*
*

- send me email (click here and
delete "zzz")

- Homepage: http://seki.csuhayward.edu
- office: South Science 429d, phone: 510-885-2691

- office hours: Tuesday/Thursday 4:00--4:45; Thursday 6:00--7:30p.m. and by appointment. I encourage you to come to scheduled office hours if possible. I'm happy to answer questions by email, which I check frequently.

Math 4901 (Senior Seminar) is designed to be a capstone experience for students who are about to graduate. It carries two units of credit, and therefore meets only once a week. This quarter we will organize it around student presentations. Each student will give 3--4 presentations in class. The other assigned work will be to read a book or article (that you haven't read before), and write a short report on it, and to do a few problems based on other lectures.

* COORDINATES: * Lectures meet Tuesdays 6:00--7:50p.m. (#12052 01) in
Sci Science 247.

* TEXT: * Fomin, Genkin, & Itenberg
* Mathematical Circles (Russian Experience)* American Mathematical
Society, Mathematical World, Vol. 7. This has some great problems.

* WEB RESOURCE: * http://seki.csuhayward.edu/4901.html
will be my Math 4901 homepage. It will include a copy of the syllabus
and list of homework assignments. I will keep this updated throughout
the quarter.

* GRADING:* Your grade will be based on 3--4 oral presentations
(in class), a report on a mathematics book or article you read, and
homework assigned and graded by your peers.

The breakdown of points is:

Presentations | Report | HW |
---|---|---|

60% | 20% | 20% |

* HOMEWORK: * Each presenter will handout a set of five exercises,
which are doable after the lecture. These should be simple enough that
they don't take a lot of time, but not so simple that they can be
answered without any thought. These will be handed in the next
week to the presenter, who will grade them.

* REPORTS: * Choose an article from the * American
Mathematical Monthly * or a book to read and write a short 5 page
report on it. If time permits, there may be presentations on these
at the end of the quarter.

Your report should be interesting to read in its own right.

- Angelica:
- John:
- George: Hubert Dreyfus: "What Computers *still* can't do"
- Leslee:
- Jeremy:
- Corri: Davis: "Mathematical Encounters of the 2nd Kind"
- Trang:
- Geurrie
- Akira
- Susanne:
- Michele: Richard Feynman: "Surely You're Joking Mr. Feynman"
- Vu:
- Angel: "Mathematics at the turn of the century", AMM 107 #1 Jan. 2000
- Blanca:
- Emily: Paulos: "Beyond Numeracy"
- Leni:
- Jacki: Theoni Pappas: "The Magic of Mathematics"
- Rick: Feynmann: "What do you care what other people think?"

* PRESENTATIONS: * Each presentation should last 10 minutes
(strictly enforced with a timer!). There will be a couple of minutes for
questions at the end of each presentation. Please handin a typed
summary of your presentation to me, and handout a homework assignment
as described above (make enough copies) to the class. You may choose your
topic from among those given below, or get approval from me for a
different one.

* TOPICS: * Here are suggested topics for each of the first three
presentations.

FIRST PRESENTATIONS:

- Pythagorean Theorem (Square with a square) [Angel]
- Pythagorean Theorem (Circle Proof) [Rick]
- Pythagorean Theorem (Another one) [Michele]
- Squareroot(2) is irrational [Susanne]
- There are infinitely many primes [Jacki]
- The rational numbers are countable
- The real numbers are uncountable [Emily]
- An interesting proof by mathematical induction [Jeremy, Akira]
- A proof that requires strong induction [George]
- The group of symmetries of an square [Leni]
- The geometry of multiplication of complex numbers
- Proof of the arithmetic-geometric mean inequality
- Law of Sines or Law of Cosines [Corri, Trang]
- Eigenvalues of a matrix [John]
- Formula for sum of geometric series [Vu]
- Derivation of the quadratic formula [Leslee]
- Evaluating determinants [Blanca]n
- Example of Newton's method for finding roots [Angelica]

SECOND PRESENTATIONS: Discuss the five "most important/interesting" facts about:

- Triangles A* [Rick]
- Triangles B* [Emily]
- Circles A*
- Circles B*
- Pascal's Triangle [Leni]
- Polynomials [Angel]
- Factoring [Corri]
- Matrices [Blanca]
- Determinants [Trang]
- Polygons (regular and irregular) [Jacki]
- Areas and surface areas [Michele]
- Logarithms and exponential functions [Susanne]
- Trigonometric functions
- Set theory operations (union, intersection, etc.) [George]
- Spheres [Akira]
- Volumes
- Complex numbers [John, Jeremy]

- Delta-epsilon definition of limits
- Finding derivatives of x^5, sqrt(x) and 1/sqrt(x) right from def.
- Proof that sin(x)/x has limit 1 as x goes to 0.
- Delta-epsilon def. of continuity and proof that polynomials are continuous.
- Product and quotient rules
- Applications of L'Hopital's rulle
- Max/min problems and the second derivative test
- Related Rate problems
- Area between graphs of curves by integration
- Integration by substitution
- Integration by parts and clever tricks
- Inverse trig functions and integration
- Partial fractions and integration
- Surface area and volumes of solids of revolution
- Taylor and Maclaurin series
- Convergence of series
- Comparison tests for series
- Ratio test for series
- Double integrals
- Triple integrals

Back to my home page.