Instructor: David Corwin (dcorwin at berkeley dot edu). In all e-mail correspondence, please include "[Math113]" in the subject line.
GSI: Julian Chaidez (jchaidez at berkeley dot edu)
Lecture: MW 5pm-6:30pm in Hearst Mining 310
GSI Office hours: GSI Office hours are tentatively in Evans 961. They are 3:30-6 MTuTh, 3-4 W and 3:30-5 F.
My Office hours: Location: Evans 749, Monday 2-3pm, Tuesday 3:45-5:45pm. Subject to change if I am away: No office hours April 30. Extra office hours 1-2pm on April 29 and 3:45-4:45pm on May 2.
Final office hours or review: Wednesday, May 8.
Final exam: Friday, May 17, 2018 3-6pm. Location HM 310 (same as class).
Prerequisites:
Text: The primary text for this course is Notes on Abstract Algebra by Alexander Paulin [P]. 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: 30% homework, 70% exams. The lowest two homework scores will be dropped. No makeups for the midterm will be given except in cases requiring special accommodation. The midterm will be on March 20, in class. Your exam grade, which counts for 70%, will be computed based on the maximum of the following two schemes: 0.25*midterm+0.75*final and 0.35*midterm+0.65*final
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 | Meeting | Topics | References | Comments | Alternative References |
---|---|---|---|---|---|
1/23 | 1 | Logistics/Syllabus, Overview of Course | Section 1.1 of [P] | ||
1/28 | 2 | Sets and Functions | Section 1.2-1.3 of [P], plus Notes on mathematical proofs - PLEASE READ | Chapter 1 of [J], | |
1/30 | 3 | Integers and Modular Arithmetic | Section 2 of [P], see these problems for optional practice. | 2.2 and 3.1 of [J], GCD, Euclidean Division and Modular Arithmetic on [W] | |
2/4 | 4 | Groups and Homomorphisms | Section 3.1 of [P], see these problems for optional practice. | 3.2 and 9.1 of [J], Groups, Group Homomorphism on [W] | |
2/6 | 5 | Subgroups, Cosets, and Lagrange's Theorem | Section 3.2 of [P], see these problems for optional practice. | HW 1 Due | 3.3, 6.1, 6.2 of [J], Subgroup, Coset, Lagrange's Theorem on [W] |
2/11 | 6 | Finitely Generated Groups | Section 3.3 of [P], see these problems for optional practice. | 4.1 of [J], Order, Generating Set, Cyclic Groups on [W] | |
2/13 | 7 | Permutation Groups and Group Actions | Section 3.4 of [P], see these problems for optional practice. | HW 2 Due | 5.1, 14.1 of [J] Permutation Group, Group Action on [W] (If you look at [W], note that all our group actions are left group actions.) |
2/18 | HOLIDAY | ||||
2/20 | 8 | The Orbit-Stabiliser Theorem and Sylow's Theorem | Section 3.5 of [P], see these problems for optional practice. | HW 3 Due | 14.1, 14.2, 15.1 of [J] |
2/25 | 9 | Quaternion Group, Begin Symmetric Groups | See the Mathworld article on the quaternion group or the group wiki article. Note that "conjugacy class" is the same as "orbit under conjugation." | See Example 1.12 of these notes. | |
2/27 | 10 | Finite Symmetric Groups | Section 3.6 of [P], see these problems for optional practice. | HW 4 Due | |
3/4 | 11 | Symmetry of Sets with Extra Structure | Section 3.7 of [P], see these problems for optional practice. | ||
3/6 | 12 | Normal Subgroups and the Isomorphism Theorems | Section 3.8 of [P], see these problems for optional practice. | HW 5 Due | Chapter 10 of [J] |
3/11 | 13 | Direct Products and Direct Sums | Section 3.9 of [P], Notes on centralizers | 9.2 of [J] | |
3/13 | 14 | Finitely Generated Abelian Groups | Section 3.10 of [P] | ||
3/18 | 15 | Finite Abelian Groups | Section 3.11 of [P] | HW 6 Due | 13.1 of [J] |
3/20 | 16 | Midterm Exam | |||
3/25-3/29 | Spring Break | ||||
4/1 | 16 | Rings and Field: Basic Definitions | Section 4.1 of [P] | 16.1, 16.2 of [J] | |
4/3 | 17 | Subrings, Ideals, and Homomorphisms | Section 4.2, 4.3 of [P] | HW 7 Due | 16.3 of [J] |
4/8 | 18 | Polynomial Rings | 4.4 of [P] | 17.1 of [J] | |
4/10 | 19 | Field of Fractions | 4.5 of [P] | HW 8 Due | 18.1 of [J] |
4/15 | 20 | Characteristic | 4.6 of [P] | 16.2 of [J] | |
4/17 | 21 | Ring Extensions, begin Principal Ideals | 4.7 of [P] and handwritten notes on Bcourses (4.7 is sparse), begin 4.8 of [P] | HW 9 Due | |
4/22 | 22 | Principal, Prime, and Maximal Ideals | 4.8 of [P] | 16.4 of [J] | |
4/24 | 23 | Factorization in Integral Domains and UFD's | up to p.64, also my notes on factorization in rings | HW 10 Due | |
4/29 | 24 | A little bit about PID's, then factorization of polynomials | my notes (see link under 4/24) | ||
5/1 | 25 | More on polynomials, overview of Galois Theory and Algebraic Geometry | my notes (see link under 4/24) | ||
5/17 | 1 | Final Exam |
Homework and Exams: