MATH 52 ASSIGNMENT TO EXPLAIN SANDZINI’S TRICK

Purpose: An important way that mathematicians gain insight into a subject they would like to understand better is by analyzing examples of interesting phenomena in this subject. These examples can suggest a general principle, and eventually lead mathematicians to the proof of a general theorem. Such a theorem provides us with the power to produce an (often endless) variety of new examples by applying the general principle to a specific situation. Generalization and application are both extremely valuable elements of the mathematician’s craft, as they extend our knowledge to new situations. The purpose of this assignment is to extend your skill in applying a general theorem, thereby practicing the art of thinking like a mathematician. Mathematicians also want to know how and why a mathematical phenomenon happens, and you will address those questions here. Finally, mathematicians need to know how to communicate their ideas effectively in order to join in the communal effort to advance the frontiers of mathematical knowledge. This assignment will also provide you with practice in communicating mathematics.

Task: You have seen the Great Sandzini perform his feat of mathematical magic. Your task is to explain the following. Devote one paragraph to each of these.

1) What the trick is.

2) How to do it.

3) Why it works.

4) A variation of the trick that you create yourself.

Details: Write your explanation with the idea that it will be read by a Math student who has learned the relevant material in the past, but has not seen the trick. The explanation of why it works (part 3) should include a clear, correct statement of the general theorem or theorems that apply, and a description of exactly how it applies in this situation.

Grading: You will be graded on

1) Organization (20 points) Is your presentation organized so as to be easily read and understood by a knowledgeable Math 52 student? Is it complete?

2) Style (20 points) Does the writing exhibit good grammar, correct spelling, neatness, clarity, and conformity with the rules of mathematical writing?

3) Accuracy (30 points) Are mathematical terminology and notation used correctly?

Are all relevant mathematical facts (theorems, propositions, etc.) stated explicitly and accurately?

4) Mathematical Reasoning (30 points) Is the connection between each theorem or proposition and the specific application of it explicitly spelled out? Are all other logical steps stated explicitly and performed correctly?

Due: Friday in class. (Final Draft)