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# Undergraduate Mathematics

# Undergraduate Mathematics

## 2020 Spring 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

##### 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 IN EARLY CHILDHOOD LEARNING

##### Mathematics 147

A study of topics in early childhood mathematics, including sets, numbers, operations, measurement, data, and geometry. The focus is on increasing conceptual understanding of mathematics, highlighting connections, and developing the ability to communicate mathematical knowledge. Problem-solving methods used by children will also be explored. Manipulatives, cooperative learning activities, and problem solving strategies are used throughout the course.

#### MATHEMATICS FOR THE ELEMENTARY TEACHER I

##### Mathematics 148

A study of topics in early childhood through early adolescence mathematics, including sets, fundamental operations of arithmetic, fundamental algorithms, and structural properties of arithmetic. The focus is on increasing conceptual understanding of mathematics, highlighting connections, and developing the ability to communicate mathematical knowledge. Problem-solving methods used by children will also be explored. Manipulatives, cooperative learning activities, and problem solving emphasized.

#### 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

##### 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

##### 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.

#### MATHEMATICS: FORM AND FUNCTION

##### Mathematics 200

An introduction to abstract and applied mathematical thinking, including exploration of career opportunities in the mathematical sciences. Centered around the dual question of "What is mathematics, and what is it good for?", this course serves as a introduction to the mathematics major and minor and includes an overview of the different emphases within the major.

#### INTRODUCTION TO STATISTICAL REASONING AND ANALYSIS

##### 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

##### Mathematics 243

A brief 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

##### 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

##### 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, the substitution rule, and applications of the integral, including volumes of revolution and average value.

#### CALCULUS AND ANALYTIC GEOMETRY II

##### Mathematics 254

Techniques of integration, introduction to differential equations, parametric equations, and infinite sequences and series.

#### CALCULUS AND ANALYTIC GEOMETRY III

##### Mathematics 255

A course in multivariable calculus. Topics include: solid analytic geometry; vectors and vector functions; functions of several variables, including limits, continuity, partial and directional derivatives, gradient vectors, and Lagrange multipliers; multiple integrals in rectangular, cylindrical, and spherical coordinates; line and surface integrals; Green's Theorem, Stokes' Theorem, and the Divergence Theorem.

#### 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 provides an introduction to mathematical proof, beginning with a discussion of formal logic. Topics include sets, functions, relations, number theory, combinatorics, and probability.

#### 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.

#### 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 processes, limits, and continuity. In addition, derivatives and integrals and their relationships to change and area will be covered.

#### COLLEGE GEOMETRY

##### Mathematics 353

This course is adapted for the prospective high school mathematics teacher. Topics include 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.

#### 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.

#### MATHEMATICAL MODELING AND SIMULATION

##### Mathematics 381

Modeling involving formulation of deterministic, stochastic and rule-based models and computer simulation in order to make predictions. Topics may include unconstrained and constrained growth models, equilibrium and stability, force and motion, predator-prey model, enzyme kinetics, data-driven models, probability distributions, Monte Carlo simulations, random walk, diffusion, cellular automaton simulations, and high performance computing.

#### 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.

#### 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.

#### 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.

#### EXPERIMENTAL DESIGN AND ANALYSIS OF VARIANCE

##### Mathematics 423

An introduction to applied experimental design with emphasis on the construction of causal knowledge, analytical techniques, and statistical publication requirements. Topics include single and multiple factor, randomized block, and repeated measure designs; model selection, underlying assumptions, inference, diagnostics, multiple comparison procedures, confidence intervals, effect sizes, and difficulties in applied research settings. The R computing platform will be used.

#### MATHEMATICAL STATISTICS

##### Mathematics 442

This course will cover moment generating functions; multivariate probability distributions including moments of linear combinations of random variables and conditional expectation; functions of random variables; sampling distributions and the Central Limit Theorem; the theory and properties of estimation; confidence intervals; and the Neyman-Pearson Lemma, likelihood ratio tests and common tests of hypotheses.

#### 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.

#### PARTIAL DIFFERENTIAL EQUATIONS

##### Mathematics 459

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

#### DYNAMICAL SYSTEMS & CHAOS

##### Mathematics 474

An analytic, geometric, and intuitive study of continuous and discrete low-dimensional nonlinear dynamical systems. The basic notions of stability, bifurcations, chaotic systems, strange attractors, and fractals are examined. Specific applications will be taken from diverse fields such as Biology, Chemistry, Economics, Engineering, and Physics.

#### INDEPENDENT STUDY

##### Mathematics 498

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