Welcome to MATH 4210/5210: Abstract Algebra I, this Fall 2024!
For the most up-to-date content, please refresh the page at each visit!
Schedule
Final Exam: Wed, Dec 18 at 6:30pm
- See Final Exam info.
Week 15 (Wed, Dec 11)
- Collected Homework
- Due on Wed, Dec 11 at the beginning of class: Homework 13 (review for final exam), hand-written
Recommended practice problems (do not submit) for quiz: practice_week15.pdf and selected solutions practice_week15sol.pdf
- Beginning of class:
Middle of class and end of class: Group quiz 13, three pages, part 1 is the first two pages and part 2 is the third page.
- Class notes week 15 (TBA): Recall mattress groups, units in Z_n; Section 14.1 Groups acting on sets including the left regular representation; Theorem 9.10 Cayley’s theorem
Week 14 (Wed, Dec 4)
- Collected Homework
- Due on Tuesday, Dec 3: Homework 12, Homework 12 solutions
- First draft due on Monday, Dec 2 if you want feedback
Recommended practice problems (do not submit): practice_week14.pdf and selected solutions practice_week14sol.pdf
- Beginning of class:
- Class notes week 14: Section 16.4 Maximal ideals and prime ideals
- Motivating example: Chapter 14 Example 12 from Gallian’s “Contemporary abstract algebra” 9th edition
Week 13 (no class the Wednesday before Thanksgiving)
Week 12 (Wed, Nov 20)
- Collected Homework
- Due on Tuesday, Nov 19: Homework 11, Homework 11 solutions
- First draft due on Monday, Nov 18 if you want feedback
Recommended practice problems (do not submit): practice_week12.pdf and selected solutions practice_week12sol.pdf
- Beginning of class:
- Class notes week 12: The rest of Section 16.3: Quotient rings and First isomorphism theorem (for rings)
Week 11 (Wed, Nov 13)
- Collected Homework
- Due on Tuesday, Nov 12: Homework 10, Homework 10 solutions
- First draft due on Monday, Nov 11 if you want feedback
Recommended practice problems (do not submit): practice_week11.pdf and selected solutions practice_week11sol.pdf
- Beginning of class:
Middle of class and end of class: Group quiz 10, 4 pages, part 1 is the first two pages and part 2 is the last two pages.
- Class notes week 11: Section 17.1 (Polynomial rings), Section 16.3 Part I: (Ring homomorphisms) and part II (Ideals)
Week 10 (Wed, Nov 6)
- Collected Homework
- Due on Tuesday, Nov 5: Homework 09, Homework 09 solutions
- First draft due on Monday, Nov 2 if you want feedback so that you can make corrections
Recommended practice problems (do not submit): practice_week10.pdf and selected solutions practice_week10sol.pdf
- Beginning of class:
- Class notes week 10: Section 16.1 (Rings) and 16.2 (Integral domains and fields)
Week 9 (Wed, Oct 30)
- Collected Homework
- Due on Tuesday, October 29: Homework 08, Homework 08 solutions
- First draft due on Monday, October 28 if you want feedback so that you can make corrections
No individual quiz this week. There will be group quizzes based on past/current materials.
- Class notes week 9: First homomorphism theorem (fundamental theorem of homormophisms), fundamental theorem of finite and finitely generated abelian groups
Midterm exam (week 8): Wed, Oct 23 at 6:30pm
See Midterm Exam info. Midterm exam solutions are posted on the course Blackboard home page.
- Collected Homework Homework 07
- Due on Tuesday, October 22: Email a picture or PDF (as an attachment) of your exam one-page cheat sheet to emily_gunawan@uml.edu (subject line: Algebra HW07 by FirstName LastName Fall 2024)
- This will be graded by completion and you can still make edits to the cheat sheet any time before the exam
- Due on Monday, October 21 if you want me to read your cheat sheet and give feedback
- Recommended practice problems (do not submit): practice_week08.pdf and selected solutions practice_week08sol.pdf
Week 7 (Wed, Oct 16)
- Collected Homework
- Due on Tuesday, October 15: Homework 06, Homework 06 solutions
- First draft due on Monday, October 14 if you want feedback so that you can make corrections
Recommended practice problems (do not submit): practice_week07.pdf and selected solutions practice_week07sol.pdf
- Beginning of class:
- Class notes week 7: Definition of conjugates of a group element, definition of conjugates of a subgroup, normal subgroups, coset multiplication, quotient groups, internal direct product
Week 6 (Wed, Oct 9)
- Collected Homework
- Due on Tuesday, October 8: Homework 05, Homework 05 solutions
- First draft due on Monday, October 7 if you want feedback so that you can make corrections
Recommended practice problems (do not submit): practice_week06.pdf and selected solutions practice_week06sol.pdf
- Beginning of class:
- Class notes week 6: Groups of complex numbers, introduction to homomorphism and isomorphism
Week 5 (Wed, Oct 2)
- Collected Homework
- Due on Tuesday, October 1: Homework 04, Homework 04 solutions
- First draft due on Monday, September 30 if you want feedback so that you can make corrections
Recommended practice problems (do not submit): practice_week05.pdf and selected solutions practice_week05sol.pdf
- Beginning of class:
- Class notes week 5: Corollaries of cosets Lagrange’s theorem; more on Dihedral groups; minimal generating set and Cayley diagram
Week 4 (Wed, Sept 25)
- Homework
- Due on Tuesday, September 24: Homework 03, Homework 03 solutions
- Recommended practice problems (do not submit): practice_week04.pdf and selected solutions practice_week04sol.pdf
- Beginning of class:
- Class notes week 4: Symmetric group, even and odd permutations, cosets and Lagrange’s theorem
Week 3 (Wed, Sept 18)
- Homework
- Due on Tuesday, September 17: Homework 02
- Recommended practice problems (do not submit): practice_week03.pdf
- Beginning of class:
End of class: Group quiz 3
- Class notes week 3: law of exponents (proof using induction), cyclic group and its Cayley graph, order of a group element and order of a group
Week 2 (Wed, Sept 11)
- Homework
- Due on Tuesday, September 10: Homework 01
- Recommended practice problems (do not submit): practice_week02.pdf
- Beginning of class:
End of class: Group quiz 2. Only half of the planned questions were handed out, see full list of questions in practice_week03.pdf
- Class notes week 2: symmetry group of regular polygons (dihedral groups) Dn, symmetric group Sn, two types of groups coming from integers modulo n, Cayley table, direct product of groups, subgroups
Week 1 (Wed, Sept 4)
Take the Welcome survey
class notes week 1: mattress group (from Group Think by Steven Strogatz) and Judson Section 3.2 (definition of groups, abelian groups, examples)