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Teaching

Topics in Analysis (Fall 2014)
 
Description: 
The course is intended to unify and solidify the topology background of students just admitted to the Master program (with possible entrance to the program from an Applied Mathematics discipline).
 

Text:

R. Engelking, General Topology. Second edition. Heldermann Verlag, Berlin, 1989.

 

Grading: 

Midterm: 40%, Final: 40%, Quizzes: 20%.

 

 

General Topology (Fall 2014)

 
Description: 

The course treats the basic notions related to continuity.  Basically, the goal is to provide a common mathematical language used by most mathematicians.

We aim to cover the first 5 chapters of Munkres' book, and if time allows (time is never going to allow though!) some elements from Algebraic Topology.

 
Prerequisites: 

Analysis I + "Mathematical Maturity", to a certain degree.

 

Text:

J.R. Munkres, Topology. Second edition. Prentice Hall Inc., Englewood Cliffs, N.J., 2000.

Other useful source:

R. Engelking, General Topology. Second edition. Heldermann Verlag, Berlin, 1989.

 

Grading: 

Midterm: 40%, Final: 40%, Quizzes: 20%

 


 

Advanced Topology I (Fall 2012)
 
Description: 

The course aims to cover the first 8 chapters of Gillman and Jerison's book. The book describes the theory of the Rings of Continuous Functions; an area of Mathematics where Algebra and Topology intersect.  

 

Prerequisites: 

The course is addressed to those who understand the meaning of each individual word in Gillman and Jerison's book title: "Rings of Continuous Functions"; none will be defined. The course will be topologically oriented, however, some knowledge of Algebra (specifically, Commutative Ring Theory) would be inevitable. 

 

Text:

L. Gillman and M. Jerison, Rings of Continuous Functions. Springer-Verlag, New York-Heidelberg, 1976.

 

Grading: 

Grading is based on assignments.

 

Assignment 1: 
1A 
1B: 2, 3, 4, 6
1C: 2
1F: 1
1G: 1, 2, 3
1H: 4
Due date: Saturday, January 26.