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# Undergraduate Mathematics

# Undergraduate Mathematics

## 2016 Spring 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

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.

#### THEORY OF INTEREST

##### Mathematics 346

This course will cover the topics of interest theory listed in the Society of Actuaries/Casualty Actuarial Society syllabus for Exam FM/2. Topics include the time value of money, annuities, loans, bonds, general cash flows and portfolios, and immunization schedules.

#### INFINITE PROCESSES FOR THE ELEMENTARY TEACHER

##### Mathematics 352

This course is primarily for pre-service elementary and middle school teachers. Students will be introduced to the concepts of calculus, which include infinite precesses, limits, and continuity. In addition, dirivatives and integrals, and their relationship to area and change will be covered.

#### COLLEGE GEOMETRY

##### Mathematics 353

The topics included in this course are foundations of Euclidean geometry, Euclidean transformational geometry, modern synthetic geometry that builds on Euclidean geometry, selected finite geometries, and an introduction to non-Euclidean and projective geometry, including their relationship to Euclidean geometry. Although the course is adapted to the prospective teacher of geometry, it will also meet the needs of those in other majors needing a background in geometry. Standards and guidelines of appropriate national and local bodies will be implemented.

#### 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.

#### PROBABILITY & STATISTICS FOR TEACHERS

##### Mathematics 359

An introduction to probability and statistics for teachers. Topics covered include counting techniques, basic probability theory, exploratory data analysis, simulation, randomization, and statistical inference. This course contains a writing component.

#### 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.

#### MODERN ALGEBRA AND NUMBER THEORY FOR THE ELEMENTARY TEACHER

##### Mathematics 415

An introduction to modern algebra with special emphasis on the number systems and algorithms which underlie the mathematics curriculum of the elementary school. Topics from logic, sets, algebraic structures, and number theory.

#### APPLIED REGRESSION ANALYSIS

##### Mathematics 420

This is a second course in regression analysis and its applications. Topics include correlation, simple and multiple linear regression, model assumptions, inference of regression parameters, regression diagnostics and remedial measures, categorical predictors, multicollinearity,and model selection. Real data re emphasized and analyzed using statistical software such as R or SAS.

#### MATHEMATICS FOR HIGH SCHOOL TEACHERS I

##### Mathematics 421

The course revisits the high school curriculum from an advanced perspective. The focus is on deepening understanding of concepts, highlighting connections and solving challenging problems. The mathematical content includes number systems, functions, equations, integers, and polynomials. Connections to geometry are emphasized throughout the course.

#### MATHEMATICAL STATISTICS

##### Mathematics 442

This course will cover moment generating functions, moments of linear combinations of random variables, conditional expection, functions of random variables, sampling distributions, the theory of estimation, Bayesian estimation, hypothesis testing, nonparametric tests, and linear models.

#### ACTUARIAL EXAMINATION PREPARATION

##### Mathematics 449

This course is designed to prepare students for Exam FM/2, the second acturial exam which tests students' knowledge and understanding of the fundamental concepts of financial mathematics. Derivatives are introduced, interest theory is reviewed, and sample questions from previous exams and practice exams from other sources are discussed.

#### 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.

#### APPLIED MATHEMATICAL ANALYSIS

##### Mathematics 458

Selected topics in ordinary differential equations: series solutions, stability, transform methods, special functions, numerical methods, vector differential calculus, line and surface integrals.

#### PARTIAL DIFFERENTIAL EQUATIONS

##### Mathematics 459

Fourier analysis, partial differential equations and boundary value problems, complex variables, and potential theory.

#### ADVANCED CALCULUS

##### Mathematics 464

This course presents a rigorous treatment of the differential and integral calculus of single variable functions, convergence theory of numerical sequences and series, uniform convergence theory of sequences and series of functions, metric spaces, functions of several real variables, and the inverse function theorem. This course contains a writing component.

#### 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.