Mathematical Thinking

Last update: December 03

*Check the end of this page for announcements and postings regularly!*

**Lecturer:** Detlef Gromoll, Math 5-116

Phone: 632-8290,
Email: *detlef@math.sunysb.edu*

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

Office Hours: M 3-4 (UG Office P-143), Th 2:30-3:30 (5-116), and by appointment

**Lecture 1:** Paul Kumpel, Math 3-120

Phone: 632-8264,
Email: *pkumpel@math.sunysb.edu*

Classes: MWF 2:15-3:10, Physics 113

Office Hours: MW 3:30-4:30 (3-120) & F 3:30-4:30 (UG Office P-143)

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**Teaching Assistants:**

Ming Xu, Email: *mxu@math.sunysb.edu*

Recitation 01: M 9:35-10:30 (Earth&Space 183)

Recitation 03: Tu 9:50-10:45 (Earth&Space 79)

Office hours: M 3-5 (2-104), W 3-5 (Math Learning Center [MLC] S-240A)

Michael Chance, Email: *mchance@math.sunysb.edu*

Recitation 02: W 3:50-4:45 (Earth&Space 181)

Office hours: TuWTh 2:30-3:30 (4-122)

Maria Ma, Email: *mx_pianogirl@yahoo.com*

Recitation 04: Th 9:50-10:45 (Earth&Space 183)

Office hours: MWF 12-1 (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 1,3,4,6,7,8. 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 Monday, December 15, 2-4:30.
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.
*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 F by noon with your TA, so will *not* be accepted in class (for R 04, it is due Th in recitation, for technical reasons). 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:**

*Week of* *Sections*

9/03-05 [Organization & Survey]

9/08-12 1.1, 1.2, 1.3

9/15-19 1.3, 1.4, 1.5

9/22-26 3.1, 3.2, 3.3

9/29-10/03 3.4, 3.5
(Test 1 - M 9/29)

10/06-10 4.1, 4.2, 4.3

10/13-17 4.4, 4.5

10/20-24 4.6, 4.7

10/27-31 6.1, 6.2
(Test 2 - M 10/27)

11/03-07 6.2, 6.3

11/10-14 6.3, 8.1

11/17-21 8.2, 8.3, 8.4

11/24-26 8.6
(Test 3 - M 11/24)

11/27-28 Thanksgiving Break

12/01-05 8.6, 8.7, 7.1

12/08-12 7.2 & Review

12/15 Final Exam

**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.ehs.stonybrook.edu/fire/disabilities.asp*

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

9/08-12 | Study 1.1 and 1.2 in detail; read through 1.3 | Homework problems:

pp15-19 2,12,16,22 pp28-32 4,6,12,14 Bonus: p32 15

9/15-19 | Review 1.2 | Study 1.3-5 in detail | Homework problems:

pp39-45 2,10,12,16 pp51-58 6,8,12,16 Bonus: p44 20

*Voting methods calculator applet*

9/22-26 | Review all of Chapter 1 for Test 1 | Study 3.1-3 in detail | Homework problems:

p133 2,12,20,30 pp138-139 12,18,22,28 pp150-153 4,26,40,46

*Financial calculator applet*

9/29-10/03 | Review 3.3 | Study 3.4-5 in detail | Homework Problems:

pp161-163 8,10,18,22 p174-180 8,12,24,28
Bonus: p162 24

*Important:* Note that this week has a different schedule! Because of the holiday, Wednesday is on a Monday schedule. So there is a lecture on W, and R01 meets as well, whereas R02 does not meet this week unless there are special arrangements.

10/07-10 | Review 3.5 | Study 4.1-3 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

*Coin-flipping applet*

10/13-17 | Review 4.3 | Study 4.4 and 4.5 in detail | Begin reading 4.6 | Homework Problems:

pp215-220 8,14,20,32 pp232-234 2,20,32,36
Bonus: p220 38

*Permutations, combinations, and factorial calculator*

10/20-24 | Review 4.4 | Study 4.5 and 4.6 in detail | Homework Problems:

pp242-244 4,8,12,18 Bonus: p244 34

10/27-31 | Review 4.6 | Study 4.7 and 6.1 in detail | Homework Problems:

p248-252 2,8,24
pp375-379 2-14 even,16,26,30 Bonus: p379 32

11/03-07 | Review 6.1 | Study 6.2 and 6.3 in detail | Homework Problems:

pp396-403 2-6 even,12,16,20 pp411-414
2-10even,16,20,24
Bonus: p403 32

(due F 11/14 noon)

*Traveling salesman problem calculator*

11/10-14 | Review 6.3 | Study 8.1 in detail | Begin reading 8.2 | Homework Problems:

pp479-480 4,12,16,18,20,22,40,46,52,56
Bonus: p480 65

(due F 11/21 noon)

11/17-21 | Review 8.1 | Study 8.2, 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 M 11/24 in class - this is also practice for Test 3)

*Check digit calculator*

12/01-05 | Review 8.4 | Study 8.6 in detail; survey 8.7 | Begin reading 7.1 | Homework Problems:

p521 2,4,6,10,13 Bonus: p521 14

(due in recitation next week 12/08-12)

*Affine cipher calculator*

*Letter frequency calculator*

*RSA and Hill Cipher calculator*

12/08-12 | Study 7.1 and 7.2 in detail | Begin final review of all course material covered | Homework Problems:

Bonus (only): pp426-428 20,28,32 pp442-444
8,12,18,28

*Note:* All remaining course work is due Monday, December 15, 5pm. Leave papers preferably with your section leaders, or drop them off in my office 5-117 by the above deadline. Extra bonus credit from homework, the exams, and a project 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 20% (or one grade).

Short Exam 1 was given M 9/29 in class (40 minutes), covering all of Chapter 1.

It will be returned in recitation during the week 10/07-10. Since R02 does not meet because of the schedule change, check with your TA during his office hours.

Short Exam 2 was given M 10/27 in class (40 minutes), covering Chapters 3 and 4.1-6.

It will be returned in recitation during the week 11/03-07.

Short Exam 3 was given M 11/24 in class (40 minutes), covering Chapter 6 and Sections 1 through 3 from Chapter 8.
It will be returned in recitation during the week 12/01-05