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

**101. Elementary Algebra. *** Open only to
summer half-term Bridge students. (Excl). *

Material covered includes integers, rationals, and real numbers;
linear, fractional, and quadratic expressions and equations, polynomials
and factoring; exponents, powers and roots; functions.

**103. Intermediate Algebra. *** Only open to
designated summer half-term Bridge students. 1 credit for students
with credit for Math. 101. 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 can elect Math. 105 for only 2 credits.
No credit granted to those who have completed or are enrolled
in Math 106. (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. *** See
Elementary Courses above. Credit usually is granted
for only one course from among Math. 112, 113, 115, 185, and 195.
(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, 186, and 196. (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 and to a number of applications of probability
to a variety of fields including genetics, economics, geology, business, and engineering. 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 1.6, 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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