Algebra, Arithmetic and Geometry
 With a View Towards Applications /2005
Class Notes
CL01 
Thu/Sept 01, 2005 
Natural Numbers

CL02 
Tue/Sept 06, 2005 
The Fundamental Theorem of Arithmetic

CL03 
Thu/Sept 08, 2005 
Monoids
 Divisibility

CL04 
Tue/Sept 13, 2005 
Factorial Monoids

CL05 
Thu/Sept 15, 2005 
Properties of pexponents
 padic valuation

CL06 
Tue/Sept 20, 2005 
Division Algorithm and GCD

CL07 
Thu/Sept 22, 2005 
Factoriality and GCD

CL08 
Tue/Sept 27, 2005 
Numbertheoretic functions

CL09 
Thu/Sept 29, 2005 
Sylvester's sieve Formula and its applications

CL10 
Tue/Oct 04, 2005 
Homomorphisms and Isomorphisms of Monoids

CL11 
Thu/Oct 06, 2005 
Categories, Examples

CL12 
Tue/Oct 11, 2005 
Rings and Homomorphisms, Examples

CL13 
Thu/Oct 13, 2005 
Unit Group of a Ring, Integral Domains and Fields

CL14 
Tue/Oct 18, 2005 
Ideals

CL15 
Thu/Oct 20, 2005 
Quotient rings

CL16 
Tue/Oct 25, 2005 
Prime rings
 Euler's theorem, Fermat's Little theorem

CL17 
Thu/Oct 27, 2005 
Modules and Algebras

CL18 
Mon/Oct 31, 2005 
Monoid rings
 Polynomial Rings

CL19 
Thu/Nov 03, 2005 
Polynomial Rings
 Universal property, substitution homomorphisms

CL20 
Tue/Nov 08, 2005 
Modules

CL21 
Thu/Nov 10, 2005 
Free Modules

CL22 
Tue/Nov 15, 2005 
Generating Systems for Modules

CL23 
Thu/Nov 17, 2005 
Cardinality of Infinite Sets

CL24 
Tue/Nov 22, 2005 
Degree of a Polynomial

CL25 
Thu/Nov 24, 2005 
Bases for Vector Spaces

CL26 
Tue/Nov 29, 2005 
Division Algorithm for Polynomials

CL27 
Thu/Dec 01, 2005 
Dimension of Vector Spaces

CL28 
Tue/Dec 06, 2005 
Yet to come

