MTH 331/431 Abstract Algebra I (Fall 2017):
 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: MWRF 10:0010:50am, room SLC 405.
 Office Hours: MWF 11:00amnoon, T 9:0011:00am, room SLC 410.
 Textbook: Tom Judson's Abstract Algebra: Theory and Applications.
An electronic version of the book is freely available here.  Sage: an opensource program for doing mathematics and is the ideal companion to Tom Judson's textbook. Sage includes many mature and powerful opensource 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 cheatsheet useful.
Consider the following LaTeX template to start: download (it is the template of our document On Proofs.)
Schedule:
Week of 
Class Topics  Remarks, Materials, Assignments 
8/28  Introduction. Preliminaries (Ch.1). Integers (Ch.2). 

9/4  Continued: Preliminaries (Ch.1). Integers (Ch.2). No class on 9/4 
Homework 1 due 9/8: All students: Ch. 1, Sect. 1.3 "Exercises" (online text), exer. 7, 9, 18(b), 19, 20(b), 21, 22(c), 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.) 
9/11  Continued: Integers (Ch.2). Groups (Ch.3)  (Baby) Homework 2 due 9/15: All students: Ch. 2, Sect. 2.3 "Exercises" (online text), exer. 2, 5, 15(d), 18. Graduate (MTH 431) students: in addition, do exer. 23. (MTH 331 students are welcome to do this problem for extra credit.) Everyone: extra credit problem is exer. 12. 
9/18  Groups (Ch.3). Study for Exam I (9/22): study guide 
Homework 3 due 9/25: All students: Section 2.3 "Exercises": exer. 28, 31, Section 3.4 "Exercises": exer. 1 (b,d), 2 (d), 7, 8, 13, 24. 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.) 
9/25  Subgroups (Ch. 3). Cyclic Groups (Ch. 4).  
10/2  Cyclic Groups (Ch. 4). Permutation Groups (Ch. 5). 
Homework 4 due 10/6: All students: Section 3.4 Exercises 16, 26, 33, 43, 47, 48 Section 4.4 Exercises 1(b) and 2(b). Graduate (MTH 431) students: in addition, do exer. 34 and 39 in Section 3.4. (MTH 331 students are welcome to do these problems for extra credit.) Extra problem for all: 45 in Section 3.4. 
10/9  Permutation Groups (Ch. 5). Fall Recess 10/1210/15 
Homework 5 due 10/18: All students: Section 4.4 Exercises 3(h and k), 4 (d), 6, 23 (a and c), 31. Section 5.3 Exercises 2 (g and j), 3 (d), 4, 6, 23. Graduate (MTH 431) students: in addition, do exer. 11 and 26 in Section 4.4 and exer. 34 in Section 5.3. (MTH 331 students are welcome to do these problems for extra credit.) Extra problems for all: 13 and 27 in Section 5.3. 
10/16  Cosets and Lagrange's Theorem (Ch. 6). Study for Exam II (10/20): study guide 

10/23  Cosets and Lagrange's Theorem (Ch. 6). Isomorphisms (Ch. 9). 
Homework 6 due 10/30: All students: Section 6.4 Exercises 1, 3, 4, 5 (b and f), 8, 11 (prove only that statements (a) and (d) are equivalent), 17. Graduate (MTH 431) students: in addition, do Exercises 18, 19. (MTH 331 students are welcome to do these problems for extra credit.) Extra problem for all: Exercise 13. 
10/30  Normal Subgroups and Factor Groups (Ch. 10).  Homework 7 due 11/8: All students: Section 9.3 Exercises 2, 3, 7, 8, 9 (do not need to proof that G is a group, prove isomorphism only), 16 (b and d), 34, 46, 50. Graduate (MTH 431) students: in addition, do Exercises 25 and 41. (MTH 331 students are welcome to do these problems for extra credit.) Extra problem for all: Exercise 24. 
11/6  Homomorphisms (Ch. 11)  Homework 8 is due 11/15: All students: Section 10.3 Exercises 1 (a,b,c,e), 5, 6, 8, 9. Graduate (MTH 431) students: in addition, do Exercises 11 and 12. (MTH 331 students are welcome to do these problems for extra credit.) Extra problem for all: Exercise 13 (a,c). 
11/13  Finite Abelian Groups (Ch. 13). Study for Exam III (11/17): study guide 

11/20  Rings (Ch. 16). Thanksgiving Recess 11/2211/26 (Tuesday follows Thursday schedule) 
Homework 9 is due 11/29: All students: Section 11.3 Exercises 2 (b,c,d,e), 4, 12, 13, 16, 18; Section 13.3 Exercises 2 and 3. Graduate (MTH 431) students: in addition, do Exercise 17 in Section 11.3. (MTH 331 students are welcome to do this problem for extra credit.) Extra problem for all: Exercise 7 (a,b) in Section 11.3. 
11/27  Rings (Ch. 16).  Homework 10 is due 12/8: All students: Section 16.6 Exercises 1 (b,h), 3 (b,d), 4(b,d,e), 8, 9, 11, 18 (c,d), 23. Graduate (MTH 431) students: in addition, do Exercises 2 and 16. (MTH 331 students are welcome to do these problems for extra credit.) Extra problem for all: Exercise 5. 
12/4  Polynomial Rings (Ch. 17).  
12/11  Takehome Final Exam is due 12/18/17, at 11am Graduate Student Presentations on 12/11/17 (Monday follows Friday schedule) 
