Credit Exclusions: A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

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 year of Math. 105/106.

Advisory Prerequisite: Only open to designated summer half-term Bridge students.

Credit Exclusions: A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

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 year of Math. 105/106.

Advisory Prerequisite: Only open to designated summer half-term Bridge students.

Credit Exclusions: A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

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 year of Math. 105/106.

Advisory Prerequisite: Only open to designated summer half-term Bridge students.

Credit Exclusions: A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

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 year of Math. 105/106.

Advisory Prerequisite: Only open to designated summer half-term Bridge students.

Credit Exclusions: A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

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 year of Math. 105/106.

Advisory Prerequisite: Only open to designated summer half-term Bridge students.

Credit Exclusions: A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

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 year of Math. 105/106.

Advisory Prerequisite: Only open to designated summer half-term Bridge students.

Credit Exclusions: A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

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 year of Math. 105/106.

Advisory Prerequisite: Only open to designated summer half-term Bridge students.

Credit Exclusions: A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

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 year of Math. 105/106.

Advisory Prerequisite: Only open to designated summer half-term Bridge students.

Credit Exclusions: A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

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 year of Math. 105/106.

Advisory Prerequisite: Only open to designated summer half-term Bridge students.

Credit Exclusions: Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: MATH 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete MATH 105 are fully prepared for MATH 115.

Content: This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 110 (Pre-Calculus (Self-Paced)) is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

Subsequent Courses: The course prepares students for MATH 115.

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

Credit Exclusions: Credit can be earned for only one of MATH 215, 255, or 285.

Background and Goals: The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof.

Content: Topics include vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation; line, surface, and volume integrals and applications; vector fields and integration; Green's Theorem and Stokes' Theorem. There is a weekly computer lab using MAPLE.

Alternatives: Math 285 (Honors Calculus III) is a somewhat more theoretical course which covers the same material. Math 255 (Applied Honors Calculus III) is also an alternative.

Subsequent Courses: For students intending to major in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math 217 (Linear Algebra). Students who intend to take only one further mathematics course and need differential equations should take Math 216 (Intro. to Differential Equations).

Advisory Prerequisite: MATH 116

Credit Exclusions: Credit can be earned for only one of MATH 216, 256, 286, or 316.

Background and Goals: For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH 216-417 (or MATH 419) and MATH 217-316. The sequence MATH 216-417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Math majors and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316.

Content: MATH 216 is a basic course on differential equations, intended for engineers and other scientists who need to apply the techniques in their work. The lectures are accompanied by a computer lab and recitation section where students have the opportunity to discuss problems and work through computer experiments to further develop their understanding of the concepts of the class. Topics covered include some material on complex numbers and matrix algebra, first and second order linear and non-linear systems with applications, introductory numerical methods, and elementary Laplace transform techniques.

Alternatives: MATH 286 (Honors Differential Equations) covers much of the same material in the honors sequence. The sequence MATH 217 (Linear Algebra)-MATH 316 (Differential Equations) covers all of this material and substantially more at greater depth and with greater emphasis on the theory. MATH 256 (Applied Honors Calculus IV) is also an alternative.

Subsequent Courses: MATH 404 (Intermediate Diff. Eq.) covers further material on differential equations. MATH 217 (Linear Algebra) and MATH 417 (Matrix Algebra I) cover further material on linear algebra. MATH 371 ((ENGR 303) Numerical Methods) and MATH 471 (Intro. To Numerical Methods) cover additional material on numerical methods.

Advisory Prerequisite: MATH 116, 119, 156, 176, 186, or 296.

Designed especially for Honors students.

Advisory Prerequisite: Permission of instructor.

Credit Exclusions: Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled MATH 513.

Many problems in science, engineering, and mathematics are best formulated in terms of matrices — rectangular arrays of numbers. This course is an introduction to the properties of and operations on matrices with a wide variety of applications. The main emphasis is on concepts and problem-solving, but students are responsible for some of the underlying theory. Diversity rather than depth of applications is stressed. This course is not intended for mathematics concentrators, who should elect MATH 217 or 513 (Honors). Topics include matrix operations, echelon form, general solutions of systems of linear equations, vector spaces and subspaces, linear independence and bases, linear transformations, determinants, orthogonality, characteristic polynomials, eigenvalues and eigenvectors, and similarity theory. Applications include linear networks, least squares method (regression), discrete Markov processes, linear programming, and differential equations.

MATH 419 is an enriched version of MATH 417 with a somewhat more theoretical emphasis. MATH 217 (despite its lower number) is also a more theoretical course which covers much of the material of MATH 417 at a deeper level. MATH 513 is an Honors version of this course, which is also taken by some mathematics graduate students. MATH 420 is the natural sequel, but this course serves as prerequisite to several courses: MATH 452, 462, 561, and 571.

Advisory Prerequisite: MATH,Three courses beyond MATH 110. Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513.

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, calculations, and derivations are emphasized. The course will make essential use of the material of MATH 116 and 215.

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, covariances. Different instructors will vary the emphasis.

Alternatives: MATH 525 (Probability Theory) is a similar course for students with stronger mathematical background and ability.

Subsequent Courses: STATS 426 (Intro. To Math. Stat.) is a natural sequel for students. MATH 423 (Mathematics of Finance) and MATH 523 (Risk Theory) include many applications of probability theory.

Advisory Prerequisite: MATH 215

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 354 or 454.

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, as is familiarity with Maple software. 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; and derivation of continuity and heat equation. Some instructors include more material on higher dimensional spaces and an introduction to Fourier series. MATH 450 is an alternative to MATH 451 as a prerequisite for several more advanced courses. MATH 454 and 555 are the natural sequels for students with primary interest in engineering applications.

Advisory Prerequisite: MATH 215, 255, or 285.

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 371 or 472.

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 proven. The course also provides an introduction to MATLAB, an interactive program for numerical linear algebra, as well as practice in computer programming. One goal of the course is to show how calculus and linear algebra are used in numerical analysis. Topics may 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, 2-point boundary value problems, and the Dirichlet problem for the Laplace equation. MATH 371 is a less sophisticated version intended principally for sophomore and junior engineering students; the sequence MATH 571-572 is mainly taken by graduate students, but should be considered by strong undergraduates. MATH 471 is good preparation for MATH 571 and 572, although it is not prerequisite to these courses.

Advisory Prerequisite: MATH 216, 256, 286, or 316; and 214, 217, 417, or 419; and a working knowledge of one high-level computer language. No credit granted to those who have completed or are enrolled in MATH 371 or 472.

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 385.

The history, development, and logical foundations of the real number system and of numeration systems including scales of notation, cardinal numbers, and the cardinal concept; and the logical structure of arithmetic (field axioms) and relations to the algorithms of elementary school instruction. Simple algebra, functions, and graphs. Geometric relationships. For persons teaching in or preparing to teach in the elementary school.

Advisory Prerequisite: One year of high school algebra or permission of the instructor.

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 385.

The history, development, and logical foundations of the real number system and of numeration systems including scales of notation, cardinal numbers, and the cardinal concept; and the logical structure of arithmetic (field axioms) and relations to the algorithms of elementary school instruction. Simple algebra, functions, and graphs. Geometric relationships. For persons teaching in or preparing to teach in the elementary school.

Advisory Prerequisite: One year of high school algebra or permission of the instructor.

This course is intended for graduate students in fields other than mathematics who require mathematical skills not otherwise available though existing courses.

Advisory Prerequisite: Graduate standing in a field other than Mathematics and permission of instructor.

Designed for individual students who have an interest in a specific topic (usually that has stemmed from a previous course). An individual instructor must agree to direct such a reading, and the requirements are specified when approval is granted.

Advisory Prerequisite: Graduate standing and permission of instructor.

Election for dissertation work by doctoral student not yet admitted as a Candidate.

Advisory Prerequisite: Election for dissertation work by doctoral student not yet admitted as a Candidate. Graduate standing.

Graduate School authorization for admission as a doctoral Candidate. N.B. The defense of the dissertation (the final oral examination) must be held under a full term Candidacy enrollment period.

Enforced Prerequisites: Graduate School authorization for admission as a doctoral Candidate