MTH 331/431 Abstract Algebra I (Fall 2019):
- What is Abstract (or Modern) Algebra?
Algebra is defined to be the study of algebraic structures. Mathematicians study algebraic structures from a general point of view, compare different structures, and find relationships between them. In this course we will study elementary number theory, groups, rings, and fields. Find more information about the course in the syllabus. - Instructor: Dr. Sofya Chepushtanova, office SLC 410, email: sofya.chepushtanova@wilkes.edu.
- Class meetings: MWF 11:00-11:50am, room SLC 411 and R 1:00-1:50pm, SLC 378.
- Office Hours: MWF 9:00-9:50am, MW 2:00-2:50am, or by appointment, room SLC 410.
- Textbook: Tom Judson's Abstract Algebra: Theory and Applications.
An electronic version of the book is freely available here. - Sage: an open-source program for doing mathematics and is the ideal companion to Tom Judson's textbook. Sage includes many mature and powerful open-source tools for mathematics, such as GAP, a system for computational discrete algebra (used for group theory). With a strength in number theory, Sage also has excellent support for rings and fields. We will be using Sage sometimes for exercises and assignments. More information about Sage is here and here.
- Reading:
- LaTeX: a markup language to typeset documents. It excels at making math and the overall layout beautiful.
You can use it to type your homework solutions. Read the tutorial here. You may find the following LaTeX cheat-sheet useful.
Consider the following LaTeX template to start: download (it is the template of document On Proofs).
Schedule:
Week of |
Class Topics | Remarks, Materials, Assignments |
8/25 | Introduction. Preliminaries. (Ch. 1) |
Introduction notes Sets and Equivalence Relations |
9/1 | No class on 9/2 (Labor Day) Integers. (Ch. 2) |
Induction and Well-Ordering Principle Division Algorith, Euclidean Algorithm, Prime Numbers Homework 1 due 9/6: All students: Ch. 1, §1.3 "Exercises" (online text), exer. 7, 9, 18(b,c), 19, 20(b), 21, 22(c,e), 25(d). Graduate (MTH 431) students: in addition, do exer. 26 and 29. (MTH 331 students are welcome to do these problems for extra credit.) Latex template for homework: here. Homework 1 Solutions |
9/8 | Groups. (Ch. 3) | Integer Equivalence Classes and Symmetries Homework 2 due 9/13: All students: Ch. 2, §2.3 "Exercises" (online text), exer. 2, 5, 12, 15(d, f), 18. Graduate (MTH 431) students: in addition, do exer. 17(c) and 23. (MTH 331 students are welcome to do these problems for extra credit.) Latex template for homework: here. Homework 2 Solutions |
9/15 | Continue on Groups. Subgroups. (Ch. 3) |
Groups: Definitions and Examples Summary of Some Groups Examples Homework 3 due 9/20: All students: Ch.2, §2.3, exer. 28, 31; Ch. 3, §3.4, exer. 1 (b,d), 2 (c,d), 6, 7, 8, 14. Graduate (MTH 431) students: in addition, do exer. 10 and 15 in Section 3.4. (MTH 331 students are welcome to do these problems for extra credit.) Latex template for homework: here. Homework 3 Solutions |
9/22 | Exam I on 9/23 (Monday) | Study for Exam I (9/23): study guide
Homework 4 due 9/27: All students: Ch. 3, §3.4, exer. 16, 26, 33, 39, 43, 48. Graduate (MTH 431) students: in addition, do exer. 34 and 47. (MTH 331 students are welcome to do these problems for extra credit.) NOTE: Extra problem for all: 45. Latex template for homework: here. |