# Mathematics (MATH)

Mathematics is the language used to understand the universe, from atomic-level chemical reactions, to the motion of the planets around the sun, and everything in between. While many graduates continue on to masters- or doctoral-level studies it’s no surprise that others use the critical thinking and reasoning skills learned at Western in a wide variety of fields including engineering, education, software programming, database management, research for business firms, and more. A degree in Mathematics can open the door to almost any career.

Western's Mathematics program provides several paths into these exciting professions. The standard major gives a sound foundation from which one can pursue advanced degrees or enter the business world with excellent quantitative skills. The secondary licensure emphasis is designed for people who want to teach in high schools or middle schools, where a shortage of well-qualified math teachers provides excellent job opportunities. The actuarial science emphasis trains students to analyze risk for the insurance and finance industries. Many actuarial science students are able to pass the first professional certification test before they graduate.

Regardless of one's major, the two mathematics minors will add quantitative skills critical to success and advancement in any profession. The standard minor provides a well-rounded set of problem solving skills and the ability to analyze complicated situations. The data analytics minor is designed to add the computational fluency which is driving nearly every profession now. This minor prepares students to analyze large data sets and extract valuable knowledge from data. These data are being produced in many fields and this minor allows students to work with professionals in other fields to derive appropriate solutions.

## Capstone Course Requirement

The following course fulfills the capstone course requirement: MATH 495 Senior Seminar

## Mathematics Courses

**MATH 098.**

**Beginning Algebra.**

**(3 Credits)**

An introduction to algebra with a review of basic arithmetic. Includes decimals, fractions, percentages, ratios, proportions, signed numbers, algebraic expressions, factoring, exponents and radicals, linear equations, and graphs. Credit does not count toward graduation. Graded Satisfactory/Unsatisfactory only.

**MATH 099.**

**Intermediate Algebra.**

**(3 Credits)**

A review of the arithmetic of fractions and decimals, percentage problems, signed numbers, arithmetic, and topics of basic algebra, including simplifying algebraic expressions, solving and graphing linear equations, basic factoring, working with algebraic fractions, and solving rational and quadratic equations. This course is designed for students who need a review of the basic algebra skills necessary to complete the required mathematics course MATH 140. Credit does not count toward graduation. Graded Satisfactory/ Unsatisfactory only. Prerequisite: ACT math score of 16 or above; SAT math score of 440 or above, MATH 098; or Accuplacer Quantitative Reasoning, Algebra, and Statistics test score of 265 or above.

**MATH 102.**

**College Algebra Skills.**

**(1 Credit)**

A review of the math skills necessary to succeed in MATH 140, College Algebra. Prerequisites: an assessment equivalent to ACT math score between 17-20; a SAT Math score between 450-530; an Accuplacer Advanced Algebra and Functions test score of 235 or above; or a Compass Algebra score between 26-44; and a high school GPA of 2.75 or higher. Co-requisite MATH 140. Note: this course is intended for those qualified students wanting to complete the Supplemental Academic Instruction (SAI) program in Math.

**MATH 103.**

**Statistical Thinking Skills.**

**(1 Credit)**

A review of the math skills necessary to succeed in MATH 113, Statistical Thinking. Prerequisites: an assessment equivalent to ACT math score between 16-20; a SAT Math score between 440-530; an Accuplacer Quantitative Reasoning, Algebra, and Statistics test score of 230 or above; and a high school GPA of 2.75 or higher; or MATH 098. Co-requisite MATH 113. Note: this course is intended for those qualified students wanting to complete the Supplemental Academic Instruction (SAI) program in Math.

**MATH 105.**

**Mathematics for the Liberal Arts.**

**(3 Credits)**

Topics may include practical applications such as personal finance and numbers in the media, along with aesthetic applications such as connections between mathematics and art or music. GT-MA1

**MATH 113.**

**Statistical Thinking (GT-MA1).**

**(3 Credits)**

A course introducing the ideas of statistical analysis. Topics include data visualization and summarization, parameter estimation, and hypothesis testing. This course emphasizes practical aspects of data analysis and makes extensive use of spreadsheets and real data. Prerequisite: ACT math score of 21 or above; SAT math score of 540 or above; MATH 099; or Accuplacer Quantitative Reasoning, Algebra, and Statistics test score of 240 or above; or co-requisite MATH 103 (SAI). GT-MA1

**MATH 140.**

**College Algebra (GT-MA1).**

**(3 Credits)**

An integration of the essential algebraic manipulations, solving equations and inequalities, polynomial functions, exponential and logarithmic functions, and techniques of graphing. Prerequisite: ACT math score of 21 or above; SAT math score of 540 or above; MATH 099; or Accuplacer Elementary Advanced Algebra and Functions test score of 245 or above; or co-requisite MATH 102 (SAI). GT-MA1

**MATH 141.**

**Precalculus (GT-MA1).**

**(4 Credits)**

This course explores the theory and applications of trigonometry, and includes an introduction to vector and matrix analysis. Topics may include the unit circle, triangle trigonometry, trigonometric functions, polar coordinates, complex numbers, vector geometry, and applied matrix techniques. Prerequisite: ACT math score of 23 or above; SAT math score of 560 or above; MATH 140 with a minimum grade of C-; or Accuplacer Advanced Algebra and Functions test with a score of 280 or above. GT-MA1

**MATH 151.**

**Calculus I (GT-MA1).**

**(4 Credits)**

A study of differential calculus, including limits, continuous functions, Intermediate Value Theorem, tangents, linear approximation, inverse functions, implicit differentiation, extreme values and the Mean Value Theorem. This course also introduces Integral calculus including anti-derivatives, definite integrals, and the Fundamental Theorem of Calculus. Prerequisite: ACT math score of 27 or above; SAT math score of 630 or above; or MATH 141 with a minimum grade of C-. GT-MA1

**MATH 197.**

**Special Topics.**

**(1-6 Credits)**

**MATH 200.**

**Discrete Mathematics.**

**(3 Credits)**

A study of the discrete mathematics necessary for computer science. Topics include logic, set theory, Boolean algebra, functions and relations, graphs, propositional and predicate calculus, proofs, mathematical induction, recurrence relations, combinatorics and discrete probability. Computer science applications are emphasized. Prerequisites: MATH 151 and CS 191 with minimum grades of “C-”.

**MATH 209.**

**Mathematics for Elementary School Teachers I.**

**(3 Credits)**

First of two courses designed for prospective elementary teachers. Emphasizes the real number system, arithmetic operations, and algebra. Explorations focus on representing, analyzing, generalizing, formalizing, and communicating patterns and structures. Content is presented using problem solving and exploration. Prerequisite: ACT math score of 23 or above; SAT math score of 560 or above; MATH 140 with a minimum grade of C-; or Accuplacer Advanced Algebra and Functions test with a score of 280 or above.

**MATH 210.**

**Mathematics for Elementary School Teachers II.**

**(3 Credits)**

Second of two courses designed for prospective elementary teachers. Emphasizes probability, data analysis, and geometry. Explorations focus on representations of data and two and three-dimensional shapes, their properties, measurements, constructions, and transformations. Prerequisite: MATH 209 with a minimum grade of “C-“.

**MATH 213.**

**Probability and Statistics.**

**(3 Credits)**

A course in the use of statistical techniques to draw knowledge from data. Topics include exploratory data analysis, descriptive statistics, t-procedures, ANOVA, chi squared procedures, regression, and non-parametric tests. Statistical software is used extensively to analyze real data sets. Prerequisite: MATH 141 with a minimum grade of C-; or instructor permission.

**MATH 220.**

**Introduction to Advanced Mathematics.**

**(3 Credits)**

Students develop and use elementary logic and set theory to construct deductive proofs with relations, functions, and some algebraic structures. Topics include indexing, equivalence relation theory, and cardinality. Prerequisite: MATH 151 with a minimum grade of C-.

**MATH 232.**

**Applied Calculus for the Managerial and Social Science.**

**(3 Credits)**

An introduction to differential and integral calculus for students majoring in business, accounting or the social sciences. The calculus is presented using a variety of real-world business and economic applications, stressing marginality, elasticity, and accumulation. Prerequisite: ACT math score of 23 or above; SAT math score of 560 or above; Math 140 with a minimum grade of “C-“; or Accuplacer Advanced Algebra and Functions test with a score of 280 or above.

**MATH 251.**

**Calculus II.**

**(4 Credits)**

Topics include techniques of integration, area computations, improper integrals, infinite series and various convergence tests, power series, Taylor's Formula, polar coordinates, and parametric curves. Prerequisite: MATH 151 with a minimum grade of C-.

**MATH 252.**

**Calculus III.**

**(4 Credits)**

Topics include calculus of functions of several variables, differentiation and elementary integration, vectors in the plane and space. Prerequisite: MATH 251 with a minimum grade of C-.

**MATH 260.**

**Applied Linear Algebra.**

**(3 Credits)**

A course in the techniques and applications of linear algebra. The core topics include solving systems of linear equations, eigenvalues and eigenvectors, matrix decomposition, the pseudoinverse and least squares approximations, and the singular value decomposition. The theory is supplemented with extensive applications and computer programming. Prerequisite: MATH 141.

**MATH 266.**

**Secondary Mathematics from an Advanced Perspective.**

**(3 Credits)**

A course designed to help Secondary Licensure Emphasis majors understand the core mathematical content of high school mathematics courses before calculus. These concepts are treated from an advanced standpoint, emphasizing connections and extensions. Topics include number systems, polynomial and transcendental functions, analytic geometry, theory of equations, and measurement. Prerequisite: MATH 151 with a minimum grade of C-.

**MATH 275.**

**Scientific Programming, Modeling, and Simulation.**

**(3 Credits)**

Designed to develop programming skills appropriate for scientific and industrial applications. Topics may include numerical solution of differential equations, singular value decomposition, and fourier analysis. Emphasis is placed on modeling, algorithm development and data visualization. Prerequisite: CIS 190 and MATH 151 with a minimum grades of C-.

**MATH 292.**

**Independent Study.**

**(1-6 Credits)**

**MATH 297.**

**Special Topics.**

**(1-6 Credits)**

**MATH 300.**

**Introduction to Mathematical Modeling.**

**(3 Credits)**

Designed to teach the basic principles of mathematical modeling and applied mathematics. Techniques from calculus, statistics, and probability are utilized to model real-world problems. Analytic and numeric tools are used to implement the models, obtain predictions and investigate underlying mechanisms. Topics include dimensional analysis, curve fitting, simulations, differential and difference equations. Prerequisites: MATH 251 and MATH 213 with minimum grades of C-.

**MATH 313.**

**Statistical Modeling and Simulation.**

**(3 Credits)**

A study of statistical techniques used to model and simulate stochastic processes. The core topics include linear and nonlinear multivariate models, generalized additive models, time series models with auto-correlated error, and mixed effects models. Emphasis is placed on computational techniques appropriate to large data sets and data visualization. Prerequisites: MATH 213 or ECON 216, MATH 260, CS190.

**MATH 314.**

**Applied Probability.**

**(3 Credits)**

A study of the basic principles of probability theory and their applications. Topics include combinational analysis, conditional probabilities, discrete and continuous random variables, and measures of centrality and variance. Emphasis is placed on applications using probability distributions (including binomial, geometric, Poisson, uniform, exponential, and normal distributions) to assess and manage risk in the fields of finance, insurance, medicine, and quality control. Prerequisite: MATH 251 with a grade "C-" or better.

**MATH 317.**

**Genome Analysis (with laboratory).**

**(3 Credits)**

This course introduces students to the appropriate mathematical techniques to answer questions about information contained in genetic sequences. These techniques may include dynamic programming, motif similarity, Bayesian models, hidden Markov models, principal component analysis, and clustering. Students use standard genome query tools to annotate genomic DNA. MATH 317 and BIOL 317 cannot both be taken for credit. Prerequisite: MATH 213 and either MATH 161 or CS 190.

**MATH 330.**

**Topics in Geometry.**

**(3 Credits)**

An introduction to modern geometries. Topics include synthetic, analytic, vector, and transformational approaches to geometry. Classification of geometries, axiomatics, and the application of geometry may also be included. Prerequisite: MATH 220 with a minimum grade of C-.

**MATH 354.**

**Differential Equations.**

**(3 Credits)**

A study of the theory and methods for solving ordinary differential equations. Prerequisite: MATH 251 with a minimum grade of "C-".

**MATH 358.**

**Introduction to Differential Equations and Linear Algebra.**

**(4 Credits)**

An introduction to ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Only one of the following courses, MATH 358 or MATH 354, may be taken for credit. Prerequisite: MATH 251 with a minimum grade of “ C-.”

**MATH 360.**

**Linear Algebra.**

**(3 Credits)**

A study of systems of linear equations, matrix operations, vector spaces, properties of determinants, eigenvalues, eigenvectors, orthogonality and least-squares. Emphasis is placed on theoretical aspects and general vector space properties with proof. Prerequisite: MATH 260, MATH 220 with a minimum grade of “C-.”

**MATH 366.**

**Methods of Teaching Secondary Mathematics.**

**(3 Credits)**

Secondary Licensure Emphasis majors learn to use the latest teaching techniques and technologies to prepare valid mathematics tests, to be able to effectively evaluate their students, to know the latest developments in secondary mathematics curriculum, and to become familiar with professional mathematics teaching organizations and their journals. Prerequisites: MATH 220 and MATH 266 with minimum grades of C-.

**MATH 370.**

**History of Mathematics.**

**(3 Credits)**

**MATH 375.**

**Numerical Methods.**

**(3 Credits)**

A study of techniques of computation for power-series calculation of functions; roots of equations; nonlinear simultaneous equations; matrices, determinants, and linear simultaneous equations; numerical integration; and differential equations. Prerequisites: MATH 251 and either CIS 275 or CIS 310 with minimum grades of C-.

**MATH 380.**

**Introduction to Cryptography.**

**(3 Credits)**

A presentation of the mathematical background to modern cryptography. Topics include symmetric and asymmetric cryptography, block ciphers, hashing, digital signatures, RSA and discrete-logarithm-based systems, and error correction. The course emphasizes rigorous mathematical formulations as well as programing algorithms. Prerequisite: MATH 151 or CS 191 with minimum grade of “C-“.

**MATH 390.**

**Introduction to Peer Tutoring in Mathematics.**

**(1 Credit)**

Strategies for tutoring mathematics at the college level, with a focus on presenting mathematical concepts and procedures, reducing anxiety, and improving study skills. May be repeated for up to four credits. Graded Satisfactory/Unsatisfactory only. Prerequisite: MATH 151 with a minimum grade of “B-” and instructor permission.

**MATH 391.**

**Seminar in Mathematics.**

**(1 Credit)**

A selected topic from areas of mathematics not usually included in the regular curriculum. Student involvement through presentations is emphasized. May be taken under different topics for a total of two credits.

**MATH 392.**

**Independent Study in Mathematics.**

**(1-4 Credits)**

**MATH 397.**

**Special Topics.**

**(1-6 Credits)**

**MATH 414.**

**Actuarial Methematics.**

**(3 Credits)**

A study of mathematical concepts useful in risk management, including multivariate probability and interest theory. Topics include the Central Limit Theorem, joint distributions, combinations of distributions, conditional and marginal probabilities, time value of money, annuities, and loans. Emphasis is placed on solving problems from the actuarial field, including applications to insurance and business. Prerequisites: MATH 252 with a minimum grade of “C-“; MATH 314 with a minimum grade of “C-”.

**MATH 451.**

**Analysis I.**

**(3 Credits)**

**MATH 456.**

**Introduction to Complex Analysis.**

**(3 Credits)**

**MATH 471.**

**Abstract Algebra I.**

**(3 Credits)**

An introduction to the theory of groups and rings. The fundamental group properties and concepts including cyclic groups, subgroups, direct products, symmetric groups, cosets, normal subgroups, and the group homomorphism theorems are discussed. Prerequisite: MATH 220 with a minimum grade of C-, and at least three upper-division mathematics credits.

**MATH 490.**

**Workshop.**

**(2 Credits)**

A study of a variety of mathematical topics generally dictated by student interest. The course may be taken for credit three times if the content of the workshop differs.

**MATH 492.**

**Independent Study.**

**(1-4 Credits)**

**MATH 495.**

**Senior Seminar.**

**(2 Credits)**

**MATH 496.**

**Senior Seminar Professional Experience.**

**(1 Credit)**

Provides students an opportunity to prepare their Senior Seminar research for the mathematics community outside of Western. Graded Satisfactory/Unsatisfactory only. Prerequisite: Instructor permission. Co-requisite: MATH 495.

**MATH 497.**

**Special Topics.**

**(1-6 Credits)**

**MATH 499.**

**Internship in Mathematics.**

**(1-12 Credits)**

Students participate in supervised field experience with a cooperating firm in the mathematics field. The sponsoring faculty member provides evaluations after the field experience is complete. A formal paper is required of the student. Specific department requirements must be met to participate in this course. Prerequisite: 18 credits of Mathematics course work, including nine upper-division credits.