Instructor: David Corwin (dcorwin at berkeley dot edu). In all e-mail correspondence, please include "[Math113]" in the subject line.
GSI: Kentaro Yamamoto
Grader: Anna Shang
Lecture: TTh 5pm-6:30pm in Etcheverry 3107
GSI Office hours: GSI Office hours are listed here
My Office hours: Location: In classroom if after class, otherwise Evans 749.
Final exam: Thursday, December 19, 2019 11:30-2:30pm. Location: classroom.
Prerequisites: If you are not familiar with writing proofs or with deductive logic, please see Notes on mathematical proofs.
Text: The primary text for this course is Notes on Abstract Algebra by Alexander Paulin, with revisions by me [P]. They will be revised throughout the semester. Students should feel free to consult other books for additional exercises and/or alternative presentations of the material. Wikipedia also has lots of great articles on the topics at hand (e.g., see articles on Abstract Algebra, Groups, Rings, Fields, and many of the other concepts we will discuss in class). Students are expected to read the relevant sections of the textbook, as the lectures are meant to complement the textbook, not replace it, and we have a lot of material to cover.
Grading: 20% homework, 2 x 20% in-class midterms (10/1 and 11/5), 40% final exam. The lowest two homework scores will be dropped. No makeups for the midterms will be given except in cases requiring special accommodation. Your exam grade will be computed based on the maximum of the following three schemes: (0.2)MT1 + (0.2)MT2 + (0.4)F; (0.2)MT1 + (0.6)F; (0.2)MT2 + (0.6)F
Website: For now, the only website is this page, http://math.berkeley.edu/~dcorwin/math113.html. I will use bcourses for solutions and other non-public information, such as my phone number.
Course policies:
Additional resources:
Course Overview: Outlined below is the rough course schedule. Depending on how the class progresses it may be subject to minor changes over the course of the semester.
Date | Lecture | Topics | References | Comments | Alternative References |
---|---|---|---|---|---|
8/29 | 1 | Logistics/Syllabus, Overview of Course | Section 1.1 of [P] | ||
9/3 | 2 | Sets and Functions | Section 1.2-1.3 of [P]. Also see Bergman's notes on sets and mathematical notation. | Chapter 1 of [J], Section 1 of [E] | |
9/5 | 3 | Integers and Modular Arithmetic | Section 2 of [P] | 2.2 and 3.1 of [J], 2.2-2.3 of [E], GCD, Euclidean Division and Modular Arithmetic on [W] | |
9/10 | 4 | Finish Modular Arithmetic, Groups | Section 3.1 of [P] | HW 1 Due | 3.0, 3.5 of [E], 3.2 and 9.1 of [J], Groups, Group Homomorphism on [W] |
9/12 | 5 | Homomorphisms, Subgroups, Cosets, and Lagrange's Theorem | Section 3.2 of [P] | 3.1, 3.3 of [E], 3.3, 6.1, 6.2 of [J], Subgroup, Coset, Lagrange's Theorem on [W] | |
9/17 | 6 | Homomorphisms, Subgroups, Cosets, and Lagrange's Theorem | Section 3.2 of [P] | HW 2 Due | 3.1, 3.3 of [E], 3.3, 6.1, 6.2 of [J], Subgroup, Coset, Lagrange's Theorem on [W] |
9/19 | 7 | Generating Sets for Groups | Section 3.3 of [P] | 3.1 of [E], 4.1, Examples 13.1-2 of [J], Order, Generating Set, Cyclic Groups on [W] | |
9/24 | 8 | Permutation/Symmetric Groups | Section 3.4 of [P] | HW 3 Due (Wednesday) | 3.2 of [E], 5.1 of [J], Permutation Group. |
9/26 | 9 | More on Symmetric Groups | Section 3.4 of [P] | 3.2 of [E], 5.1 of [J] Permutation Group | |
10/1 | Midterm 1 | ||||
10/3 | 10 | More on Symmetric Groups, Group Actions | Section 3.5 of [P] | 3.2, 3.6 of [E], 5.1, 14.1 of [J], Group Action on [W] (If you look at [W], note that all our group actions are left group actions.) | |
10/8 | 11 | Group Actions and the Orbit-Stabiliser Theorem | Section 3.5, 3.5.1 of [P] | 3.2, 3.6 of [E], 5.1, 14.1 of [J], Group Action on [W] (If you look at [W], note that all our group actions are left group actions.) | |
10/10 | 12 | Conjugacy Classes and Sylow's Theorem. CLASS CANCELLED: read this material | Section 3.5.2-3 of [P] | HW 5 Due | 3.7, 3.8 of [E], 14.2, 15.1 of [J] |
10/15 | 13 | Symmetry of Sets with Extra Structure | Section 3.6 of [P] | Chapter 12 of [J] | |
10/17 | 14 | Normal Subgroups and the Isomorphism Theorems | Section 3.7 of [P] | 3.4, 3.5 of [E], Chapter 10 of [J] | |
10/22 | 15 | Direct Products and Direct Sums, Begin Abelian Groups | Section 3.8 of [P], begin Section 3.9 of [P] | 9.2 of [J] | |
10/24 | 16 | Finite and Finitely Generated Abelian Groups | Section 3.9-10 of [P] | 13.1 of [J] | |
10/29 | 17 | Rings and Field: Basic Definitions | Section 4.1 of [P] | 16.1, 16.2 of [J] | |
10/31 | 18 | Subrings, Ideals, and Homomorphisms | Section 4.2, 4.3 of [P] | 16.3 of [J] | |
11/5 | Midterm 2 | ||||
11/7 | 19 | Polynomial Rings, Ring Extensions | 4.4, 4.5 of [P] | 17.1 of [J] | |
11/12 | 20 | Finish Polynomial Rings, Field of Fractions | 4.6 of [P] | 18.1 of [J] | |
11/14 | 21 | Briefly finish Field of Fractions, then Characteristic | 4.7 of [P] | 16.2 of [J] | |
11/19 | 22 | Prime and Maximal Ideals | 4.8 of [P] | ||
11/21 | 23 | Factorization in Integral Domains | 5.1 of [P] | 16.4 of [J] | |
11/26 | 24 | Finish Unique Factorization, Remainder Theorem for Polynomials, begin PID | 5.2, 5.3 of [P] | 17.2, 18.2 of [J] | |
11/27-12/2 | Thanksgiving Break | ||||
12/3 | 26 | More on PIDs, overview of Galois Theory and Algebraic Geometry (if time) | 5.3, 5.4 of [P] | 17.2, 18.2 of [J] | |
12/5 | 27 | Review Session for Final Exam (possibly after class) | |||
12/17 | Final Exam |
Homework and Exams: