The Washington State University Vancouver Catalog

Mathematics

The online catalog includes the most recent changes to courses and degree requirements that have been approved by the Faculty Senate, including changes that are not yet effective.

Mathematics

cas.vancouver.wsu.edu/mathematics
Science & Engineering Building (VSCI), Room 130
360-546-9620

Academic Director: Amy Wharton, Ph.D.; Academic Coordinator: Emily Earhart; Faculty: Alexander Dimitrov, Ph.D.; David Hill, Ph.D.; Bala Krishnamoorthy, Ph.D.; Paul Krouss, Ph.D.; Eric Mapes, Ph.D.; Leslie New, Ph.D.; Rocio Sotomayer, Ph.D.; Nikolay Strigul, Ph.D.

Mathematics and statistics courses offered at WSU Vancouver are primarily in support of Biology and Environmental Science degrees and other major degrees of study. All students who enroll in mathematics courses are responsible for satisfying the prerequisite(s). One way to satisfy a prerequisite is to obtain an appropriate score on the ALEKS Mathematics placement exam. All new WSU students are urged to take the ALEKS exam. The ALEKS exam is not needed for students who have already completed the prerequisite college mathematics course or for transfer students who have already satisfied General Education Requirements (GERs) and do not intend to take a mathematics course at WSU. See studentaffairs.vancouver.wsu.edu/student-affairs/math-placement-faq for more information.

Middle Level Math Endorsement: Washington State University's Middle Level Math Endorsement program is designed for new (including teacher candidates) and experienced teachers who wish to add an additional endorsement or expertise in middle level mathematics to their current certificate.

A mathematics minor requires 18 hours of approved mathematics courses, with at least 9 hours of 300-400-level credits taken in residence at WSU or through WSU-approved education abroad or educational exchange courses. Check with a Sciences advisor for a current list of approved courses. Courses required for the minor may not be taken pass/fail and minimum 2.0 GPA is required in these courses.

 




Schedules of Studies

Honors students complete the Honors College requirements which replace the UCORE requirements.


Applied Option (120 Credits)

Mathematics Major Core Requirements

In addition to the UCORE requirements and the College of Arts and Sciences requirements, a mathematics major is required to take 13 core courses and a minimum of 4 additional 300-400-level MATH courses specified by a chosen option. Options include: Actuarial Science, Applied Mathematics, Theoretical Mathematics. Courses required for the major may not be taken pass/fail, and a 2.0 minimum GPA is required.

Admission to the Major Requirements

1. Applications for admission to the major are accepted at any time during fall and spring semesters. Decisions are made within ten working days of receipt of application. Application forms are available in the Mathematics Department office.
2. Applications are evaluated, and admission decided, by a faculty committee.
3. Applicants must have a cumulative GPA of at least 2.0.
4. The mathematics core consists of MATH 171, 172, and 220. These courses (or their equivalent for transfer students) must be completed before application.
5. Students with at least a 2.5 GPA in the mathematics core will be admitted automatically. Those with less than a 2.0 GPA in the mathematics core will normally not be admitted. Others will be considered on a case-by-case basis.
6. Appeals related to admission decisions are considered by the department chairperson.
7. Students who are denied admission may reapply after completing at least 12 more credits, whereupon decisions are based on grades in mathematics, science, and computer science courses; cumulative GPA and grade patterns; and a personal interview.
8. Admitted students whose cumulative GPA or GPA in MATH courses numbered 171 and above falls below 2.0 for two consecutive semesters, or who are academically deficient, are subject to release from the major.
9. Applications for readmission are handled in the same manner as admission applications for those previously denied.
First Year
First TermCredits
Arts [ARTS]3
Biological Sciences [BSCI] with lab4
ENGLISH 101 [WRTG]3
MATH 171 [QUAN]4
Second TermCredits
CPT S 1214
HISTORY 105 [ROOT]3
MATH 172 or 1824
MATH 220 or 2302 or 3
Social Sciences [SSCI]3
Second Year
First TermCredits
Humanities [HUM]3
MATH 273 or 2832
MATH 3013
PHYSICS 201 [PSCI]3
PHYSICS 211 [PSCI]1
Foreign Language, if needed, or Electives4
Second TermCredits
Arts [ARTS], Humanities [HUM], or Social Sciences [SSCI]3
MATH 3153
MATH 3981
STAT 3603
Foreign Language, if needed, or Electives4
Complete Writing Portfolio
Third Year
First TermCredits
Diversity [DIVR]3
MATH 300 [M]3
MATH 4203
Applied Mathematics Option Course13
Electives3
Second TermCredits
ENGLISH 402 [WRTG] [M]3
MATH 421 [M]3
Applied Mathematics Option Course13
Electives6
Fourth Year
First TermCredits
MATH 401 [M]3
Applied Mathematics Option Course13
Electives9
Second TermCredits
MATH 402 [M]3
MATH 464 [CAPS]3
Applied Mathematics Option Course13
Electives6
Exit Interview

Footnotes
1Applied Mathematics Required Option Courses: a) MATH 364 and two of MATH 325, 416, 448, 453, 456, or 466; or b) CPT S 122, MATH 364, 448, and one of MATH 416, 440, or 466; or c) three of MATH 340, 415, 440, 448, and 486.

Secondary Teaching Option Without Certification (120 Credits)

Mathematics Major Core Requirements

Courses required for the major may not be taken pass/fail, and a 2.0 minimum GPA is required.


Admission to the Major Requirements

  1. Applications for admission to the major are accepted at any time during fall and spring semesters. Decisions are made within ten working days of receipt of application. Application forms are available in the Mathematics Department office.
  2. Applications are evaluated, and admission decided, by a faculty committee.
  3. Applicants must have a cumulative GPA of at least 2.0.
  4. The mathematics core consists of MATH 171, 172, and 220. These courses (or their equivalent for transfer students) must be completed before application.
  5. Students with at least a 2.5 GPA in the mathematics core will be admitted automatically. Those with less than a 2.0 GPA in the mathematics core will normally not be admitted. Others will be considered on a case-by-case basis.
  6. Appeals related to admission decisions are considered by the department chairperson.
  7. Students who are denied admission may reapply after completing at least 12 more credits, whereupon decisions are based on grades in mathematics, science, and computer science courses; cumulative GPA and grade patterns; and a personal interview.
  8. Admitted students whose cumulative GPA or GPA in MATH courses numbered 171 and above falls below 2.0 for two consecutive semesters, or who are academically deficient, are subject to release from the major.
  9. Applications for readmission are handled in the same manner as admission applications for those previously denied.

First Year
First TermCredits
Biological Sciences [BSCI] with lab4
HISTORY 105 [ROOT]3
Humanities [HUM]3
MATH 171 [QUAN]4
Second TermCredits
Arts [ARTS]3
ENGLISH 101 [WRTG]3
MATH 1724
MATH 220 2
PSYCH 105 [SSCI]3
Second Year
First TermCredits
Arts [ARTS], Humanities [HUM], or Social Sciences [SSCI]3
ENGLISH 201 [WRTG] or 301 [WRTG]3
MATH 2163
MATH 2732
PHYSICS 201 [PSCI]3
PHYSICS 211 [PSCI]1
Second TermCredits
Diversity [DIVR]3
MATH 3013
MATH 3153
MATH 3981
Electives6
Complete Writing Portfolio
Third Year
First TermCredits
MATH 300 [M]3
MATH 330 3
MATH 4033
Foreign Language, if necessary, and/or Electives6
Second TermCredits
MATH 320 [M]3
STAT 360 or 4433
300-400-level MATH Electives13
Foreign Language, if necessary, and/or Electives6
Fourth Year
First TermCredits
MATH 401 [M]3
MATH 4313
Electives9
Second TermCredits
MATH 432 [CAPS]3
300-400-level MATH Electives13
300-400-level Electives3
Electives6
Exit Interview

Footnotes
1MATH Elective courses include any 3-credit 300-400-level MATH courses not required to fulfill a major requirement.


Courses

The online catalog includes the most recent changes to courses and degree requirements that have been approved by the Faculty Senate, including changes that are not yet effective. Courses showing two entries of the same number indicate that the course information is changing. The most recently approved version is shown first, followed by the older version, in gray, with its last-effective term preceding the course title. Courses shown in gray with only one entry of the course number are being discontinued. Course offerings by term can be accessed by clicking on the term links when viewing a specific campus catalog.


Mathematics (MATH)

Spring 2022 Summer 2022 Fall 2022 


100 Basic Mathematics 2 Course Prerequisite: A minimum ALEKS math placement score of 1%. Review of basic arithmetic and elementary algebra. No credit earned toward degree. S, F grading.

101 Intermediate Algebra 3 Fundamental algebraic operations and concepts. No credit earned toward degree.

103 Algebra Methods and Introduction to Functions 3 Course Prerequisite: MATH 100 with an S, MATH 101 with a C or better, or a minimum ALEKS math placement score of 40%. Fundamental algebraic operations and concepts, linear systems and inequalities, polynomial and rational functions, introduction to exponential and logarithmic functions. Typically offered Fall, Spring, and Summer.

105 [QUAN] Exploring Mathematics 3 Course Prerequisite: MATH 101, 103, or 251, each with a C or better, or STAT 212 with a C or better, or a minimum ALEKS math placement score of 45%. Nature and scope of modern mathematics, and its relationships to other disciplines. Typically offered Fall, Spring, and Summer.

106 College Algebra 3 Course Prerequisite: MATH 101 with a C or better, or MATH 103 with a C or better, or a minimum ALEKS math placement score of 70%. Graphs, properties and applications of polynomial, rational, exponential and logarithmic functions. Typically offered Fall, Spring, and Summer.

108 Trigonometry 2 Course Prerequisite: MATH 106 with a C or better. Graphs, properties and applications of trigonometric functions. Typically offered Fall, Spring, and Summer.

108 (Effective through Spring 2022) Trigonometry 2 Course Prerequisite: MATH 106 with a C or better. Graphs, properties and applications of trigonometric functions. Typically offered Fall, Spring, and Summer.

110 Mathematics Acceleration 1 (0-3) Course Prerequisite: A minimum ALEKS math placement score of 25%. Individualized instruction on mathematical skills to enhance the mathematical background necessary for success in one of MATH 103, 106, or 171. Typically offered Fall and Spring. S, F grading.

111 Mathematics Tutorial for MATH 201 1 Course Prerequisite: Concurrent enrollment MATH 107. Student-centered group tutorial focusing on skill improvement for success in MATH 201. S, F grading.

115 Math 105 Tutorial 2 Tutorial for MATH 105 focusing on concept development and mastery; skill proficiency. S, F grading.

116 Math 106 Tutorial 2 Tutorial for MATH 106 focusing on concept development and mastery; skill proficiency. S, F grading.

140 [QUAN] Calculus for Life Scientists 4 (3-3) Course Prerequisite: MATH 106 with a C or better and MATH 108 with a C or better, or a minimum ALEKS math placement score of 80%. Enrollment not allowed if credit already earned for MATH 171 or 202 except by department consent. Differential and integral calculus with emphasis on life science applications. By department consent, credit may be allowed for two of MATH 140, 171, or 202. Typically offered Fall, Spring, and Summer.

171 [QUAN] Calculus I 4 (3-3) Course Prerequisite: MATH 106 with a C or better and MATH 108 with a C or better, or a minimum ALEKS math placement score of 83%. Enrollment not allowed if credit already earned for MATH 140 or 202 except by department consent. Differential and integral calculus of one variable with associated analytic geometry. By department consent, credit may be allowed for two of MATH 140, 171, or 202. Typically offered Fall, Spring, and Summer.

172 Calculus II 4 (3-3) Course Prerequisite: MATH 171 with a C or better. Techniques and applications of one-variable calculus; estimations; series, derivative of a vector function. Credit not granted for both MATH 172 and 182. Typically offered Fall, Spring, and Summer.

201 Mathematics for Business and Economics 3 Course Prerequisite: MATH 101 with a C or better, MATH 103 with a C or better, or a minimum ALEKS math placement score of 65%. Mathematical analysis using polynomial, exponential, and logarithmic functions; linear systems, linear programming and mathematics of finance, for business/economic applications and modeling. Typically offered Fall, Spring, and Summer.

202 [QUAN] Calculus for Business and Economics 3 Course Prerequisite: MATH 106 with a C or better, MATH 201 with a C or better, or a minimum ALEKS math placement score of 80%. Enrollment not allowed if credit already earned for MATH 140 or 171 except by department consent. Differential calculus of the polynomial, exponential, and logarithmic functions; focus on unconstrained and constrained optimization, single and partial differentiation. By department consent, credit may be allowed for two of MATH 140, 171, or 202. Typically offered Fall, Spring, and Summer.

216 Discrete Structures 3 Course Prerequisite: MATH 108 with a C or better, OR MATH 140, 171, 172, 182, or 202 (concurrent enrollment also allowed). Discrete mathematics, trees, graphs, elementary logic, and combinatorics with application to computer science. Recommended preparation: Programming course. Typically offered Spring.

220 Introductory Linear Algebra 2 Course Prerequisite: MATH 171 or concurrent enrollment. Enrollment not allowed if credit already earned for MATH 225 or 230. Solving linear systems, matrices, determinants, subspaces, eigenvalues, orthogonality. Credit not granted for more than one of MATH 220, 225, and 230. Typically offered Fall, Spring, and Summer.

225 Linear Algebra with Modern Applications 3 Course Prerequisite: MATH 106 or higher. Enrollment not allowed if credit already earned for MATH 220 or 230. Solving linear systems, matrices, determinants, subspaces, eigenvalues, orthogonality, machine learning, AI, computer graphics, and economic models. Credit not granted for more than one of MATH 220, 225, and 230. (Crosslisted course offered as MATH 225, DATA 225.)

225 (Effective through Summer 2022) Linear Algebra with Modern Applications 3 Course Prerequisite: MATH 106 or higher. Enrollment not allowed if credit already earned for MATH 220 or 230. Solving linear systems, matrices, determinants, subspaces, eigenvalues, orthogonality, machine learning, AI, computer graphics, and economic models. Credit not granted for more than one of MATH 220, 225, and 230.

251 Fundamentals of Elementary Mathematics I 3 (2-2) Course Prerequisite: MATH 101, 103, 105, 106, or 201, each with a C or better, or STAT 212 with a C or better, or a minimum ALEKS math placement score of 45%. Comprehensive development of number systems emphasizing place-value, integers, rational numbers, and associated algorithms; methods of problem solving. Typically offered Fall.

252 [QUAN] Fundamentals of Elementary Mathematics II 3 (2-2) Course Prerequisite: MATH 251 with a C or better. Inquiry-based approach to fundamental concepts: measurement, geometrical constructions, similarity, congruence, symmetry, probability, counting principles, measures of central tendency, and distributions. Required preparation: One year of high school geometry. Typically offered Spring.

273 Calculus III 2 Course Prerequisite: MATH 172 with a C or better, or MATH 182 with a C or better. Calculus of functions of several variables. Credit not granted for both MATH 273 and 283. Typically offered Fall, Spring, and Summer.

300 Mathematical Computing 3 Course Prerequisite: MATH 220, 225, or 230; admitted to the major in Mathematics. Examination of some current computer software for solving mathematical problems. Recommended preparation: MATH 315. Typically offered Odd Years - Fall.

301 Introduction to Mathematical Reasoning 3 Course Prerequisite: MATH 220, 225, or 230, each with a C or better. Mathematical arguments and the writing of proofs. Typically offered Odd Years - Spring.

302 Theory of Numbers 3 Course Prerequisite: MATH 172 with a C or better, or MATH 182 with a C or better; MATH 301 with a C or better. Divisibility properties of integers; congruences; Diophantine equations; quadratic residues.

303 [M] Geometry for the Middle School Teacher 3 Course Prerequisite: MATH 252. Topics in 2D and 3D geometry including technology-based reasoning and exploration, deductive arguments, transformational and proportional reasoning, and non-Euclidean geometries.

315 Differential Equations 3 Course Prerequisite: MATH 273 or 283, each with a C or better; and MATH 220, 225, or 230, each with a C or better, or concurrent enrollment. Linear differential equations and systems; series, numerical and qualitative approaches; applications. Typically offered Fall, Spring, and Summer.

320 [M] Elementary Modern Algebra 3 Course Prerequisite: MATH 220, 225, or 230, each with a C or better; MATH 301. Algebra as a deductive system; number systems; groups, rings, and fields. Typically offered Even Years - Spring.

325 Elementary Combinatorics 3 Course Prerequisite: MATH 220, 225, or 230, each with a C or better. Introduction to combinatorial theory: counting methods, binomial coefficients and identities, generating functions, occurrence relations, inclusion-exclusion methods.

330 Methods of Teaching Secondary School Mathematics 3 Course Prerequisite: MATH 301 or concurrent enrollment. New curricula and pedagogical techniques for secondary school mathematics. Typically offered Even Years - Fall.

340 Introduction to Mathematical Biology 3 Course Prerequisite: MATH 140 with a C or better, or MATH 172 with a C or better, or MATH 182 with a C or better; BIOLOGY 101, BIOLOGY 102, BIOLOGY 106, or BIOLOGY 107. Mathematical biology and development of mathematical modeling for solutions to problems in the life sciences. (Crosslisted course offered as MATH 340, BIOLOGY 340). Typically offered Even Years - Spring.

351 Algebraic Thinking for the Middle School Teacher 3 Course Prerequisite: MATH 252 with a C or better. Algebraic reasoning, classes of functions, translation among models, analytical rule, tables of data, context and coordinate graphs.

352 Probability and Data Analysis for Middle School Teachers 3 Course Prerequisite: MATH 251 and 252; or STAT 360. Probability and statistics in relation to middle school mathematics and real world problems through visualization, hands-on activities, and technology.

364 Principles of Optimization 3 Course Prerequisite: MATH 202, 220, 225, or 230. Algebra of linear inequalities; duality; graphs, transport networks; linear programming; special algorithms; nonlinear programming; selected applications.

398 Mathematical Snapshots 1 Course Prerequisite: MATH 172 or MATH 182. Character, life work, and historical importance of mathematicians from various eras and branches of mathematics. Typically offered Odd Years - Fall.

401 [M] Introduction to Analysis I 3 Course Prerequisite: MATH 301 with a C or better. Properties of sets and sequences of real numbers; limits, continuity, differentiation and integration of functions; metric spaces. Typically offered Odd Years - Fall.

402 [M] Introduction to Analysis II 3 Course Prerequisite: MATH 401. Sequences of functions, power series, multivariable calculus, inverse and implicit function theorems, Lagrange multipliers, change of variable in multiple integrations.

403 Euclidean and Non-Euclidean Geometry 3 Course Prerequisite: MATH 301 with a C or better. Geometry as a deductive system of logic; postulational systems; projective and non-Euclidian geometries.

405 Introduction to Financial Mathematics 3 Course Prerequisite: MATH 172 or 182. Introduction to financial mathematics including the basics of annuities, stocks, bonds, and financial derivatives.

415 Intermediate Differential Equations 3 Course Prerequisite: MATH 315. Linear systems; qualitative theory (existence, uniqueness, stability, periodicity); boundary value problems; applications.

416 Numerical Simulations for Probabilistic Models 3 Course Prerequisite: STAT 360; CPT S 121, CPT S 251, or MATH 300. Efficient generation of random variables; statistical analysis and validation techniques; variance reduction; Markov Chain Monte Carlo methods; applications include complex systems, financial models, and Bayesian computation. Credit not granted for both MATH 416 and MATH 516. Required preparation must include probability and statistics and programming experience. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

420 Linear Algebra 3 Course Prerequisite: MATH 220, 225, or 230, each with a C or better; MATH 301 with a C or better. Vector spaces, linear transformations, diagonalizability, normal matrices, inner product spaces, orthogonality, orthogonal projections, least-squares, SVD.

421 [M] Algebraic Structures 3 Course Prerequisite: MATH 301 with a C or better. Properties of algebraic structures and their homomorphisms, semi-groups, groups, rings, unique factorization domains, fields. Typically offered Spring.

425 Conceptual Aspects of Mathematics 3 Course Prerequisite: By instructor permission. Exploration of conceptual models for thinking about mathematical ideas; activities and discussions of mathematical thinking and instruction. (Crosslisted course offered as TCH LRN 425, MATH 425).

431 Intersections of Culture and Mathematics 3 Course Prerequisite: MATH 301 with a C or better. Gender/race/ethnicity differences; social consequences; cultural influences on development and learning of mathematics; role of women, people of color in mathematics. Credit not granted for both MATH 431 and 531. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

432 [CAPS] Mathematics for College and Secondary Teachers 3 Course Prerequisite: MATH 301 with a C or better. Pre-algebra, algebra functions and geometry examined from an advanced perspective, for secondary and lower level college teachers. Typically offered Odd Years - Fall.

440 Applied Mathematics I: PDEs 3 Course Prerequisite: MATH 315. Applied partial differential equations; Fourier series; Bessel functions and Legendre polynomials as harmonics for disks and balls; Laplace, heat, and wave equations; separation of variables and D'Alambert's formula. Credit not granted for both MATH 440 and MATH 540. Required preparation must include differential equations. Offered at 400 and 500 level. Typically offered Fall. Cooperative: Open to UI degree-seeking students.

448 Numerical Analysis 3 Course Prerequisite: MATH 315 with a C or better; one of CPT S 121, 131, or MATH 300, with a C or better. Fundamentals of numerical computation; finding zeroes of functions, approximation and interpolation; numerical integration (quadrature); numerical solution of ordinary differential equations. (Crosslisted course offered as MATH 448, MATH 548, CPT S 430, CPT S 530). Required preparation must include differential equations and a programming course. Offered at 400 and 500 level.

453 Graph Theory 3 Course Prerequisite: MATH 220, 225, or 230. Graphs and their applications, directed graphs, trees, networks, Eulerian and Hamiltonian paths, matrix representations, construction of algorithms. (Crosslisted course offered as MATH 453, MATH 553, CPT S 453, CPT S 553). Required preparation must include linear algebra. Recommended preparation: MATH 301. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

456 Introduction to Statistical Theory 3 Course Prerequisite: STAT 430 or 443. Sampling distributions; hypothesis testing and estimation; maximum likelihood; likelihood ratio tests; theory of least squares; nonparametrics. (Crosslisted course offered as STAT 456, MATH 456). Credit not granted for more than one of STAT/MATH 456 or STAT 556. Recommended preparation: One 3-credit 400-level STAT or probability course. Offered at 400 and 500 level.

464 [CAPS] Linear Optimization 3 Course Prerequisite: MATH 273 or MATH 283. Linear and integer programming; optimization problems; applications to economic and military strategies; rectangular games; minimax theory. Recommended preparation: MATH 301. Typically offered Spring.

466 Optimization in Networks 3 Course Prerequisite: MATH 364. Formulation and solution of network optimization problems including shortest path, maximal flow, minimum cost flow, assignment, covering, postman, and salesman. Credit not granted for both MATH 466 and MATH 566. Required preparation must include linear programming. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

486 Mathematical Methods in Natural Sciences 3 Course Prerequisite: MATH 315. Introduction to mathematical modeling of natural processes; methods include dimensional and scaling analysis, perturbation theory, field theory of continuum mechanics, calculus of variations, and Markov chains; applications to physics, chemistry, biology, and engineering. Credit not granted for both MATH 486 and MATH 586. Required preparation must include differential equations. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

490 Topics in Mathematics V 1-3 May be repeated for credit; cumulative maximum 9 credits. Course Prerequisite: By instructor permission. Special topics in mathematics.

494 Seminar in Mathematical Biology 1 May be repeated for credit; cumulative maximum 4 credits. Course Prerequisite: MATH 140 with a C or better, or MATH 172 with a C or better, or MATH 182 with a C or better; BIOLOGY 101, BIOLOGY 102, BIOLOGY 106, or BIOLOGY 107. Oral presentation of research approaches, research results and literature review of mathematical biology including mathematical modeling of biological systems. (Crosslisted course offered as MATH 494, BIOLOGY 494). Cooperative: Open to UI degree-seeking students. S, F grading.

499 Special Problems V 1-4 May be repeated for credit. Independent study conducted under the jurisdiction of an approving faculty member; may include independent research studies in technical or specialized problems; selection and analysis of specified readings; development of a creative project; or field experiences. S, F grading.

500 Proseminar 1 May be repeated for credit; cumulative maximum 2 credits. S, F grading.

501 Real Analysis 3 Metric spaces, convergence, continuous functions, infinite series, differentiation and integration of functions of one and several variables. Required preparation must include advanced calculus or real analysis.

502 Introduction to Functional Analysis 3 Course Prerequisite: MATH 501. Normed linear spaces, Banach spaces, introduction to Hilbert space, linear operators. Required preparation: Advanced linear algebra.

511 Advanced Linear Algebra 3 Spectral theory, Schur's theorem, normality, Jordan canonical forms, hermitian matrices, variational inequalities, matrix norms, eigenvalue localization, matrix perturbation theory. Required preparation must include second level undergraduate linear algebra. Cooperative: Open to UI degree-seeking students.

512 Ordinary Differential Equations 3 Existence of solutions; linear systems; qualitative behavior, especially stability; periodic solutions. Required preparation must include a year-long sequence in advanced calculus or real analysis. Cooperative: Open to UI degree-seeking students.

516 Numerical Simulations for Probabilistic Models 3 Efficient generation of random variables; statistical analysis and validation techniques; variance reduction; Markov Chain Monte Carlo methods; applications include complex systems, financial models, and Bayesian computation. Credit not granted for both MATH 416 and MATH 516. Required preparation must include probability and statistics and programming experience. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

524 Algebraic Topology 3 Algebraic techniques (groups, homomorphisms, etc) to study connectivity of spaces; topics include simplicial complexes, homology, relative homology, Meyer-Vietoris sequences, categories and functors, cohomology, and duality in manifolds. Recommended preparation: real analysis and abstract algebra.

525 General Topology 3 Sets, metric spaces, topological spaces; continuous mappings, compactness, connectedness, local properties, function spaces, and fundamental groups. Required preparation must include a year-long sequence in advanced calculus or real analysis. Cooperative: Open to UI degree-seeking students.

529 Computational Topology 3 Topological techniques combined with algorithms to find structure in data; simplicial complexes from point clouds, algorithms for homology and persistent homology, mapper and topological data analysis, optimal homology problems. Recommended preparation: mathematical maturity at senior undergraduate level and some experience with computer programming.

531 Intersections of Culture and Mathematics 3 Gender/race/ethnicity differences; social consequences; cultural influences on development and learning of mathematics; role of women, people of color in mathematics. Credit not granted for both MATH 431 and 531. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

532 Advanced Mathematical Thinking 3 Course Prerequisite: Graduate standing in mathematics. Current theories about how humans learn to think mathematically at the advanced level. Cooperative: Open to UI degree-seeking students.

533 Teaching College Mathematics 1 May be repeated for credit; cumulative maximum 3 credits. Course Prerequisite: Graduate standing in Mathematics or Statistical Science. Theory and practice of mathematics instruction at the collegiate level.

535 Research Paradigms in Mathematics Education 3 Course Prerequisite: MATH 534. Current research paradigms in math education research; critique research designs used in current mathematics education research article; design and carry out a research project. Cooperative: Open to UI degree-seeking students.

536 Statistical Computing 3 (2-3) Generation of random variables, Monte Carlo simulation, bootstrap and jackknife methods, EM algorithm, Markov chain Monte Carlo methods. (Crosslisted course offered as STAT 536, MATH 536). Recommended preparation: STAT 530, 548, 556, or equivalent. Cooperative: Open to UI degree-seeking students.

536 (Effective through Summer 2022) Statistical Computing 3 (2-3) Course Prerequisite: STAT 556. Generation of random variables, Monte Carlo simulation, bootstrap and jackknife methods, EM algorithm, Markov chain Monte Carlo methods. (Crosslisted course offered as STAT 536, MATH 536). Recommended preparation: One 3-credit 400-level probability or STAT course. Cooperative: Open to UI degree-seeking students.

540 Applied Mathematics I: PDEs 3 Applied partial differential equations; Fourier series; Bessel functions and Legendre polynomials as harmonics for disks and balls; Laplace, heat, and wave equations; separation of variables and D'Alambert's formula. Credit not granted for both MATH 440 and MATH 540. Required preparation must include differential equations. Offered at 400 and 500 level. Typically offered Fall. Cooperative: Open to UI degree-seeking students.

544 Advanced Matrix Computations 3 Advanced topics in the solution of linear systems, singular value decomposition, and computation of eigenvalues and eigenvectors (Francis's algorithm). (Crosslisted course offered as MATH 544, CPT S 531). Required preparation must include numerical analysis. Cooperative: Open to UI degree-seeking students.

545 Numerical Analysis of Parabolic and Hyperbolic PDEs 3 Numerical solutions of parabolic and hyperbolic partial differential equations with emphasis on finite difference methods; topics include: finite difference; stability, consistency, and convergence; shocks; conservation of forms. Required preparation must include numerical analysis. Cooperative: Open to UI degree-seeking students.

548 Numerical Analysis 3 Fundamentals of numerical computation; finding zeroes of functions, approximation and interpolation; numerical integration (quadrature); numerical solution of ordinary differential equations. (Crosslisted course offered as MATH 448, MATH 548, CPT S 430, CPT S 530). Required preparation must include differential equations and a programming course. Offered at 400 and 500 level.

553 Graph Theory 3 Graphs and their applications, directed graphs, trees, networks, Eulerian and Hamiltonian paths, matrix representations, construction of algorithms. (Crosslisted course offered as MATH 453, MATH 553, CPT S 453, CPT S 553). Required preparation must include linear algebra. Recommended preparation: MATH 301. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

555 Topics in Combinatorics 3 May be repeated for credit; cumulative maximum 6 credits. Combinatorics, generating functions, recurrence relations, inclusion-exclusion, coding theory; experimental design, graph theory. Cooperative: Open to UI degree-seeking students.

563 Mathematical Genetics 3 Mathematical approaches to population genetics and genome analysis; theories and statistical analyses of genetic parameters. (Crosslisted course offered as MATH 563, BIOLOGY 566). Required preparation must include multivariate calculus, genetics, and statistics. Cooperative: Open to UI degree-seeking students.

564 Convex and Nonlinear Optimization 3 Convex sets and functions; operations preserving convexity; linear, quadratic, and conic optimization; duality theory; unconstrained smooth optimization; interior point methods. Required preparation must include advanced multivariate calculus, and a programming language. Recommended preparation: Knowledge in linear optimization and numerical linear algebra. Cooperative: Open to UI degree-seeking students.

565 Nonsmooth Analysis and Optimization with Applications 3 Course Prerequisite: MATH 564. Extended real-valued functions; continuity and convexity; subgradient, conjugate functions and optimality condition; alternating minimization; projected subgradient methods; alternating direction methods of multipliers; applications in statistical learning. Required preparation must include real analysis and command of a programming language. Cooperative: Open to UI degree-seeking students.

566 Optimization in Networks 3 Formulation and solution of network optimization problems including shortest path, maximal flow, minimum cost flow, assignment, covering, postman, and salesman. Credit not granted for both MATH 466 and MATH 566. Required preparation must include linear programming. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

567 Integer and Combinatorial Optimization 3 Theory and applications of integer and combinatorial optimization including enumerative, cutting plane, basis reduction, relaxation and matching methods. Required preparation must include linear optimization. Cooperative: Open to UI degree-seeking students.

568 Statistical Theory I 3 Probability spaces, combinatorics, multidimensional random variables, characteristic function, special distributions, limit theorems, stochastic processes, order statistics. (Crosslisted course offered as STAT 548, MATH 568). Recommended preparation: Calculus III and one 3-credit 400-level probability course. Cooperative: Open to UI degree-seeking students.

569 Statistical Theory II 3 Course Prerequisite: STAT 548 or MATH 568. Statistical inferences; estimation and testing hypotheses; regression analysis; sequential analysis and nonparametric methods. (Crosslisted course offered as STAT 549, MATH 569). Cooperative: Open to UI degree-seeking students.

574 Topics in Optimization 3 May be repeated for credit; cumulative maximum 12 credits. Advanced topics in the theory and computing methodology in optimization with emphasis on real-life algorithmic implementations. Required preparation must include advanced multivariable calculus and a programming language. Typically offered Spring. Cooperative: Open to UI degree-seeking students.

579 Mathematical Modeling in the Biological and Health Sciences 3 Techniques, theory, and current literature in mathematical modeling in the biological and health sciences, including computational simulation. (Course offered as BIOLOGY 579, MATH 579). Cooperative: Open to UI degree-seeking students.

581 Topics in Mathematics V 1-3 May be repeated for credit. Topics in mathematics. Cooperative: Open to UI degree-seeking students.

583 Topics in Applied Mathematics V 1-3 May be repeated for credit. Topics in applied mathematics. Cooperative: Open to UI degree-seeking students.

586 Mathematical Methods in Natural Sciences 3 Introduction to mathematical modeling of natural processes; methods include dimensional and scaling analysis, perturbation theory, field theory of continuum mechanics, calculus of variations, and Markov chains; applications to physics, chemistry, biology, and engineering. Credit not granted for both MATH 486 and MATH 586. Required preparation must include differential equations. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

587 Topics in Algebra and Linear Algebra V 1-3 May be repeated for credit. Advanced topics in algebra and linear algebra. Recommended preparation: Two semesters of linear algebra and one semester of abstract algebra.

588 Topics in Computational Math V 1-3 May be repeated for credit. Advanced topics in computational mathematics. Recommended preparation: one semester of numerical analysis.

589 Topics in Analysis V 1-3 Advanced topics in mathematical analysis. Recommended preparation: one semester of graduate analysis.

591 Seminar in Mathematical Biology 1 May be repeated for credit; cumulative maximum 10 credits. Current research in mathematical biology. S, F grading.

592 Seminar in Analysis 1 May be repeated for credit; cumulative maximum 10 credits. Current research in analysis. S, F grading.

594 Mathematics Education Seminar 1 May be repeated for credit; cumulative maximum 10 credits. Current research in mathematics education. S, F grading.

600 Special Projects or Independent Study V 1-18 May be repeated for credit. Independent study, special projects, and/or internships. Students must have graduate degree-seeking status and should check with their major advisor before enrolling in 600 credit, which cannot be used toward the core graded credits required for a graduate degree. S, F grading.

702 Master's Special Problems, Directed Study, and/or Examination V 1-18 May be repeated for credit. Independent research in special problems, directed study, and/or examination credit for students in a non-thesis master's degree program. Students must have graduate degree-seeking status and should check with their major advisor/committee chair before enrolling for 702 credit. S, U grading.

800 Doctoral Research, Dissertation, and/or Examination V 1-18 May be repeated for credit. Course Prerequisite: Admitted to the Mathematics PhD program. Independent research and advanced study for students working on their doctoral research, dissertation and/or final examination. Students must have graduate degree-seeking status and should check with their major advisor/committee chair before enrolling for 800 credit. S, U grading.

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