MATH 245, Discrete Structures
Spring 2010, Project guidelines

• All projects are to be done in groups, unless you are really strongly opposed to group work, or have a schedule that doesn't work with other people's schedules. You may work with a partner or in a group of three. You may change groups for the different projects.
• Projects 1 and 2 consist of picking a section from the book, reading the section, writing a summary of the main ideas of the section, solving some sample problems, and giving a 5-minute presentation in class. The list of topics for both projects is given below. Each group must choose a different topic. The summary of the section needs to be typed, and should be 2-5 pages long, including solved problems. Before the presentation, I will ask you to do a practice presentation in my office to make sure that it makes sense and will be useful to your peers. Each summary will be worth 15 points, and each presentation will be worth 10 points. Each group must choose a different topic.
• Project 3 will require more original work. Choose one of the topics below and solve the problem as directed. For the first three projects, you will have to do some additional research, while problems 4 and 5 are more difficult and do not require any additional work. Like with projects 1 and 2, you will write up your solution, and present it to the class on the last day of class, in five minutes or less. The written solution is worth 35 points, and the presentation is worth 15 points. Different groups may choose the same project, though every project should be done at least by one group.

Project 1 will be assigned on Monday, March 15, and will be due on Friday, March 26, though you can start working on it earlier if you wish.
Project 1 topics:

1. 3.1. Divisors
2. 3.2. Consequences of Well-Ordering
3. 3.3. Euclid’s Algorithm and Lemma
4. 3.4. Rational Numbers
5. 3.5. Irrational Numbers
6. 3.6. Modular Arithmetic
7. 4.5. Strong Induction
8. 4.6. The Binomial Theorem

Project 2 will be assigned on Monday, April 26, and will be due on Wednesday, May 5.
Project 2 topics:

1. 5.4. Special Functions
2. 5.5. General Set Constructions
3. 5.6. Cardinality
4. 6.5. Applications of Combinations
5. 6.6. Correcting for Overcounting
6. 7.1. Inclusion-Exclusion
7. 7.2. Multinomial Coefficients
8. 7.3. Generating Functions
9. 7.4. Counting Orbits
10. 7.5. Combinatorial Arguments
11. 8.2. Matrices and Special Graphs
12. 8.3. Isomorphisms
13. 8.4. Invariants
14. 8.5. Directed Graphs and Markov Chains
15. 9.4. Planar Graphs

Project 3 will be assigned on Wednesday, May 5, and will be due on Friday, May 21.
Project 3 topics:

1. Work on the following activity:
   http://www.colorado.edu/education/DMP/activities/graph/ddghnd03.html.
   When you are finished, contact me so I can give you further instructions.
2. ``Zoo Redo." Work on the following activity:
   http://www.colorado.edu/education/DMP/activities/graph/gklhnd04.html .
   When you are finished, contact me so I can give you further instructions.
3. Work on the following activity:
   http://www.colorado.edu/education/DMP/activities/graph/gklhnd04.html .
   When you are finished, contact me so I can give you further instructions.
4. Work on the following activity:
   http://www.colorado.edu/education/DMP/activities/iteration_recursion/jaehnd07.html .
5. Work on the following activity:
   http://www.colorado.edu/education/DMP/activities/counting/olchnd04.html.