# Courses in MATHEMATICS (DIVISION 428)

103. Intermediate Algebra. Two or three years of high school mathematics; or Math. 101 or 102. 1 credit for students with credit for Math. 101 or 102. No credit for students with credit for Math. 105 or 106. (Excl).

Material covered includes review of algebra; linear, quadratic, polynomial and rational functions and their graphs; logarithmic and exponential functions and their graphs. The material is the first half of Mathematics 105/106. Text: ALGEBRA AND TRIGONOMETRY by Larson and Hostetler.

105. Algebra and Analytic Trigonometry. See table. Students with credit for Math. 103 or 104 can elect Math. 105 for only 2 credits. No credit for students with credit for Math 106. (Excl).

Material covered includes review of algebra; linear, quadratic, polynomial and rational functions and their graphs; logarithmic and exponential functions and their graphs; triangle trigonometry, trigonometric functions and their graphs. Text: ALGEBRA AND TRIGONOMETRY by Larson and Hostetler.

109. Pre-Calculus. Two years of high school algebra. No credit for students who already have 4 credits for pre-calculus mathematics courses. (N. Excl).

Standard lecture version of Math 110. Material covered includes linear, quadratic, and absolute value equations and inequalities; algebra of functions; trigonometric identities; functions and graphs: trig and inverse trig, exponential and logarithmic, polynomial and rational; analytic geometry of lines and conic sections.

THE ELEMENTARY CALCULUS SEQUENCE CONSISTS OF FOUR COURSES OF 4 CREDITS EACH: Math . 115, 116, 215, and 216. The first three of these are calculus in content; Math. 216 is an introduction to differential equations. As an alternative fourth course, Math. 217 (Linear Algebra), will be offered as a 4 credit alternative for those students who require linear algebra, rather than differential equations, early in their programs. After completing Math. 217, students who require an introductory course in differential equations may elect 3 credit Math. 316 (Differential Equations) which is intended to cover the material of Math. 216 and Math. 404.

For students who elect Math. 216 as the fourth course of the elementary calculus sequence, Math. 417 (Matrix Algebra I) will continue to be the appropriate first course in linear algebra.

115. Analytic Geometry and Calculus I. See table. (Math. 107 may be elected concurrently.) Credit is granted for only one course from among Math. 112, 113, 115, and 185. (N.Excl).

Topics covered in this course include functions and graphs, derivatives; differentiation of algebraic and trigonometric functions and applications; definite and indefinite integrals and applications. Daily assignments are given. There are generally two or three one-hour examinations and a uniform midterm and final.

116. Analytic Geometry and Calculus II. Math. 115. Credit is granted for only one course from among Math. 114, 116, and 186. (N.Excl).

Transcendental functions, techniques of integration, introduction to differential equations, vectors, conic sections, infinite sequences and series. The course generally requires two one-hour examinations and a uniform midterm and final exam. Text: CALCULUS AND ANALYTIC GEOMETRY by Thomas and Finney, seventh edition.

215. Analytic Geometry and Calculus III. Math. 116. (N.Excl).

Topics covered include vector algebra and calculus, solid analytic geometry, partial differentiation, multiple integrals and applications. There are generally daily assignments and class examinations in addition to midterm and final examinations.

216. Introduction to Differential Equations. Math. 215. (N.Excl).

Topics covered include first order differential equations, linear differential equations with constant coefficients, vector spaces and linear transformations, differential operators, systems of linear differential equations, power series solutions, and applications. There are generally several class examinations and regular assignments.

417. Matrix Algebra I. Three terms of college mathematics. No credit granted to those who have completed 513. (N.Excl).

The course covers basic linear algebra and touches on several of its applications to many different fields. Emphasis is on introducing a diversity of applications rather than treating a few in depth. Topics emphasized include a review of matrix operations, vector spaces, Gaussian and Gauss-Jordan algorithms for linear equations, subspaces of vector spaces, linear transformations, determinants, orthogonality, characteristic polynomials, eigenvalue problems, and similarity theory. Applications include linear networks, least squares method (regression), discrete Markov processes, linear programming, and differential equations. The class is elected by a cross section of students, and usually includes some graduate students. The class format is lecture/discussion.

425/Stat. 425. Introduction to Probability. Math. 215. (N.Excl).

This course is a basic introduction to the mathematical theory of probability. Course topics include fundamental concepts, random variables, expectations, variance, covariance, correlation, independence, conditional probability, Bayes' Theorem, distributions, random walks, law of large numbers and central limit theorem. By itself the course provides a basic introduction to probability and, when followed by Statistics 426 or Statistics 575, the sequence provides a basic introduction to probability and statistics.

450. Advanced Mathematics for Engineers I. Math. 216 or 286. (N.Excl).

Topics include: vector analysis, line and surface integrals, Stokes' and Divergence Theorems, Fourier Series and Mean Square Convergence, Implicit functions, Separation of Variables for heat and wave equation.

471. Introduction to Numerical Methods. Math. 216 or 286 and some knowledge of computer programming. (N.Excl).

Basic mathematical methods used in computing. Polynomial interpolation. Numerical integration. Numerical solution of ordinary differential equations. Linear systems. Monte Carlo Techniques. Round-off error. Students will use a digital computer to solve problems. (Intended for graduates and more qualified undergraduates. Others should elect Math. 371).