MATH 380: Homework Assignments
Turn in your homework assignment to me (in class or my office) before 4:00 PM on the due date.
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UPDATED: Wednesday, December 9, 2009 at 14:28
| Set | Homework Problems | Reading Assignment | Due Date |
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| Sec. 1.1: 2(a,b), 3, 5, 6, 7, 9, 10 | |||
| Sec. 1.2: 3, 6, 7, 9, 11, 13, 17, 18, 19 Hint: "Give a geometric description" means to describe in words, but you can use a picture to help with your description. To "illustrate a simple bijection" I would be happy with a well labeled picture, indicating where various points are mapped to. "Investigate the correspondence" means you should determine (with proof) if the correspondence is or is not surjective, injective, or bijective. |
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| Sec. 1.3: 10 Sec. 1.4: 1, 2, 3, 7, 10, 13, 14a (Can you do #6?) |
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| Sec. 1.5: 1, 4, 6, 7, 8, 9, 11, 12, 13 | |||
| Sec. 1.6: 3, 4, 5, 7, 9, 10 For most of the ambient isotopies, you will not be writing a formula. Instead you may need to draw a series of pictures to illustrate your isotopy, with a simple explanation where necessary. Overzealous students may want to actually create the animation itself using computer technology. (Automatic A if you do....) (Read #11 and #12 about "triangulation". You don't have to do them, but it is a very important concept that we may make use of later.) |
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| Sec. 2.1: 2, 3, 4, 9 Sec. 2.2: 3, 5, 6, 8, 14, 15 (Read 11, 12, and 13 of Sec. 2.2 about "unknotting and unlinking". You don't have to do them, but they are interesting.) |
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| Exam Questions: The exam coming up will cover Sections 1.1-1.6 and 2.1-2.4 of the textbook. Each student should submit a possible exam question coming from the material of Chapter 1 or Section 2.1-2.4. Submit one question by Thursday, October 8, and if I choose to include your question then you will receive 5 bonus points on the exam. | |||
| Sec. 2.3: 3, 4, 6, 8, 11 Sec. 2.4: 1, 2, 10 |
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| Exam 1 will be given on Thursday, Oct. 15: The exam will be a take-home exam and will cover all of Sections 1.1-1.6 and 2.1-2.4 of the textbook. You will NOT be allowed to use your textbook, notes or any other aid, and you must work alone. You must hand in the exam by 3:00 on Monday, Oct. 19. It will be similar to the homework. To practice for the exam, review the homework problems, do some extra problems similar to the homework problems, and know ALL of the relevant definitions and theorems. | --- Hand in Monday, October 19 |
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| Sec. 2.5: 1, 2, 5, 7, 14(a) | |||
| Sec. 2.6: 2, 4, 6, 7, 9, 10 Hint: Reading the last paragraph of Section 2.6 may help you with #9 and #10. |
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| Sec. 2.7: 3, 5, 8, 10 (You will use exercise 4, but you do not have to prove it.) Sec. 3.1: 2, 3, 4, 5 |
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| Sec. 3.2: 4, 6, 7, 8 Sec. 3.3: 1, 3, 4, 6(a,b), 7 (Read 6(c,d), 8, and 10. You don't have to do them, but they are interesting.) |
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| Exam Questions: The exam coming up will cover Sections 2.5-2.7 and 3.1-3.5 of the textbook. Each student should submit a possible exam question coming from the material of these sections. Submit one question by Tuesday, November 10, and if I choose to include your question then you will receive 5 bonus points on the exam. | |||
| Sec. 3.4: 1, 3, 4, 6, 10, 11 Sec. 3.5: 1, 4 (You might want to consider doing #2, and feel free to give it to me!) |
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| Exam 2 will be given on Thursday, Nov. 19: The exam will be a take-home exam and will cover all of Sections 2.5-2.7 and 3.1-3.5 of the textbook. You will NOT be allowed to use your textbook, notes or any other aid, and you must work alone. You must hand in the exam by 10:00 AM (in class) on Tuesday, Dec. 1. It will be similar to the homework. To practice for the exam, review the homework problems, do some extra problems similar to the homework problems, and know ALL of the relevant definitions and theorems. | --- Hand in Tuesday, December 1 |
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| Sec. 4.1: 2 (b-e), 3(b,c), 6, 7, 9 (Read 8 (b,c) for a description of projective space P3.) (Remember that to show something is a n-manifold, you just need to find a neighborhood homeomorphic to an open n-ball around any point.) Sec. 4.2: 3, 4, 5, 6, 8(a,b,c), 9 (SPECIAL INSTRUCTIONS: Do 8a, then the extra problem below, THEN do 8b and 8c.) Problem 8(a2): Triangulate Bn for n=0,1,2,3,4 with the simplest possible triangulation. (A drawing for B4 is not necessary but may help.) Make a chart whose entries are the number of vertices, edges, faces, 3-cells, 4-cells, 5-cells and 6-cells for each Bn so that the k-th row would list the number of cells in Bk-1. For example, the third row would say: B2: 3 3 1 0 0 0 0 since it has 3 vertices, 3 edges, 1 face, and no 3-cells, 4-cells, 5-cells, or 6-cells. Make an educated guess to fill in the chart to include B5 and B6. Determine the Euler characteristic of Bn for all n. |
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...Yeah right! Have a great and safe break! |
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Click here to complete the evaluation |
completed by Tuesday, December 15 |
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| Sec. 4.3: 5, 6, 7, 8 Sec. 4.4: 7, 8, 9 |
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| Sec. 6.1: 2, 3, 4, 6(a) Sec. 6.2: 1 Sec. 6.3: 3, 5, 7. Also show h : π1(X,x0) → π1(X,x1), as defined in class, is an isomorphism. Sec. 6.4: 12(d), 13, 14, 16, 17 (Hint: These problems require almost no effort!) |
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Exam |
The Final Exam is on Thursday, December 17, 8:00-11:00 am, in class (Sturges 105): The exam is a "nonstandard" exam. Click here for more details, and we will discuss it in class on Tuesday, December 8. | ||