m225project

Math 225

Fall 2008

Miniprojects

The following is a long list of what I am calling "Miniprojects". They are either one or more problems from the text or problems of my own devising (or someone else's devising in the math department) related to the content covered in each section. They are intended to be interesting, fun, and perhaps challenging, and might also preview later topics in this or other courses in Math or Computer Science. Some of the topics are just fun and games, some are very mathematical, a few are very applicable to computer science, so your interest level in each miniproject will vary depending on your own personal interests and on what you want to get out of this course. Therefore, I do not expect you to do every one of these miniprojects (although you certainly may if you wish!). The "Miniproject" component of your grade will consist of the best 30 scores you get on the miniprojects that you submit. Although I haven't written miniprojects for the entire semester yet, I do expect to write, on average, about two for each section, which will mean that there will be on the order of 60 choices available to you. You may do as few as 30 miniprojects if you wish, or you may do all of them, or any number in between. This also means that if you do poorly on one of them, you may do an extra one to replace the poor score. It also means that if you choose to do the first thirty miniprojects, you can be done with them halfway through the semester.

I intend for this part of your grade to pique your interest, be at least a little enjoyable, and to help your grade overall. However, in order for that to occur, you do have to keep up. I would expect each one to take anywhere from 30 minutes to complete to a couple of hours, depending on your interest, prior knowledge, and sometimes creativity. But this means that you won't be able to do all of your projects in the last week of the class, at least not if you wish to pass any of your final exams. Therefore, I will institute some due dates. The miniprojects for those sections covered on an exam will be due the class day after the exam. For example, I expect Exam 1 to cover sections 1.1-1.4 and will be on Friday, September 12. Therefore, any of the miniprojects from sections 1.1, 1.2, 1.3, or 1.4 will be due on Monday, September 15. I chose this for the due date because you would otherwise have little to do (for this class anyway) at that time. However, to make the most efficient use of your time I would suggest that you look at the miniprojects for the sections as we finish the section, and do any that you like immediately. You may turn in the miniprojects early if you finish them early (although I am not likely to grade them early, I do promise not to lose them!). There will be five exams, so this will break the miniprojects into five chunks. Therefore, a good rule of thumb is to do at least six miniprojects per exam. Note: Miniprojects that are on the material between the fifth exam and the final exam will be due the day of the final exam, rather than the day after.

Your solutions should include a printout of the problem (or at least the first page), so that I know which one you are doing, and should be well-written and legible. If your handwriting is atrocious, this means that you might want to type them, at least if there are not too many mathematical symbols, diagrams, or tables, but I do not require that they be typed. My guess is that it will be rare for you to turn in your initial work - you will most likely have to clean up the scratch work, dead ends, etc. for a copy that is appropriate for grading.

Recap:

Do at least 30.

Minimum goal is at least six per exam.

Extras will replace low scores.

Due the day after the exam on the relevant section.

Well-written, legible solution (not just an answer).

Include the miniproject statement.

Projects: This is the final list of projects for Fall 2008. There are a total of 81 projects to choose from.

Section 1.1 - Logic problem (note: You need to write out a solution, not just give the answer. See the handout for #65 for an example.)

Section 1.2 - NAND and NOR

Section 1.3 - Lewis Carroll

Section 1.4 - Properties of Real Numbers

Section 1.4 - Prenex normal form

---------------- Any of the above that you wish to do are due on Thursday, September 11. ---------------------

Section 1.5 - Proofs

Section 1.5 - Rules of Inference

Section 1.5 - Logical Arguments

Section 1.6 - Proofs

Section 1.6 - Connected proofs

Section 1.6 - Errors in Proofs

Section 1.7 - The 3x + 1 Conjecture

Section 1.7 - Bits Around a Circle

Section 1.7 - Blackboard Odd

Section 1.7 - Tilings with Dominoes

Section 1.7 - Tilings with Tetrominoes

Section 1.7 - Chomp

Section 1.7 - O'Ekaki

---- Any of the ones from sections 1.5, 1.6, or 1.7 that you wish to do are due on Thursday, September 25. ----

Section 2.2 - Symmetric Difference

Section 2.2 - Multisets

Section 2.2 - Fuzzy Sets

Section 4.1 - Tilings

Section 4.1 - Chomp and Strong Induction

Section 4.1 - Modular Arithmetic

Section 8.1 - Irreflexive/Asymmetric/Inverse/Complementary

Section 8.1 - Concrete Problem and Properties

Section 8.1 - Reflexive/Irreflexive and Combining Relations

Section 8.1 - Rⁿ Symmetric

Section 8.3 - Inverse and Complementary Relations

Section 8.3 - Properties Galore (Note: This project counts as three projects: I'll grade it out of 30. If you get 23, I'll record the grades as 10+10+3.)

--- Any of the ones from sections 2.2, 4.1, 8.1, or 8.3 that you wish to do are due on Thursday, October 16. ---

Section 8.5 - Partitions

Section 8.5 - Dogs Playing Tricks

Section 8.5 - Divisibility

Section 8.5 - Monkeys and Nuts

Section 8.5 - Magic Squares

Section 8.6 - Posets and Cartesian Products

Section 8.6 - Partitions using Partial Orderings

Section 8.6 - Dense Posets

Section 9.1 - MSUM Buildings

Section 9.1 - NCC Football with data file Schedule/Results

Section 9.2 - Graphs