Math 103A, Fall 2022

Modern Algebra I

## Announcements:

##

## Course Information

Modern Algebra I

- 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.

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.

## Course Schedule (items in gray may change)

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.

- 20% Homework, 20% First Midterm, 20% Second Midterm, 40% Final Exam.
- 20% Homework, 20% Best Midterm, 60% Final Exam

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 |