Mathematics (MATH)

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.

This course covers the interpretation and evaluation of numerical information in context. Students learn how to identify strengths and limitations of information sources and methods; how uncertainty affects data collection and analysis; and the role of hypothesis testing and confidence intervals in research. 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 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 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.

MATH 110 and MATH 210 form a sequence that is designed for future elementary and middle school teachers to develop mathematical knowledge for teaching by deeply examining concepts in mathematics that include number sense, number systems (whole numbers, integers, rational numbers and real numbers), meanings and properties of operations, ratio and proportion, functions and algebra, number theory, geometry, measurement, probability, and statistics. Problem-solving, reasoning, representations, connections and communication form the foundation through which learning will take place. Priority registration will be given to Inclusive Early Childhood Education, Elementary Education, Middle Grades Education, and Special Education majors. Other majors may enroll during open enrollment. MATH 110 may be used for general education credit in quantitative reasoning.

This course is designed for future elementary and middle school teachers to develop mathematical knowledge for teaching by deeply examining concepts in mathematics including: number sense, number systems (whole numbers, integers, rational numbers and real numbers), and meaning and properties of operations. These mathematical concepts will be explored through the lens of the Standards of Mathematical Practice. Problem solving, reasoning, representation, connections and communication form the foundation through which learning will take place.

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, MATH 156, MATH 205 or MATH 235, except with the consent of the department head.

Polynomial, rational, exponential and logarithmic functions and applications, systems of equations and inequalities, sequences. An appropriate ALEKS placement score is required in order to enroll.

Covers same topics as MATH 155. MATH 156 will meet five times a week for students requiring more instructional time.

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.

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.

This course is a one semester overview of calculus for students who do not intend further coursework in calculus. Topics include: limits; derivatives; application of derivatives in business, the social sciences and the natural sciences; integrals; and the Fundamental Theorem of Calculus. Throughout, the focus is on algebraic, exponential and logarithmic functions. May be used for general education credit.

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

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

MATH 110 and MATH 210 form a sequence that is designed for future elementary and middle school teachers to develop mathematical knowledge for teaching by deeply examining concepts in mathematics that include number sense, number systems (whole numbers, integers, rational numbers and real numbers), meanings and properties of operations, ratio and proportion, functions and algebra, number theory, geometry, measurement, probability, and statistics. Problem solving, reasoning, representations, connections and communication form the foundation through which learning will take place. The MATH 110/MATH 210 sequence is restricted to those seeking teaching licensure in the PreK-8 range.

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.

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.

An introduction to applied statistics that is more in-depth than MATH 220 and is encouraged for students majoring or minoring in STEM fields. Descriptive statistics, data collection, frequency distributions, sampling distributions and the Central Limit Theorem, estimation, confidence intervals, 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. May be used for general education credit.

MATH 231 and MATH 232 form a two-semester sequence that combines a first university course in calculus with review of functions. The sequence offers rigorous coverage of calculus that can serve as a foundation for later courses typical for science, engineering or mathematics majors, while reviewing the properties of algebraic, trigonometric, exponential and logarithmic functions necessary to support that coverage. Topics in MATH 231 include: properties of functions, graphing, properties of polynomials, limits, continuity, differentiation and applications of the derivative. Each topic is treated in the context of algebraic functions. This course may be used for general education credit. Not open to students who have already earned credit in MATH 234 or MATH 235.

MATH 231 and MATH 232 form a two-semester sequence that combines a first university course in calculus with review of functions. It offers rigorous coverage of calculus that can serve as a foundation for later courses typical for science, engineering or mathematics majors, while reviewing the properties of algebraic, trigonometric, exponential and logarithmic functions necessary to support that coverage. Topics in MATH 232 include: properties and differentiation of trigonometric, exponential and logarithmic functions; L'Hôpital's Rule; Riemann sums; integrals; and the Fundamental Theorem of Calculus. 

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.

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.

Calculus I is a first university course in calculus. It offers rigorous coverage that can serve as a foundation for later courses typical for science, engineering or mathematics majors. Topics include: limits, continuity, derivatives, applications of derivatives, Riemann sums, integrals and the Fundamental Theorem of Calculus. Each topic is treated in the context of algebraic, trigonometric, exponential and logarithmic functions. This course may be used for general education credit.

Calculus II continues the development of differential and integral calculus. It offers rigorous coverage that can serve as a foundation for later courses typical for science, engineering or mathematics majors. Topics include: applications of the definite integral; integration techniques; improper integrals; sequences and series; and Taylor series.

Vectors. Multivariate calculus.

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

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

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.

This course is an introduction to programming for data science using a modern programming language.

This course provides an introduction to relational database queries. Students will learn about organizing, cleaning, summarizing and transforming data in preparation for exploration, visualization and analysis.

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.

Topics include experimental and survey design, distributions, variation, chance, sampling variation, computer simulation, bootstrapping, estimation and hypothesis testing using real data generated from classroom experiments and large databases.

Independent study in mathematics under faculty supervision.

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.

Students will explore vector spaces, linear transformations, matrices, determinants, systems of linear equations, and eigenvalues and eigenvectors.

This course is designed for future elementary and middle school teachers to develop mathematical knowledge for teaching by deeply examining concepts in mathematics including: expressions, equations and inequalities, functions, systems of equations and inequalities, and some calculus connections. Problem solving, reasoning, representation, connections and communication form the foundation through which learning will take place.

This course is designed for future elementary and middle school teachers to develop mathematical knowledge for teaching by deeply examining concepts in mathematics including: strategies for proving geometric arguments, properties of and relationships among geometric figures (particularly right triangles leading to basic trigonometric functions), geometric transformations, and geometric constructions. Problem solving, reasoning, representation, connections and communication form the foundation through which learning will take place.

This course covers sequences, discrete calculus and difference equations, derivatives and integrals, and concepts of differential equations and applications.

This course is designed for future elementary and middle school teachers to develop mathematical knowledge for teaching by deeply examining concepts in mathematics including: experimental and theoretical probability, graphical representations, measures of center, measures of spread, variation, permutations and combinations. Problem solving, reasoning, representation, connections and communication form the foundation through which learning will take place.

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

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

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

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.

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

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

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

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.

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.

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.

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

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.

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

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.

This course will cover 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.

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.

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.

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

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.

This is an introductory course on machine learning with focus on regression and classification methods. The objective is to familiarize students with some basic models and algorithms for machine learning and prepare them for research or industry application of machine learning techniques. Several software libraries and publicly available datasets will be used to illustrate the application of these techniques. The emphasis will be on machine learning algorithms and application, with some broad explanation of the underlying principles.

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.

Introduces the student to the application of vector calculus to the description of fluids. The Euler equation, viscosity and the Navier-Stokes equation will be covered.

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.

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.

Data and AI for Defense/Diplomacy is a project-based course that tackles mission-driven real world problems from the Departments of State and Defense, the intelligence community and other federal departments and agencies. Students use the Lean Launch Pad Methodology, mathematical modeling, operations research, data science and AI to develop implementable minimal viable products and potential solutions. The course provides students the opportunity to address critical problems facing the U.S. government today, addressing current national security and foreign policy problems. Students engage with stakeholders from a range of government agencies, academia and industry.

This course presents an overview of the role of mathematical concepts in financial applications. Topics include continuous time finance, optimization, numerical analysis and applications in asset pricing.

A quantitative treatment of the theory and method of financial securities pricing to include an examination of closed form pricing models such as the Black-Scholes and its various derivatives as well as numerical solution techniques such as binomial methods.

This course covers limits, continuity, differentiation, sequences, series, integration and selected topics.

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

This course covers topics in the history of mathematics spanning ancient times to the present.

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.

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.

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.

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.

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

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.

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

An introduction to groups, rings and fields.

An introduction to groups, rings and fields.

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.

This course covers metric spaces, limits, continuous maps and homeomorphisms, connectedness, compact topological spaces, and applications.

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.

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.

This course is the study and analysis of algorithms used to solve nonlinear equations and systems of linear and nonlinear equations. Students will learn iterative methods for matrices and Newton-type methods as well as numerical differential and integral calculus. Students will perform programming using a high-level language and/or software packages.

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.

An introduction to algorithm design techniques and the mathematical analysis of algorithms. Techniques covered include divide-and-conquer, greedy, backtracking, network flow and dynamic programming. The classes P and NP are introduced and intractable problems are discussed. This is a proof-intensive course. Students may not receive credit for both CS 412 and CS 452.

This course is a mathematics capstone course primarily for mathematics majors seeking secondary teaching licensure. It consists of a review of some mathematical topics in the high school curriculum, such as trigonometry, calculus and statistics, highlighting the interconnectedness of advanced mathematics to the secondary curriculum.

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

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.

Independent study in mathematics under faculty supervision. Only offered with the consent of the department head.

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.

This is the first of a 3-course sequence completed over three semesters for a total of 6 credits. The distribution of the 6 credits will be determined by the project advisor.

This is the second of a 3-course sequence completed over three semesters for a total of 6 credits. The distribution of the 6 credits will be determined by the project advisor.

This is the third of a 3-course sequence completed over three semesters for a total of 6 credits. The distribution of the 6 credits will be determined by the project advisor.

This course will explore topics important to the mathematical experiences of students in K-5 classrooms including addition, subtraction, multiplication, division, place value, and properties of whole numbers. Relevant connections to the history of mathematics will also be included.

The course is designed to develop an understanding of topics from algebra: variables, patterns, and functions; modeling and interpreting graphs; linear and non-linear functions, connecting these ideas to underlying concepts in primary and middle grades mathematics. Attention will be given to interpreting and assessing students' work and learning. Relevant connections to the history of mathematics will also be included.

This course is designed to help participants develop understanding in: theoretical development of math and students' learning of math within content strands of rational numbers and proportional reasoning; development of pedagogical knowledge of rational numbers and proportional reasoning appropriate for K-8 Mathematics Teacher Specialists; and assessment of K-8 students' mathematical conceptions through interviews. Relevant connections to the history of mathematics will also be included.

The course will develop students' understanding of probabilistic structures, reasoning, data analysis and exploration. These structures will be related to real world problem solving. Attention will also be given to children's thinking, how they learn this basic mathematics, their problem solving strategies, and how they construct their understanding of our number system and arithmetic. Relevant connections to the history of mathematics will also be included.

Explorations of foundations of informal measurement and geometry in one, two, and three dimensions. The van Hiele model for geometric learning is used as a framework for how children understand measurement and geometric relationships. Visualization, spatial reasoning, and geometric modeling are stressed. Transformational geometry, congruence, similarity, and geometric constructions will be discussed and relevant connections to history of mathematics will be included.

A course to update and broaden secondary teachers' capability and point-of-view with respect to topics in analysis. Applications of concepts such as limits, continuity, differentiation and integration. May be taken for graduate credit and for certificate renewal by secondary school teachers.

A course to update and broaden secondary teachers' capability and point-of-view with respect to topics in discrete mathematics. May be taken for graduate credit for certificate renewal by secondary school teachers.

From advanced viewpoint, an investigation of topics in algebra from high school curriculum. Theory of equations, polynomial rings, rational functions and elementary number theory. Course may be taken for graduate credit for certificate renewal by secondary school teachers.

Topics in geometry of concern to secondary teachers in their work and provision for background and enrichment. Various approaches to study of geometry, including vector geometry, transformational geometry and aximoatics. Course may be taken for graduate credit and for certificate renewal by secondary school teachers.

This course provides an introduction to statistics and statistical methods, including descriptive and inferential techniques, as well as regression and analysis of variance, using a modern programming language to perform analyses.

Study of selected topics not otherwise covered in the regular offerings of the department. May be repeated for credit when course content changes.

Topics in the history of mathematics of particular concern to secondary teachers in their work and provision for background and enrichment. Selected topics spanning ancient times to the present. Course may be taken for graduate credit and for certificate renewal by secondary school teachers.

AP probability and statistics topics sampling, experimentation and anticipating patterns. These include Bayes's theorem; binomial, geometric, uniform, normal, t and Chi-square random variables and the mean and variance of linear combinations of random variables. Sampling distributions and central limit theorem, unbiased point estimates of population parameters and the variance of point estimates. Types of generalizations and conclusions that can be drawn including cause and effect. Course may be taken for graduate credit and for certificate renewal by secondary teachers.

AP statistics topics exploring data and statistical inference. Correlation and simple linear regression, interpretation of residual plots, influential points and transformations. Logic of significance testing including hypotheses, errors, p-values and power. Statistical inference methods (confidence intervals, significance tests, and the relationship between one- and two-side tests and confidence intervals) for proportions and means, the slope of a regression line and the Chi-Square tests. Course may be taken for graduate credit and for certificate renewal by secondary teachers.

The design of biological experiments and applications of statistical techniques in ecology, cell biology, physiology, behavior, systematics, genetics, and evolution. Emphasis will be placed on relevant concepts in experimental design and statistical analysis, decision making related to selecting appropriate experimental designs and analysis techniques, and the practical application of design and analysis for graduate research projects.

Continued preparation in anticipation of the comprehensive examination. Course may be repeated.