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Homework for Abstract Algebra I

Math 171, Spring 2013, Harvey Mudd College
Prof. Orrison

Unless stated otherwise, homework is due on Tuesdays at the beginning of class. Also, the Focus Problems listed below are problems that you should ponder and sincerely attempt to solve because they will help you better understand important and useful ideas and techniques. Even though you will not be submitting your solutions to the Focus Problems, please keep in mind that they will be considered fair game for the exams.

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1. Due Tue. 1/29: Groups

Reading — Sections 1.1-1.5, Communicating Mathematics through Homework, and Prof. Su's Advice.
Focus Problems — (1.1) 8, 26, 27. (1.2) 12. (1.3) 4, 6.
Problems — (1.1) 22, 25, 31. (1.2) 3. (1.3) 2, 11.
Rewrites Due — Tue. 2/12. Remember to attach your original assignment under your rewrites, and that rewritten solutions must be fully rewritten.

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2. Due Tue. 2/5: Homomorphisms and Quotient Groups

Reading — Section 1.6 and Section 3.1.
Focus Problems — (1.6) 2, 13, 14, 20, 21. (3.1) 22, 24, 25, 32, 40, 42, 43.
Problems — (1.6) 16, 18, 23. (3.1) 1, 36, 41.
Rewrites Due — Tue. 2/19.

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3. Due Tue. 2/12: Cosets and Isomorphism Theorems

Reading — Sections 3.2-3.3.
Focus Problems — (3.2) 5, 7, 12, 16, (3.3) 1, 4, 10.
Problems — (3.2) 4, 20, 22. (3.3) 3, 8, 9.
Rewrites Due — Tue. 2/26.

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4. Due Tue. 2/26: Group Actions, Centralizers, Normalizers,...

Reading — Section 1.7 and Section 2.2.
Focus Problems — (1.7) 4, 15, 16. (2.2) 2, 3, 5.
Problems — (1.7) 17, 18, 19. (2.2) 7, 9, 10.
Rewrites Due — Tue. 3/12.

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5. Due Tue. 3/5: Cyclic Groups and the Class Equation

Reading — Sections 2.3-2.5 and Sections 4.1-4.3.
Focus Problems — (2.4) 2, 14. (4.2) 8. (4.3) 11, 24, 25.
Problems — (2.3) 15, 24. (4.3) 1, 3, 6, 13.
Rewrites Due — Tue. 4/2.

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6. Due Tue. 3/12: Sylow's Theorems

Reading — Section 4.5.
Focus Problems — (4.5) 2, 4, 13, 14, 15, 16.
Problems — (4.5) 1, 3, 5, 17, 18, 30.
Rewrites Due — Tue. 4/16.

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7. Due Tue. 4/2: Rings

Reading — Section 7.1.
Focus Problems — (7.1) 4, 6, 11, 13, 17, 20.
Problems — (7.1) 7, 8, 9, 14, 15, 16.
Rewrites Due — Tue. 4/16.

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8. Due Tue. 4/9: Ring Homomorphisms and Quotient Rings

Reading — Section 7.3.
Focus Problems — (7.2) 6, 7. (7.3) 1, 18, 34, 35.
Problems — (7.2) 10, 13. (7.3) 13, 26, 28, 29.
Rewrites Due — N/A.

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9. Due Tue. 4/16: Properties of Ideals

Reading — Section 7.4.
Focus Problems — (7.4) 2, 4, 8, 11, 19, 26.
Problems — (7.4) 7, 23, 24, 30, 31, 32.
Rewrites Due — N/A.

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10. Due Tue. 4/30: Euclidean Domains and PIDs

Reading — Sections 8.1-8.2.
Focus Problems — (8.1) 1, 2, 5, 11, 12. (8.2) 4.
Problems — (8.1) 3, 4, 6. (8.2) 1, 2, 3.
Rewrites Due — N/A.
Note — This is the last homework for the semester.

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