Course Content
UNIT 0: Preliminaries
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0.1 Properties of Integers
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0.2 Modular Arithmetic
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0.3 Complex Numbers
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0.4 Mathematical Induction
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0.5 Equivalence Relations
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0.6 Functions (Mappings)
UNIT 1: Introduction to Groups
UNIT 2: Groups
UNIT 3: Finite Groups; Subgroups
UNIT 4: Cyclic Groups 75
UNIT 5: Permutation Groups
UNIT 6: Isomorphisms
UNIT 7: Cosets and Lagrange’s Theorem
UNIT 8: External Direct Products
UNIT 9: Normal Subgroups and Factor Groups
UNIT 10: Group Homomorphisms
UNIT 11: Fundamental Theorem of Finite
UNIT 12: Introduction to Rings
UNIT 13: Integral Domains
UNIT 14: Ideals and Factor Rings
UNIT 15: Ring Homomorphisms
UNIT 16: Polynomial Rings
UNIT17: Factorization of Polynomials
UNIT 18: Divisibility in Integral Domains
UNIT 19: Vector Spaces
UNIT 20: Extension Fields
UNIT 21: Algebraic Extensions
UNIT 22: Finite Fields
UNIT 23: Sylow Theorems
UNIT 24: Finite Simple Groups
UNIT 24: Finite Simple Groups
UNIT 25: Generators and Relations
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