 MAT103
Franklin College
Erich Prisner

# MAT103 College Algebra

 Schedule Topics PageRank Project NEW: Sample Midterm Study Guide

## Writing Component

You have to write one research paper of about three pages length on a mathematical subject related to the topics we cover in class. Each student is assigned a topic from the list below. The topics vary in mathematical difficulty, so check with me when you have made a choice whether I consider this topic appropriate for you. You have to give me a first draft two weeks after you have chosen the topic, a second draft one week after the first draft, and the paper two more weeks later, so overall you have five weeks for the whole project.

For some of the topics you need sources, for some you don't. If you use sources, please cite and quote correctly and completely, also internet sources. A good but brief introduction for writing research papers (based on the MLA Handbook for Writers of Research Papers) can be found here. Read also Stephen B Maurer's notes and Stephen L. Kleiman's notes for writing mathematical papers.

For the technical side, note that Word contains a formula editor.

### List of topics

1. Triangle inside square
2. A work word problem
3. A puzzle leading to several equations with several unknowns
4. (Addition method) is not possible this semester!
5. (A thermostat word problem) is not possible this semester!
6. Shoelaces
7. A family of radical equations
9. Composition of piecewise defined functions
10. Number of variables versus number of equations
11. The inverse function of a composed function
12. (Traveling salesman problem) is not possible this semester!
14. Finding the better fence
15. Finding the better fence II
16. Solving cubic equations
17. T-Shirt production
18. The complex plane
19. Composition of functions I
20. Composition of functions II
21. A polynomial of high degree
22. Mixture problem I
23. Mixture problem II
24. Two boats on the river
25. (The invention of logarithms) is not possible this semester!
26. (Proofs in Mathematics) is not possible this semester!
27. Triangular mixture problem
28. (The old liar) is not possible this semester, but have a look on the solution!
29. Integer zeros of a polynomial
30. (Inequalities) is not possible this semester!
31. The old liar II
32. (Benjamin Franklin and magic squares) is not possible this semester!
33. A cinema word problem
34. Sharing Coconuts
35. (Arabian Algebra) is not possible this semester!
36. Tartaglia, Cardano, and the cubic and quartic formula
37. Abel and the impossibility of the quintic formula
38. Placing Restaurants
39. Upstream-Downstream-Upstream
40. Mixture Problem III
41. Absolute Value
42. Absolute Value and two variables
43. Triangle inside square II
44. Page Rank I
45. Page Rank II
46. Folding Paper
47. Factoring a polynomial
48. Factoring a polynomial II
49. Production
50. ........
51. ........
52. ........
53. ........

The grading will be based on

• Mathematical knowledge (Does the student understand the mathematics necessary to treat the problem? Is the mathematical treatment correct?)
• Organization (Are the ideas presented in a logical and structured way? Does the student make an attempt to explain formulas or result in a nontechnical way? Is there an appropriate introduction and conclusion?)
• Mechanics (This addresses spelling, grammar, word choice, citing correctly, and so on)
• Originality (Does the student show original and independent thoughts on the topic? Is he or she maybe discussing generalizations? You can get 5 extra credit points here.)

Erich Prisner, August 2003