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# Undergraduate Mathematics

# Undergraduate Mathematics

## 2023 Fall Term

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#### SUPPORT FOR COLLEGE ALGEBRA

##### MATH 124

This course is designed to enrich the MATH 142 College Algebra course. It is dedicated to support students by identifying and addressing skills that require review as well as create a structure that will support student success and improve math study skills. In addition to the pursuit of algebraic skills essential for success in MATH 142 and subsequent college-level mathematics courses, students will engage in activities to improve motivation, mindfulness, and mindset.

#### QUANTITATIVE REASONING

##### MATH 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, business, and education.

#### COLLEGE ALGEBRA

##### MATH 142

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. Applications to other disciplines are used to enhance conceptual understanding.

#### FINITE MATHEMATICS FOR BUSINESS AND SOCIAL SCIENCES

##### MATH 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

##### MATH 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

##### MATH 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

##### MATH 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.

#### TRIGONOMETRY

##### MATH 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

##### MATH 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.

#### APPLIED CALCULUS SURVEY FOR BUSINESS AND SOCIAL SCIENCES

##### MATH 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 250 and MATH 253.

#### CALCULUS AND ANALYTIC GEOMETRY I

##### MATH 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

##### MATH 254

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

#### CALCULUS AND ANALYTIC GEOMETRY III

##### MATH 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.

#### PROBLEM SOLVING FOR MATHEMATICS TEACHERS

##### MATH 270

Students will learn a variety of problem solving strategies applicable in elementary and secondary school. The applications will cover many different areas of mathematics. Students will also practice solving challenging problems from various math competitions and learn to prepare students for such contests.

#### DISCRETE MATHEMATICS

##### MATH 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.

#### PUTNAM COMPETITION AND PROBLEM SOLVING

##### MATH 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.

#### INTRODUCTION TO ANALYSIS

##### MATH 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.

#### EUCLIDEAN GEOMETRY

##### MATH 333

The topics included in this course are foundations of two-dimensional Euclidean geometry and transformational geometry, with emphasis on topics most relevant for prospective mathematics teachers. The approach of the course is not a precise, axiomatic development, but rather emphasizes intuitive thinking, problem solving, and proof writing. The course includes an introduction to dynamic geometry software (such as Geometer's Sketchpad or GeoGebra).

#### APPLIED PROBABILITY THEORY

##### MATH 343

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

#### MATRICES AND LINEAR ALGEBRA

##### MATH 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

##### MATH 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.

#### BEGINNING ALGEBRA

##### MATH 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.

#### MATHEMATICS FOR HIGH SCHOOL TEACHERS II

##### MATH 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.

#### INTRODUCTION TO ABSTRACT ALGEBRA

##### MATH 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.

#### COMPLEX VARIABLES

##### MATH 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.

#### DYNAMICAL SYSTEMS & CHAOS

##### MATH 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.

#### MATH INTERNSHIP

##### MATH 493

#### INDEPENDENT STUDY - UNDERGRADUATE RESEARCH

##### MATH 498R

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

#### SUPPORT FOR QUANTITATIVE REASONING

##### MATH 93

This course is designed to enrich the MATH 139 Quantitative Reasoning course. It is dedicated to support students by identifying and addressing skills that require review as well as create a structure that will support student success and improve math study skills. In addition to the pursuit of algebraic skills essential for success in MATH 139 and subsequent college-level mathematics courses, students will engage in activities for understanding and reducing test anxiety and will create strategies to improve motivation, mindfulness, and mindset.