MATH 301/601

## Math 301/601, Sec 02, Abstract Algebra I, Spring 2023

Here are Solutions to Exam I.
Here are Solutions to Exam II.

### Assignments:

This will be updated regularly.
• Due 5/11. Read Ch. 19, do problems A.1, B.1,2, E.1,2, H.1,4,7. (601 students only: try problems in F.)
• Due 5/9. Read Ch. 18. Do problems A.4 B.3,5 C.3,6 D.4 F.1,2
• Due 5/4. Do problems Ch 17, H.3,4. I.4,5. J.3,5. Read Ch. 18, do problm A.1,4.
• Due 5/2. Read Ch. 17, try problem A.4, and read problem C.1.
• Due 4/27 (no class 4/25). Ch 15 do problems A.1,2,5 B.2, C.1,2,3 E.1,2,3,6. Read Ch. 16 and do problems A.1, C.1-3, E.1-3. Challenge problem: I.1-5.
• Due 4/20. Handwrite corrections to all exams to submit in class.
• Due 3/30. Ch. 14 do problems A. 3, D.1(a), 2, 6, E. 1,5, F.1. Read Ch. 15.
• Due 3/28. Read Ch 14. Do problems A.1,2 B.3-5, C. 2,8, G.1
• Due 3/23. Read Ch. 13, and do problems A.1,3. B.1,2. C.1,5. D.1,2,3 E.1,2.
• Due 3/21. Read Ch 12 and do problems A.1, B.2,4 C.2, D.1.
• Due 3/16. Read Ch 12. Do problems in Ch 11, D. 4, 5. Also:
1) Find all subgroups of a cyclic group with 90 elements (e.g. Z_90, with operation addition modulo 90).
2) Show that if p is prime, then for every integer j from 1 to p-1, there is an integer k with j*k modulo p equal to 1. Conclude that {1,2...,p-1} is a group with operation "multiplication modulo p".
• Due 3/14. Read Ch. 11 do problems A. 1,3 B. 3,4 C. 1,2 D. 1,4,5.
• Due 3/9. Do problems Appendix B, 1,5,8,12,13. Ch 10, do problems E. 1,2. (You can also try working through G.1 to G.5. I will present solutions in class.)
• Due 3/7. Read Ch. 10 and do problems B. 2,6, C. 3,5, D. 1,2. Review Appendix B (consider problems 1,5,8,12,13.)
• Due 3/2. Study for exam I.
• Due 2/28. Do problems in Ch 9, A.1,2,3, C.1,2,4 D.2, E.1,2.
• Due 2/23. Do problems in Ch 8. B.1, C.1-3, F.1,2, G.4, H.1,2.
• Due 2/16. Read Ch. 8. Do problems A.1c,2c,3c B.1,4, D.1,2,3.
• Due 2/14. Read Ch. 6. and do problems A2, B1, C4, D5, E2. Read Ch 7 and do problems A.1,3. B.2,3. F.1-4.
• Due 2/9. Do problems from Ch. 5 D.1, 8(uses Ch.4 G.1), E.1,4,6,7. F.2 (students in 601 do F.3).
• Due 2/7. Read Ch. 4, do problems A.1,4. B.1,2,5. C.1-4. D.1,8. (Students in 601, do problem G). Read Ch. 5, do problems A,1,5. (Students in 601, do A.7, B.1)
• Due 2/2. Read Ch.3 and do problems A.1,4, B.1,4, C.1-3, D(all). Students registered for 601 do problem E(all) as well.
• Due 2/7. Read Ch. 1. These are meant to motivate the book and its subject. The mathematical details will be filled in during the course, but try to extract the basic concepts.
• Due 1/31. Read Preface and Appendix A, 345-347. Also read Ch. 2, p. 19-21, and do Problems A.1,4,5. B.1,5,6. D.1,2,3. Be prepared to present solutions in class.

### Course Information:

This course is an introduction to algebraic structures, including the theory of groups, rings and fields.
• Location: Tuesdays and Thurdays, 10:05-11:55, Kiely 273.
• Textbook: "A Book of Abstract Algebra," second edition, by Charles C. Pinter.
• Grading: The final grade will be based on two preliminary exams (30% each), and the final exam (40%). Homework assignments will generally not be graded, but are essential for progress in the course. The letter grades will correspond to the student's display of content knowledge: A (great), B (good), C (little to good), D or F (little or none). The letter grade F is always given for cheating or plagarism. In this case, I will seek academic and disciplinary sanctions. See The CUNY Policy on Academic Integity.
• Exams: The two preliminary exams are in class on March 2nd and April 4th. The final exam is Thursday, May 18th, 11am-1pm in Kiely 273.

### Contact Information:

• Instructor: Scott Wilson
• Email: scott dot wilson AT qc.cuny.edu
• Office: Kiley 609.
• Office hours: Tuesday, Thursday 1:35-2:05, or by appointment.