# Undergraduate Courses in Mathematics

**118. APPLIED MATHEMATICS 3 cr.** Introduction to the use of mathematics to model various aspects of everyday life. Topics include application of graphs and networks to urban services and business efficiency, planning and job scheduling, interpreting data for decision-making, digital information representation, growth, voting systems, and fair division.

**119. QUANTITATIVE ANALYSIS. 3 cr. **Introduction to the study of numbers and subsequent analysis of quantified data using mathematical techniques in studying problems in the context of various disciplines. Mathematical techniques include displaying and describing data, making statistical inferences from data, and building models by fitting functions to data.

**122. ELEMENTARY STATISTICS (DATA 122) 3 cr.** Describing data by graphs and measures, sampling distributions, confidence intervals and tests of hypotheses for one and two means and proportions, Chi-square tests, correlation and regression. Methods are illustrated in the context of quantitative research, with applications in disciplines such as sports, psychology, and social and natural sciences. Use of appropriate statistical software.

**130. APPLIED CALCULUS. 3 cr. P**rerequisite: placement by the Math Department. Limits, derivatives, definite and indefinite integrals of polynomial, exponential, and logarithmic functions. Focus on concepts and applications, particularly those pertaining to business fields. Use of a computer algebra system to facilitate computation.

**133-134. CALCULUS AND ANALYTIC GEOMETRY IA-IB 3 cr. each.** Prerequisite: placement by the Math Department. Sequence covers the same calculus topics as MT 135 with algebra review integrated into the course as needed. The MT 133-134 sequence will count as one course in Division IV of the Core, but neither MT 133 nor MT 134 will count as a Core course individually. *Note:* MT 133-134 will satisfy the MT 135 or equivalent prerequisites and requirements listed throughout the *Bulletin.* Academic credit will not be given for both MT 134 and MT 135.

**135. CALCULUS AND ANALYTIC GEOMETRY I 4 cr.** Prerequisite: placement by the Math Department. Functions, limits, continuity, differentiation, differentiation rules, optimization, antiderivatives, definite integrals. Fundamental Theorem of Calculus, improper integrals, applications of integrals, including probability. (See “Note” in MT 133-134.)

**136. CALCULUS AND ANALYTIC GEOMETRY II 4 cr.** Prerequisite: MT 135 or equivalent. Second course in a three-semester calculus sequence. Parametric curves, differentials, related rates, techniques of integration, additional applications of integrals, introduction to differential equations, polar coordinates, sequences, and series.

**142. INTRODUCTION TO DISCRETE MATHEMATICS 3 cr. **Mathematical foundations for computer science. Possible topics include: number representation and computation; deductive inference such as proof by induction; data representation as graphs and trees; analysis of time and space complexity of algorithms; Boolean algebra and computer logic; and encryption.

**160. MATHEMATICS AND CREATIVITY 3 cr.** Mathematics as a creative discipline. Examples of what pure mathematics is and what mathematicians do. The nature of mathematical reasoning and proof and their essential role in human thought.

**162. MATHEMATICS FROM NON-WESTERN CULTURES 3 cr.** Introduction to mathematics developed in non-Western and Native American societies, and illustrations of modern mathematical ideas within non-Western cultures. Topics include arithmetic in positional number systems, arithmetic and geometric sequences, methods of solving linear equations, geometry and symmetry, and games.

**171. FOUNDATIONS OF EARLY CHILDHOOD MATHEMATICS 4 cr.** Prerequisite: MT 160 or MT 200. Focus on understanding, from an advanced standpoint, the mathematics taught in elementary school. Curriculum issues, methods, instructional resources, and assessment strategies for grades pre-K through 3 will be addressed.

**175. FOUNDATIONS OF ELEMENTARY MATHEMATICS 3 cr. **For students seeking licensure in Early Childhood Education or Middle Childhood Education with Mathematics concentration. Explores elements of mathematical thinking — reasoning and proof, problem-solving, pattern-finding — and their impact on elementary quantitative concepts and structure. Focus on the development of the real number system and its structure as utilized in Elementary Mathematics.

**176. TOPICS IN EARLY CHILDHOOD MATH 4 cr. **Prerequisite: MT 175 or chair permission. For students seeking licensure in Early Childhood Education. Continued exploration of mathematics taught in elementary school from an advanced standpoint. Topics include number theory, measurement, geometry, symmetry, statistics. Demonstrations of how various models — visual, verbal, physical, writing — are used to convey mathematical instruction in an elementary school setting.

**199. SPECIAL TOPICS IN MATH 1-3 cr.** Subject announced in schedule of classes.

**200. EXPLORATIONS IN MATHEMATICS 3 cr.** Introduction to the nature of mathematics emphasizing the exploration that leads to deep ideas as well as connections between different areas. Models and development of deeper mathematical thinking using concepts that have advanced the discipline.

**221. COMBINATORICS, PROBABILITY AND STATISTICS FOR MIDDLE SCHOOL MATHEMATICS. 3 cr. **Recursive relationships, counting techniques with applications to theoretical probability, principles of data collection and analysis, graphical and numerical representations of data, principles of statistical inference via resampling, and other techniques.

**223. INTERMEDIATE STATISTICS (DATA 260) 3 cr.** Prerequisite: DATA/MT 122 or DATA/MT 228 or DATA/MT 229 or EC 208. Power analysis, factorial and repeated measures, analysis of variance, nonparametric procedures, contingency tables, introduction to multiple regression. Use of appropriate statistical software.

**225. ACTUARIAL MATHEMATICS. 3 cr. **Prerequisite: MT 135 or MT 130. Theory of interest: time value of money, annuities, and cash flow. Mathematical models of loans, bonds, general cash flows, and portfolios. Quantitative analysis of financial economics: derivatives, options, forwards, futures, swaps. Prepares students to take Society of Actuaries exam 2/FM.

**228. STATISTICS FOR THE BIOLOGICAL SCIENCES (DATA 228) 3 cr.** Exploratory data analysis, probability fundamentals, sampling distributions and the Central Limit Theorem, estimation and tests of hypotheses through one-factor analysis of variance, simple linear regression, and contingency tables using appropriate statistical software. Course content in biology context.

**229. PROBABILITY AND STATISTICS (DATA 229) 3 cr.** Prerequisite: MT 135. Probability, discrete and continuous distributions, sampling distributions and the Central Limit Theorem, introduction to data analysis, estimation and hypothesis testing, simple linear regression and correlation; exact, normal-theory, and simulation-based inference; use of appropriate statistical software. Methods are illustrated in the context of quantitative research, with applications in various disciplines.

**233. CALCULUS AND ANALYTIC GEOMETRY III 4 cr.** Prerequisite: MT 136. Calculus of vector-valued functions; partial differentiation; multiple, line, and surface integrals.

**234. ELEMENTARY DIFFERENTIAL EQUATIONS 3 cr. **Prerequisite: MT 136. A first course in ordinary differential equations. First order equations and applications, linear equations with constant coefficients, linear systems, Laplace transforms, numerical methods of solution.

**241. NUMERICAL AND ALGEBRAIC CONCEPTS FOR MIDDLE SCHOOL MATHEMATICS TEACHERS. 3 cr.** Prerequisite or corequisite: MT 175. For students seeking licensure to teach mathematics in grades 4-9. Topics include properties of the integers, rational and irrational numbers, algebra and algebraic thinking, sequences, functions and sets. How to communicate in the precise language of mathematics, make connections among mathematical systems, and construct valid mathematical arguments and proofs.

**242. INTRODUCTION TO LINEAR ALGEBRA 3 cr.** Prerequisite: MT 130 or MT 135. Matrix operations, systems of linear equations, vector spaces, subspaces, bases and linear independence, eigenvalues and eigenvectors, diagonalization of matricies, linear transformations, determinants and applications.

**251. GEOMETRY FOR MIDDLE SCHOOL MATHEMATICS TEACHERS 3 cr.** Prerequisite: MT 135. For students seeking licensure to teach mathematics in grades 4-9. Examination of geometric concepts related to the middle-school curriculum. Axiomatic foundations and transformational geometry. The use of teaching manipulatives and dynamic geometry software to promote understanding. Emphasis on various types of mathematical reasoning needed to establish geometric credibility.

**271. DISCRETE MATHEMATICS AND MATRIX ALGEBRA 3 cr.** Prerequisite/corequisite: MT 136. Introduction to mathematical proof and logic, sets, functions and relations, counting principles, graphs, matrix operation, and mathematical induction.

**288. NETWORK ANALYSIS 3 cr. **Introduction to the mathematical and computational theory of network analysis with applications in globalization studies and other social sciences. Fundamentals of graph theory and matrix algebra. Measures of networks, including concepts of centrality and structural balance. Study of large-scale structure of networks. Computational representation of and algorithms on networks. Independent student project.

**299. SPECIAL TOPICS IN MATH 1-3 cr. **Subject announced in schedule of classes.

**301. METHODS IN PURE MATHEMATICS 3 cr. **Prerequisite or corequisite: MT 136. Introduction to basic mathematical terminology and the techniques of abstract mathematics in the context of discrete mathematics. Topics include proof and logic, inductive and deductive reasoning, mathematical induction, sets, functions and relations, and counting principles.

**399. INDEPENDENT STUDY IN MATHEMATICS 1-4 cr. **Prerequisites: permission of chair and instructor. For the student seeking a research project under faculty supervision

**421. MATHEMATICAL STATISTICS (DATA 421) 3 cr.** Prerequisites: DATA/MT 229, MT 233. Moment generating functions, transformations, properties of estimators, foundations of hypothesis tests, one- and two-factor analysis of variance, and nonparametric analyses.

**422. APPLIED STATISTICS (DATA 422) 3 cr. **Prerequisite: DATA 260/MT 223 or chair permission. Multi-factor analysis of variance, interaction, serial correlation, time series, forecasting, multivariate data, categorical data; data reduction; simulation; analysis of large datasets; use of appropriate statistical software.

**424. APPLIED REGRESSION ANALYSIS (DATA 424) 3 cr. **Prerequisite: DATA 260/MT 223 or chair permission. Multiple linear regression, collinearity, model diagnostics, variable selection, nonlinear models, logistic regression; use of appropriate statistical software.

**425. OPERATIONS RESEARCH 3 cr.** Prerequisite: MT 271 or 301. Linear programming, sensitivity analysis and duality, queuing theory, topics from networks, decision making, game theory, Markov chains, dynamic programming, and simulation.

**4 31. INTRODUCTION TO REAL ANALYSIS 3 cr. **Prerequisite: MT 233, 271, or 301. Rigorous mathematical treatment of the fundamental ideas of calculus: sequences, limits, continuity, differentiation, and integration.

**432. ADVANCED CALCULUS OF SEVERAL VARIABLES 3 cr.** Prerequisites: MT 233. Development of and motivation for vector‑valued functions, calculus of functions of several variables, implicit functions and Jacobians, multiple integrals, and line integrals.

**436. INTRODUCTION TO COMPLEX ANALYSIS 3 cr.** Prerequisite: MT 271 or 301 or permission of department chair. Complex number plane, analytic functions, integration of complex functions, sequences and series, residue theorem, evaluation of real integrals.

** 441. INTRODUCTION TO ABSTRACT ALGEBRA 3 cr.** Prerequisite: MT 271 or 301. Groups, homomorphisms, permutations, quotient groups, rings, ideals, integral domains, fields, polynomial rings and factorization.

**442. LINEAR ALGEBRA AND VECTOR SPACES 3 cr. **Prerequisite: MT 271 or 301; MT 242. Proof-based introduction to algebra of matrices, linear systems, abstract vector spaces, linear transformations, eigenvectors, and applications.

**450. EUCLIDEAN AND NONEUCLIDEAN GEOMETRY 3 cr.** Prerequisite: MT 271 or 301 or permission of department chair. Alternative ways of investigating the Euclidean plane, including transformational geometry; examination of the parallel postulate and how it can be changed to create new geometries; hyperbolic geometry.

**452. ELEMENTARY TOPOLOGY 3 cr.** Prerequisite: MT 271 or 301. Topological spaces, homeomorphisms, connected spaces, compact spaces, regular and normal spaces, metric spaces, and topology of surfaces.

**453. DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS 3 cr. **Prerequisite: MT 233. Introduction to the qualitative study of di
erential equations and related dynamical systems. Topics include first-order di
erential equations, planar systems and their dynamical classification, general nonlinear systems and their equilibria, closed orbits, limit sets, discrete systems, and applications to mechanics.

**468. THEORY OF NUMBERS 3 cr.** Prerequisite: MT 271 or 301. Divisibility theorems, numbertheoretic functions, primitive roots, quadratic congruences and reciprocity, partitions.

**469. HISTORY OF MATHEMATICS 3 cr.** Prerequisite: MT 271 or 301. Study of mathematics from its origins to its present state. Topics include the development and impact of geometry, algebra, number theory, irrational numbers, analytic geometry, calculus, nonEuclidean geometry, and infinite sets.

**479. COMBINATORICS AND GRAPH THEORY 3 cr.** Prerequisite: MT 271 or 301. Pigeonhole principle, inclusion and exclusion, recurrence relations and generating functions, combinatorial designs, the theory of graphs, graphical optimization problems.

**480. SPECIAL TOPICS cr. TBA.** Readings about, reports on, and investigation of selected material and topics.

**491. SENIOR SEMINAR IN MATHEMATICS 3 cr. **Prerequisites: MT 271 or 301 and senior standing. Culminating experience of the mathematics major, requiring students to demonstrate mathematical skills through common readings, class discussions, presentations, and written assignments.

**499. INDEPENDENT STUDY IN MATHEMATICS 1-4 cr.** Prerequisite: permission of chair and instructor. For the student seeking a research project under faculty supervision.

*For graduate courses in mathematics, click here. *