Mathematical Thinking

Last update: November 24, 2004

*This page will be updated at least once a week. Check for announcements and postings regularly, mostly at the bottom of the page!*

**Lecturer:** Detlef Gromoll, Math 5-110

Phone: 632-8286,
Email: *detlef@math.sunysb.edu*

Classes: MF 12:50-2:10pm, Engineering 145

Office Hours: M 3-4, F 11-12 (both UG Office P-143), W 2:30-3:30 (5-110), and by appointment

**Teaching Assistants:**

Ruth Cuevas

Email: *pguzzone@aol.com*

Recitation 01: M 9:35-10:30 (Physics 130)

Office hours: M 10:45-12:15 & Th 10-11:30 Math Learning Center [MLC] S-240A

Daniel Robles-Llana, Math 6-117

Email: *daniel@insti.physics.sunysb.edu*

Recitation 02: W 3:50-4:45 (Chemistry 128)

Recitation 03: Tu 9:50-10:45 (Union 231)

Office hours: Tu 4-5 & F 5-6 (Math 6-117), F 1-2 Math Learning Center [MLC] S-240A

Karen Cumbo

Email: *karencumbo@optonline.net*

Recitation 04: Th 9:50-10:45 (Physics 128)

Office hours: Tu 2:40-3:50 & Th 11-12:40 Math Learning Center [MLC] S-240A

**About this Course:** There is much more to mathematics than just calculations and solving equations. In this course we will examine several mathematical topics accessible to students with an understanding of high-school mathematics. These will be selected from among the following: voting methods; the mathematics of money; probability; graphs, paths and networks; tilings and polyhedra; number theory. (*3 credits*)

**Prerequisites:** Equivalent of MAP 103, or level 2+ on the mathematics placement examination, or permission of instructor.

**Text:** George Gilbert, Rhonda Hatcher: *Mathematics - Beyond the Numbers*, John Wiley & Sons (2000).

The course will cover material from Chapters 1,3,4,6,8. The textbook is intended to be read. Study the assigned sections before the lecture. This will greatly increase your comprehension, and enable you to ask intelligent questions in class. Further optional reading will be suggested below.

**Grading:** There will be 3 short tests, 40 minutes each, about once a month; all given in class - *no makeups*. If one short exam is missed because of a serious (documented) illness or emergency, the semester grade will be determined based on the balance of the work in the course. A final examination will be held on Friday, December 17, 11-1:30 (Period 2).
Students are expected to ensure when they register for this course that they will be available for the final examination, and that they do not have too many final exams on that date.
The final course grades in MAT 118 will be determined as follows:

Homework/Recitation/Quizzes 35%, Short Tests 10% each, Final Exam 35%

We will give up to 10% extra credit for a project, to be assigned later. You can do at most two projects.

*Incompletes* will be granted only if documented circumstances beyond your control prevent you from completing the course work, according to strict University rules.

**Recitation/Homework:** You can not learn mathematics without doing mathematics. It is essential to actively take part in the recitation and to solve problems: Each week a homework assignment will be posted further down on this page (usually M or Tu). It is due the following week by F noon with your TA, so will *not* be accepted in class. Homework will be graded, returned, and discussed. While you may work together with others in the class (which can be a rewarding experience), write up your own solutions in your own words. Since homework earns credit, it is assumed that everyone submitting particular problems has solved them individually. The goal of the homework is to understand the material, not to merely hand in some paper. Late homework will *not* be accepted.

**Approximate Course Schedule:**

*Weeks of* *Sections*

8/30-9/17 1.1 through 1.5

Short Test 1 - M 9/20 [in class, on Chapter 1 - finish all assigned homework]

9/20-10/08 3.1 through 3.5

10/11-10/29 4.1 through 4.7

Short Test 2 - F 11/05 [in class, on Chapters 3 and 4 - finish all assigned homework]

11/08-11/19 6.1 through 6.3

11/22-12/10 8.1 through 8.4, 8.6

Short Test 3 - F 12/03 [in class, on Chapter 6; **note time change**]

Final Exam - F 12/17 [in our classroom; cumulative, slight emphasis on Chapter 8]

**Special Needs:**
If you have a physical, psychological, medical or learning disability that
may impact your course work, please contact Disability Support Services,
ECC (Educational Communications Center) Building, room 128, (631) 632-6748.
They will determine with you what accommodations are necessary and
appropriate. All information and documentation is confidential.

Students requiring emergency evacuation are encouraged to discuss their
needs with their professors and Disability Support Services. For procedures
and information, go to the following web site.

*http://www.stonybrook.edu/facilities/ehs/fire/disabilities.shtml*

**Week by Week Details:** Assignments are listed here.

8/30-9/03 | Study 1.1 and 1.2 in detail | Homework problems:

pp15-19 2,12,16,22 pp28-32 4,6,12,14 Bonus: p32 15 [due by noon, F 9/10]

9/06-10 | Review 1.2 | Study 1.3 and 1.4 in detail | Homework problems:

pp39-45 2,10,12,16 Bonus: p44 20
[due by 5pm, W 9/15]

9/13-17 | Review 1.3 and 1.4 | Study 1.4 and 1.5 in detail | Homework problems:

pp51-58 6,8,12,16 Bonus: p61 3
[due by noon, F 9/24. Review Ch 1 and homework for Test 1]

*Voting methods calculator applet*

9/20-24 | Study 3.1 in detail, begin reading 3.2 | Homework problems:

p133 2,12,20,30 pp138-139 12,18,22,28
[due by noon, F 10/01]

9/27-10/01 | Review 3.2 | Study 3.3-4 in detail | Homework problems:

pp150-153 4,26,40,46 pp161-163 8,10,18,22 Bonus: p162 24
[due by noon, F 10/08]

10/04-10/08 | Review 3.4 | Study 3.5 in detail and review Ch. 3 |
Homework problems:

pp174-180 8,12,24,28 Bonus: p180 2
[due by noon, F 10/15]

*Financial calculator applet*

10/11-15 | Study 4.1 through 4.3 in detail; begin reading 4.4 | Homework Problems:

pp192-195 2,14,28 pp200-201 2,18

pp205-206 2,8,10,12 Bonus: p195 32
[due by noon, F 10/22]

*Coin-flipping applet*

10/18-22 | Review 4.3 | Study 4.4 and 4.5 in detail | Begin reading 4.6 | Homework Problems:

pp215-220 8,14,20,32 Bonus: 38 pp232-234 2,20,22,32,36 Bonus: 38
[due by noon, F 10/29]

*Permutations, combinations, and factorial calculator*

10/25-29 | Review 4.5 | Study 4.6 and 4.7 in detail | Homework Problems:

pp242-244 4,8,12,18 Bonus: 34
p248-252 2,8,24
[due by noon, F 11/05]

11/01-05 | We will review Chapters 3 and 4 for Friday's Test 2 on M in class.

11/08-12 | Study 6.1 and the first half of 6.2 in detail | Homework Problems:

pp375-379 2-14 even,16,26,30 Bonus: 32
pp396-403 2-6 even,12,16,20

[due by noon, W 11/24 - note that W is a correction day and on a F schedule!]

11/15-19 | Review 6.1 | Study 6.2 and 6.3 in detail | Homework Problems:

pp411-414 2-10even,16,20,24 Bonus: 32
[due by noon, M 11/29, as preparation for Test 3]

*Traveling salesman problem calculator*

11/22-24 | Review 6.3 | Study 8.1 in detail | Read 8.2 | Homework Problems:

pp479-480 4,12,16,18,20,22,40,46,52,56
Bonus: 65
[due by noon, F 12/03]

11/29-12/03 | Review 8.2 | Study 8.3 and 8.4 in detail | Homework Problems:

pp486-487 2-20 even,26,32,36,42
pp493-495 4,12,20,26,28,30
Bonus: p487 46

[due by noon, F 12/10]

*Check digit calculator*

12/06-10 | Review 8.4 | Study 8.6 in detail | Homework Problems:

pp502-504 2,8,14,18,20
p521 2,4,6,10,13 Bonus: 14

[do as soon as you can; absolute deadline: Final, Friday 12/17]

Begin final review of all course materials covered.

*Affine cipher calculator*

*Letter frequency calculator*

*Important:* Note above time change of Test 3 to F 12/03.

*Note:* All remaining course work is due Friday, December 17, by the end of the Final (you may submit papers with the exam). Preferably, leave work already earlier with your section leaders. Extra bonus credit from homework, the exams, and up to two projects below will be counted altogether as additional input, which we will use to improve your course grade based just on the regular scores by up to 25% (or one grade).

**Projects:** You can submit work on (not more than) two of the following problems. Some may require a little more careful reading of the material and examples in the relevant sections. If you choose two projects, then one should be a writing exercise, the other a project. Of course, partial solutions will earn partial credit.