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 versions prior to Fall 2000.

Course Numbers Policy
Definitions of Course Characteristics (pdf)
Course Descriptions Frequently Asked Questions

Course Descriptions: Search Results

MTH 100E  Intermediate Algebra Workshop for the Mathematics Enrichment Program

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: 1   Lab Hours: 4
Corequisite:
MTH 1825 concurrently
Restrictions:
Approval of department.
Description:
Enrichment topics in intermediate algebra for students in the Mathematics Enrichment Program.
Effective Dates:
FALL 2013 - Open


MTH 101  Quantitative Literacy I

Semester:
Fall of every year
Credits:
Total Credits: 3
Prerequisite:
(MTH 1825 or MTH 103) or designated score on Mathematics Placement test
Description:
Quantitative literacy including applications to health and risk, science, and the environment.
Effective Dates:
FALL 2016 - Open


MTH 102  Quantitative Literacy II

Semester:
Spring of every year
Credits:
Total Credits: 3
Prerequisite:
(MTH 1825 or MTH 103) or designated score on Mathematics Placement test
Description:
Quantitative literacy including applications to finance, economics, and politics.
Effective Dates:
FALL 2016 - Open


MTH 103  College Algebra

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
(MTH 1825) or designated score on Mathematics Placement test
Not open to students with credit in:
MTH 116
Description:
Number systems; functions and relations; exponents and logarithms; elementary theory of equations; inequalities; and systems of equations.
Semester Alias:
LBS 117
Effective Dates:
FALL 2013 - Open


MTH 103E  College Algebra Workshop for the Mathematics Enrichment Program

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: 1   Lab Hours: 4
Corequisite:
MTH 103 concurrently
Restrictions:
Approval of department.
Description:
Enrichment topics in college algebra for students in the Mathematics Enrichment Program.
Effective Dates:
FALL 2013 - Open


MTH 110  Finite Mathematics and Elements of College Algebra

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: 5   Lecture/Recitation/Discussion Hours: 5
Prerequisite:
(MTH 1825) or designated score on Mathematics Placement test
Not open to students with credit in:
MTH 112
Description:
Functions and graphs. Equations and inequalities. Systems of equations. Matrices. Linear programming. Simplex algorithm. Probability and statistics.
Effective Dates:
FALL 2013 - Open


MTH 112  Finite Mathematics: Applications of College Algebra

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
(MTH 103) or designated score on Mathematics Placement test
Not open to students with credit in:
MTH 110
Description:
Combinatorics, probability and statistics, mathematics of finance, geometry, transition matrices, and linear programming. The course emphasizes applications and includes work using spreadsheets.
Semester Alias:
MTH 106
Effective Dates:
FALL 2013 - Open


MTH 114  Trigonometry

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
MTH 103
Not open to students with credit in:
MTH 116
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.
Semester Alias:
MTH 104
Effective Dates:
FALL 2013 - Open


MTH 116  College Algebra and Trigonometry

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: 5   Lecture/Recitation/Discussion Hours: 5
Prerequisite:
(MTH 1825) or designated score on Mathematics Placement test
Not open to students with credit in:
MTH 103
Description:
Functions and graphs. Equations and inequalities. Exponential and logarithmic functions. Trigonometric functions. Systems of equations. Binomial theorem.
Semester Alias:
LBS 117
Effective Dates:
FALL 2013 - Open


MTH 124  Survey of Calculus I

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total 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:
FALL 2013 - Open


MTH 126  Survey of Calculus II

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total 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:
FALL 2013 - Open


MTH 132  Calculus I

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
(MTH 103 and MTH 114) or (MTH 116 or designated score on Mathematics Placement test )
Not open to students with credit in:
LB 118 or MTH 152H
Description:
Limits, continuous functions, derivatives and their applications. Integrals and the fundamental theorem of calculus.
Effective Dates:
FALL 2013 - Open


MTH 133  Calculus II

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total 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 or 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:
FALL 2013 - Open


MTH 152H  Honors Calculus I

Semester:
Fall of every year
Credits:
Total 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 or MTH 132
Description:
Limits, continuous functions, derivatives, integrals, fundamental theorem of calculus. Special emphasis on concepts and theory.
Effective Dates:
FALL 2013 - Open


MTH 153H  Honors Calculus II

Semester:
Fall of every year, Spring of every year
Credits:
Total 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 or 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:
FALL 2013 - Open


MTH 1825  Intermediate Algebra

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Description:
Properties of real numbers. Factoring. Roots and radicals. First and second degree equations. Linear inequalities. Polynomials. Systems of equations.
Effective Dates:
FALL 2013 - Open


MTH 201  Elementary Mathematics for Teachers I

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
(MTH 103 or MTH 110 or MTH 116 or MTH 124 or MTH 132 or MTH 152H or LB 118) 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 K-8 teaching. Place value and models for arithmetic, mental math, word problems, and algorithms. Factors, primes, proofs, and prealgebra. Fractions, ratios, rates, and percentages. Negative, rational, and real numbers. Special emphasis on the appropriate sequential order for teaching.
Effective Dates:
FALL 2013 - Open


MTH 202  Elementary Mathematics for Teachers II

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
MTH 201
Restrictions:
Open to students in the Education Major or in the Special Education-Learning Disabilities Major or in the Child Development major or in the Teacher Certification Internship Year Studies Program.
Description:
A continuation of MTH 201. Geometry, measurement, and elementary data analysis.
Effective Dates:
FALL 2013 - Open


MTH 234  Multivariable Calculus

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total 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:
FALL 2013 - Open


MTH 235  Differential Equations

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total 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:
SUMMER 2017 - Open


MTH 254H  Honors Multivariable Calculus

Semester:
Fall of every year, Spring of every year
Credits:
Total 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:
FALL 2013 - 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:
FALL 2013 - Open


MTH 299  Transitions

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total 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:
FALL 2013 - Open


MTH 301  Foundations of Higher Mathematics

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
(MTH 133 or MTH 153H or LB 119) and MTH 202
Restrictions:
Open to students in the Mathematics Elementary Teaching Major or in Mathematics-Elementary Disciplinary Teaching Minor or approval of department.
Description:
Elementary set theory including permutations, combinations, cardinality theorems, relations, functions and quotient sets. Basic principles of logic and proof techniques. Elementary number theory and abstract algebra.
Effective Dates:
FALL 2015 - Open


mth 304  Algebra for Elementary and Middle School Teachers

Semester:
Fall of every year
Credits:
Total Credits: 3
Prerequisite:
(MTH 201 and MTH 202 and MTH 301) and completion of Tier I writing requirement
Restrictions:
Open to undergraduate students in the College of Education or in the Department of Teacher Education. Approval of department.
Description:
Algebra needed for understanding connections between topics of algebra and the mathematics taught in elementary and middle school.
Interdepartmental With:
Teacher Education
Administered By:
Mathematics
Effective Dates:
FALL 2013 - Open


mth 305  Functions and Calculus for Elementary and Middle School Teachers (W)

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
(MTH 304) and completion of Tier I writing requirement
Description:
Functions and calculus needed for understanding connections between topics of calculus and the mathematics taught in middle school.
Interdepartmental With:
Teacher Education
Administered By:
Mathematics
Effective Dates:
FALL 2013 - Open


MTH 309  Linear Algebra I

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
((MTH 133 or MTH 153H or LB 119) and completion of Tier I writing requirement) and (MTH 299 or approval of department)
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:
FALL 2017 - 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: 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:
SUMMER 2017 - Open


MTH 314  Matrix Algebra with Applications

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
MTH 133 or MTH 153H or LB 119
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 Mathematics Minor 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-Elementary Disciplinary Teaching Minor or in Mathematics-Secondary Disciplinary Teaching Minor.
Description:
Problem-solving and applications in matrix algebra for scientists and engineers. Vectors, matrices, linear transformations, inner products, dimension, eigenvalues and eigenvectors. Applications to systems of equations and to geometry.
Effective Dates:
FALL 2013 - Open


MTH 317H  Honors Linear Algebra

Semester:
Fall of every year, Spring of every year
Credits:
Total 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.
Not open to students with credit in:
MTH 309
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:
FALL 2017 - Open


MTH 320  Analysis I

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total 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:
SUMMER 2015 - Open


MTH 327H  Honors Introduction to Analysis

Semester:
Fall of every year, Spring of every year
Credits:
Total 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:
SUMMER 2015 - Open


MTH 330  Higher Geometry

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
MTH 301 or 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:
FALL 2013 - Open


MTH 340  Ordinary Differential Equations I

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total 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:
SUMMER 2015 - Open


MTH 347H  Honors Ordinary Differential Equations

Semester:
Spring of every year
Credits:
Total 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:
SUMMER 2015 - Open


MTH 360  Theory of Mathematical Interest

Semester:
Fall of every year, Spring of every year
Credits:
Total 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:
FALL 2013 - Open


MTH 361  Financial Mathematics for Actuaries I

Semester:
Fall of every year, Spring of every year
Credits:
Total 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:
FALL 2015 - Open


MTH 396  Capstone in Mathematics for Secondary Education (W)

Semester:
Spring of every year
Credits:
Total 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.
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:
FALL 2013 - Open


MTH 411  Abstract Algebra II

Semester:
Fall of every year, Spring of every year
Credits:
Total 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:
SUMMER 2017 - Open


MTH 414  Linear Algebra II

Semester:
Fall of every year
Credits:
Total 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:
FALL 2013 - Open


MTH 415  Applied Linear Algebra

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
(MTH 235 or MTH 340 or MTH 347H) and (MTH 309 or MTH 314 or MTH 317H)
Not open to students with credit in:
MTH 414
Description:
Matrices and linear algebra. General linear systems of equations. Least squares minimization techniques. Eigenvalues and eigenvectors, spectral decompositions, and exponentials.
Effective Dates:
FALL 2015 - Open


MTH 416  Introduction to Algebraic Coding

Semester:
Fall of every year
Credits:
Total 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:
FALL 2013 - Open


MTH 417  Topics in Number Theory

Semester:
Spring of even years
Credits:
Total 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:
FALL 2013 - Open


MTH 418H  Honors Algebra I

Semester:
Fall of every year
Credits:
Total 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:
SUMMER 2015 - Open


MTH 419H  Honors Algebra II

Semester:
Spring of every year
Credits:
Total 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:
FALL 2013 - Open


MTH 421  Analysis II

Semester:
Fall of every year, Spring of every year
Credits:
Total 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:
SUMMER 2015 - Open


MTH 425  Complex Analysis

Semester:
Fall of every year, Spring of every year
Credits:
Total 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:
SUMMER 2015 - Open


MTH 428H  Honors Complex Analysis

Semester:
Fall of every year
Credits:
Total 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:
SUMMER 2015 - Open


MTH 429H  Honors Real Analysis

Semester:
Spring of every year
Credits:
Total 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:
SUMMER 2015 - Open


MTH 432  Axiomatic Geometry

Semester:
Spring of every year
Credits:
Total 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:
FALL 2013 - Open


MTH 441  Ordinary Differential Equations II

Semester:
Fall of every year
Credits:
Total 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:
FALL 2015 - Open


MTH 442  Partial Differential Equations

Semester:
Spring of every year
Credits:
Total 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:
FALL 2015 - Open


MTH 451  Numerical Analysis I

Semester:
Fall of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
(CSE 131 or CSE 231) and (CSE 131 or CSE 231) and (MTH 235 or MTH 340 or MTH 347H)
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.
Semester Alias:
MTH 351
Effective Dates:
FALL 2015 - Open


MTH 452  Numerical Analysis II

Semester:
Spring of every year
Credits:
Total 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:
SPRING 2016 - Open


mth 455  Actuarial Models I

Semester:
Fall of every year
Credits:
Total 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:
Mathematics
Administered By:
Statistics and Probability
Effective Dates:
FALL 2014 - Open


mth 456  Actuarial Models II

Semester:
Spring of every year
Credits:
Total 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:
Mathematics
Administered By:
Statistics and Probability
Effective Dates:
FALL 2014 - Open


MTH 457  Introduction to Financial Mathematics

Semester:
Spring of every year
Credits:
Total 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:
FALL 2015 - Open


mth 458  Financial Mathematics for Actuaries II

Semester:
Fall of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
MTH 361 and STT 441
Recommended Background:
MTH 235 or MTH 340 or MTH 347H
Description:
Evaluate and construct interest rate models. Rational valuation of derivative securities using put-call parity and calculation of European and American options. Risk management techniques using the method of delta-hedging.
Interdepartmental With:
Statistics and Probability
Administered By:
Mathematics
Effective Dates:
FALL 2015 - Open


mth 459  Construction and Evaluation of Actuarial Models

Semester:
Spring of every year
Credits:
Total 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:
Mathematics
Administered By:
Statistics and Probability
Effective Dates:
FALL 2014 - Open


MTH 461  Metric and Topological Spaces

Semester:
Fall of every year
Credits:
Total 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:
FALL 2013 - Open


MTH 481  Discrete Mathematics I

Semester:
Fall of every year, Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
MTH 309
Description:
Binomial and multinomial theorems. Graphs and digraphs, graph coloring. Generating functions, asymptotic analysis, trees. Representing graphs in computers.
Effective Dates:
FALL 2013 - Open


MTH 482  Discrete Mathematics II

Semester:
Spring of every year
Credits:
Total 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:
FALL 2013 - 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:
FALL 2013 - Open


MTH 491A  Actuarial Internship

Semester:
Summer of every year
Credits:
Total 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:
FALL 2013 - Open


MTH 491B  Teamwork Experience

Semester:
Fall of every year, Spring of every year
Credits:
Total 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:
FALL 2013 - Open


MTH 492H  Undergraduate Thesis (W)

Semester:
Fall of every year, Spring of every year, Summer of every year
Credits:
Total 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:
FALL 2014 - Open


MTH 496  Capstone in Mathematics (W)

Semester:
Fall of every year, Spring of every year
Credits:
Total 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:
SUMMER 2015 - Open


MTH 810  Error-Correcting Codes

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 411 or MTH 414 or MTH 415
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:
FALL 1995 - Open


MTH 818  Algebra I

Semester:
Fall of every year
Credits:
Total 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:
FALL 1995 - Open


MTH 819  Algebra II

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 818
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:
FALL 1995 - Open


MTH 828  Real Analysis I

Semester:
Fall of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 421 and MTH 461
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:
FALL 1995 - Open


MTH 829  Complex Analysis I

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 421 and MTH 425
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:
FALL 1995 - Open


MTH 840  Chaos and Dynamical Systems

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
(MTH 441 and MTH 320 and MTH 414) and some experience with mathematical software such as Mathematica or Matlab.
Description:
Chaotic or random motions in differential and difference equations.
Effective Dates:
SPRING 2002 - Open (Interim Delete - SUMMER 2018)


MTH 841  Boundary Value Problems I

Semester:
Fall of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 414 and MTH 421
Description:
Methods for solving boundary and initial value problems for ordinary and partial differential equations.
Effective Dates:
FALL 1995 - Open


MTH 842  Boundary Value Problems II

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 841
Description:
Continuation of MTH 841.
Effective Dates:
FALL 1995 - Open


MTH 843  Survey of Industrial Mathematics

Semester:
Fall of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
((MTH 414 or MTH 415) or Some familiarity with mathematical software such as Mathematica, Matlab, etc.) and (MTH 421 and MTH 442)
Restrictions:
Open only to master's students in the Industrial Mathematics major or approval of department.
Description:
Fundamentals of mathematical modeling in government and industry, including modes of industrial communication.
Effective Dates:
FALL 1999 - Open


MTH 844  Projects in Industrial Mathematics

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
((MTH 414 or MTH 415) or some familiarity with mathematical software such as Mathematica or Matlab.) and (MTH 421 and MTH 442 and MTH 843)
Restrictions:
Open only to master's students in the Industrial 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:
SPRING 2002 - Open


MTH 847  Partial Differential Equations I

Semester:
Fall of every year
Credits:
Total 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:
FALL 2015 - Open


MTH 848  Ordinary Differential Equations

Semester:
Fall of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 414 and MTH 421
Description:
Existence and uniqueness theorems. Theory of linear differential equations. Floquet theory. Stability theory and Poincare-Bendixson theory. Green's functions and boundary value problems.
Effective Dates:
FALL 1995 - Open


MTH 849  Partial Differential Equations

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 414 and MTH 421
Description:
Cauchy-Kowalewski theorem. Characteristics. Initial-boundary value problems for parabolic and hyperbolic equations. Energy methods, boundary value problems for elliptic equations, potential theory. Green's function, maximum principles, Schauder's method.
Effective Dates:
FALL 1995 - Open


MTH 850  Numerical Analysis I

Semester:
Fall of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 414 and MTH 421
Description:
Convergence and error analysis of numerical methods in applied mathematics.
Effective Dates:
FALL 1995 - Open


MTH 851  Numerical Analysis II

Semester:
Fall of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 850 and MTH 852
Description:
Spectral methods for boundary value problems, eigenvalue problems, and time-dependent problems. Trigonometric and Chebyshev polynomials. Fast Fourier transforms.
Effective Dates:
FALL 2013 - Open


MTH 852  Numerical Methods for Ordinary Differential Equations

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 850
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:
FALL 2013 - Open


MTH 864  Geometric Topology

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 421
Description:
Topology of surfaces and higher dimensional manifolds, studied from combinatorial, algebraic or differential viewpoints.
Semester Alias:
MTH 464
Effective Dates:
SPRING 1999 - Open (Interim Delete - SUMMER 2018)


MTH 868  Geometry and Topology I

Semester:
Fall of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
(MTH 411 and MTH 421) 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:
SPRING 1995 - Open


MTH 869  Geometry and Topology II

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 868
Description:
Continuation of MTH 868.
Effective Dates:
FALL 1995 - Open


mth 879  Teaching College Mathematics

Semester:
Fall of even years
Credits:
Total 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.
Description:
Curriculum materials, case studies, approaches to teaching and student learning of particular mathematics topics.
Semester Alias:
SME 879
Interdepartmental With:
Counseling, Educational Psychology and Special Education, Mathematics, Teacher Education
Administered By:
Mathematics Education
Effective Dates:
SUMMER 2013 - Open


MTH 880  Combinatorics

Semester:
Fall of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 411 or MTH 482
Description:
Enumerative combinatorics, recurrence relations, generating functions, asymptotics, applications to graphs, partially ordered sets, generalized Moebius inversions, combinatorial algorithms.
Effective Dates:
FALL 1995 - Open


MTH 881  Graph Theory

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 880
Description:
Graph theory, connectivity, algebraic and topological methods. Networks, graph algorithms, Hamiltonian and Eulerian graphs, extremal graph theory, random graphs.
Effective Dates:
FALL 1995 - 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:
Approval of department.
Description:
Individualized study for Master's level students.
Effective Dates:
SUMMER 2002 - Open


MTH 910  Commutative Algebra

Semester:
Fall of odd years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 819
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:
FALL 2014 - Open


MTH 912  Group Theory I

Semester:
Fall of even years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 819
Description:
Permutation groups, solvable and nilpotent groups, simple groups. Representation and character theory. Extension theory and cohomology groups.
Effective Dates:
FALL 1995 - Open


MTH 913  Group Theory II

Semester:
Spring of odd years
Credits:
Total 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:
FALL 1995 - Open


MTH 914  Lie Groups and Algebras

Semester:
Fall of odd years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 819
Description:
Nilpotent and semisimple algebras, the ad joint representation, root spaces, Weyl groups, Dynkin diagrams, classification of simple algebras.
Effective Dates:
FALL 2014 - Open


MTH 916  Introduction to Algebraic Geometry I

Semester:
Fall of even years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 818 and MTH 819
Description:
Affine and projective algebraic varieties and their properties. Morphisms and singularities. Schemes and coherent sheaves. Sheaf cohomology and other related topics.
Effective Dates:
FALL 2004 - Open


MTH 917  Introduction to Algebraic Geometry II

Semester:
Spring of odd years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 916
Description:
Continuation of MTH 916.
Effective Dates:
SPRING 2005 - Open


MTH 918  Number Theory I

Semester:
Fall of even years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
MTH 819 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:
FALL 2014 - Open


MTH 919  Number Theory II

Semester:
Spring of odd years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
MTH 918 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:
SPRING 2015 - Open


MTH 920  Functional Analysis

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 828
Restrictions:
Open to graduate students in the College of Natural Science 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:
FALL 2016 - Open


MTH 921  Operator Theory

Semester:
Fall of even years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 829 and MTH 920
Restrictions:
Open to doctoral students in the College of Natural Science 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:
FALL 2016 - Open


MTH 922  Harmonic Analysis

Semester:
Fall of odd years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 829 and MTH 920
Description:
Fourier series, mean and pointwise convergence, conjugate functions, Fourier transform, Plancherel theorem, Paley-Wiener theorem, interpolation of operators, Hausdorff-Young thoerem.
Effective Dates:
FALL 2009 - Open


MTH 925  Random Variables and Stochastic Processes

Semester:
Fall of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Restrictions:
Open to doctoral students in the College of Natural Science 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:
FALL 2016 - Open


MTH 928  Real Analysis II

Semester:
Spring of odd years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 828
Restrictions:
Open to doctoral students in the College of Natural Science 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:
SPRING 2017 - Open


MTH 929  Complex Analysis II

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 828 and MTH 829
Description:
Phragmen-Lindelof method. Hadamard's theorem, Runge's thoerem, Weierstrass factorization theorem, Mittag-Leffler theorem, and Picard's theorem. Poisson integrals, Harnack's inequality, Dirichlet problem. Hp-spaces and Blaschke products.
Effective Dates:
FALL 1995 - FALL 2017


MTH 930  Riemannian Geometry I

Semester:
Fall of even years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 869
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:
SUMMER 2006 - Open


MTH 931  Riemannian Geometry II

Semester:
Spring of odd years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 930
Description:
Continuation of MTH 930.
Effective Dates:
SUMMER 2006 - Open


MTH 935  Complex Manifolds I

Semester:
Fall of odd years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 829 and MTH 869
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:
FALL 1995 - Open


MTH 936  Complex Manifolds II

Semester:
Spring of even years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 935
Description:
Continuation of MTH 935.
Effective Dates:
FALL 1995 - Open


MTH 940  Topics in Partial Differential Equations for Applied Math

Semester:
Fall of odd years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 828
Restrictions:
Open to doctoral students in the College of Natural Science 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:
FALL 2016 - Open


MTH 941  Applied Analysis II

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 940
Description:
Fixed point theorems. Variational methods. Applications to nonlinear integral and elliptic differential equations. Semigroup theory.
Effective Dates:
FALL 1995 - FALL 2017


MTH 942  Regularity for Second Order Elliptic Equations

Semester:
Fall of even years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 848 and MTH 849
Restrictions:
Open to doctoral students in the College of Natural Science 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:
FALL 2016 - Open


MTH 943  Hyperbolic and Dispersive Equations

Semester:
Spring of odd years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 942
Restrictions:
Open to doctoral students in the College of Natural Science. 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:
SPRING 2017 - Open


MTH 950  Numerical Methods for Partial Differential Equations I

Semester:
Spring of odd years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 852
Description:
Finite difference methods for ordinary and partial differential equations.
Effective Dates:
SPRING 2000 - Open


MTH 951  Numerical Methods for Partial Differential Equations II

Semester:
Spring of even years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Description:
Finite element methods for ordinary and partial differential equations.
Effective Dates:
SPRING 2008 - Open


MTH 960  Algebraic Topology I

Semester:
Fall of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 869
Description:
Cohomology, products, duality, basic homotopy theory, bundles, obstruction theory, spectral sequences, characteristic classes, and other related topics.
Effective Dates:
SPRING 1995 - Open


MTH 961  Algebraic Topology II

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 960
Description:
Continuation of MTH 960.
Effective Dates:
FALL 1995 - Open


MTH 970  Dynamics I

Semester:
Fall of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
(MTH 868 or concurrently) and MTH 869 or approval of department
Restrictions:
Open to doctoral students in the College of Natural Science or approval of department.
Description:
Flows and diffeomorphisms, examples, topological and smooth conjugacy, recurrence and limit sets, circle diffeomorphisms, symbolic spaces and expanding maps, structural stability of expanding maps, Perron-Frobenius theorem and discrete Markov processes, topological entropy and volume growth, zeta function, homological growth, linearization, bifurcation theory.
Effective Dates:
FALL 2016 - Open


MTH 971  Dynamics II

Semester:
Spring of every year
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
(MTH 868 or concurrently) and (MTH 869 or concurrently)
Restrictions:
Open to doctoral students in the College of Natural Science or approval of department.
Description:
Hyperbolic theory, Anosov systems, invariant manifold theory, geodesic flows on Riemannian manifolds, structural stability theorems, generic properties, horseshoe diffeomorphisms, basic theory of Hamiltonian systems on manifolds, variational principles, Lagrangian and Hamiltonian mechanics, Poisson brackets. Introduction to completely integrable systems.
Effective Dates:
SPRING 2017 - Open


MTH 988  Representation Theory I

Semester:
Fall of odd years
Credits:
Total Credits: 3   Lecture/Recitation/Discussion Hours: 3
Prerequisite:
MTH 819 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:
FALL 2015 - Open


MTH 989  Representation Theory II

Semester:
Spring of even years
Credits:
Total 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:
SPRING 2016 - 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:
Approval of department.
Description:
Individualized study for doctoral level students.
Effective Dates:
SUMMER 2000 - 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:
Approval of department.
Description:
Advanced topics in algebra.
Effective Dates:
FALL 1992 - 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:
Approval of department.
Description:
Advanced topics in analysis.
Effective Dates:
FALL 1992 - 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:
Approval of department.
Description:
Advanced topics in geometry.
Effective Dates:
FALL 1992 - 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:
Approval of department.
Description:
Advanced topics in applied mathematics.
Effective Dates:
SUMMER 2002 - Open


MTH 995  Special Topics in Numerical Analysis and Operations Research

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:
Approval of department.
Description:
Advanced topics in numerical analysis or operations research.
Effective Dates:
FALL 1992 - 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:
Approval of department.
Description:
Advanced topics in topology.
Effective Dates:
FALL 1992 - 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:
Approval of department.
Description:
Doctoral dissertation research.
Effective Dates:
FALL 2014 - Open