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# Undergraduate Mathematics

# Undergraduate Mathematics

## 2018 Fall Term

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#### QUANTITATIVE REASONING

##### Mathematics 139

A quantitative reasoning course which includes topics from college algebra ( such as functions, linear, exponential and logarithmic models), statistics, and probability. Emphasizes modeling, problem-solving and applications. Designed for students whose programs do not require further coursework in pre-calculus or calculus. Appropriate for students majoring and minoring in areas such as the arts, humanities, social sciences, and education.

#### MATHEMATICAL IDEAS

##### Mathematics 140

Designed to give students a broad understanding and appreciation of mathematics. Includes topics not usually covered in a traditional algebra course. Topics encompass some algebra, problem solving, counting principles, probability, statistics, and consumer mathematics. This course is designed to meet the University Proficiency Requirement for students who do not wish to take any course having MATH 141 as a prerequisite.

#### FUNDAMENTALS OF COLLEGE ALGEBRA

##### Mathematics 141

A functional approach to algebra with emphasis on applications to different disciplines. Topics include linear, exponential, logarithmic, quadratic, polynomial and rational equations and functions, systems of linear equations, linear inequalities, radicals and rational exponents, complex numbers, variation. Properties of exponents, factoring, and solving linear equations are reviewed.

#### FINITE MATHEMATICS FOR BUSINESS AND SOCIAL SCIENCES (GM)

##### Mathematics 143

Mathematical preparation for the understanding of quantitative methods in management and social sciences. Topics include sets, relations, linear functions, interest, annuities, matrices, solution of linear systems by graphical, algebraic, Gauss-Jordan, and inverse methods, linear programming by graphical and simplex methods, counting and probability. College of Business and Economics majors must take this course on a conventional grade basis.

#### MATHEMATICS FOR THE ELEMENTARY TEACHER I (GM)

##### Mathematics 148

A study of sets, whole numbers, fractions, integers, decimals and real numbers, basic arithmetic operations and their properties, standard and alternative algorithms and estimations strategies; problem-solving, proportional reasoning and algebraic thinking. Manipulatives and cooperative learning activities are used throughout the course. For elementary education majors.

#### MATHEMATICS FOR THE ELEMENTARY TEACHER II

##### Mathematics 149

Topics in probability and statistics, with emphasis on descriptive techniques. Investigations in geometric figures, measurement, construction, transformations, congruent and similar geometric figures. Problem solving strategies, manipulatives, and cooperative learning activities are emphasized throughout the course.

#### COLLEGE ALGEBRA (GM)

##### Mathematics 150

Study of polynomial, radical, rational, piecewise, exponential, and logarithmic functions, including basic graphs, transformations, inverses, and combining functions; solving equations and inequalities both algebraically and graphically is explored. The course also includes an introduction to vectors.

#### TRIGONOMETRY (GM)

##### Mathematics 151

Study of trigonometric functions including basic graphs, transformations, and inverses; trigonometric functions are studied through the unit circle and right triangle approaches. Also studied are trigonometric identities, equations, and applications, including Law of Sines and Law of Cosines, as well as polar coordinates.

#### PRECALCULUS (GM)

##### Mathematics 152

Study of polynomial, radical, rational, piecewise, exponential, logarithmic, and trigonometric functions, including basic graphs, transformations, inverses, and combining functions; solving equations and inequalities both algebraically and graphically is explored. In addition, trigonometric functions are studied through the unit circle and right triangle approaches. Also studied are vectors, trigonometric identities, trigonometric equations, and polar coordinates.

#### THE LOGIC OF CHESS

##### Mathematics 177

A study of logic particularly as it is used in the game of chess and, most particularly, in chess strategy and the end game of chess. The rules are taught to those who are not already acquainted with the game.

#### INTRODUCTION TO STATISTICAL REASONING AND ANALYSIS (GM)

##### Mathematics 230

A course on the principles, procedures and concepts surrounding the production, summarization and analysis of data. Emphasis on critical reasoning and interpretation of statistical results. Content includes: probability, sampling, and research design; statistical inference, modeling and computing; practical application culminating in a research project.

#### SHORT CALCULUS FOR BUSINESS AND SOCIAL SCIENCES (GM)

##### Mathematics 243

A general survey of the calculus. Topics covered include limits, differentiation, max-min theory, exponential and logarithmic functions, and integration. Business and social science applications are stressed.

#### APPLIED CALCULUS SURVEY FOR BUSINESS AND SOCIAL SCIENCES (GM)

##### Mathematics 250

An applied calculus course covering elementary analytic geometry, limits, differentiation, max-min theory, exponential and logarithmic functions, integration, functions of several variables, and elementary differential equations. Some computer topics may be included. A student may earn credit for only one of MATH 243, MATH 250, and MATH 253.

#### CALCULUS AND ANALYTIC GEOMETRY I (GM)

##### Mathematics 253

Review of algebraic and trigonometric functions, transcendental functions, limits, study of the derivative, techniques of differentiation, continuity, applications of the derivative, L' Hopital's Rule and indeterminate forms, the Riemann integral, Fundamental Theorem of Calculus, and substitution rule.

#### CALCULUS AND ANALYTIC GEOMETRY II

##### Mathematics 254

Techniques of integration, applications of the integral, introduction to differential equations, polar coordinates and conic sections, infinite sequences and series. This course includes a writing component.

#### CALCULUS AND ANALYTIC GEOMETRY III

##### Mathematics 255

Solid analytic geometry, vectors and vector functions, functions of several variables, multiple integrals and their applications.

#### INTRODUCTION TO R

##### Mathematics 263

This course will cover basic topics in R, a statistical computing framework. Topics include writing R functions, manipulating data in R, accessing R packages, creating graphs, and calculating basic summary statistics.

#### DISCRETE MATHEMATICS

##### Mathematics 280

This course will supply a thorough grounding in the mathematical topics which are central to the study of computer science, and which form the basis for many modern applications of mathematics to the social sciences. Topics covered will include sets, logic, Boolean algebra and switching circuits, combinatorics, probability, graphs, trees, recursion, and algorithm analysis. Expressing mathematical ideas and writing proofs will be emphasized.

#### PUTNAM COMPETITION AND PROBLEM SOLVING

##### Mathematics 281

Preparation for the William Lowell Putnam Competition. Includes advanced problem solving techniques in pure mathematics. Review of previous examination problems and related material. May be repeated for a total of four credits. Satisfactory/No Credit only.

#### INDEPENDENT STUDY

##### Mathematics 298

Study of a selected topic or topics under the direction of a faculty member. Repeatable. Department Consent required.

#### INTRODUCTION TO ANALYSIS

##### Mathematics 301

A first course in real analysis. Topics include properties of the real numbers, convergence of sequences, monotone and Cauchy sequences, continuity, differentiation, the Mean Value Theorem, and the Riemann integral. Emphasis is placed on proof-writing and communicating mathematics.

#### APPLIED STATISTICS

##### Mathematics 342

This course will cover the basics of statistical testing, regression analysis, experimental design, analysis of variance, and the use of computers to analyze statistical problems. This course contains a writing component.

#### APPLIED PROBABILITY: THEORY AND PRACTICE

##### Mathematics 343

Sets and counting, probability spaces, discrete and continuous random variables, mathematical expectation, discrete and continuous distributions with applications and probabilistic computing using R.

#### MATRICES AND LINEAR ALGEBRA

##### Mathematics 355

Systems of linear equations, matrices and determinants, finite dimensional vector spaces, linear dependence, bases, dimension, linear mappings, orthogonal bases, and eigenvector theory. Applications stressed throughout.

#### DIFFERENTIAL EQUATIONS

##### Mathematics 361

Ordinary differential equations: general theory of linear equations, special methods for nonlinear equations including qualitative analysis and stability, power series and numerical methods, and systems of equations. Additional topics may include transformation methods and boundary value problems. Applications stressed throughout.

#### APPLIED NONPARAMETRIC STATISTICS

##### Mathematics 362

This course covers theory and applications of commonly used distribution-free tests such as the sign test and the Wilcoxon signed rank test. Other topics include: the Kruskal-Wallis and Friedman tests for analysis of variance, nonparametric regression, and nonparametric bootstrapping.

#### PROBLEM SOLVING FOR THE ELEMENTARY TEACHER

##### Mathematics 370

This course is primarily for pre-service elementary and middle school teachers. Students will learn a variety of problem solving strategies applicable in elementary and middle school. The applications will cover many different areas of mathematics.

#### DEVELOPMENT OF MATHEMATICS

##### Mathematics 375

A study of the development of mathematical notation and ideas from prehistoric times to the present. Periods and topics will be chosen corresponding to the backgrounds and interests of the students.

#### BEGINNING ALGEBRA

##### Mathematics 41

A course for those who need to strengthen their basic algebra skills. Topics include properties of the real numbers, linear and quadratic equations, linear inequalities, exponents, polynomials, rational and radical expressions, and systems of linear equations. The course credits count towards the semester credit load and GPA, but are not included in the 120 credit graduation requirement.

#### GEOMETRY FOR THE ELEMENTARY TEACHER

##### Mathematics 416

A study of the intuitive, informal geometry of sets of points in space. Topics include elementary constructions, coordinates and graphs, tessellations, transformations, problem solving, symmetries of polygons and polyhedra, and use of geometry computer software.

#### MATHEMATICS FOR HIGH SCHOOL TEACHERS II

##### Mathematics 422

The course continues the exploration of the high school curriculum from an advanced perspective that was started in MATH 421. The focus is on deepening understanding of concepts, highlighting connections and solving challenging problems. The mathematical content includes congruence, distance, similarity, trigonometry, area, and volume. Connections to algebra are emphasized throughout the course.

#### TOPOLOGY

##### Mathematics 431

An introduction to point-set topology, including such topics as topological spaces, mappings, connectedness, compactness, separation axioms, metric spaces, complete spaces, product spaces and function spaces.

#### GRAPH THEORY

##### Mathematics 450

This course will examine basic concepts and applications of graph theory. Topics covered will be selected from trees, connectivity, paths and cycles, coloring, matching and covering problems, digraphs, and network flows.

#### INTRODUCTION TO ABSTRACT ALGEBRA

##### Mathematics 452

An introductory survey of abstract algebra and number theory with emphasis on the development and study of the number systems of integers, integers mod n, rationals, reals, and complex numbers. These offer examples of and motivation for the study of the classical algebraic structures of groups, rings integral domains and fields. Applications to algebraic coding theory and crystallography will be developed if time allows.

#### NUMERICAL ANALYSIS

##### Mathematics 471

Emphasis on numerical algebra. The problems of linear systems, matrix inversion, the complete and special eigenvalue problems, solutions by exact and iterative methods, orthogonalization, gradient methods. Consideration of stability and elementary error analysis. Extensive use of microcomputers and programs using a high level language. This course contains a writing component.

#### WORKSHOP

##### Mathematics 49

Variable credit course offering with a defined topic. Repeatable with a change of topic.