Courses in Mathematics (Division 428)

See Mathematics introductory paragraph under the Spring half-term listing for information describing the elementary Mathematics courses.

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 granted to those who have completed or are enrolled in Math. 105 or 106. (Excl).

This course is an in-depth review of high school algebra. It covers linear, quadratic, and polynomial functions and their graphs.

105. Algebra and Analytic Trigonometry. Students with credit for Math. 103 or 104 can elect Math. 105 for only 2 credits. No credit granted to those who have completed or are enrolled in Math 106 or 107. (Excl).

This is a course in college algebra and trigonometry with an emphasis on functions and graphs. Functions covered are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Students completing Math 105/106 are fully prepared for Math 115. Text: Algebra and Trigonometry by Larson and Hostetler, 2nd ed.

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

See description under Spring-half.

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

See description under Spring-half.

215. Analytic Geometry and Calculus III. Math. 116 or 186. (Excl).

See description under Spring-half.

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

See description under Spring-half.

417. Matrix Algebra I. Three courses beyond Math. 110. No credit granted to those who have completed or are enrolled in 513. No credit granted to those who have completed 217. (Excl).

See description under Spring-half.

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

Background and Goals. This course introduces students to useful and interesting ideas of the mathematical theory of probability. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts and calculations are emphasized over proofs. The stated prerequisite is fully adequate preparation. Content. Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, co-variances, central limit theorem. Different instructors will vary the emphasis between these two theories. The material corresponds to most of chapters 1-7 and part of 8 of A First Course in Probability, 3rd ed. (S. Ross) with the omission of sections 2.6, 7.7-7.9, and 8.4-8.5 and many of the long examples.

450. Advanced Mathematics for Engineers I. Math. 216, 286, or 316. (Excl).

Background and Goals. Although this course is designed principally to develop mathematics for application to problems of science and engineering, it also serves as an important bridge for students between the calculus courses and the more demanding advanced courses. Students are expected to learn to read and write mathematics at a more sophisticated level and to combine several techniques to solve problems. Some proofs are given and students are responsible for a thorough understanding of definitions and theorems. Students should have a good command of the material from Math 215, and 216 or 316, which is used throughout the course. A background in linear algebra, e.g. Math 217, is highly desirable. Contents. Topics include a review of curves and surfaces in implicit, parametric, and explicit forms; differentiability and affine approximations; implicit and inverse function theorems; chain rule for 3-space; multiple integrals; scalar and vector fields; line and surface integrals; computations of planetary motion, work, circulation, and flux over surfaces; Gauss' and Stokes' Theorems, derivation of continuity and heat equation. Some instructors include more material on higher dimensional spaces and an introduction to Fourier series. This corresponds to Chapters 2, 3, 5, 7, and 8 and sometimes 4 of Vector Calculus, 3rd ed. (Marsden and Tromba).

471. Introduction to Numerical Methods. Math. 216, 286, or 316; and 217, 417, or 419; and a working knowledge of one high-level computer language. (Excl).

Background and Goals. This is a survey of the basic numerical methods which are used to solve scientific problems. The emphasis is evenly divided between the analysis of the methods and their practical applications. Some convergence theorems and error bounds are proved. The course also provides an introduction to MATLAB, an interactive program for numerical linear algebra, as well as practice in computer programming. Contents. Topics include computer arithmetic, Newton's method for non-linear equations, polynomial interpolation, numerical integration, systems of linear equations, initial value problems for ordinary differential equations, quadrature, partial pivoting, spline approximations, partial differential equations, Monte Carlo methods. This corresponds to chapters 1-6 and sections 7.3-4, 8.3, 10.2, and 12.2 of Numerical Analysis, 4th ed. (Burden and Faires).


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