions:
Open to doctoral students in the Applied Mathematics Major or in the Mathematics Major. Approval of department.
Description:
Doctoral dissertation research.
Effective Dates:
FS24 - Open