# Mathematics & Statistics - Courses

## Courses typically taught by the Department of Mathematics and Statistics

- MATH 103. The Nature of Mathematics

3 credits. Offered fall, spring, summer.

Topics such as geometry, computing, algebra, number theory, history of mathematics, logic, probability, statistics, modeling and problem solving intended to give students insight into what mathematics is, what it attempts to accomplish and how mathematicians think. May be used for general education credit. - MATH 105. Quantitative Literacy and Reasoning

3 credits. Offered fall, spring, summer.

Applications and interpretation of numerical information in context. Selection and use of appropriate tools: scientific notation, percentages, descriptive summaries, absolute and relative changes, graphs, normal and exponential population models, and interpretations of bivariate models. Making informed decisions and effectively communicating them. Identifying limitations of information sources, assessing reasonableness of results, and basic concepts of confidence amid uncertainty. Not open to majors in mathematics or statistics. May be used for general education credit. Not open to students who have previously earned credit in courses requiring MATH 105 competency except with consent of the Mathematics and Statistics department head. - MATH 107. Fundamentals of Mathematics

3 credits. Offered fall, spring, summer.

MATH 107 and MATH 108, along with MATH 207, form a sequence that covers the topics of sets, logic, numeration systems, development of real numbers, number operations, number theory, geometry, measurement, algebra, functions, probability and data analysis. Sequence is required for early childhood, elementary, or middle school teacher licensure. May be used for general education credit. - MATH 108. Fundamentals of Mathematics II

3 credits. Offered fall, spring, summer.

MATH 107 and MATH 108, along with MATH 207, form a sequence that covers the topics of sets, logic, numeration systems, development of real numbers, number operations, number theory, geometry, measurement, algebra, functions, probability and data analysis. Sequence is required for early childhood, elementary, or middle school teacher licensure.

*Prerequisite: MATH 107 with a grade of “C-” or better and a passing score on Basic Skills Test.* - MATH 135. Elementary Functions

4 credits. Offered spring.

Algebraic, exponential, logarithmic and trigonometric functions; matrices and matrix solutions to systems of linear equations; vectors. Not open to students who have previously earned credit in MATH 155, 156, 205 or 235, except with the consent of the department head. - MATH 155. College Algebra

3 credits. Offered fall, spring, summer.

Polynomial, rational, exponential and logarithmic functions and applications, systems of equations and inequalities, sequences.

*Prerequisite: Demonstration of proficiency in algebra at an intermediate level. A test is required to determine placement in MATH 155 or MATH 156. Not open to students who have previously earned credit in MATH 135, MATH 156, MATH 205, MATH 205, MATH 232 or MATH 235.* - MATH 167. Topics in Mathematics (Math/Stat Intro Seminar)

1 to 3 credits. Offered fall, spring.

Topics or projects in mathematics which are of interest to the lower-division student. May be repeated for credit when course content changes. Topics or projects selected may dictate prerequisites. Students should consult the instructor prior to enrolling for this course. - MATH 199. Algebra/Precalculus Gateway

1 credit. Offered fall, spring.

Review of fundamental mathematics required to be successful in MATH 205 or MATH 231, including graphs of functions, factoring, simplifying, solving equations and inequalities, and exponential/logarithmic/trigonometric functions. Self-paced study with required proctored tests. Students needing more instruction should register for MATH 155 instead.

*Corequisite: MATH 231 or MATH 205 with appropriate calculus placement score.* - MATH 205. Introductory Calculus I

3 credits. Offered fall, spring, summer.

Topics from differential and integral calculus with applications to the social, behavioral or life sciences and business or management.

*Prerequisite: MATH 135 or MATH 155 or MATH 156 or sufficient score on the mathematics placement exam. Not open to mathematics or physics majors or to students who have already earned credit in MATH 232 or MATH 235.* - MATH 207. Fundamentals of Mathematics III

3 credits. Offered fall, spring, summer.

A continuation of topics listed in the MATH 107-108 description will be covered. The MATH 107-108-207 sequence fulfills the requirements for licensure of prospective early childhood, elementary, or middle school teachers.

*Prerequisite: MATH 107 and MATH 108 with a grade of “C-” or better.* - MATH 220. Elementary Statistics

3 credits. Offered fall, spring, summer.

Descriptive statistics, frequency distributions, sampling, estimation and testing of hypotheses, regression, correlation and an introduction to statistical analysis using computers. May be used for general education credit.

*Prerequisite: MATH 105 with a grade of “C-” or better or sufficient score on the Mathematics Placement Exam.* - MATH 220H. Elementary Statistics – Honors

3 credits. Offered fall, spring.

Descriptive statistics, frequency distributions, sampling, estimation and testing of hypotheses, regression, correlation and an introduction to statistical analysis using computers. May be used for general education credit.

*Prerequisite: Honors Students* - MATH 227. Discrete Structures I

3 credits. Offered on demand. Crosslisted with: CS 227

An introduction to discrete mathematical structures including functions, relations, sets, logic, matrices, elementary number theory, proof techniques, basics of counting, graphic theory, discrete probability, digital logic, finite state machines, integer and floating point representations.

*Prerequisite: CS 159. Corequisite: CS 159.* - MATH 229. Introduction to Applied Statistics Using R

3 credits. Offered fall, spring.

An introduction to applied statistics that is more rigorous than MATH 220 intended for students majoring in mathematics or statistics. Descriptive statistics, data collection, frequency distributions, sampling distributions and the Central Limit Theorem, estimation and testing of hypotheses, simple linear regression, correlation, and chi-square test of independence are covered. Emphasis is on the analysis and interpretation of real data in context. Uses the R programming language.

*Prerequisite: Sufficient statistics and calculus placement scores. The calculus placement score requirement may be waived for students with “C-” or better in MATH 231.*

Not open to students with credit in MATH 220, MATH 220H, MATH 318, MATH 329 or equivalent. - MATH 231. Calculus with Functions I

3 credits. Offered fall, spring, summer.

MATH 231 and MATH 232 form a sequence that combines first-semester calculus with algebra and trigonometry. The sequence is designed for students whose pre-calculus skills are not strong enough for MATH 235. Calculus material in MATH 231 includes limits and derivatives of algebraic functions and their applications. May be used for general education credit. Not open to students who have already earned credit in MATH 234 or MATH 235.

*Prerequisite: MATH 155, MATH 156 or sufficient score on the Mathematics Placement Exam. MATH 231-MATH 232 together are equivalent to MATH 235 for all prerequisites.* - MATH 232. Calculus with Functions II

3 credits. Offered fall, spring, summer.

A continuation of MATH 231. Calculus topics include limits and derivatives of transcendental functions, the theory of integration and basic integration techniques. NOTE: MATH 231-232 together are equivalent to MATH 235 for all prerequisites. Not open to students who have already earned credit in MATH 234 or MATH 235.

*Prerequisite: MATH 231 with a grade of “C-” or better.* - MATH 233. Calculus with Modeling I

3 credits. Offered on demand.

MATH 233 and MATH 234 form a sequence that combines first-semester calculus with pre-calculus for students with skills not strong enough for MATH 235. Calculus is motivated by static and dynamic models in the context of scientific applications. MATH 233 includes limits, continuity, summation, and the definite integral as accumulation of change and as the limit of Riemann sums. May be used for general education credit.

*Prerequisite: MATH 155, MATH 156 or sufficient score on the Mathematics Placement Exam. MATH 233-234 together are equivalent to MATH 235 for all prerequisites. Not open to students who have already earned credit for MATH 232 or MATH 235.* - MATH 234. Calculus with Modeling II

3 credits. Offered on demand.

MATH 233 and MATH 234 form a sequence that combines first-semester calculus with pre-calculus for students with skills not strong enough for MATH 235. Calculus is motivated by static and dynamic models in the context of scientific applications. MATH 234 includes differentiation and antidifferentiation, including trigonometric functions, as well as the fundamental theorem of calculus.

*Prerequisite: MATH 233 with a grade of “C-” or better. Not open to students who have already earned credit for MATH 235. MATH 233-234 together are equivalent to MATH 235 for all prerequisites. Not open to students who have already earned credit for MATH 235.* - MATH 235. Calculus I

4 credits. Offered fall, spring, summer.

Differential and integral calculus of functions of one variable. Sequences and infinite series. MATH 235 may be used for general education credit. MATH 235 is not open to students who have already earned credit in MATH 232 or MATH 234.

*Prerequisite: Sufficient score on the Mathematics Placement Exam.* - MATH 236. Calculus II

4 credits. Offered fall, spring, summer.

Differential and integral calculus of functions of one variable. Sequences and infinite series.

*Prerequisite: MATH 232 or MATH 234 or MATH 235 with a grade of “C-” or better.* - MATH 237. Calculus III

4 credits. Offered fall, spring, summer.

Multivariate calculus.

*Prerequisite: MATH 236 with a grade of C- or better.* - MATH 238. Linear Algebra with Differential Equations

4 credits. Offered fall, spring, summer.

Matrices; determinants; vector spaces; linear transformations; eigenvalues and eigenvectors; separable, exact and linear differential equations; and systems of linear differential equations.

*Prerequisite: MATH 236. Not open to students with credit in MATH 300 or MATH 336 without departmental permission.* - MATH 245. Discrete Mathematics

3 credits. Offered fall, spring.

Logic, set theory, relations and functions, mathematical induction and equivalent forms, recurrence relations, counting techniques.

*Prerequisite: MATH 236. Corequisite: MATH 236.* - MATH 248. Computers & Numerical Algorithms

4 credits. Offered fall, spring.

Programming in a high-level computer language. Applications of numerical algorithms to problems basic to areas such as mathematics, the sciences, and economics and finance. This course is not open to students who have previously earned credit in MATH/CS 448.

*Prerequisite: MATH 236. Corequisite: MATH 236 and permission of instructor.* - MATH 268. Data Analysis and Visualization

3 credits. Offered spring.

This course is intended to give students hands-on experience on the basics of the data analysis techniques using R. It will focus on data management, data visualization, data exploration using descriptive data summaries, the basics of model building and the basics of inference. Topics include data management (creating data frames, splitting data, efficient data search); exploratory data analysis; data visualization; major distributions (univariate and multivariate); numerical summaries and outlier detections; and the basics of dimension reduction using principle component analysis and exploratory factor analysis.

*Prerequisite: MATH 220, or MATH 318 and permission of instructor.* - MATH 297. Undergraduate Research

1 to 4 credits. Offered on demand.

Students pursue research in a selected area of mathematics and/or statistics. Student must make arrangements with a supervising instructor prior to registration. Course may be repeated. - MATH 300. Linear Algebra

3 credits. Offered fall, spring.

Vector spaces, linear transformations, matrices, determinants, systems of linear equations, and eigenvalues and eigenvectors.

*Prerequisite: MATH 236; Not open for credit to students with credit in MATH 238.* - MATH 304. Principles of Algebra

3 credits. Offered fall, spring.

Algebraic structures, number systems, matrices, groups, rings, factors and solutions to equations, graph theory.

*Prerequisite: C- or better in MATH 107, MATH 108, and MATH 207.* - MATH 305. Principles of Geometry

3 credits. Offered fall, spring.

Finite geometries, geometric transformations, constructions, geometry of inversion, projective geometry, non-Euclidean geometry.

*Prerequisite: C- or better in MATH 107, MATH 108, and MATH 207.* - MATH 306. Principles of Analysis

3 credits. Offered fall, spring.

Sequences, discrete calculus and difference equations, derivatives and integrals, concepts of differential equations and applications.

*Prerequisite: C- or better in MATH 107, MATH 108, and MATH 207.* - MATH 307. Principles of Probability and Statistics

3 credits. Offered fall, spring.

Descriptive statistics, measures of central tendency and dispersion, correlation, probability, probability distributions and statistical inference.

*Prerequisite: C- or better in MATH 107, MATH 108, and MATH 207.* - MATH 309. SAS Programming and Data Management

3 credits. Offered fall, spring.

Use of statistical software to manage, process and analyze data. Writing of statistical programs to perform simulation experiments.

*Prerequisite: Prerequisite: MATH 220, MATH 229, MATH 318 or equivalent.* - MATH 310. Elementary Number Theory

3 credits. Offered Spring 2020, Fall 2021, Spring 2023, Fall 2024, Spring 2026 etc.

Properties of integers and prime numbers, divisibility, congruence, residues and selected topics.

*Prerequisite: MATH 245 or consent of the instructor.* - MATH 315. Real Number System

3 credits. Offered Fall 2019, Spring 2021, Fall 2022, Spring 2024, Fall 2025 etc.

A development of the real number system through a systematic approach to the natural numbers, integers, rationals and irrationals.

*Prerequisite: MATH 245 or consent of the instructor.* - MATH 318. Introduction to Probability and Statistics

4 credits. Offered fall, spring, summer.

This class covers descriptive statistics, counting, probability axioms, discrete and continuous univariate random variables, expected values of random variables and sums of independent random variables, and sampling distributions. It also covers the Central Limit Theorem, single and two sample inference for proportions and means, chi-square test of independence, simple linear regression and correlation. Not open to students with credit in MATH 229 or MATH 329.

*Prerequisite: MATH 236.* - MATH 321. Analysis of Variance and Experimental Design

3 credits. Offered fall, spring.

Introduction to basic concepts in statistics with applications of statistical techniques including estimation, test of hypothesis, analysis of variance and topics in experimental design.

*Prerequisite: MATH 220, MATH 229, MATH 318 or equivalent.* - MATH 322. Applied Linear Regression

3 credits. Offered fall, spring.

Introduction to basic concepts and methods in regression analysis and the application of these models to real-life situations.

*Prerequisite: MATH 220, MATH 229, MATH 318 or equivalent.* - MATH 324. Applied Nonparametric Statistics

3 credits. Offered spring.

Methods of analyzing data from non-normal populations including binomial tests, contingency tables, use of ranks, Kolmogorov-Smirnov type statistics and selected topics.

*Prerequisite: MATH 220, MATH 229, MATH 318 or equivalent.* - MATH 325. Survey Sampling Methods

3 credits. Offered fall.

Theory and practice of sampling including stratified random samples, discussion of simple random samples, cluster sampling, estimating sample size, ratio estimates, subsampling, two-state sampling and analysis of sampling error.

*Prerequisite: MATH 220, MATH 229, MATH 318 or equivalent.* - MATH 326. Statistical Quality Control

3 credits. Offered on demand.

Uses and concepts of probability and sampling procedures. Acceptance sampling by attributes and variables, Shewhart concepts of process control, control chart process capability studies, reliability and life testing. Design of sampling plans.

*Prerequisite: MATH 318* - MATH 327. Categorical Data Analysis

3 credits. Offered fall, spring.

Exact inference for population proportions, comparison of population proportions for independent and dependent samples, two- and three-way contingency tables, Chi-square tests of independence and homogeneity, Chi-square goodness-of-fit tests, and Poisson and logistic regression.

*Prerequisite: MATH 220, MATH 229, MATH 318 or equivalent.* - MATH 328. Time Series Analysis

3 credits. Offered fall even years. Crosslisted with FIN 328.

Regression and exponential smoothing methods for forecasting nonseasonal and seasonal time series, stochastic processes, Box-Jenkins’ autoregressive and moving average models.

*Prerequisite: MATH 238 or MATH 300; and MATH 318 or MATH 329.* - MATH 329. Introduction to Probability and Theoretical Statistics

3 credits. Offered fall.

This course covers counting, probability axioms, discrete and continuous univariate random variables, expected values of random variables and sums of independent random variables. It also discusses theoretical underpinnings of sampling distributions and the Central Limit Theorem, computer simulation, two-sample estimation and inference for proportions and means, and estimation and inference including verification of assumptions in simple linear regression. Uses the R programming language.

*Prerequisite: MATH 236 and “C-” or better in MATH 229. MATH 220 with a grade of “B-” or better may be substituted for MATH 229 by permission if student has suitable experience with R. Not open to students with credit in MATH 318.* - MATH 336. Elementary Differential Equations

3 credits. Offered fall, spring.

Development of techniques for obtaining, analyzing and graphing solutions to differential equations, with emphasis on first and second order equations.

*Prerequisite: MATH 236; Not open for credit to students with credit in MATH 238.* - MATH 337. Methods of Applied Calculus

3 credits. Offered spring 2020, fall 2021, spring 2023, fall 2024, spring 2026 etc.

Laplace transforms, power series and their application to differential equations. Vector differential and integral calculus; parametric curves; coordinate systems; line, surface and volume integrals; and gradient, divergence, and curl including the theorems of Green, Stokes and Gauss.

*Prerequisite: MATH 237; and MATH 238 or MATH 336.* - MATH 340. Mathematical Modeling I – Optimization

3 credits. Offered fall even years.

Linear and nonlinear optimization with an emphasis on applications in the sciences, economics and social sciences. Techniques studied include the simplex, Newton, and Lagrange methods and Kuhn-Tucker theory. Software packages will be used to implement these methods.

*Prerequisite: MATH 237; and MATH 238 or MATH 300 or consent of instructor.* - MATH 341. Non-Linear Dynamics and Chaos

3 credits. Offered spring. Crosslisted with PHYS 341.

Introductory study of nonlinear dynamics and chaos intended primarily for upper-level undergraduates in science or mathematics. Topics include stability, bifurcations, phase portraits, strange attractors, fractals, and selected applications of nonlinear dynamics in pure and applied science. Computers may be utilized for simulations and graphics.

*Prerequisite: MATH 238 or (MATH 300 and MATH 336); and MATH 248.* - MATH 342. Mathematical Models in Biology

3 credits. Offered spring. Crosslisted with BIO 342.

Introduction to dynamical models (discrete and continuous time) applied to biology. Tools of mathematical analysis from linear and nonlinear dynamics will be taught, including stability analysis of equilibrium, as well as appropriate use of software packages. Emphasis will be on model development and interpretation in the context of applications, including effective written and oral presentation.

*Prerequisite: MATH 232 or MATH 235 or equivalent.* - MATH 353. Graph Theory

3 credits. Offered fall 2020, spring 2022, fall 2023, spring 2025, fall 2026 etc.

Graphs and their applications. Possible topics include trees, Euler paths and Hamiltonian circuits, planar graphs, digraphs, adjacency matrices, connectivity and coloring problems.

*Prerequisite: MATH 245 or instructor consent.* - MATH 354. Introduction to Biometrics

4 credits. Offered spring. Crosslisted with BIO 454

This course discusses the role of statistics in biological research and interpretation of biological phenomena. The course will cover topics of sampling, correlation, regression analysis, tests of hypotheses, commonly observed distributions in natural populations, nonparametric tests, goodness-of-fit tests and ANOVA. In order to fully comprehend the statistical analysis of those publications, students will review approximately half a dozen publications from different fields of biology.

*Prerequisite: MATH 220, MATH 229, MATH 318 or equivalent.* - MATH 358. Introduction to Machine Learning

3 credits. Offered spring. Crosslisted with DATA 358. - MATH 360. Complex Variables

3 credits. Offered fall 2019, spring 2021, fall 2022, spring 2024, fall 2025 etc.

Introduction to algebraic properties of complex numbers, analytic functions, harmonic functions, mappings of elementary functions, contour integration, series, residues, and poles and conformal mappings. Emphasis on computations and applications to fluid and heat flow.

*Prerequisite: MATH 237.* - MATH 367. Introduction to Acoustics

3 credits. Offered spring. Crosslisted with PHYS 367.

This course represents an introduction to sound, hearing, and vibration. Architectural, biological and environmental acoustics will also be discussed. Students will develop an ability to use mathematical models and experimental techniques to study problems in acoustics and to transfer this knowledge to analogous situations. They will also develop an ability to conduct a semester-long research or expository project and present it in written and oral form to an audience of peers.

*Prerequisite: MATH 236.* - MATH 368. Statistical Computing

3 credits. Offered fall.

This course is an intensive introduction to statistical computing with R. It intends to develop core computing skill to complement traditional course work in statistics and lay the groundwork for further study for data analytics and data mining. The class will cover the basics of programming in R; visualization of multivariate data; generating random variables; bootstrap, jackknife and permutation methods; Monte Carlo methods in inference; and Monte Carlo Integration and Variable reduction. - MATH 410. Advanced Calculus I

3 credits. Offered fall, spring.

Limits, continuity, differentiation, sequences, series, integration and selected topics.

*Prerequisite: MATH 238 or MATH 300; and MATH 245 or consent of the instructor.* - MATH 411. Advanced Calculus II

3 credits. Offered spring.

Limits, continuity, differentiation, sequences, series, integration and selected topics.

*Prerequisite: MATH 410.* - MATH 415. History of Mathematics

3 credits. Offered spring.

Topics in the history of mathematics spanning ancient times to the present.

*Prerequisite: MATH 245 or instructor consent.* - MATH 421. Applied Multivariate Statistical Analysis

3 credits. Offered fall.

Multivariate statistical methods with applications. Topics include canonical correlation, clustering, discriminant analysis, factor analysis, multivariate analysis of variance, multiple regression, multidimensional scaling and principal component analysis.

*Prerequisite: MATH 300 or MATH 238 and MATH 321 or MATH 322.* - MATH 423. Stochastic Process

3 credits. Offered spring odd years.

Sequences and classes of random variables. Applications to physical, biological, social and management sciences. Topics include Markov chains, branching processes, the Poisson process, queuing systems and renewal processes.

Sequences and classes of random variables. Applications to physical, biological, social and management sciences. Topics include Markov chains, branching processes, the Poisson process, queuing systems and renewal processes.

*Prerequisite: MATH 238 or MATH 300; and MATH 318 or MATH 329.* - MATH 424. Statistical Decision Theory

3 credits. Offered spring even years.

Development and use of probability and statistics for strategic decision making with applications. Topics include decision flow diagrams, analysis of risk and risk aversion, utility theory, Bayesian statistical methods, the economics of sampling, sensitivity analysis and collective decision making.

*Prerequisite: MATH 318 or MATH 329.* - MATH 425E. Statistical Genomics

3 credits. Offered spring.

This course will cover key statistical concepts and methods necessary for extracting biological insights from high throughput genomic experiments. The topics include: discrete probability distributions (binomial, Poisson, negative binomial, and multinomial), joint probability distributions, conditional probabilities, prior and posterior probabilities, and Bayesian inference. Students will learn how to access high throughput genomic data from public websites, relevant preprocessing and analyses methods. This course will also study gene network, groups and patterns using cluster and principal component analysis.*Prerequisite: MATH 321 or MATH 322.* - MATH 426. Probability and Mathematical Statistics I

3 credits. Offered fall.

Derivations and proofs of probability theorems, discrete and continuous univariate and multivariate random variables, conditional distributions, mathematical expectations, functions of random variables, moment generating functions, properties and derivation of estimators including the method of moments and maximum likelihood estimation.

*Prerequisite: MATH 318 or MATH 329.* - MATH 427. Probability and Mathematical Statistics II

3 credits. Offered spring.

Limiting distributions, sampling theory and distributions, theory and applications of estimation and hypothesis testing.

*Prerequisite: MATH 426.* - MATH 428. Statistical Consulting

3 credits. Offered spring.

Training and experience in statistical consulting emphasizing oral and written communication, interview, report writing and presentation skills. Participate in significant interdisciplinary consulting project that will require meeting with the client, creating reports summarizing the client’s problem and an analysis performed by the students, and explanation of results using language that can be understood by the client. Students are required to meet with clients outside of class meeting times.

*Prerequisite: MATH 318 or MATH 329; MATH 321, at least junior standing and MATH 322. Corequisite: MATH 322.* - MATH 429. Research Project in Statistics

1 to 3 credits. Offered on demand.

Experience in the design, data collection, and analysis for a survey or experiment.

*Prerequisite: Consent of the instructor.* - MATH 430. Abstract Algebra I

3 credits. Offered fall, spring.

An introduction to groups, rings and fields.

*Prerequisite: MATH 238 or MATH 300; and MATH 245 or consent of the instructor.* - MATH 431. Abstract Algebra II

3 credits. Offered spring.

An introduction to groups, rings and fields.

*Prerequisite: MATH 430.* - MATH 434. Advanced Linear Algebra

3 credits. Offered spring.

A proof-based linear algebra course covering such topics as vector spaces, linear transformations and matrices, eigenvalues and eigenvectors, inner product spaces, and canonical forms.

*Prerequisite: MATH 245 and either MATH 238 or MATH 300.* - MATH 435. Introduction to Topology

3 credits. Offered fall.

Metric spaces, limits, continuous maps and homeomorphisms, connectedness, compact topological spaces and applications.

*Prerequisite: MATH 238 or MATH 300 and MATH 245.* - MATH 440. Fourier Analysis and Partial Differential Equation

3 credits. Offered fall.

Elementary applied partial differential equations, the heat equation, Laplace’s equation, the wave equation; Fourier series and boundary value problems. Both theory and problem-solving will be included.

*Prerequisite: MATH 238 or MATH 336.* - MATH 441. Analysis and Dynamics of Differential Equations

3 credits. Offered spring.

Analysis of qualitative properties and dynamics of linear and non-linear ordinary differential equations, including topics such as existence, uniqueness, phase portraits, stability and chaos, with applications in the sciences.

*Prerequisite: MATH 238 OR MATH 300 and MATH 336; AND MATH 245 or MATH 440 OR Instructor Permission.* - MATH 448. Numerical Analysis

3 credits. Offered fall 2020, spring 2022, fall 2023, spring 2025, fall 2026 etc. Crosslisted with CS 448.

Study and analysis of algorithms used to solve nonlinear equations and systems of linear and nonlinear equations. Iterative methods for matrices and Newton-type methods. Numerical differential and integral calculus. Programming using a high-level language and/or software packages.

*Prerequisite: MATH 237; MATH 238 or MATH 300; and MATH 248.* - MATH 449. Numerical Analysis for Differential Equations

3 credits. Offered fall 2019, spring 2021, fall 2022, spring 2024, fall 2025 etc. Crosslisted with CS 449.

Study and analysis of numerical techniques to solve ordinary and partial differential equations, including Euler, Runge-Kutta, Picard, finite-difference and finite-element methods. Programming using a high-level language and/or software packages.

*Prerequisite: MATH 237; MATH 238 or MATH 336; and MATH 248.* - MATH 470. Connections in Mathematics

3 credits. Offered spring.

This course is a mathematics capstone course primarily for math majors with secondary education minors. It covers a variety of topics, each designed to develop the interconnectedness of advanced mathematics to the secondary curriculum.

*Prerequisite: MATH 318 or MATH 329; MATH 410, MATH 430 and MATH 475. Corequisite: MATH 318 or MATH 329; MATH 410, MATH 430 and MATH 475.* - MATH 475. Fundamental Concepts of Geometry

3 credits. Offered fall.

Origin and development of Euclidean and other geometries including axiomatic systems, mathematical proof and special topics from incidence geometry.

*Prerequisite: MATH 245 or consent of the instructor.* - MATH 485. Selected Topics

1 to 4 credits. Offered on demand.

Topics in advanced mathematics or statistics which are not covered in the regularly offered courses. Offered only with approval of the department head; may be repeated for credit when course content changes.

*Prerequisite: Permission of the instructor.* - MATH 486. Independent Study

1 to 3 credits. Offered on demand.

Independent study in mathematics under faculty supervision. Only offered with the consent of the department head. - MATH 497. Undergraduate Research

1 to 4 credits. Offered on demand.

Students pursue advanced research in a selected area of mathematics and/or statistics. Student must make arrangements with a supervising instructor prior to registration. Offered only with consent of the department head. Repeatable up to 6 credits. - MATH 499A. Honors

1 to 4 credits. Offered on demand.

*Prerequisite: Consent of the SHP supervisor.* - MATH 499B. Honors Thesis

3 credits. Offered on demand. - MATH 499C. Honors Thesis

3 credits. Offered on demand.