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.
- First
Midterm. [Practice Midterm] Friday Oct. 21. Will cover Chapters 0, 1, 2, and 3. You may bring one 8.5x11 sheet of paper with notes on it to the exam.
- Second Midterm. [Practice Midterm] Friday Nov. 18. Will cover Chapters 4, 5, and 6. You may bring one 8.5x11 sheet of paper with notes on it to the exam.
- Final Exam. [Practice Final] Friday Dec. 9 from 8:00 AM to 11:00 AM. Will cover Chapters 1, 2, 3, 4, 5, 6, 7, 9, and 10.
Grading: Your final grade will be the maximum of the following two weighted averages:
- 20% Homework, 20% First Midterm, 20% Second Midterm, 40% Final Exam.
- 20% Homework, 20% Best Midterm, 60% Final Exam
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
|