Homework Homework will be posted on this webpage, and collected in class on the due date. No late homework will be accepted. Collaboration policy Reasonable collaboration is permitted on homework. However, the homework you submit should reflect your own understanding of the material. You are not allowed to copy solutions from other students or other sources. Your final solutions should always be written in your own words. You should write down the name of your collaborator(s) for each problem that you have collaborated on. Submission Please put the following information at the top of your homework: your name, the due date, Math 245, and the assignment number. The homework problems will be mostly chosen from 2nd edition of EC1. Difficulty Levels and Weights Each problem has a difficulty factor [d], such as [3-]. This is converted into a weight w(d), as follows. w(1-) = 0.1, w(1) = 0.3, w(1+) = 0.5 w(2-) = 1, w(2) = 2, w(2+) = 3 w(3-) = 5, w(3) = 8, w(3+) = 12 w(4-) = 18, w(4) = 25, w(4+) = 50 w(5-), w(5): depends on solution For each homework, I will assign a few problems, most (if not all) of them will be rated as [2], [2+], [3-]. You only need to hand in your "best" one or two problems, as indicated on each assignment. Please indicate clearly which problem each solution belongs to. Although you only need to submit one or two problems, I expect you to work on a range of problems throughout the quarter. In particular, I expect the average weight of the problems you work on to be at least 2.5, which is the average of the weight ofs a [2] problem and a [2+] problem. Of course, it is better to turn in a [2] problem with a perfect solution than a [3-] problem with an incorrect solution. Grading Each submitted problem is worth 10 points. Your score on a problem will be the number of points you receive times the difficulty factor. For example, if you receive 9 out of 10 points on a [2+] problem, your score for that problem is 9 x w(2+) = 9 x 3 = 27 points. The 10-point score reflects the quality of your submitted solution, including both the correctness of the mathematics and the clarity and completeness of the written argument. Having the right idea is important, but a correct idea by itself does not constitute a complete solution. I will not give full credit to a solution that has the correct idea but does not clearly explain why the argument works. To encourage you to work on more difficult problems, you may submit a [2+] or [3-] problem from the previous homework assignment in place of a problem on the current assignment. For example, for Homework 2, you may submit a [3-] problem from Homework 1. For a letter grade of A or A- on the homework component, I expect an average score of 22.5 points per submitted problem. Thus, it is highly recommended that you submit at least one problem with difficulty level [2+] or higher for each homework. Working on a [3-] problem once a while is a good way to increase your score. Help During Office Hours I am happy to discuss homework problems with you during office hours. However, because the difficulty level of a problem affects its weight in the grading, the amount of guidance I provide will generally decrease as the difficulty level increases. For a [2-] or [2] problem, I am happy to discuss the problem with you and, if needed, gradually provide substantial hints and ideas. For a [2+] problem, I will provide some hints or partial ideas, but I will expect you to work out the main argument yourself. For a [3-] problem, I expect you to develop the main idea and solution essentially on your own. I may give a small hint if you are stuck, but I will generally not provide the main idea or outline of the solution. If you have developed the mathematical ideas but are having difficulty turning them into a clear written proof, I am happy to help you formulate and organize your argument. However, the final submitted solution should still be your own work. In general, the more difficult the problem, the more you should expect to work through the key ideas yourself before coming to office hours. Proofs Some problems may ask for an elegant proof or a combinatorial proof. Please ask me if you are not sure what is meant by either of these terms. Homework Schedule The due dates below are tentative and may be adjusted during the quarter. Homework 1 due Wednesday 10/7. (Make sure that you read the above instruction.) Homework 2 due Wednesday 10/14. Homework 3 due Wednesday 10/21. Homework 4 due Wednesday 10/28. Homework 5 due Wednesday 11/4. Homework 6 due Friday 11/13. Homework 7 due Friday 11/20. Homework 8 due Wednesday 12/2.