Math 103A, Fall 2022
Modern Algebra I


Announcements:

  • During finals week I will have office hours Wednesday 3:00-4:30 and Thursday 3:30-5:00
  • I have reduced the assignment of HW 9 to: Chapter 8 problems 10, 52 and Chapter 10 problems 15, 24
  • During the week of the second midterm, my office hours will be Wednesday 11-12 and 2-4.
  • I'm sick today (Nov. 7) and am doing everything remote. Lecture notes for recorded Lecture Nov. 7 (video on Canvas). My office hours are at zoom id 976 2314 0201.
  • On Monday Nov. 7 my office hours will be 11:00 - 11:30 and 4:00 - 4:30 (rather than 11:00 - 12:00).
  • During the week of the first midterm, my office hours will be Wednesday 11-12 and 2-4.


Course Information

Professor: Brandon Seward (pronouns: they/them or he/him)
Email: bseward@ucsd.edu
Lecture: MWF 10:00-10:50 in Peterson room 102
Lecture Recordings: On our Canvas page under the Media Gallery tab
Lecture Notes: Chapters 0 , 1 and 2, 3, 4, 5, 6, 7, 9, 8, 10
Office Hours: Mon. 11-12 and Wed. 2-4 in AP&M 5739

Teaching Assistant: Qingyuan Chen (pronouns: he/him)
Email: qic069@ucsd.edu
B01 Discussion: Fri. 5:00-5:50 in Center Hall room 203
B02 Discussion: Fri. 6:00-6:50 in Center Hall room 203
Office Hours: Tues. 1-3 and Thurs. 1-3 in Humanities and Social Sciences Building (HSS) 3062

Course Descritption:
First course in a two-quarter introduction to abstract algebra with some applications. The emphasis is on group theory. Topics include: definitions and basic properties of groups, properties of isomorphisms, and subgroups. No previous knowledge of abstract algebra will be assumed, but students will be expected to be able to understand and write basic proofs, as covered in Math 109.

Math 103 vs Math 100: Math 100ABC and Math 103AB are course sequences that cover similar material. Math 100 is more challenging, goes into greater depth, and focuses more on theory, while Math 103 provides basic and practical knowledge with an emphasis on examples and applications. You cannot recieve credit for both sequences, so you must choose between the two. If you plan to go to graduate school in math then you should strongly consider taking Math 100 instead of Math 103.

Textbook: Contemporary Abstract Algebra by Joseph A. Gallian, 9th edition. We will cover most of Chapters 0 through 10, and perhaps Chapter 11 if we have time. An electronic version of the textbook is available to you through our Canvas page. Important: Your student account will be automatically charged for the electronic textbook unless you OPT-OUT by October 8th. Instructions on how to opt out can be found here: https://solve.redshelf.com/hc/en-us/articles/360013142634-How-to-Opt-Out.

Homework: Homework will be assigned regularly and due on Wednesdays at 11:59 PM. No late homework will be accepted, but your two lowest homework scores will be dropped when computing your final grade. On each assignment, a few problems will be graded for correctness, while the others will be graded simply for completion. We will use Gradescope for turning in homework. When registering for gradescope, please register using your "@ucsd.edu" email address and use Entry Code E7676E.

Homework 0 (Due Wednesday Sept. 28): Chapter 0 problems 2 and 3.
Homework 1 (Due Wednesday Oct. 5): Chapter 0 problems 11, 13, 14, 16, 18, 28, 38, 60
Homework 2 (Due Wednesday Oct. 12): Chapter 2 problems 11, 12, 14, 15, 18, 32, 35, 40, 47
Homework 3 (Due Wednesday Oct. 19): Chapter 3 problems 10, 13, 20, 22, 28, 46, 61, 71, 73
Homework 4 (Due Wednesday Oct. 26): Chapter 4 problems 1, 9, 10, 12, 38, 41, 53, 61, 67
Homework 5 (Due Wednesday Nov. 2): Chapter 5 problems 2, 3, 5, 22, 29, 31, 32, 34, 43
Homework 6 (Due Wednesday Nov. 9): Chapter 5 problems 8, 9, 15, 19, 55 and Chapter 6 problems 1, 7, 37, 39
Homework 7 (Due Wednesday Nov. 16): Chapter 6 problems 26, 28, 32, 59 and Chapter 7 problems 1, 5, 6, 16, 36
Homework 8 (Due Wednesday Nov. 30): Chapter 7 problems 7, 15 and Chapter 9 problems 12, 14, 17, 18, 32, 52
Homework 9 (Due Friday Dec. 2): Updated: Chapter 8 problems 10, 52 and Chapter 10 problems 15, 24 (previously listed as: Chapter 8 problems 6, 8, 10, 52 and Chapter 10 problems 9, 15, 24, 31, 35)

Exams: All exams will be in-person. If you miss a midterm no makeup exam will be given. Instead your final exam will count towards 60% of your final grade.
Grading: Your final grade will be the maximum of the following two weighted averages:
Special Accommodations: Students requiring accommodations should provide an OSD letter of certification and OSD accommodation recommendation as soon as possible.


Course Schedule (items in gray may change)

Week
Monday
Wednesday
Friday
0


September 23
Chapter 0
Well ordering principle, division algorithm
1
September 26
Chapter 0
gcd, Euclid's lemma

September 28 (HW 0 Due)
Chapter 0
fundamental theorem of arithmetic, modular arithmetic, equivalence relations and partitions

September 30
Chapters 0 and 2
Equivalence relations and partitions

Definition of groups, examples
2
October 3
Chapter 2
Definition of groups, examples

October 5 (HW 1 Due)
Chapters 1 and 2
Examples of groups, elementary properties of groups
October 7
Chapter 3
Order of groups and elements, subgroups, one-step subgroup test

3
October 10
Chapter 3
Two-step subgroup test, finite subgroup test
October 12 (HW 2 Due)
Chapter 3
Examples of subgroups: powers of an element, the center, centralizers

October 14
Chapter 4
Properties of cyclic groups

4
October 17
Chapters 4
Classification of subgroups of cyclic groups

October 19 (HW 3 Due)
Review
October 21
First Midterm
Practice Midterm
5
October 24
Chapter 5
Fundamental theorem of cyclic groups
Definition and notation, array notation
October 26 (HW 4 Due)
Chapter 5
Cycle notation, products of disjoint cycles

October 28
Chapter 5
Orders of permutations, products of 2-cycles

6
October 31
Chapters 5 and 6
Odd and even permutations, the alternating group A_n

Isomorphisms, examples, Cayley's Theorem
November 2 (HW 5 Due)
Chapter 6
Examples of isomorphisms, Cayley's Theorem, properties of isomorphisms

November 4
Chapter 6
Properties of isomorphisms, automorphisms, inner automorphisms, Aut(Z_n)

7
November 7
Chapter 7
Cosets, Lagrange's Theorem
November 9 (HW 6 Due)
Chapters 7 and 9
Consequences of Lagrange's Theorem
Normal subgroups, examples
November 11
Veterans Day Holiday
8
November 14
Chapter 9
Factor groups, examples

November 16 (HW 7 Due)
Review
November 18
Second Midterm
Practice Midterm
9
November 21
Chapters 9 and 8
Cauchy's Theorem for Abelian Groups
Direct products, orders of elements
November 23 (HW 8 Due)
Chapters 8 and 10
Orders of elements
Homomorphisms, kernels, examples

November 25
Thanksgiving Holiday

10 November 28
Chapter 10
Properties of homomorphisms, examples
November 30
Chapter 10
First isomorphism theorem
December 2 (HW 9 Due)
Review
11
Friday December 9, 8:00 AM -- 11:00 AM
Final Exam
Practice Final