**Prerequisite Course:** Math 116

**Textbook:** *Abstract Algebra* by I. N. Herstein, Third
Edition, Prentice Hall, 1996.

**Other Books:**

Ay�e Berkman: Monday 8.40-9.30 and 13.40-14.30

Arzu Zabun: Tuesday 13.40-15.30 (until 23 April)

Ayberk Zeytin: Anytime (after 23 April)

Two midterm exams (30 points each) and a final exam (40 points).

Week 1: Motivation for groups and examples. Subgroups, cyclic groups.

Week 2: Equivalence relations, partitioning. Congruence modulo a subgroup, left and right cosets. Lagrange's Theorem and its corollaries.

Week 3: Examples of homomorphisms and isomorphisms. Cayley's Theorem. Kernels. Normal subgroups.

Week 4: Quotient groups. Homomorphism Theorems.

Week 5: Direct Products. Classification of finite abelian groups.

Week 6: More on permutations. Review. Exam 1.

Week 7: Even/odd permutations. Class Equation. Sylow Theorems. (End of group theory!)

Week 8: Definitions and examples of rings, integral domains, division rings, fields. Ideals and ring homomorphisms.

Week 9: Prime and maximal ideals. Polynomial rings.

Week 10: Maximal ideals in F[x]. Irreducibility criteria for polynomials over rationals.

Week 11: Field of quotients. Examples of fields. Field extensions.

Week 12: Algebraic elements. Minimal Polynomials.

Week 13: Review. Exam 2.

Week 14: Three impossible constructions.

Some warm-up exercises from Chapter 1: 1.1, 2.13, 3.10, 3.25, 3.26, 3.30, 3.31, 7.22, 7.25.

Section 2.1: 1(e,f), 3, 4, 9, 13, 18, 21, 23, 24, 26, 27.

Section 2.2: 2.

Section 2.3: 1, 4, 5, 7, 11, 19, 20, 21, 26, 29, 30.

Section 2.4: 5, 12, 13, 16, 17, 18, 27, 29, 30.

Section 2.5: 1, 6, 9, 13, 14, 17, 20, 24, 28, 29c, 36.

Section 2.6: 8, 11, 12, 13, 15, 17, 18.

Section 2.7: 2, 4, 5, 6, 7.

Section 2.9: 1, 2, 3, 4, 5.

Section 2.10: All

Section 3.2: 15, 16, 17, 20, 22, 23, 24, 25.

Section 3.3: 1, 2, 3, 5, 8.

Section 2.11: 2, 3, 5, 9, 15, 20.

Section 4.1: 2, 3, 9, 13b, 15, 20, 21, 28, 30.

Section 4.2: 2, 3, 4.

Section 4.3: 2, 6, 12, 19, 20, 21, 23, 24.

Section 4.4: See the exercise sheet.

Section 4.5: 1, 8, 9, 12, 16, 20.

Section 4.6: 3, 6, 8, 9, 13.

Section 4.7: Fill out the details in the proof of Theorem 4.7.1.

Section 5.1: 1, 7, 8, 9, 10.

Section 5.3: 1, 5, 7, 12, 14.