mat118 homework S2007

## MAT 118 Mathematical Thinking

### Spring 2007

Index
Course Description
Teaching Staff, Office Hours
Syllabus and Schedule
Homework

## Homework

Note: Homework will start immediately with the first week of classes, M 1/22. Assignments will be posted for several weeks in advance. They always correspond to the material covered in lecture during a particular week, and they are due in recitation the following week. Your TA may make adjustments. Solutions are to be submitted in writing for grading; papers should be well written using complete sentences and arguments. Recitation leaders may assign additional odd numbered problems which are to be prepared for discussion, possible presentation, or quizzes. We also refer to the "homework" paragraph on the course description page.

```Section/Pages   Problems       Bonus    Due Week of

1.1/15-19        2 12 16 22
1.2/28-32        4  6 12 14     15      1/29

1.3/39-45        2 10 12 16     20
1.4/51-58        6  8 12 16
1.5/61-62                        3      2/5

Voting methods calculator applet

3.1/133          2 12 20 30
3.2/138-139     12 18 22 28
3.3/150-151      4 26           28      2/12

3.3/152-153           40 46
3.4/161-163      8 10 18 22     24      2/19

Financial calculator applet

3.5/174-180      8 12 24 28     42
4.1/192-195      2  8 14 28             2/26

4.2/200-201      2  6 12 24
4.3/205-206      2  8 10 12     16      3/5

Coin-flipping applet

4.4/215-220      8 14 20 32
4.5/232-234      2 20 22 32 36  38      3/12

4.6/242-244      4  8 12 18     34
4.7/248-252      2  8 24                3/19

Permutations, combinations, and factorial calculator

6.1/375-379      2-14 even
16 26 30     32
6.2/396-403      2- 6 even
12 16 20             3/26

6.3/411-414      2-10 even     p403
16 20 24     32      4/9

Traveling salesman problem calculator

7.1/426-428      2- 8 even
10-16 even
18 28 32
7.2/442-444      2-10 even
18 28        32      4/16

7.3/456-460      2- 8 even
12 22 38     39
8.1/479-480      4 12 16 18 20
22 40 46 52 56  65      4/23

Check digit calculator

8.2/486-487      2-20 even
26 32 36 42     46
8.3/493-495      4 12 20
26 28 30
8.4/502-504      2  8 14 18 20          4/30

Affine cipher calculator

Letter frequency calculator

The following assignment must be completed in preparation for the Final,
although it can not be discussed in recitation anymore. Submission is optional
but recommended for bonus credit. See the discussion of all deadlines below.

8.6/521          2  4  6 10 13  14

RSA and Hill Cipher calculator

The last assignment is completely optional.  But again, submission before the

8.7/532-534      4  8 10 16     20

```

Projects: You can work on one or two projects from the categories A,B,C below and submit them for credit. The absolute deadline for turning in any remaining course work is May 15, 7:30pm - the end of our Final Exam. We strongly recommend not to wait that long. Each project is worth up to 10% of the course grade; scores will reflect the quality of your effort. We encourage you to tackle a more challenging task, which will be judged generously. You cannot submit more than two projects, and if you do two, they must be chosen from different categories.

(A) (General)   Build a model of one of the following three regular or semiregular polyhedra:
dodecahedron, icosahedron, truncated icosahedron (soccer ball, buckyball)
Use a paper or cardboard template consulting online resources such as
http://isotropic.org/polyhedra/
http://www.mathsisfun.com/geometry/model-construction-tips.html
http://www.stevepasos.com/ai/fod/escher_assignment/
Ready made construction kits with sticks or similar may not be utilized. You can actually keep your model, just sign and show it at the end of any lecture, for instant evaluation and extra credit - also present it in recitation.

(B) (Writing)   The optimal format might be about 2-3 typewritten pages - double spaced.
Include examples to support your arguments whenever possible.
1.   Writing Exercise 4 on p180 in Chapter 3
2.   Writing Exercise 4 on p415 in Chapter 6
3.   Writing Exercise 4 on p460 in Chapter 7

(C) (Problems)   Explain all details; make use of applets where applicable.
1.   Project 4 on pp63-64 in Chapter 1
2.   Project 4 on p265 in Chapter 4
3.   Project 8 on p535 in Chapter 8

Detlef Gromoll
Math Dept Stony Brook University
detlef@math.sunysb.edu
January 19, 2007