All mathematics courses require a minimum of one year each of high school algebra and geometry. In order to accommodate diverse backgrounds and interests, several course options are open to beginning mathematics students. Some courses preparatory to the calculus are offered in pairs: a recitation format and a self-paced version of the same material. The even-numbered course of each pair is self-paced. Department policy limits a student to a total of 4 credits for courses numbered 110 and below.

MATH 103/104 is the first half of MATH 105/106; MATH 107/108 is the second half. MATH 112 is designed for students of business and social sciences who require only one term of calculus. The sequence 113-114 is designed for students of the life sciences who require only one year of calculus. The sequence 115-116-215-216 is appropriate for most students who want a complete introduction to the calculus. Students planning to concentrate in mathematics should take Math 217 instead of Math 216. Math 217 is designed to provide a smoother transition to the more theoretical material in upper-division mathematics courses. Each of MATH 112, 113, 115, 185, and 195 is a first course in calculus; credit ordinarily can be received for only one course from this list. Math 109/110 is designed for students whose preparation includes all of the prerequisites for calculus but who are unable to complete one of the calculus courses successfully. Math 109/110 will be offered as a 7-week course during the second half of each term.

Admission to MATH 185 or 195 requires permission of a mathematics Honors advisor (1210 Angell Hall). Students who have performed well on the College Board Advanced Placement exam may receive credit and advanced placement in the sequence beginning with Math 115. Other students who have studied calculus in high school may take a departmental placement examination during the first week of the fall term to receive advanced placement WITHOUT CREDIT in the MATH 115 sequence. No advanced placement credit is granted to students who elect MATH 185. Students electing MATH 195 receive advanced placement credit after Math 296 is satisfactorily completed.

NOTE: [For most Mathematics courses the Cost of books and materials is $25-50] [WL:3 for all courses]

**101. Elementary Algebra. *** (2). (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. *** 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. (2). (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 in Bulletin. 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. (4). (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. (2). (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.

**115. Analytic Geometry and Calculus I. *** See
table in Bulletin. (Math. 107 may be elected concurrently.) Credit
is granted for only one course from among Math. 112, 113, 115, and 185. (4). (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. (4). (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. (4). (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. (4). (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. (3). (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. (3). (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. (4). (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. (3). (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).

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