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Math 0413 Term Paper

Option 1:

Write a paper about mathematical proofs. Start your paper by addressing the following issues (∼ 1 page):

(1) What are proofs and their purposes

(2) The importance and limitations of proofs

(3) Different types of proofs and how to construct them (you should mention at least the

following four kinds: direct proof, proof by mathematical induction, proof by contrapositive, and proof by contradiction.)

The rest of your paper will be made up of proofs for the following four problems assigned during the semester (they will be part of the regular homework):

HW Part 2, Problem 2.4  (use mathematical induction )

HW Part 5, Problem 5.1  (use direct proof)

HW Part 5, Problem 5.7  (use proof by contradiction)

HW Part 10, Problem 10.7  (use proof by contrapositive)

Option 2:

Write an expository article on a mathematical topic of your choice. Some suggested topics are listed below, but you are not limited to that list. Your paper should be interesting and comprehensible to a reader who does not already know your topic.  It must include some non-trivial mathematical content such as proofs.

Suggested Topics:

Probability theory and games of chance The Axiom of Choice

Public key cryptography

Proofs of the Pythagorean Theorem Conic sections


The golden ratio

Algebraic and transcendental numbers Geometry of space curves