Mathematics 30A.H1
Mathematical Excursions
Fall 2009
MWF 12:50-1:45 (202 Brower Hall)
Instructor: Dr. Raymond Greenwell
Office: 100C Adams Hall, 463-5573
E-mail: matrng@hofstra.edu
Home: (516) 705-6575
Fax: (516) 463-6596
Web page: http://people.hofstra.edu/rgreenwell
Office Hours: M 1:55-3:25; WF 1:55-2:50 (Adams 100C); M 6:00-7:30 (Republic Hall Lounge)
or by appointment or whenever you can catch me.
Text: The Heart of Mathematics (2nd ed.) by Burger and Starbird
Additional text on reserve in library: Mastering Mathematics: How
to Be a Great Math Student, by Richard Smith
For turnitin.com: class ID: 2748432; enrollment password: tannenbaum
The purpose of this course is to give students who are not math majors a view of what mathematics is about. We will cover a variety of topics in math, most of which will be new to everyone in the class, yet elementary enough to learn even for those without a strong background in math. The topics will include problem solving, numbers, infinity, and geometry. This is an honors section that will go more deeply into these topics than is done in a typical section of Math 30A.
Your grade will be based on three tests (worth roughly 100 points each), a final exam (worth roughly 200 points), a short paper (roughly 6 pages, but the exact length isn't important, worth roughly 80 points), and other occasional miscellaneous assignments (worth no more than 80 points). The paper, due November 16, should demonstrate that you have learned about and can explain some concept in elementary mathematics not covered in class. A separate handout will give more details on choosing a topic and writing the paper. By October 9 you are to send me an email message containing the following three items: the topic of your paper, a paragraph summarizing what you intend to cover in your paper, and a list of the references you will be using.
If you miss a test, it will count as a zero unless you have a very convincing excuse, in which case your grade will be based on the two tests that you take. Grades of Incomplete will not be given except for extraordinary circumstances.
Below is the minimum daily homework assignment; you should do as many additional problems as you have time for. The more you do, the more you learn. Turn in the homework two class days after it is assigned. To be counted, the homework must be turned in on time with all the work showing. Late homework will not be accepted unless illness prevents you from attending class. Each of you will grade homework at least one day. Your homework grade will be averaged with your lowest test grade, assuming that improves your grade.
Since you are responsible for everything said in class, be sure to get the notes from someone else if you are absent. This syllabus is subject to change; stay tuned for the latest update.
All students are expected to abide by the University's Policy on Academic Honesty (p. 52 of the Hofstra University General Bulletin 2009-2010).
If you have any concerns regarding a physical, psychological and/or learning disability that may have an impact upon your performance in this course, appropriate accommodations can be made on an individualized, as-needed basis after the needs, circumstances and documentation have been evaluated by the Office of Services for Students with Disabilities. All disability-related information will be kept confidential.
Learning Goal: Students will apply analytical reasoning across academic disciplines.
Date |
Sec. |
Page |
Assignment |
Description |
W 9-2 |
Ch. 1 |
28 |
Do any 8. #8, 9, and 14 are worth 2. #15 is worth 4. |
problem solving |
F 9-4 |
Ch. 1 |
|
continued |
|
W 9-9 |
2.1 |
46 |
6,8,11,12,14,16,17,18, 20 |
counting |
F 9-11 |
2.2 |
58 |
7,8,16,18,21,26,32,36,37 |
Fibonacci numbers |
M 9-14 |
2.2 |
|
continued |
|
W 9-16 |
2.3 |
77 |
7,8,9,17,19,20,26,32,35,36 |
prime numbers |
F 9-18 |
2.4 |
90 |
6,7,13,14,19,26,28,32,33,37 |
modular arithmetic |
| M 9-21 | 2.4 | continued | ||
| W 9-23 | 2.5 | 107 | 7,9,11,12,13,16,17(ans:4),19 | public secret codes |
F 9-25 |
2.5 |
|
continued |
|
W 9-30 |
2.6 |
118 |
8,12,18,26,29,30,36,40 |
irrational numbers |
F 10-2 |
2.6 |
|
continued |
|
M 10-5 |
review |
|||
W 10-7 |
Test 1 |
|||
F 10-9 |
2.7 |
132 |
7,8,10,15,22,29,33,37,38 |
real numbers |
M 10-12 |
4.1 |
213 |
6,8,10,13,15,16,18,20 |
Pythagorean theorem |
W 10-14 |
4.2 |
228 |
7,10,12,20,21 |
art gallery theorem |
F 10-16 |
4.3 |
245 |
9,12,13,16,17,19 |
golden rectangle |
M 10-19 |
4.3 |
continued |
||
W 10-21 |
4.4 |
263 |
6,8,10,12,17,18 |
pinwheel pattern |
F 10-23 |
4.5 |
285 |
8,9,11,14,16 |
platonic solids |
M 10-26 |
4.5 |
continued |
||
W 10-28 |
4.6 |
300 |
17(ans:2),18(2.46),19(2.236),20(2.83),26,27,30, extra exercise |
non-Euclidean geometry |
| F 10-30 | 4.7 | 321 | 6,7,8,13,15,16,19 | fourth dimension |
| M 11-2 | review | |||
| W 11-4 | Test 2 | |||
F 11-6 |
6.1 |
407 |
2,5 |
fractal overview |
M 11-9 |
6.2 |
423 |
13,14,15(Step 1 by hand, steps 2-4 on web site), 30,31(start with .20638),32(do by hand, then try other starting points on the web site and describe what happens),38,39 |
dynamical systems |
W 11-11 |
6.2 |
continued |
||
F 11-13 |
6.3 |
452 |
13,14,20,21,23,24,34,35,39 |
fractals |
M 11-16 |
6.3 |
continued |
||
W 11-18 |
6.4 |
476 |
7,8,12-15,29-30,31-34,35,36,38(Hint: After using the quadratic formula, calculate (-1+2i)2.) |
Julia and Mandelbrot sets |
F 11-20 |
6.4 |
|
continued |
|
| M 11-23 | 6.5 | 494 | 7,10,12,14,16,22,23,31,33 | chaos |
| M 11-30 | 6.6 | 510 | 7,9,11,12,15,16,18,19,21 | fractal dimension |
| W 12-2 | 6.6 | continued | ||
F 12-4 |
review |
|||
M 12-7 |
Test 3 |
|||
W 12-9 |
review |
Friday, December 18, 10:30-12:30: The Final Exam!
"Where mathematical reasoning can be had, it's as great folly to make use of any other, as to grope for a thing in the dark, when you have a candle standing by you." John Arbuthnot (1667-1735)