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• 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.

Class Information

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:

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

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