# 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, 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 I 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. **prerequisite: 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.** 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” under MT 133-134 above.)

**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.

**160. MATHEMATICS AND CREATIVITY 3 cr.** Mathematics and the men and women who have contributed to it. Topics in modern mathematics and examples of mathematical creativity are emphasized, as well as the student’s reaction to and thoughts on selected readings concerning the nature of mathematics and mathematics as a creative art.

**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, games.

**171. FOUNDATIONS OF EARLY CHILDHOOD MATHEMATICS 4 cr.** Prerequisite: MT 160. 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. Explorations of the 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: counting numbers, fractions, integers, operations, algebraic properties and some of their applications in measurement, geometry and statistics.

**176. TOPICS IN EARLY CHILDHOOD MATHEMATICS 4 cr. **Pre-requisite: MT 175

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.

**MT 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. Methods of measurement on data sets. Graphical and numerical representations of data. principles of statistical inference.

**223. STATISTICS FOR PSYCHOLOGICAL RESEARCH 3 cr.** Prerequisite: MT 122. Power analysis, factorial and repeated measures analysis of variance, nonparametric procedures, contingency tables, introduction to multiple regression. Use of appropriate statistical software.

**MT 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. Content from this courses will prepare students to Society of Actuaries Exam 2/FM.

**228. STATISTICS FOR THE BIOLOGICAL SCIENCES 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 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 disciplines including sports, psychology, and social and natural sciences.

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

**241. NUMERICAL AND ALGEBRAIC CONCEPTS FOR MIDDLE SCHOOL MATHEMATICS TEACHERS. 3 cr.** Prerequisites: MT 135; and MT 160 or MT 200. For students seeking licensure to teach mathematics in grades 4-9. Topics include properties of the integers, rational and irrational numbers, sequences, functions, counting techniques, and probability. Students will learn to communicate in the precise language of mathematics, to make connections among mathematical systems, and to construct valid mathematical arguments and proofs.

**242. INTRODUCTION TO LINEAR ALGEBRA 3 cr.** Prerequisite: MT 136. Algebra of matrices, linear systems, vector spaces, linear transformations, eigenvectors, applications, with emphasis on computation and conceptual understanding. (May not be counted toward the mathematics majors.)

**251. GEOMETRY FOR MIDDLE SCHOOL MATHEMATICS TEACHERS 3 cr.** Prerequisites: MT 135; and MT 160 or MT 200. For students seeking licensure to teach mathematics in grades 4-9. Examination of geometric concepts related to the curriculum of the middle school. Axiomatic foundations and transformational geometry. The use of teaching manipulatives and dynamic geometry software to promote understanding. An emphasis on various types of mathematical reasoning needed to establish geometric credibility.

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

**322. (Now 424) APPLIED REGRESSION ANALYSIS 3 cr. **Prerequisite: MT 123 or 223 or 228 or 229.** **Multiple linear regression, collinearity, model diagnostics, variable selection, nonlinear models; autocorrelation, time series, and forecasting; use of appropriate statistical software.

**342. INTRODUCTION TO LINEAR ALGEBRA 3 cr.** Prerequisite: MT 271. Algebra of matrices, linear systems, vector spaces, linear transformations, eigenvectors, applications.

**421. MATHEMATICAL STATISTICS II 3 cr.** Prerequisites: MT 229, 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 3 cr.** Prerequisites: MT 223 or MT 228 or MT 229. Two factor analysis of variance; categorical data analysis, logistic regression, factor analysis, simulation, analysis of large datasets; use of appropriate statistical software.

**424. (Prev. 322) APPLIED REGRESSION ANALYSIS 3 cr. **Prerequisite: MT 123 or 223 or 228 or 229.** **Multiple linear regression, collinearity, model diagnostics, variable selection, nonlinear models; autocorrelation, time series, and forecasting; use of appropriate statistical software.

**425. OPERATIONS RESEARCH 3 cr.** Prerequisite: MT 271. 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 136, 271. 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, 271. Development of and motivation for vector‑valued functions, calculus of functions of several variables, implicit functions and Jacobians, multiple integrals, line integrals.

**436. INTRODUCTION TO COMPLEX ANALYSIS 3 cr.** Prerequisite: MT 271 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. Groups, homomorphisms, permutations, quotient groups, rings, ideals, integral domains, fields, polynomial rings and factorization.

**450. EUCLIDEAN AND NON‑EUCLIDEAN GEOMETRY 3 cr.** Prerequisite: MT 271 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. Topological spaces, homeomorphisms, connected spaces, compact spaces, regular and normal spaces, metric spaces, and topology of surfaces.

**468. THEORY OF NUMBERS 3 cr.** Prerequisite: MT 271. Divisibility theorems, number‑theoretic functions, primitive roots, quadratic congruences and reciprocity, partitions.

**469. HISTORY OF MATHEMATICS 3 cr.** Prerequisite: MT 271. 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, non‑Euclidean geometry, and infinite sets.

**479. COMBINATORICS AND GRAPH THEORY 3 cr.** Prerequisite: MT 271. 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.

**499. INDEPENDENT STUDY IN MATHEMATICS 1-4 cr.** Prerequisite: consent of chair and instructor. Designed for the student who wants to undertake a research project supervised by a faculty member.

*For graduate courses in mathematics, click here. *