Lecture Notes for Math 3613
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Lecture 1: Elements of Mathematical Logic
Lecture 2: Methods of Proof
Lecture 3: Methods of Proof, cont'd
Lecture 4: Methods of Proof, cont'd
Lecture 5: Review of Set Theory
Lecture 6: Functions
Lecture 7: The Division Algorithm
Lecture 8: Divisibility
Lecture 9: Divisibility, Cont'd
Lecture 10: Review
Lecture 11: Congruence and Congruence Classes
Lecture 12: Modular Arithmetic
Lecture 13: The Structure of Z_p when p is Prime
Lecture 14: Definition and Examples of Rings
Lecture 15: Basic Properties of Rings
Lecture 16: Homorphisms and Isomorphisms of Rings
Lecture 17: Polynomial Arithmetic and the Division Algorithm
Lecture 18: Divisibility in F[x]
Lecture 19: Irreducible Polynomials and Unique Factorization
Lecture 20: Polynomial Functions, Roots, and Reducibility
Lecture 21: Definition and Examples of Groups
Lecture 22: Basic Properties of Groups
Lecture 23: Subgroups
Lecture 24: Group Homomorphisms
Lecture 25: Examples of Groups and Group Properties
