Senior and Graduate Math Course Offerings 2006 Summer
| MATH 4377 Advanced Linear Algebra (Summer I)(section# 06264) | |
| Time: | 12:00-2:00PM - MTWTH - 202-SEC |
| Instructor: | M. Ru |
| Prerequisites: | Math 2431 and minimum 3 hours of 3000 level math. |
| Text(s): | Linear Algebra and Its Applications, Fourth Edition by Gilbert Strang, Thomson Brooks/Cole 2006. |
| Description: | Solving Linear Equations, general theory of vector spaces and linear maps, algebra of polynomials, determinants. |
| MATH 4378 Advanced Linear Algebra II (Summer I) (section# 06265) | |
| Time: | 1200-0200PM - MTWTH - 201-SEC |
| Instructor: | Murray |
| Prerequisites: | Math 4377 or consent of instructor. |
| Text(s): | Linear Algebra and Its Applications, Fourth Edition by Gilbert Strang, Thomson Brooks/Cole 2006. |
| Description: | Topics to be covered in this course include linear equations, vector spaces, polynomials, linear transformations and matrices. |
| MATH 5333 Analysis (Summer I)(section# 06284) | |
| Time: | On line course (arrange time) |
| Instructor: | Etgen |
| Prerequisites: | Consent of instructor. |
| Text(s): | Analysis by Steven R. Lay, 4th ed. |
| Description: | A survey of the concepts of limit, continuity, differentiation and integration for functions of one variable and functions of several variables; selected applications. |
| MATH 5383: Number Theory (Online)(section#06285) | |
| Time: | arrange |
| Instructor: | M. Ru |
| Prerequisites: | Graduate standing or consent of instructor. |
| Text(s): | Discovering Number Theory by Jeffrey J. Holt and John W. Jones, W.H. Freeman and Company, New York, 2001. |
| Description: | Number theory is a subject that has interested people for thousand of years. This course is a one-semester long graduate course on number theory. Topics to be covered include divisibility and factorization, linear Diophantine equations, congruences, applications of congruences, solving linear congruences, primes of special forms, the Chinese Remainder Theorem, multiplicative orders, the Euler function, primitive roots, quadratic congruences, representation problems and continued fractions. There are no specific prerequisites beyond basic algebra and some ability in reading and writing mathematical proofs. The method of presentation in this course is quite different. Rather than simply presenting the material, students first work to discover many of the important concepts and theorems themselves. After reading a brief introductory material on a particular subject, students work through electronic materials that contain additional background, exercises, and Research Questions, using Java applets. The research questions are typically more open ended and require students to respond with a conjecture and proof. We then present the theory of the material which the students have worked on, along with the proofs. The homework problems contain both computational problems and questions requiring proofs. It is hoped that students, through this course, not only learn the material, learn how to write the proofs, but also gain valuable insight into some of the realities of mathematical research by developing the subject matter on their own. |
| MATH 5385 Statistics (Summer IV)(section# 06286) | |
| Time: | On line course |
| Instructor: | Peters |
| Prerequisites: | Math 1432: Calculus II or consent of instructor. |
| Text(s): | Applied Statistics with Microsoft Exceel, by Gerald Keller, Duxbury 2001. ISBN:0534382029 |
| Description: | Fundamentals of probability and statistics. Descriptive and inferential methods of statistics. |
| MATH 5397 Discrete Mathematics (Summer I )(section# 07848) | |
| Time: | On line course |
| Instructor: | Kaiser |
| Prerequisites: | |
| Text(s): | Discrete Mathematics and Its Applications, Kenneth H. Rosen, fifth edition. McGraw Hill, ISBN 0-07-242434-6 and lecture notes on Basic Set Theory, an axiomatic approach. Recommended book: "Introduction to Set Theory" by Karel Hrbacek and Thomas Jech, Second Edition, ISBN 0-8247-7074-9 |
| Description: | Syllabus: Chapter 1, Chapter 3 (3.3), Chapter 7 (7.1, 7.4, 7.5, 7.6) from the Rosen book. The Zermelo Fraenkel Axioms; Cardinals, Ordinals and the Axiom of Choice in form of my own posted notes. Note: For the online 5397 courses, students have to turn in HW by e-mail and as LaTex files. |
| MATH 6304 Theory of Matrices (Summer III)(section# 07990) | |
| Time: | 0100-0200PM - MTWTH - 348-PGH |
| Instructor: | Dinesh Singh |
| Prerequisites: | |
| Text(s): | Matrix Theory by Horn and Johnson |
| Description: | This course is designed for the use of graduate students of mathematics, engineering, the physical sciences and economics for whom matrix theory is relevant and useful. The emphasis shall be on canonical forms and the spectral theorem with applications. The course is good for students of pure mathematics and it is algorithmic enough so that numerical students can also gain from it. |
| MATH 6397 Logic with Applications (Summer I) (section# 07852) | |
| Time: | 10:00-12:00n - MTWTH - 345-PGH |
| Instructor: | K. Kaiser |
| Prerequisites: | |
| Text(s): | Logic for Applications, second edition, by Anil Nerode and Richard A. Shore, Text and Monographs in Computer Science, Springer Verlag. |
| Description: | Propositional Logic, Predicate Logic, Ultraproducts of Relational Systems with Applications to Algebra and Analysis. |
| MATH 6397: Convex Sets (Summer IV)(secton#07859) | |
| Time: | 10:00-12:00n - MTWTH - 345-PGH |
| Instructor: | G. Johnson |
| Prerequisites: | Linear algebra and analysis. |
| Text(s): | TBA |
| Description: | This will be a careful study of convex sets in real inner product spaces. Rotundness, supporting planes, unique nearest points, unique farthest points and characterizations of convexity. |