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 curse options are open to beginning mathematics students. Courses preparatory to the calculus are offered in pairs: a lecture/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. Each
of * Math 112, 113, 115, 185, * and * 195 * is a first course in calculus;
credit 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.

**102. Elementary Algebra (Self-Paced). *** (2). (Excl). *

Self-paced version of Mathematics 101. 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). *

Standard lecture version of Mathematics 104. Review of elementary algebra; rational and quadratic equations; properties of relations, functions, and their graphs; linear and quadratic functions, inequalities, logarithmic and exponential functions and equations. Equivalent to the first half of Mathematics 105/106.

*Section 002 – Permission of Comprehensive Studies Program (CSP). *
This CSP section is designed for students who want better preparation and are willing to devote the necessary effort to do so. The required extra
class time is provided for in-depth analysis of central concepts and group
problem-solving.

**104. Intermediate Algebra (Self-Paced). *** Two to three years high
school mathematics; or Math. 101. One credit for students with credit for
Math. 101. No credit for students with credit for Math. 105 or 106. (2).
(Excl) *

Self-paced version of Math 103. Material covered includes rational and quadratic equations; properties of relations, functions, and their graphs; linear and quadratic functions; inequalities; logarithmic and exponential functions and equations. Course content is equivalent to the first half of Mathematics 105/106.

**105. Algebra and Analytic Trigonometry. *** See table. Students with
credit for Math. 103 or 104 can only elect Math. 105 for 2 credits. No credit
for students with credit for Math 106. (4). (Excl). *

Standard lecture version of Math 106. This course provides passage to
Math 115 for students with weak or incomplete high school mathematics backgrounds.
Students with good mathematics preparation but no trigonometry can elect
Math 107 concurrently with Math 115. Topics covered include number systems, factoring, exponents and radicals, linear and quadratic equations, polynomials, exponential and trigonometric functions, graphs, triangle solutions, and curve sketching. The text has been * Fundamentals of Algebra and Trigonometry *
(Fourth Edition) by Swokowski.

**106. Algebra and Analytic Trigonometry (Self-Paced). *** See table.
Students with credit for Math. 103 or 104 can only elect Math. 106 for 2
credits. No credit for students with credit for Math 105. (4). (Excl). *

Self-paced version of Math 105. There are no lectures or sections. Students
are assigned to tutors in the Mathematics Laboratory and work at their own
pace. Progress is measured by tests following each chapter which must be
passed with at least 80% success for the student to move on to the next
chapter. Up to five versions of each chapter test may be taken to reach this level. Midterms and finals are administered when a group of students
is ready for them. More detailed information is available from the Mathematics
Department office. The text has been * Algebra and Trigonometry: A Functions
Approach * by Keedy and Bittenger.

**107. Trigonometry. *** See table. No credit granted to those who have
completed 105 or 106. (2). (Excl). *

Standard lecture version of Math 108. This course provides the trigonometry
background needed for Math 115. Students with a history of poor performance
in high school mathematics, with or without trigonometry, who plan to continue
in mathematics usually need a more general training than is offered in Math
107, and should elect Math 105 or 106. The text for Math 107 has been Keedy
and Bittinger, * Trig, Triangles, and Functions, * Third Edition.

*Sections 002 and 003 – Permission of Comprehensive Studies Program (CSP). *
These CSP sections are designed for students who want to be certain that they are highly prepared for calculus and are willing to devote the necessary
effort to do so. These CSP sections cover the complete departmental syllabus
and also include precalculus material. The required extra class time is
provided for in-depth analysis of central concepts and group problem-solving.
Material covered includes: triangle solutions, trigonometric functions, graphs and equations, curve sketching, and the analytic geometry of lines
and conic sections. The text has been * Trigonometry: A Functions Approach, *
by Keedy and Bittenger.

**108. Trigonometry (Self-Paced). *** Two or three years of high school
mathematics; or Math. 101. One credit for students with credit for Math.
101. No credit for students with credit for Math. 105 or 106. (2). (Excl). *

Self-paced version of Math 107. Material covered includes circular functions, graphs and properties; trigonometric identities; functions of angles; double and half-angle formulas; inverse functions; solving triangles; laws of sines and cosines.

**109. Pre-Calculus. *** Two years of high school algebra. No credit
for students who already have 4 credits for pre-calculus mathematics courses.
(2). (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.

**110. Pre-Calculus (Self-Paced). *** Two years of high school algebra.
No credit for students who already have 4 credits for pre-calculus mathematics
courses. (2). (Excl). *

Self-paced version of Mathematics 109. See Math 109 for description.

*Note *: Math 112 is a single term calculus course designed primarily
for pre-business and social science students. The course neither presupposes
nor covers any trigonometry. Math 113-114 is a special two-term calculus
sequence for students in the biological sciences. Math 113 begins with a
number of pre-calculus topics; the introduction to calculus is gradual.
Neither 112 nor 113 nor 114 meshes with the standard sequence. Students
who want to keep open the option of going beyond introductory calculus should
elect the standard sequence. Credit is allowed for only one of the first
term calculus courses: 112, 113, 115, 185, 195.

**112. Brief Calculus. *** Three years of high school mathematics or
Math. 105 or 106. Credit is granted for only one course from among Math.
112, 113, 115, and 185. (4). (N.Excl). *

This is a one-term survey course that provides the basics of elementary
calculus. Emphasis is placed on intuitive understanding of concepts and not on rigor. Topics include differentiation with application to curve sketching
and maximum-minimum problems, antiderivatives and definite integrals. Trigonometry
is not used. The text has been Hofman, * Calculus for the Social, Managerial, and Life Sciences, * Second Edition. This course does not mesh with any
of the courses in the regular mathematics sequences.

**113. Mathematics for Life Sciences I. *** Three years of high school
mathematics or Math. 105 or 106. Credit is granted for only one course from
among Math. 112, 113, 115, and 185. (4). (N.Excl). *

Mathematics 113 and 114 constitute a two-term sequence designed for
students anticipating study in fields such as biology, zoology, botany, natural resources, microbiology, medical technology and nursing. Students
in the life sciences who may need a more thorough mathematics background
should elect one of the regular mathematics sequences. The material covered
includes logic, set theory, algebra, calculus, matrices and vectors, probability
and differential equations. Examples are chosen from the life sciences.
The text has been Arya and R. Lardner, * Mathematics for Biological Sciences *
(Second Edition).

*Section 007 – Permission of Comprehensive Studies Program (CSP). *
This CSP section is designed for students who want to be certain that they
develop a thorough understanding of calculus and are willing to devote the
effort necessary on calculus. This section requires extra discussion time
for in-depth analysis of central concepts and group problem-solving.

**114. Mathematics for Life Sciences II. *** Math. 113. Credit is granted
for only one course from among Math. 114, 116, and 186. (4). (N.Excl). *

See Mathematics 113.

**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. (4). (N.Excl). *

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

*Sections 010 and 022: Permission of Comprehensive Studies Program (CSP). *
These CSP sections are designed for students who want to be certain that they develop a thorough understanding of calculus and are willing to devote the effort necessary on calculus. These sections require extra discussion
time for in-depth analysis of central concepts and group problem-solving.

**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, vectors in R to the nth power and matrices, solutions of systems of linear equations by Gaussian elimination, determinants, conic sections, infinite sequences and series. The course generally requires three one-hour examinations and a uniform midterm and final exam.

*Section 042: Permission of Comprehensive Studies Program (CSP). * This
CSP section is designed for students who want to be certain that they develop
a thorough understanding of calculus and are willing to devote the effort
necessary on calculus. This section requires extra discussion time for in-depth
analysis of central concepts and group problem-solving.

**185. Analytic Geometry and Calculus. *** Permission of the Honors
advisor. Credit is granted for only one course from among Math. 112, 113, 115. (4 each). (N.Excl). *

First of a three course sequence, 185/186/285. Topics covered in this course are the same as those for Math 115. Students who elect Math 185/186 cannot also receive Advanced Placement credit for Math 115/116.

**195. Honors Mathematics. *** Permission of the Honors advisor. (4).
(N.Excl). *

Functions of one variable and their representation by graphs. Limits
and continuity. Derivatives and integrals, with applications. Parametric
representations. Polar coordinates. Applications of mathematical induction.
Determinants and systems of linear equations. Text: L. Gillman and R.H.
McDowell * Calculus, * Second Edition. The course is part of the Honors
sequence Mathematics 195, 196, 295, 296. Students must bring basic competence
in high-school algebra and trigonometry. They need not be candidates for
a mathematical career; but they should be willing to regard mathematics
not only as a logical system and as a tool for science, but also as an art.
Evaluation will be based on homework, examinations, and participation in
discussions. The division of class-time between lectures and discussions
will be determined informally according to the students' needs. Students
will be encouraged to establish informal study groups.

**215. Analytic Geometry and Calculus III. *** Math. 116. (4). (N.Excl). *

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

**216. Introduction to Differential Equations. *** Math. 215. Students
with credit for Math. 117 can only elect Math. 216 for 3 credits. (3; 4
beginning IIIa 1982). (N.Excl). *

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

**247. Mathematics of Finance. *** Math. 112 or 115. (3). (N.Excl). *

This course is designed for students who seek an introduction to the mathematical concepts and techniques employed by financial institutions such as banks, insurance companies, and pension funds. Actuarial students, and other mathematics concentrators, should elect Math 424 which covers the same topics but on a more rigorous basis requiring considerable use of the calculus. Topics covered include: various rates of simple and compound interest, present and accumulated values based on these; annuity functions and their application to amortization, sinking funds and bond values; depreciation methods; introduction to life tables, life annuity, and life insurance values. The course is not part of a sequence. Students should possess financial calculators.

**285. Analytic Geometry and Calculus. *** Permission of the Honors
advisor. (4 each). (N.Excl). *

Topics covered in this courses are the same as those for Math 215/216.

**289. Problem Seminar. *** (1). (N.Excl). May be repeated for credit
with permission. *

One of the best ways to develop mathematical abilities is by solving problems using a variety of methods. Familiarity with numerous methods is a great asset to the developing student of mathematics. Methods learned in attacking a specific problem frequently find application in many other areas of mathematics. In many instances, an interest in mathematics and an appreciation of mathematics is better developed by solving problems than by receiving formal lectures on specific topics. The student receives an opportunity to participate more actively in his education and development. This course is intended only for those superior students who have exhibited both ability and interest in doing mathematics. The course is not restricted to Honors students.

**295. Honors Analysis I. *** Math. 196. (4). (N.Excl). *

This course is devoted to the study of functions of several real variables. Topics covered include: (1) Elementary linear algebra: subspaces, bases, dimension, and solution of linear systems by Gauss elimination. (2) Elementary topology: open, closed, compact, and connected sets. Continuous and uniformly continuous functions. (3) Differential and integral calculus for vector-valued functions of a scalar. (4) Differential calculus for scalar valued functions on R to the nth power. (5) Linear transformations: null space, range, matrices, calculations, return to linear systems, norm of a linear transformation. (6) Differential calculus of vector valued mappings on R to the nth power: derivative, chain rule, implicit function theorem, inverse function theorem. Math 296 picks up where 295 ends.

**300/EECS 300. Mathematical Methods in System Analysis. *** Math. 216
or the equivalent. No credit granted to those who have completed 448. (3).
(N.Excl). *

This is a lecture course required for all electrical and computer engineering
students. The primary focus is the operational mathematics necessary for the solution of linear system problems, but the coverage also includes Fourier
series and transforms, and functions of a complex variable, which are needed
in other areas as well. The topics and the times allotted are as follows:
Laplace transforms with particular reference to the solution of differential
equation (2 weeks), linear systems – concepts and solution techniques (3
weeks), Fourier series and the steady state response of systems (2 weeks), theory of functions of a complex variable, leading up to integration in the complex plane (4 weeks), Fourier transforms (2 weeks), and Laplace transform
inversion (1 week). The course grade is determined from graded weekly homework
assignments, two or three hourly quizzes and the final examination. Text: * Mathematical Methods in Electrical Engineering, * by Thomas B.A. Senior
(Cambridge Univ. Press, 1986) (Senior)

**312. Applied Modern Algebra. *** Math. 116, or permission of mathematics
advisor. (3). (N. Excl). *

This course is an introduction to algebraic structures having applications in such areas as switching theory, automata theory and coding theory, and useful to students in mathematics, applied mathematics, electrical engineering and computer science. It introduces elementary aspects of sets, functions, relations, graphs, semigroups, groups, rings, finite fields, partially ordered sets, lattices, and Boolean algebras. Computer oriented applications are introduced throughout.

**350/Aero. Eng. 350. Aerospace Engineering Analysis. *** Math. 216
or the equivalent. (3). (N.Excl). *

This is a three-hour lecture course in engineering mathematics which
continues the development and application of ideas introduced in Math 215
and 216. The course is required in the Aerospace Engineering curriculum, and covers subjects needed for subsequent departmental courses. The major
topics discussed include vector analysis, Fourier series, and an introduction
to partial differential equations, with emphasis on separation of variables.
Some review and extension of ideas relating to convergence, partial differentiation, and integration are also given. The methods developed are used in the formulation
and solution of elementary initial- and boundary-value problems involving, e.g., forced oscillations, wave motion, diffusion, elasticity, and perfect-fluid theory. There are two or three one-hour exams and a two-hour final, plus
about ten homework assignments, or approximately one per week, consisting
largely of problems from the text. The text is * Mathematical Methods in the Physical Sciences * by M.L. Boas.

**371/Engin. 303. Numerical Methods. *** Engineering 103 and preceded
or accompanied by Math. 216. (3). (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. (Graduates and more qualified undergraduates should elect Math. 471).

**385. Mathematics for Elementary School Teachers. *** One year each
of high school algebra and geometry. No credit granted to those who have
completed 485. (3). (Excl). *

Mathematics 385 is an integrated treatment of arithmetic and geometric
concepts important to elementary teachers. Principal emphasis is placed
on the number systems of elementary mathematics: whole numbers, integers, and rational numbers. The School of Education requires successful completion
of Math 385 before the student teaching experience. The text has been Professor
Krause's * Mathematics for Elementary Teachers, * published by Prentice
Hall. The course consists of two hours of lecture and one hour of discussion
per week. Grades are principally determined by midterm and final examination
scores, but the quality of homework performance, as evaluated in the discussion
sections, has bearing on the final grade.

**404. Differential Equations. *** Math. 216 or 286. (3). (N.Excl). *

This is a second course in differential equations which reviews elementary techniques and delves into intermediate methods and equations. Emphasis varies slightly with individual instructor and student needs but usually includes power series expansions about ordinary points and regular singular points, series solutions of second-order differential equations, simultaneous linear equations (solutions by matrices), Laplace transform, numerical methods, nonlinear equations, and phase-plane methods. The format is lecture/discussion, and the course is often elected by engineering students and students of the natural, physical and social sciences.

**412. First Course in Modern Algebra. *** Math. 215 or 285, or permission
of instructor. No credit granted to those who have completed 512. Students
with credit for 312 should take 512 rather than 412. (3). (N.Excl). *

This course assumes a level of mathematical maturity and sophistication consistent with advanced level courses. It is a course elected primarily by mathematics majors including teaching certificate candidates and by a small number of master's degree candidates. Normally it is the first "abstract" course encountered by students in mathematics. Most students continue with Mathematics 513 for which Mathematics 412 serves as a prerequisite. Course topics include basic material on sets with special emphasis on mappings, equivalence relations, quotients and homomorphisms; groups and subgroups; rings, integral domains and polynomial rings; and fields and simple extensions. Students seeking a more comprehensive presentation should consider Mathematics 512.

**413. Calculus for Social Scientists. *** Not open to freshmen, sophomores
or mathematics concentrators. (3). (N.Excl). *

A one-term course designed for students who require an introduction to the ideas and methods of the calculus. The course begins with a review of algebra and then surveys analytic geometry, derivatives, maximum and minimum problems, integrals, integration, and partial derivatives. Applications to business and economics are given whenever possible, and the level is always intuitive rather than highly technical. This course should not be taken by those who have had a previous calculus course or plan to take more than one or two further courses in mathematics. The course is specially designed for graduate students in the social sciences.

**416. Theory of Algorithms. *** Math. 312 or 412 or ECE 367; and CCS
374. (3). (N. Excl). *

This course will introduce the students to various algorithms used to solve mathematical problems. We will discuss the efficiency of these methods and areas of current research. The interaction between mathematics and computer science will be stressed. Topics will include: enumerative algorithms and their relation to sieve methods and sequence counting; generative algorithms designed to output all possible objects of a given type; algorithms for selecting an object at random; and graphical algorithms useful in circuit design and flow problems. Some elementary complexity analysis will be included with discussion of run and storage space restrictions, asymptotic methods, and NP completeness. The class format will be lecture/discussion. The grades will be based on homework and take-home exams.

**417. Matrix Algebra I. *** Three terms of college mathematics. No
credit granted to those who have completed 513. (3). (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.
The text has been * Linear Algebra and Its Applications * by Strang.

**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.

**448. Operational Methods for Systems Analysis. *** Math. 450 or 451.
No credit granted to those who have completed 300. (3). (N.Excl). *

Introduction to complex variables. Fourier series and integrals. Laplace
transforms; application to systems of linear differential equations; theory
of weighting functions, frequency response function, transfer function;
stability criteria, including those of Hurwitz-Routh and Nyquist. Text has
been Kaplan's * Operational Methods for Linear Systems. *

**450. Advanced Mathematics for Engineers I. *** Math. 216 or 286.
No credit granted to those who have completed 305. (4). (N.Excl). *

Topics in advanced calculus including vector analysis, improper integrals, line integrals, partial derivatives, directional derivatives, and infinite
series. Emphasis on applications. Text: Kaplan's * Advanced Calculus *
(Second Edition).

**451. Advanced Calculus I. *** Math. 215 and one course beyond Math.
215; or Math. 285. Intended for concentrators; other students should elect
Math. 450. (3). (N.Excl). *

Single variable calculus from a rigorous standpoint. A fundamental course for further work in mathematics.

**454. Fourier Series and Applications. *** Math. 216 or 286. Students
with credit for Math. 455 or 554 can elect Math. 454 for 1 credit. (3).
(N.Excl). *

Othogonal functions. Fourier series, Bessel function, Legendre polynomials
and their applications to boundary value problems in mathematical physics.
The text will probably be Churchill's * Fourier Series and Boundary Value
Problems, * Third Edition.

**471. Introduction to Numerical Methods. *** Math. 216 or 286 and some
knowledge of computer programming. (3). (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. The text is Burden, Faires, and Reynolds, * Numerical Analysis. * (Intended for graduates and more qualified undergraduates.
Others should elect Math. 371).

**481. Introduction to Mathematical Logic. *** Math. 412 or 451; or
permission of instructor. (3). (N.Excl). *

The course covers the syntax and semantics of the languages of propositional
and first-order predicate logic. In the first third of the course, the notion
of a formal language is introduced and propositional connectives, tautologies, and the notion of tautological consequence is studied. The heart of the
course is the study of first-order predicate languages and their models.
The completeness and compactness theorems are proved and applications such
as non-standard analysis will be covered. No background in logic is required, but a student should be familiar with some abstract mathematics and have
experience in constructing proofs. Evaluation is by problem sets and exams, either take-home or in-class. The usual text is * A Mathematical Introduction
to Logic * by H.B. Enderton.

**486. Concepts Basic to Secondary Mathematics. *** Math. 215. (3).
(N.Excl). *

Mathematics 486 is a specialized course for junior and senior math majors
and minors who may teach high school mathematics. The purpose of the course
is to strengthen students' understandings of the basic mathematical concepts that underlie the algebra, geometry, and pre-calculus math taught in high
schools. The principal emphasis is on algebraic ideas. Six or seven units
are ordinarily covered. A possible sequence of topics for the 1981 Fall
Term is: * Absolute Value; Number Theory; Logic and Set Theory; Development of Elementary Algebra from the Field Axioms; Mathematical
Induction; Theory of Equations * (including the solution by radicals
of 3rd and 4th degree equations and a brief introduction to Galois Theory); * Problem Solving * (centered around the kinds of problems encountered
in Math Contests). This is a required course for high school math teachers.
It should be completed before student teaching. The calculus sequence is
a prerequisite. In many ways, the course supplements Math 412, providing
concrete examples for abstract concepts encountered in Math 412. Taking
486 prior to Math 412 would be helpful. The course is a combination of lecture
and discussion. One homework paper is required each week. It is expected that each paper will reflect between six and ten hours work on problem sets.
Grades are principally determined by the quality of these papers. The two-hour
final examination counts for about 20% of the final grade. No text is used.
Students are given mimeographed material over each topic. This includes
assigned problems and explanatory material. There are many helpful library
texts on Number Theory, Theory of Equations, Logic, and Set Theory, but
in general it is essential that the student attend all lectures and participate
in the discussion in order to be properly prepared for the assignments.

**490. Introduction to Topology. *** Math. 450 or 451. (3). (N.Excl). *

The topology of subsets of Euclidean space. Simplicial complexes, simplicial approximation, manifolds and fixed point theorems. Concurrent registration in advanced calculus and Math 412 (or 417) will be useful but not necessary. Topological ideas permeate much of modern mathematics, and this course will stress developing one's intuition about the subject.

**525/Stat. 510. Probability Theory. *** Math.
450 or 451; or permission of instructor. Students with credit for Math.
425/Stat. 425 can elect Math. 525/Stat. 510 for 1 credit. (3). (N.Excl). *

This course covers basic topics in probability, including random variables, distributions, conditioning, independence, expectation and generating functions, special distributions and their relations, transformations, non-central distributions, the multivariate normal distribution, convergence concepts, and limit theorems.

University of Michigan | College of LS&A | Student Academic Affairs | LS&A Bulletin Index

This page maintained by LS&A Academic Information and Publications, 1228 Angell Hall

The Regents of the University of Michigan,

Ann Arbor, MI 48109 USA +1 734 764-1817

Trademarks of the University of Michigan may not be electronically or otherwise altered or separated from this document or used for any non-University purpose.