Algebra, Arithmetic and Geometry
 With a View Towards Applications /2005
Lectures
L01 
Thu/Sept 01, 2005 
Natural Numbers

L02 
Tue/Sept 06, 2005 
The Fundamental Theorem of Arithmetic

L03 
Thu/Sept 08, 2005 
Monoids
 Divisibility

L04 
Tue/Sept 13, 2005 
Factorial Monoids

L05 
Thu/Sept 15, 2005 
Properties of pexponents
 padic valuation

L06 
Tue/Sept 20, 2005 
Division Algorithm and GCD

L07 
Thu/Sept 22, 2005 
Factoriality and GCD

L08 
Tue/Sept 27, 2005 
Numbertheoretic functions

L09 
Thu/Sept 29, 2005 
Sylvester's sieve Formula and its applications

L10 
Tue/Oct 04, 2005 
Homomorphisms and Isomorphisms of Monoids

L11 
Thu/Oct 06, 2005 
Categories, Examples

L12 
Tue/Oct 11, 2005 
Rings and Homomorphisms, Examples

L13 
Thu/Oct 13, 2005 
Unit Group of a Ring, Integral Domains and Fields

L14 
Tue/Oct 18, 2005 
Ideals

L15 
Thu/Oct 20, 2005 
Quotient rings

L16 
Tue/Oct 25, 2005 
Prime rings
 Euler's theorem, Fermat's Little theorem

L17 
Thu/Oct 27, 2005 
Modules and Algebras

L18 
Mon/Oct 31, 2005 
Monoid rings
 Polynomial Rings

L19 
Thu/Nov 03, 2005 
Polynomial Rings
 Universal property, substitution homomorphisms

L20 
Tue/Nov 08, 2005 
Modules

L21 
Thu/Nov 10, 2005 
Free Modules

L22 
Tue/Nov 15, 2005 
Generating Systems for Modules

L23 
Thu/Nov 17, 2005 
Cardinality of Infinite Sets

L24 
Tue/Nov 22, 2005 
Degree of a Polynomial

L25 
Thu/Nov 24, 2005 
Bases for Vector Spaces

L26 
Tue/Nov 29, 2005 
Division Algorithm for Polynomials

L27 
Thu/Dec 01, 2005 
Dimension of Vector Spaces

L28 
Tue/Dec 06, 2005 
Yet to come

