MATH 46 Abstract Algebra

We will cover properties of integers, permutations, groups, alternating groups, groups of symmetries, quotient groups, sets, mappings, isomorphisms, homomorphisms, rings, fields, polynomials. The syllabus of the class is available here Syllabus. . We will be using the book by Judson:

Abstract Algebra: Theory and Applications, by Thomas W. Judson.

Lectures:

Lecture 0: Abstract Algebra.

Lectures 1 and 2: Sets, relations, maps.

Lecture 3: Integers.

Lecture 4: Groups and examples.

Lecture 5+6: Subgroups.

Lecture 7: Cyclic groups.

Lecture 8: Cosets and Lagrange.

Lecture 9: Symmetric groups.

Lecture 10: Dihedral groups.

Lecture 11: Group homomorphism and normal subgroups.

Lecture 12-13: Isomorphism Theorems.

Lecture 14-15: Characters.

Lecture 16: Abelian groups.

Lecture 17: Introduction to rings.

Lecture 18: Integral domains and fields.

Lecture 19: Ring homomorphisms and ideals.

Lecture 20: Maximal and prime ideals.

Lecture 21: Rings of polynomials.

Lecture 22: Rings of polynomials II.

Homework:

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