Instructor: Dr. Debrup Chakraborty
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Day |
Time |
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Monday |
1600 hrs to 1800 hrs |
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Wednesday |
1200 hrs to 1400 hrs |
Willingness
to read and write proofs.
This course
will deal with basic algebraic structures like groups, rings, fields and vector
spaces. Specific problems related to applications of such algebraic structures
in certain problems of computer science will be explored. Specifically, we plan
to explore some elementary coding theory. This can give you a good background
for future courses like Computational Arithmetic and Cryptography and
Coding.
The
textbook for the course will be:
Topics in Algebra, by I.N. Herstein
We shall
also refer to some parts of:
A Computational Introduction to Number Theory
and Algebra by V. Shoup
(This book
is available online at: http://www.shoup.net)
We will
have four home works (60%), two tests (40%)
Problem set 1 (To be discussed on Oct, 2)
Home work 1 (Due on Sept, 27)
Home work 2 (Due on Nov, 8)
Home work 3 (Due on Nov, 20)
Home work 4 (Due on Dec, 5)
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Aug 28 |
Sets |
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Aug 30 |
Relations
and Equivalence Relations |
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Sep 4 |
Functions |
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Sep 6 |
Integers |
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Sep 11 |
Groups:
Introduction |
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Sep 13 |
Supgroups |
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Sep 18 |
Cosets |
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Sep 20 |
Normal
Subgroups |
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Sep 25 |
Group
Homomorphism |
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Sep 27 |
Permutation
Groups |
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Oct 2 |
Congugacy |
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Oct 4 |
Sylows
Theorems |
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Oct 9 |
Introduction
to Coding Theory |
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Oct 11 |
Test 1 |
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Oct 16 |
Rings and
fields: Introduction |
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Oct 18 |
Basic
properties of Rings and Fields |
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Oct 23 |
Ring
Homomorphism and Quotient rings |
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Oct 25 |
Polynomial
Rings |
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Oct 30 |
Polynomial
Rings |
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Nov 1 |
Vector
Spaces |
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Nov 6 |
Vector
Spaces |
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Nov 8 |
Extension
Fields |
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Nov 13 |
Finite
Fields |
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Nov 15 |
More
number theory: Quadratic Residues |
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Nov 20 |
More
about primes: Primality Testing |
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Nov 22 |
Test 2 |
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Nov 27 |
Review
and ending!! |
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