Recommended Reading: Math SciFi. Science Fiction Arxiv.

See Boolean Notation. A short article about Boolean Algebra notation.

See Peirce. A excerpt from the writings of Charles Sanders Peirce, American philosopher and mathematician (1839-1914). In this article, Peirce gives his "sign of illation", a symbol for implication that is a combination of the Boolean negation sign and the Boolean plus sign. He also has a worthwhile discussion of the nature of logic.

See Boolean Algebra. A short article about Boolean Algebra and some ideas related to it, including switching circuits, Laws of Form, recursions and circuits that count.

See Even/Odd. An article by David Joyce about Even and Odd Numbers.

See Peano Axioms for a list of the Peano axioms for the natural numbers and a list of problems to prove, using these axioms. Compare these axioms with the discussion in the article by David Joyce on Even and Odd.

See Set Theory. This is an appendix from the book "Topology and Geometry" by Glen Bredon. The appendix is a concise but complete synopsis of basic set theory and goes beyond what is in Eccles. In particular, you will find discussion of well-ordering of sets, and in Theorem B18 the equivalence of a number of set theoretic principles such as well-ordering and the axiom of choice. You will also find a proof of the Cantor-Schroeder-Bernstein Theorem (B15 and B20). You do not need to read this whole appendix, but I DO ask you to look at Theorem B27. There you will find a beautiful proof that the real numbers have the same cardinality as P(N) where N is the natural numbers. The proof includes a proof that the set of finite subsets of N is countable (can you give an independent proof of this fact?). The proof of Theorem 27 uses the concept of continued fractions.

See Wang Algebra for a clever approach to graphs and spanning trees.

Remark. By now the assignments below are only approximate. I will revise this to a summary of the actual assignments in a few days. Please keep copies of the drafts of your writing assignments that have been approved for no further rewrites.

First Assignment: (Due in the second week of the course.)

1. Find an example of one or two pages of writing that you feel to be really excellent. Make a photo-copy of this sample and bring it to class. Please be prepared to read from your writing sample! This writing sample need not be about mathematics. It can be from any part of your reading experience.

2. Choose a simple piece of mathematics that you know well.

Find someone with whom you can discuss this topic or to whom you can teach the topic. Discuss or teach as the case may be. Then write a one page explanation of the topic, in your own words.

(Examples: a proof of the Pythagorean Theorem, why the sum of the angles of triangle is pi, how to solve a quadratic equation, what is a set and what is an infinite set, Euclid's proof that there are infinitely many prime numbers, the concept of probability, what is calculus, what is projective geometry ...)

Again, it will be best if you choose your own topic. The point is simplicity, not complexity. Choose a simple direct message in relation to the topic. Write a concise and readable single page.

3. Think about topics that you would like to explore for the first essay. We will brainstorm about that essay in the second class.

See Geometry This is a one page summary of some remarks that we made about geometry in class.

Choose a topic for the first essay and prepare a first draft to be discussed in the next class.

Continue working on the first essay. Prepare a second draft to hand in (and keep a copy for yourself).

Prepare an essay on a new topic. This is the third essay in the course.