Abstract Algebra I and Number Theory, MTH 310-03
Tentative Schedule and Homework Assignments
Chapter numbers refer to:
Abstract Algebra, 2nd Ed., Thomas Hungerford, Cengage Learning 1996 Chapters 1-7, ISBN13: 978-0030105593.
Prof. Meierfrankenfeld's Notes
Piazza Forum:
This is a question-and-answer pantform created for our class, where we can discuss solutions to class assignments. You can access it using the following link: piazza.com/msu/fall2014/mth310/home
| L | Date | Chapter and Topic | HW | Comment |
| 1 | 8/27 | 1.1: The Division Algorithm | Due 08/291.1: 1a,d, 5, 8, 9. Problem statements can be found here. | Read Section 1.2 before Friday's class. |
| 2 | 8/29 | 1.2: Divisibility | Due 09/051.2: 1d, 3, 10, 16, 17, 20, 21, 25-bonus.Problem statements can be found here. | |
| 9/1 | Labor Day - no class | |||
| 3 | 9/3 | 1.2: Continued | ||
| 4 | 9/5 | 1.3: Prime Numbers | Due 09/121.3: 2, 4, 10, 25-bonusProblem statements can be found here. | Read Section 1.4. Think about problems 7 and 15. |
| 5 | 9/8 | 1.3: Continued | Due 09/121.3: 12a, 15, 16, 22 | |
| 6 | 9/10 | 2.1: Congruence and Congruence Classes | Due 09/192.1: 6, 10, 13a, 22, 23 | |
| 7 | 9/12 | 2.2: Modular Arithmetic | Due 09/192.2: 1d, 2d, 7, 8 | |
| 8 | 9/15 | 2.3: The Structure of Zp, When p is Prime | Due 09/192.3: 5, 6 | Suggested reading: Ch. 12 on Public-Key Cryptography |
| 9 | 9/17 | 2.3: Continued 3.1: Definition and Examples of Rings | Due 09/262.3: 7e, 8, 9, 10, 11a | |
| 10 | 9/19 | 3.1: Continued | Due 09/263.1: 19, 24, 26 | |
| 9/22 | Last day to withdraw with tuition refund | |||
| 11 | 9/22 | 3.1: Continued 3.2: Basic Properties of Rings | Due 09/263.1: 5a,c,e, 6, 9, 18, 31 | |
| 12 | 9/24 | 3.2 - Continued | Due 10/033.2: 5, 6, 11, 12 | |
| 13 | 9/26 | 3.2 - Continued | Due 10/033.2: 18, 19, 26, 28 | Read Section 3.3. |
| 14 | 9/29 | 3.3 - Isomorphisms and Homomorphisms | Due 10/103.3: 6, 9, 13, 16 | |
| 15 | 10/1 | Review | Review for exam 1 | |
| 16-M | 10/3 | Midterm Exam | The exam will cover Chapters I and II, and sections 3.1 and 3.2. | |
| 17 | 10/6 | 3.3 - Continued | Due 10/103.3: 19, 28, 33a,b,c,e, 39-bonus | |
| 18 | 10/8 | Discussion and 4.1 | ||
| 19 | 10/10 | 4.1 - Polynomial Arithmetic | Due 10/174.1: 1a, 4, 6a,c,d,e, 8, 10 | |
| 20 | 10/13 | 4.1 - The Division Algorithm for Polynomials 4.2 - Divisibility in F[x] | Due 10/174.1: 5c,d, 16, 18, 14-bonus4.2: 3, 4 | Reading assignment: read the proof of Theorem 4.5 before Wednesday's class and be prepared to discuss it. |
| 21 | 10/15 | 4.2 - continued | Due 10/244.2: 5d, 7, 10, 12, 13, 14 | See Piazza for a hint on problem 10. |
| 10/15 | Last day to withdraw with no grade reported | |||
| 22 | 10/17 | 4.3 - Irreducibles and Unique Factorization | Due 10/244.3: 2, 5, 6, 9a |
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| 23 | 10/20 | 4.3 - continued | Due 10/244.3: 8, 12, 22a, 23a |
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| 24 | 10/22 | 4.4 - Polynomial Functions, Roots, and Reducibility | Due 10/314.4: 1a, 3c, 4b, 6a,c, 7, 8f, 14a, 15 |
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| 25 | 10/24 | 4.5 - Irreducibility in Q[x] | Due 10/314.5: 5c, 7b |
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| 26 | 10/27 | 5.1 - Congruence in F[x] and Congruence-Classes | Due 10/315.1: 1a, 2, 8, 10, 11, 13 |
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| 27 | 10/29 | 5.2 - Congruence-Class Arithmetic | Due 11/75.2: 2, 6, 9, 14a |
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| 28 | 10/31 | 5.2 - continued | Due 11/75.2: 8, 11 |
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| 29 | 11/3 | 5.3 - The Structure of F[x]/(p(x)) When p(x) is Irreducible | Due 11/75.3: 1a,b, 5, 8 |
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| 30 | 11/5 | 6.1 - Ideals and Congruence | Due 11/196.1:2, 6b, 7b, 9, 12a |
Note - the HW is due on Wednesday |
| 31 | 11/7 | 6.2 - Quotient Rings and Homomorphisms | ||
| 32 | 11/10 | Review | Review for exam 2 | |
| 33 | 11/12 | Review | Partial solutions to the review problems | |
| 34-M | 11/14 | Midterm Exam | ||
| 35 | 11/17 | 6.2 - continued | Due 11/266.2: 3, 4, 5, 8a, 10, 11, 19, 33-bonus |
Note - the HW is due on the Wednesday before Thanksgiving. If you can't attend class, please make arrangements to turn it in early. |
| 36 | 11/19 | 7.1 - Definition and Examples of Groups | Due 11/267.1: 5, 7, 8, 10, 13a |
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| 37 | 11/21 | 7.1 - continued | Due 11/267.1: 17, 24, 25 |
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| 38 | 11/24 | 7.2 - Basic Properties of Groups | Due 12/57.2: 5, 7, 11, 13, 19 |
Visual Group Theory |
| 39 | 11/26 | 13.1 - The Chinese remainder Theorem | ||
| 11/28 | Thanksgiving - no class | |||
| 40 | 12/1 | 7.3 - Subgroups | Due 12/57.3: 1, 3a, 12, 14, 23 |
Office hours on Tuesday are moved to 10 am-noon. |
| 41 | 12/3 | 7.3 - continued Review | Consider the following, but do not turn in: 7.3: 2, 6, 11, 15, 17, 18 |
Last quiz is on Wednesday, instead of Friday. |
| 42 | 12/5 | Review | Review sheet Partial solutions |
Please take the survey requesting your feedback on MTH 299. |
| 12/9 | Office Hours 10:30 am - 1:00 pm | C-137 Wells Hall | ||
| E | 12/10 | Final Exam 10:00 am - noon |