FALL 2003 COURSES

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Mathematics Course Descriptions:

MATH. 70100 - Functions of a Real Variable

M/W, 10:15-11:30 a.m., Rm. 5417, 4.5 credits, Prof. Kaplan, [45295]

 

MATH. 70300 - Functions of Complex Variable

M/W, 12:30-1:45 p.m., Rm. 5417, 4.5 credits, Prof. Randol, [45298] 

 

MATH. 70500 - Algebra I

T/R, 2:00-3:15 p.m., Rm. 5417, 4.5 credits, Prof. Moskowitz, [45301]

 

MATH. 70700 - Topology I

T/R, 11:45 a.m.-1:00 p.m., Rm. 5417, 4.5 credits, Prof. Bendersky, [45303]

 

MATH. 70900 - Differential Geometry I

M/W, 2:00-3:15 p.m., Rm. 6417, 4.5 credits, Prof. Rocha, [45306]   

 

MATH. 71100 - Logic I

M/W, 4:15-5:30 p.m., Rm. 6417, 4.5 credits, Prof. Mate, [45310]    

 

MATH. 81700 - Topology II

T/R, 2:00-3:15 p.m., Rm. 4433 (T) & 4419 (R), 4.5 credits, Prof. Vasquez, [45313] 

 

MATH. 82530 Topol, Riemann Surf & Strings

T, 10:30 a.m.-12:30 p.m., Rm. 4422, 3 credits, Prof. Sullivan, [45325]

NOTE: Class will start on 9/16/03

 

MATH. 83530 - Algebra II

M, 4:15-6:15 p.m., Rm. 5417, 3 credits, Prof. Szpiro, [45316]

 

MATH. 87100 - Group Theory
F, 11:45 a.m.-1:45 p.m., Rm. 6417, 3 credits, Prof. Baumslag, [45326]

The objective of this course is to cover, not necessarily in any detail, many of the basic topics in group theory. A tentative list of subjects that will be touched on include the following: 

Finite groups, the Jordan--Holder theorem, the Krull-Remak-Schmidt theorem, classification of finite simple groups, extension theory,  abelian groups, countable abelian groups, varieties of groups, nilpotent, solvable and generalized solvable groups, hyperbolic and automatic groups, free groups, groups given by generators and defining relations and algorithmic problems about groups.  

The textbook for the course will be Rotman's book: An Introduction to  Group Theory (revised edition). 

Additional references:  

A.G. Kurosh, The theory of groups, Volumes 1 and 2. Chelsea Publishing Company, New York. 

W. Magnus, A. Karrass and D. Solitar, Combinatorial Group Theory. Chelsea Publishing Company, New York. 

R.C. Lyndon and P.E. Schupp, Combinatorial Group Theory.  Chelsea Publishing Company, New York. 

G. Baumslag, Topics in Group Theory. Birkhauser. 

MATH 89901: Indep. Research in Analysis        1-12 cr.

MATH 89902: Indep. Research in Alg. & Num. Theory   1-12 cr.

MATH 89903: Indep. Research in Geom. & Topology    1-12 cr.

MATH 89904: Indep. Research in Logic   1-12 cr.

MATH 89905: Indep. Research in Applied Math.    1-12 cr.

MATH 90000: Dissertation Supervision  1 cr. 

SEE ALSO

CSC 80040 Algebraic and Numerical Computation

T, 6:30-8:30pm, Victor Pan [45473]

Algebraic and numerical computing is the cornerstone of modern computations in sciences, engineering, and signal processing.  It is a huge cache of topics for study and research in both computer  science and mathematics. Systematic comparison of algebraic and numerical techniques for algorithm design and analysis simplifies study in both areas. The students from the CS and Math Programs learn fundamentals as well as selected research topics, eventually leading to PhD defenses (17 in the last 8 years in both programs).

Because of the variety of the available topics the subjects in the seminar can be partly adjusted to the students’ interests and background.  Sample topics considered for this  semester include:
 a) Structured (e.g., Toeplitz, Hankel,   Cauchy, and Pick) matrices,
omnipresent in modern  computing, signal and image processing, and many
areas of math, and closely related to fundamental algebraic computations
with polynomials and rational functions. This subject is treated both
algebraically and numerically based on the instructor's recent book and
several papers, many of them joint with his PhD students.

b) Polynomial and rational interpolation.

c) Solving a polynomial equation (the  central and most influential problem in math for 4 millennia and still highly important in computer algebra), with possible extension to fundamentals of the solution of  systems of multivariate polynomial equations.

d) Algebraic techniques for coding and cryptography.

The seminar resumes with new topics and new students every semester. The students are divided into the entry level group and the advanced group, the instructor meets separately for 2 hours per week with each group. The students in the entry level group study the fundamentals and  eventually join the group of advanced students. The instructor supplies survey and research papers as handouts, in addition to his books currently on display by both Math and CS Programs. Good progress in learning is sufficient for high grades, but
Computer Science students are also encouraged to implement new algorithms devised in the seminar,  math. students to  solve the relevant open problems in math.

 

 

CSC 80040 Topics in Algorithms and Their Analysis: Contemporary Cryptoanalysis

Fri. 2 :00- 4 :00pm, Michael Anshel [45474]

 

CSC 85020 Topics in Theoretical Computer Science : Computability and Complexity

Wed 2:00- 4:00pm, Stathis Zachos [45488]

                                                   Last Updated on  9/11/03