## MATH Course Descriptions

MATH 136 – CALCULUS I. (4
semester hours) GEN ED D-II | QR

Prerequisites: Four years of high school mathematics, including Algebra II, geometry, and trigonometry, and satisfactory score on Math Placement Exam and Math Placement Trig Exam; or MATH 117 or MATH 118, with grade of C or better.

A course in one-variable calculus including topics from analytic geometry. Limits, derivatives, integration, and applications of polynomial, rational, trigonometric, and transcendental functions. Includes lecture and recitation.

MATH 137 – CALCULUS II. (4 semester hours)

Prerequisites: MATH 136 with a grade of C or better.

A second course in one-variable calculus including topics from analytic geometry. Methods of integration, sequences and series, polar and parametric functions. Includes lecture and recitation.

MATH 237 – MULTIVARIABLE CALCULUS. (4 semester hours)

Prerequisite: MATH 137 with a grade of C or better.

Topics in real-valued functions of several variables including directional derivatives, implicit functions, gradient, Taylor’s Theorem, maxima, minima, and Lagrange multipliers. Differential calculus of vector-valued functions including chain rule and Inverse Function Theorem. Multiple integrals, line integrals, surface integrals, Stokes’ and Green’s Theorems.

MATH 305 – INTRODUCTION TO MATHEMATICAL MODELING. (3 semester hours)

Prerequisite: MATH 137 with a grade of C or better.

Theory and computer implementation of mathematical models. Deterministic, stochastic, discrete, continuous, and matrix models. Introduction to advanced topics such as linear algebra, differential and difference equations, probability, stochastic processes, and dynamical systems.

MATH 307 – INTRODUCTION TO LINEAR ALGEBRA. (3 semester hours)

Prerequisites: MATH 137 with a grade of "C" or better or Math 136 with a grade of "A" or Math 142 with a grade of "A".

Systems of linear equations, matrix algebra, vector spaces, inner product spaces, linear transformations, eigenvectors, quadratic forms.

MATH 310 – INTRODUCTION TO DISCRETE MATHEMATICS. (3 semester hours)

Prerequisite: MATH 137 with a grade of C or better.

Introduction to discrete topics. Development of skills in abstraction and generalization. Set theory, functions and relations, mathematical induction, elementary propositional logic, quantification, truth tables, validity; counting techniques, pigeonhole principle, permutations and combinations; recurrence relations and generating functions; elementary graph theory, isomorphisms, trees.

MATH 331 – DIFFERENTIAL EQUATIONS. (3 semester hours)

Prerequisite: MATH 137 with a grade of C or better

Methods of solution of differential equations, existence and nature of solutions, Laplace transform method, infinite series, numerical solutions, and applications.

MATH 382 – PROBABILITY AND STATISTICS I. (3 semester hours)

Prerequisite: MATH 310 with a grade of C or better. Prerequisite or corequisite: MATH 237.

Axioms and laws of probability; discrete and continuous probability distributions; multivariate distributions; random variables; expectation; moment generating functions; Central Limit Theorem.

MATH 405 – NUMERICAL ANALYSIS I. (3 semester hours)

Prerequisites: MATH 237 or 307 or 310, and CS 180 or CS 230, all with grades of C or better.

Computer arithmetic, roots of equations, polynomial approximation and interpolation, numerical differentiation and integration. Computer solutions of problems will be required.

MATH 435 – PARTIAL DIFFERENTIAL EQUATIONS. (3 semester hours)

Prerequisites: MATH 237, 307, and 331 all with grades of C or better.

Equations of first and second order; elliptic, hyperbolic and parabolic equations; Sturm-Liouville theory; applications to equations of mathematical physics using separation of variables and Fourier series.

MATH 482 – PROBABILITY AND STATISTICS II. (3 semester hours)

Prerequisites: MATH 237 and MATH 382 with grades of C or better.

Multivariate probability distributions; sampling distributions, statistical inference; point and interval estimation, properties of estimators; hypothesis testing; regression and correlation; analysis of variance; non-parametric methods.

MATH 497 – SENIOR SEMINAR IN MATHEMATICAL ECONOMICS. (1 semester hour)

Prerequisite or corequisite: Senior standing and admitted to the major in mathematical economics.

This course is designed to integrate the ideas and techniques students have encountered in their work in mathematics and economics. Students will study research articles and/or undertake independent investigations in mathematical economics. Equivalent to ECON 497.

STAT 301 – INTRODUCTORY PROBABILITY AND APPLIED STATISTICS. (3 semester hours)

Prerequisite: MATH 136 or MATH 142, with a grade of C or better.

A calculus-based introduction to applied statistics, with emphasis on analysis of real data. Curve fitting, probability models, estimation and testing for means and proportions, quality control; use of computers for data analysis and simulation.

Prerequisites: Four years of high school mathematics, including Algebra II, geometry, and trigonometry, and satisfactory score on Math Placement Exam and Math Placement Trig Exam; or MATH 117 or MATH 118, with grade of C or better.

A course in one-variable calculus including topics from analytic geometry. Limits, derivatives, integration, and applications of polynomial, rational, trigonometric, and transcendental functions. Includes lecture and recitation.

MATH 137 – CALCULUS II. (4 semester hours)

Prerequisites: MATH 136 with a grade of C or better.

A second course in one-variable calculus including topics from analytic geometry. Methods of integration, sequences and series, polar and parametric functions. Includes lecture and recitation.

MATH 237 – MULTIVARIABLE CALCULUS. (4 semester hours)

Prerequisite: MATH 137 with a grade of C or better.

Topics in real-valued functions of several variables including directional derivatives, implicit functions, gradient, Taylor’s Theorem, maxima, minima, and Lagrange multipliers. Differential calculus of vector-valued functions including chain rule and Inverse Function Theorem. Multiple integrals, line integrals, surface integrals, Stokes’ and Green’s Theorems.

MATH 305 – INTRODUCTION TO MATHEMATICAL MODELING. (3 semester hours)

Prerequisite: MATH 137 with a grade of C or better.

Theory and computer implementation of mathematical models. Deterministic, stochastic, discrete, continuous, and matrix models. Introduction to advanced topics such as linear algebra, differential and difference equations, probability, stochastic processes, and dynamical systems.

MATH 307 – INTRODUCTION TO LINEAR ALGEBRA. (3 semester hours)

Prerequisites: MATH 137 with a grade of "C" or better or Math 136 with a grade of "A" or Math 142 with a grade of "A".

Systems of linear equations, matrix algebra, vector spaces, inner product spaces, linear transformations, eigenvectors, quadratic forms.

MATH 310 – INTRODUCTION TO DISCRETE MATHEMATICS. (3 semester hours)

Prerequisite: MATH 137 with a grade of C or better.

Introduction to discrete topics. Development of skills in abstraction and generalization. Set theory, functions and relations, mathematical induction, elementary propositional logic, quantification, truth tables, validity; counting techniques, pigeonhole principle, permutations and combinations; recurrence relations and generating functions; elementary graph theory, isomorphisms, trees.

MATH 331 – DIFFERENTIAL EQUATIONS. (3 semester hours)

Prerequisite: MATH 137 with a grade of C or better

Methods of solution of differential equations, existence and nature of solutions, Laplace transform method, infinite series, numerical solutions, and applications.

MATH 382 – PROBABILITY AND STATISTICS I. (3 semester hours)

Prerequisite: MATH 310 with a grade of C or better. Prerequisite or corequisite: MATH 237.

Axioms and laws of probability; discrete and continuous probability distributions; multivariate distributions; random variables; expectation; moment generating functions; Central Limit Theorem.

MATH 405 – NUMERICAL ANALYSIS I. (3 semester hours)

Prerequisites: MATH 237 or 307 or 310, and CS 180 or CS 230, all with grades of C or better.

Computer arithmetic, roots of equations, polynomial approximation and interpolation, numerical differentiation and integration. Computer solutions of problems will be required.

MATH 435 – PARTIAL DIFFERENTIAL EQUATIONS. (3 semester hours)

Prerequisites: MATH 237, 307, and 331 all with grades of C or better.

Equations of first and second order; elliptic, hyperbolic and parabolic equations; Sturm-Liouville theory; applications to equations of mathematical physics using separation of variables and Fourier series.

MATH 482 – PROBABILITY AND STATISTICS II. (3 semester hours)

Prerequisites: MATH 237 and MATH 382 with grades of C or better.

Multivariate probability distributions; sampling distributions, statistical inference; point and interval estimation, properties of estimators; hypothesis testing; regression and correlation; analysis of variance; non-parametric methods.

MATH 497 – SENIOR SEMINAR IN MATHEMATICAL ECONOMICS. (1 semester hour)

Prerequisite or corequisite: Senior standing and admitted to the major in mathematical economics.

This course is designed to integrate the ideas and techniques students have encountered in their work in mathematics and economics. Students will study research articles and/or undertake independent investigations in mathematical economics. Equivalent to ECON 497.

STAT 301 – INTRODUCTORY PROBABILITY AND APPLIED STATISTICS. (3 semester hours)

Prerequisite: MATH 136 or MATH 142, with a grade of C or better.

A calculus-based introduction to applied statistics, with emphasis on analysis of real data. Curve fitting, probability models, estimation and testing for means and proportions, quality control; use of computers for data analysis and simulation.

Dr.
David K. Neal, Lead Academic
Advisor

Department of Mathematics

COHH 4108

Western Kentucky University

Bowling Green, KY 42101

270.745.6213

Department of Mathematics

COHH 4108

Western Kentucky University

Bowling Green, KY 42101

270.745.6213

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