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# Courses in Mathematics

This page was created at 6:38 PM on Sun, Jun 30, 2002.

## Summer Half-Term Courses

### MATH 417. Matrix Algebra I.

#### Instructor(s):

Prerequisites: 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 Math. 513. (3).

Credits: (3).

Course Homepage: No homepage submitted.

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 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.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

### MATH 419. Linear Spaces and Matrix Theory.

#### Instructor(s):

Prerequisites: Four terms of college mathematics 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. (3).

Credits: (3).

Course Homepage: No homepage submitted.

Math 419 covers much of the same ground as Math 417 but presents the material in a somewhat more abstract way in terms of vector spaces and linear transformations instead of matrices. There is a mix of proofs, calculations, and applications with the emphasis depending somewhat on the instructor. A previous proof-oriented course is helpful but by no means necessary. Basic notions of vector spaces and linear transformations: spanning, linear independence, bases, dimension, and matrix representation of linear transformations; determinants; eigenvalues, eigenvectors, Jordan canonical form, and inner-product spaces; unitary, self-adjoint, and orthogonal operators and matrices, and applications to differential and difference equations.

Math 417 is less rigorous and theoretical and more oriented to applications. Math 217 is similar to Math 419 but slightly more proof-oriented. Math 513 is much more abstract and sophisticated. Math 420 is the natural sequel, but this course serves as prerequisite to several courses: Math 452, 462, 561, and 571.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

### MATH 425 / STATS 425. Introduction to Probability.

#### Instructor(s):

Prerequisites: Math. 215, 255, or 285. (3).

Credits: (3).

Course Homepage: No homepage submitted.

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. 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, and covariances. Different instructors will vary the emphasis. Math 525 is a similar course for students with stronger mathematical background and ability. Stat 426 is a natural sequel for students interested in statistics. Math 523 includes many applications of probability theory.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

### MATH 450. Advanced Mathematics for Engineers I.

#### Instructor(s):

Prerequisites: Math. 215, 255, or 285. (4).

Credits: (4).

Course Homepage: No homepage submitted.

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.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

### MATH 471. Introduction to Numerical Methods.

#### Instructor(s):

Prerequisites: Math. 216, 256, 286, or 316; and 217, 417, or 419; and a working knowledge of one high-level computer language. (3).

Credits: (3).

Course Homepage: No homepage submitted.

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.

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### MATH 485. Mathematics for Elementary School Teachers and Supervisors.

#### Instructor(s):

Prerequisites: One year of high school algebra. No credit granted to those who have completed or are enrolled in Math. 385. (2). May not be included in a concentration plan in mathematics. Does not apply to any math degree programs.

Credits: (3; 2 in the half-term).

Course Homepage: No homepage submitted.

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.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

#### Instructor(s):

Prerequisites: Graduate standing in a field other than mathematics. (1-4). (INDEPENDENT).

Credits: (1-4).

Course Homepage: No homepage submitted.

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

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Instructor

### MATH 700. Directed Reading and Research.

#### Instructor(s):

Credits: (1-3).

Course Homepage: No homepage submitted.

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.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Instructor

### MATH 990. Dissertation/Precandidate.

#### Instructor(s):

Prerequisites: Election for dissertation work by doctoral student not yet admitted as a Candidate. Graduate standing. (1-4). (INDEPENDENT). May be repeated for credit.

Credits: (1-8; 1-4 in the half-term).

Course Homepage: No homepage submitted.

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

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Instructor

### MATH 995. Dissertation/Candidate.

#### Instructor(s):

Prerequisites: Graduate School authorization for admission as a doctoral Candidate. Graduate standing. (4). (INDEPENDENT). May be repeated for credit.

Credits: (8; 4 in the half-term).

Course Homepage: No homepage submitted.

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.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

## Spring Half-Term Courses

### MATH 417. Matrix Algebra I.

#### Instructor(s):

Prerequisites: 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 Math. 513. (3).

Credits: (3).

Course Homepage: No homepage submitted.

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 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.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

### MATH 425 / STATS 425. Introduction to Probability.

#### Instructor(s):

Prerequisites: Math. 215, 255, or 285. (3).

Credits: (3).

Course Homepage: No homepage submitted.

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. 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, and covariances. Different instructors will vary the emphasis. Math 525 is a similar course for students with stronger mathematical background and ability. Stat 426 is a natural sequel for students interested in statistics. Math 523 includes many applications of probability theory.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

### MATH 425 / STATS 425. Introduction to Probability.

#### Instructor(s):

Prerequisites: Math. 215, 255, or 285. (3).

Credits: (3).

Course Homepage: No homepage submitted.

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. 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, and covariances. Different instructors will vary the emphasis. Math 525 is a similar course for students with stronger mathematical background and ability. Stat 426 is a natural sequel for students interested in statistics. Math 523 includes many applications of probability theory.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

### MATH 451. Advanced Calculus I.

#### Instructor(s):

Prerequisites: Math. 215 and one course beyond Math. 215; or Math. 255 or 285. Intended for concentrators; other students should elect Math. 450. (3).

Credits: (3).

Course Homepage: No homepage submitted.

Background and Goals. This course has two complementary goals: (1) a rigorous development of the fundamental ideas of calculus, and (2) a further development of the student's ability to deal with abstract mathematics and mathematical proofs. The key words here are "rigor" and "proof"; almost all of the material of the course consists in understanding and constructing definitions, theorems (propositions, lemmas, etc.), and proofs. This is considered one of the more difficult among the undergraduate mathematics courses, and students should be prepared to make a strong commitment to the course. In particular, it is strongly recommended that some course which requires proofs (such as Math 412) be taken before Math 451.

Content. Topics covered include: logic and techniques of proofs; sets, functions, and relations; cardinality; the real number system and its topology; infinite sequences, limits, and continuity; differentiation; integration; the Fundamental Theorem of Calculus; infinite series; and sequences and series of functions.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

### MATH 454. Boundary Value Problems for Partial Differential Equations.

#### Instructor(s):

Prerequisites: Math. 216, 256, 286, or 316. Students with credit for Math. 354 can elect Math. 454 for one credit. (3).

Credits: (3).

Course Homepage: No homepage submitted.

This course is devoted to the use of Fourier series and other orthogonal expansions in the solution of boundary-value problems for second-order linear partial differential equations. Emphasis is on concepts and calculation. The official prerequisite is ample preparation. Classical representation and convergence theorems for Fourier series; method of separation of variables for the solution of the one-dimensional heat and wave equation; the heat and wave equations in higher dimensions; spherical and cylindrical Bessel functions; Legendre polynomials; methods for evaluating asymptotic integrals (Laplace's method, steepest descent); Fourier and Laplace transforms; applications to linear input-output systems; analysis of data smoothing and filtering; signal processing; time-series analysis; and spectral analysis. Both Math 455 and 554 cover many of the same topics but are very seldom offered. Math 454 is prerequisite to Math 571 and 572, although it is not a formal prerequisite, it is good background for Math 556.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

#### Instructor(s):

Prerequisites: Graduate standing in a field other than mathematics. (1-4). (INDEPENDENT).

Credits: (1-4).

Course Homepage: No homepage submitted.

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

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Instructor

### MATH 561 / IOE 510 / SMS 518. Linear Programming I.

#### Instructor(s):

Prerequisites: Math. 217, 417, or 419. (3). CAEN lab access fee required for non-Engineering students.

Credits: (3).

Lab Fee: CAEN lab access fee required for non-Engineering students.

Course Homepage: No homepage submitted.

Formulation of problems from the private and public sectors using the mathematical model of linear programming. Development of the simplex algorithm: duality theory and economic interpretations. Postoptimality (sensitivity) analysis: applications and interpretations. Introduction to transportation and assignment problems: special purpose algorithms and advanced computational techniques. Students have opportunities to formulate and solve models developed from more complex case studies and use various computer programs.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

### MATH 700. Directed Reading and Research.

#### Instructor(s):

Credits: (1-3).

Course Homepage: No homepage submitted.

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.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Instructor

### MATH 990. Dissertation/Precandidate.

#### Instructor(s):

Prerequisites: Election for dissertation work by doctoral student not yet admitted as a Candidate. Graduate standing. (1-4). (INDEPENDENT). May be repeated for credit.

Credits: (1-4).

Course Homepage: No homepage submitted.

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

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Instructor

### MATH 995. Dissertation/Candidate.

#### Instructor(s):

Prerequisites: Graduate School authorization for admission as a doctoral Candidate. Graduate standing. (4). (INDEPENDENT). May be repeated for credit.

Credits: (4).

Course Homepage: No homepage submitted.

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.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Instructor

## Spring/Summer Term Courses

#### Instructor(s):

Prerequisites: Graduate standing in a field other than mathematics. (1-4). (INDEPENDENT).

Credits: (1-4).

Course Homepage: No homepage submitted.

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

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Instructor

### MATH 700. Directed Reading and Research.

#### Instructor(s):

Credits: (1-3).

Course Homepage: No homepage submitted.

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.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Instructor

### MATH 990. Dissertation/Precandidate.

#### Instructor(s):

Prerequisites: Election for dissertation work by doctoral student not yet admitted as a Candidate. Graduate standing. (1-8). (INDEPENDENT). May be repeated for credit.

Credits: (1-8; 1-4 in the half-term).

Course Homepage: No homepage submitted.

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

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 1

### MATH 995. Dissertation/Candidate.

#### Instructor(s):

Prerequisites: Graduate School authorization for admission as a doctoral Candidate. Graduate standing. (8). (INDEPENDENT). May be repeated for credit.

Credits: (8; 4 in the half-term).

Course Homepage: No homepage submitted.

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.

 Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Instructor

### Undergraduate Course Listings for MATH.

This page was created at 6:38 PM on Sun, Jun 30, 2002.