# 2015-2016 Mathematics Courses

 MATH 095 Elementary Algebra (3) Properties of the real number system, linear equations and inequalities, graphing, exponents, operations with algebraic expressions, factoring, and problem solving. Prerequisite: Pre-algebra or placement test. Offered every semester. MATH 105 Intermediate Algebra (3) Brief review of basic algebra, linear equations and inequalities, graphs, functions, systems of equations, factoring, rational expressions, radicals, and quadratic equations. Prerequisite: MATH 095 or placement test. Offered every semester. MATH 120 Quantitative Reasoning, LE (4) An introduction to contemporary mathematics through a survey of several practical and interesting uses of mathematics in society, including topics in logic, geometry, probability and statistics, with some attention given to historical background. Prerequisite: MATH 105 or placement test. MATH 141 College Algebra, LE (4) Linear and quadratic equations and inequalities, complex numbers, graphs, modeling, functions including polynomial, rational, exponential, and logarithmic, systems of equations and matrices, sequences and series. Prerequisite: MATH 105 or placement test. Offered every semester. MATH 142 Trigonometry, LE (2) The study of trigonometric functions and their graphs, applications to navigation and surveying problems, modeling cyclic behavior, complex numbers, polar coordinates, and vectors. Prerequisite: MATH 141 or placement test. Offered every semester. MATH 143 Precalculus, LE (4) Similar to College Algebra (MATH 141), but accelerated; emphasizes functions and other topics needed for success in Calculus. Also includes coverage of trig functions sufficient to satisfy the MATH 142 prerequisite for MATH 201 and 201B and Physics 151 and 211. Prerequisite: B+ or better in Math 105, or Math ACT at least 24, or Math SAT at least 560. Offered every semester. MATH 150 Elementary Statistics, LE (4) An introduction to the use of statistics as a valuable tool for analyzing data in a variety of fields. Topics in elementary descriptive and inferential statistics, including the normal, binomial, Student t, and chi-square distributions, correlation and regression, confidence intervals, and hypothesis testing. Prerequisite: MATH 105 or placement test. Offered every semester. MATH 200/300 Special Topics (1–4) Prerequisite: consent of mathematics faculty. Offered on sufficient demand. MATH 201 Calculus I, LE (4) Functions, graphs and limits. Differential calculus of algebraic, trigonometric, exponential, and logarithmic functions with applications to geometry, the physical and life sciences, and economics. Prerequisite: MATH 142 or MATH 143 or consent of instructor or placement test. Offered every semester. MATH 201B Calculus for the Life Sciences, LE (4) Differential calculus. Applications in biological sciences, including discrete difference methods, exponential growth and decay, and initial value problems. Prerequisite: MATH 142 or MATH 143 or consent of instructor or placement test. Offered every semester. MATH 202 Calculus II (4) Integral calculus of algebraic, trigonometric, exponential, and logarithmic functions with applications to geometry, the physical and life sciences, and economics. Sequences and series. Taylor’s theorem. Introduction to differential equations. Prerequisite: MATH 201 or 201B or placement test. Offered every semester. MATH 203 Multivariate Calculus (4) Vectors in n-space, differential calculus in several variables, vector fields, integration and its applications in several variables, line, surface, volume, and flux integrals. Green’s, Stokes’, and the divergence theorems. Prerequisite: MATH 202. Offered every Fall semester. MATH 210 Discrete Mathematics (4) Topics in sets, logic, elementary counting including permutations and combinations, finite probability, sequences and mathematical induction. Prerequisite: MATH 201 or 201B. Offered every semester. MATH 211 Introduction to Linear Algebra (4) Vector algebra in 2-3 dimensional space, linear systems and matrices. Linear algebra in Rn, linear transformations, eigenvalues and eigenvectors. Programming in Matlab. Prerequisite: MATH 201 or 201B. Offered every Fall semester. MATH 240 Statistics for the Sciences, LE (4) An introduction to probability and statistics using real world data from the sciences. Covers descriptive and inferential statistics. Focuses on the meaning and interpretation of p-values (with respect to hypothesis testing), explained via sampling distributions and sampling error. Explains the central importance of normal distributions. Regression, correlation, confidence intervals, comparisons of proportions and means, goodness of fit, and analysis of variance (ANOVA) will be covered, along with relevant tests. The importance of experimental design will also be discussed. Prerequisite: MATH 141 or math 143. Offered every semester. MATH 306 Introduction to Statistical Methods (2) Covers topics in elementary statistics, including distributions, correlation and regression, confidence intervals, hypothesis testing, and non-parametric statistical methods. Prerequisite: MATH 201 or 201B. Offered every odd May term. MATH 308 Putnam Seminar (1) Preparation for the William Lowell Putnam Mathematical competition. May be taken twice for credit. Prerequisites: MATH 211. Offered every Fall semester. MATH 310 Probability and Statistics (4) Introduction to probability theory including combinatorial analysis, conditional probability, discrete and continuous random variables, expectation and variance, jointly distributed random variables, and sampling theory. Prerequisite: MATH 202. Offered every odd Fall semester. MATH 311 Linear Algebra II (4) Rigorous treatment of Euclidean space, linear systems, theory of Gaussian elimination, determinants, and inverses. General vector spaces, linear transformations, quadratic forms, and least squares. Eigenvalues and eigenvectors, diagonalization. Includes Matlab programming. Prerequisites: MATH 210 and 211. MATH 312 Abstract Algebra (4) Sets, relations and functions. Number theory. Rings, fields and groups. Galois theory. Prerequisites: MATH 203, 210, 211. Offered every Spring semester. MATH 314 Foundations of Geometry (4) Modern axiomatic development of plane geometry and related systems. Includes investigation of finite geometry and hyperbolic geometry. Prerequisite: MATH 201 or 201B. Pre- or co-requisite: MATH 210. MATH 321 Advanced Calculus (4) A proof based class in which many of the results assumed in Calculus are proven. Topics include point set topology of real numbers, a rigorous treatment of limits for sequences and functions, continuity and differentiability. Prerequisites: MATH 203, 210, 211 and junior or senior status. Offered every Fall semester. MATH 323 Complex Analysis (4) Functions of one complex variable, analyticity, Cauchy-Riemann equations, derivatives and integrals of complex functions, complex series, and residue theory. Prerequisites: MATH 203, 210. MATH 340 History of Mathematics (3) A survey of the history of mathematics, from antiquity to the modern period. Prerequisites: MATH 202, 210. Offered every Spring semester. MATH 341 Topology (4) An introduction to topology. Topics include open and closed sets, continuity, compactness, quotient spaces, and product spaces. Applications of topology may include metric topology, knot theory, classification of surfaces, and the fundamental group. Prerequisite: MATH 210. MATH 362 Topics in Applied Mathematics (4) A range of applied mathematics topics building on a foundation of linear algebra, differential equations, and discrete mathematics. Possible topics include optimization, numerical analysis, algorithm analysis and design, algorithms on graphs and trees, math modeling, dynamical systems, and statistical learning theory. May be taken more than once for credit with instructor’s approval. Prerequisites: MATH 211; or MATH 201 or 201B and PHYS 309. Offered every Fall semester. MATH 363 Differential Equations (4) Topics include a review of methods for solving linear systems; non-linear systems, Laplace transform and power series methods of solving equations; topics from partial differential equations; heat equation, Laplace’s equation, wave equation, and Fourier series methods. Prerequisite: MATH 202. Offered every even Spring semester. MATH 387 Undergraduate Teaching (1) For teaching assistants in lower division mathematics problem-solving courses. A maximum of two credit hours of MATH 387 may be applied toward the major or minor. Prerequisite: consent of program director. MATH 401 Directed Studies (1–4) A tutorial-based course used only for student-initiated proposals for intensive individual study of topics not otherwise offered in the Mathematics Program. Prerequisites: junior or senior standing and consent of instructor and school dean. MATH 440 Internship (1–8) Offers students the opportunity to integrate classroom knowledge with practical experience. Prerequisites: junior or senior standing (for transfer students, at least 15 hours completed at Westminster or permission of instructor), minimum 2.5 GPA, and consent of program director and Career Center internship coordinator. MATH 485 Senior Seminar (2) This class will collaboratively review the core areas of undergraduate mathematics and build a more complete and integrated view of mathematics. All students will be required to take the Mathematics ETS exam at the conclusion of the course. Teaching and academic majors must register for the Senior Seminar during the spring semester of their senior year. Students who will be student teaching during that semester may take it the previous year. Prerequisites: Senior standing and graduation expected by the following December or permission of the instructor. Offered every Spring semester.