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# Undergraduate Mathematics

# Undergraduate Mathematics

## 2015 Fall Term

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#### 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 in mathematics for those students who do not wish to take any course which has MATH 141 as a prerequisite. ACT Math subscore 19-23 (SAT 460-550)

#### 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. ACT Math subscore 19-23 (SAT 460-550)

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

##### Mathematics 143

Mathematical preparation for the understanding of various quantitative methods in modern management and social sciences. Topics included are sets, relations, linear functions, interest, annuities, matrix theory, the solution of linear systems by the graphical, algebraic, Gauss-Jordan, and inverse methods, linear programming by graphical and simplex methods, counting and probability, and decision theory. 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. All students will prepare a mathematics based activity and present it at an area elementary school.

#### ELEMENTARY FUNCTIONS (GM)

##### Mathematics 152

Review of algebraic functions, inequalities, mathematical induction, theory of equations, exponential and logarithmic functions, circular functions, trigonometric identities and equations, inverse trigonometric functions, solution of triangles.

#### 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. Unreq: ECON 245, PSYCH 215, SOCIOLGY 295

#### 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.

#### 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.

#### 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.

#### INTRODUCTION TO ANALYSIS

##### Mathematics 301

The main emphasis of this course is to introduce students to mathematical proofs. Students will learn to read and write proofs in mathematics by writing proofs of theorems about limits, sets of real numbers, and continuous functions. If time permits, other topics may include derivative and integration theorems, theory of open and closed sets, and cardinality of sets.

#### 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.

#### 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.

#### 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 have a sound background in basic arithmetic, but who have not been exposed to algebra, or who need to strengthen their basic algebra skills. Topics include properties of the real numbers, linear and quadratic equations, linear inequalities, exponents, polynomials, rational expressions, the straight line, and systems of linear equations. The course counts towards the semester credit load and will be computed into the grade point average. It will not, however, be included in the credits necessary for graduation. It may be taken for a conventional grade or on a satisfactory/no credit basis. Prereq: MATH 040 or equivalent demonstration of capability. Students cannot receive credit for MATH 041 if they have been waived from the Mathematics Proficiency Requirement. Not available to students who have satisfied the University Proficiency requirement in mathematics.

#### 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.

#### PROBABILITY THEORY

##### Mathematics 441

Probability spaces, discrete and continuous random variables, mathematical exceptation, discrete and continuous distributions.

#### 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.

#### ABSTRACT ALGEBRA

##### Mathematics 453

This course is a continuation of MATH 452 with emphasis on ring and field theory. Topics include a review of group theory, polynomial rings, divisibility in integral domains, vector spaces, extension fields, algebraic extension fields, finite fields, etc.

#### COMPLEX VARIABLES

##### Mathematics 463

This course is a study of the algebra and geometry of complex numbers, the properties of analytic functions, contour integration, the calculus of residues and the properties of power series.

#### WORKSHOP

##### Mathematics 49

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

#### INDEPENDENT STUDY

##### Mathematics 498

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

#### INDEPENDENT STUDY - UNDERGRADUATE RESEARCH

##### Mathematics 498R

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