Homework
The geometric idea behind the famous identity, $\sum_{k=1}^n k = \frac{n^2 + n}{2}$.
The only way to learn math is to do math. If you don't work on exercises, you never become confident in solving problems. Ideally you should attempt all the homework on your own at first, realizing that there will be problems that may take some chin scratching before you can solve them. Running into problems and making mistakes is normal, just try to learn from the mistakes you do make.
When studying and doing homework, don't simply strive to get an answer: try to really understand what's going on, and why the manipulations you perform actually give you the answer. To quote the mathematician Paul Halmos,
Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
Homework will be taken up at the start of class. Late homework will not be accepted!
Due: Tuesday January 13, 2015
- Read Ch. 1 of Silverman.
Due: Thursday January 15, 2015
- Read Chs. 2 and 3 of Silverman.
- Create an account on the Sage Math Cloud (http://cloud.sagemath.org) using your @clemson.edu email address.
Due: Tuesday January 20, 2015. (Key to graded problems.).
- Exercises from Silverman, Ch. 1: 1.1, 1.5, and 1.6.
- Exercises from Silverman, Ch. 2: 2.1, 2.7, and 2.8
- Exercises from Silverman, Ch. 3: 3.2, 3.3, and 3.5
Of these problems, only numbers 1.6, 2.1, and 3.3 were collected and graded.
Due: Tuesday, January 27, 2015
- Exercises from Silverman, Ch. 5: 5.3, 5.4
- Exercises from Silverman, Ch. 6: 6.1, 6.4, 6.6
Of these problems, only numbers 5.3 and 6.4 were collected and graded.
Due: Thursday, January 29, 2015 Extended to Tuesday, February 3
Due: Thursday, February 5, 2015
- Exercises from Silverman, Ch. 7: 7.1, 7.2, 7.4
- Exercises from Silverman, Ch. 8: 8.3, 8.4, 8.9
Due: Tuesday, February 10, 2015
Due: Tuesday, February 17, 2015
- Exercises from Silverman, Ch. 9: 9.2, 9.3
- Exercises from Silverman, Ch. 10: 10.1, 10.3
- Exercises from Silverman, Ch. 11: 11.2, 11.3, 11.7, 11.10
Due: Thursday, February 19, 2015
Due: Thursday, April 2
- Exercises from Silverman, Ch. 21: 21.1, 21.3.
- Exercises from Silverman, Ch. 22: 22.1, 22.2, 22.7
Due: Tuesday, April 7
- Exercises from Silverman, Ch. 28: 28.3, 28.4, 28.7
- Exercises from Silverman, Ch. 29: 29.2, 29.3, 29.4