- Title: Introduction to Abstract Algebra (Group Theory)
- Instructor: Trevor Wilson (twilson@math.uci.edu)
- Lectures: 11:00–11:50 a.m. MWF in MSTB 122
- Office hours: 1:30–3:30 p.m. on Mondays, or by appointment, in 510V Rowland Hall
- TA: Adrian Ferenc (aferenc@uci.edu)
- Text: A First Course in Abstract Algebra, 7th edition, by John B. Fraleigh

You may collaborate on the homework with other students and seek help from any source. As always, you must credit your collaborators and cite your sources.

Midterm exam (white) and solutions

Midterm exam (yellow) and solutions

- Oct. 3 (F) Section 0 exercises 3, 11, 12adf; Section 1 (no exercises for section 1)
- Oct. 6 (M) Section 2 exercises 12, 16, 23ab
- Oct. 8 (W) Section 2 exercises 5, 8, 34
- Oct. 10 (F) Section 3 exercises 4, 5, 6

- Oct. 13 (M) Section 3 exercises 30, 32, 33ab
- Oct. 15 (W) Section 3 exercises 17ab, 22; Section 4 exercise
3.
*Hint for 3.17ab: write $a \ast b$ as $\phi(\phi^{-1}(a \ast b))$ or $\phi^{-1}(\phi(a \ast b))$ and then try to express this in terms of multiplication "$\cdot$" and the functions $\phi$ and $\phi^{-1}$, which you know.* - Oct. 17 (F) Section 4 exercises 8, 14, 20. In exercise 14 we leave $n$ fixed when forming the structure. So it asks: do $1 \times 1$ diagonal matrices with the stated property form a group under multiplcation? Do $2 \times 2$ diagonal matrices with the stated property form a group under multiplcation? And so on. It turns out that the same argument works for all $n$, so we state and prove it for general $n$. For exercise 20b, recall that $U_4$ denotes the group of complex fourth roots of unity: $\{1,i,-1,-i\}$ under complex multiplication. In exercise 20c, "structurally the same as" means "isomorphic to". Proving associativity by checking all triples of elements is tedious, so we can use the shortcut of finding an isomorphism with a structure whose operation is already known to be associative.

- Oct. 20 (M) Sections 4, 5
- Oct. 22 (W) Section 5
- Oct. 24 (F) Section 6 (Cyclic Groups)

- Oct. 27 (M) Section 6
- Oct. 29 (W) Section 8 (Groups of Permutations)
- Oct. 31 (F) Section 8

- Nov. 3 (M) Review
- Nov. 5 (W) Midterm Exam
- Nov. 7 (F) Section 9 (Orbits, Cycles, and the Alternating Groups)

- Nov. 10 (M) Section 9
- Nov. 12 (W) Section 9
- Nov. 14 (F) Section 9

- Nov. 17 (M) Section 10 (Cosets and the Theorem of Lagrange)
- Nov. 19 (W) Section 10
- Nov. 21 (F) Section 11 (Direct Products and Finitely Generated Abelian Groups)

- Nov. 24 (M) Section 11
- Nov. 26 (W) Section 13 (Homomorphisms)
- Nov. 28 (F) Thanksgiving Holiday

- Dec. 1 (M) Section 13
- Dec. 3 (W) Section 14 (Factor Groups)
- Dec. 5 (F) Section 14

- Dec. 8 (M) Section 15 (Factor Group Computations and Simple Groups)
- Dec. 10 (W) Section 15
- Dec. 12 (F) Review

- Dec. 19 (F) 8:00–10:00 a.m. Final Exam

- 15% homework
- 15% quizzes
- 30% midterm exam
- 40% final exam