MHF 3404 - HISTORY OF MATHEMATICS FLORIDA INT'L UNIV

PROJECTS 1 & 2 (March. 3rd)  SPRING 2009

Pick two of the following 4 topics and write a 4 to 6 page (1.5 space, 1” L/R margins) paper
            on each of the two topics you choose. By a 4-page paper, we mean 4 complete pages. If you
            have to exceed 6 pages, you may do so, but try to avoid making the paper too long or technical.
The paper should be aimed at students with your background (students who have successfully
            mastered Calculus I & II) and have an idea of what a proof is (especially, proofs in Euclidean
            Geometry).   Write the paper as a continuous essay with the references at the end

            THE  FOUR TOPICS :

1. The Origin of the Deductive Method of Proof and its success with Euclidean Geometry.

2.   The Origin of the Calculus & its Applications to the Natural Sciences in the 17th century.

3.   The Origin of the Hindu-Arabic Numerals and Modern Number Systems (Negative,
 Rational, Algebraic, Real, and Complex  Numbers).

            4.   The Solvability of Polynomial Equations of degree less than or equal to four and the
                  Unsolvability of Polynomial Equations, in general, of degree greater than four. 

                               THE SOURCES you may wish to consult are:

1. Standard Encyclopedias such as Encyclopedia Brittanica & Mathematical Encyclopedias

2. Handbooks & Textbooks on Mathematics and on the History of Mathematics

3. Wolfram Math World (http://mathworld.wolfram.com/)

4. Wikipedia (http://en.wikipedia.org/wiki/Main_Page)

Be careful with on-line information (like #4 )as they are not considered reliable but they can lead

you to reliable sources. The kind of things that you are expected to include in your paper are:

1. An introductory paragraph that describes in a non-technical way the topic under discussion.

2. The history of the topic under discussion and the people involved in its solution.

3. Some details of the situation and the standard approach to the topic

4. A concluding paragraph about the significance & importance of the topic under discussion.

            5.   Include at least 5 different sources & indicate where these sources were used in your essay.

Be careful with on-line information like #5 as they are not considered reliable but they can lead

you to reliable sources.  You should only quote things when they are particularly relevant, very

revealing and nicely said.  Otherwise, just express everything in your own word in the way you
understand them.  Never include any statement in your paper that you do not understand. 

            DEADLINES: One paper is due in class by Feb.12th and the other by Mar. 26th, 2009.

BONUS QUESTION #1 (Due Feb.12th).  In triangle ABC, BD bisects angle ABC to meet AC
            in D and CE bisects angle ACB to meet AB in E.  If BD = CE, does it follow that angle ABC = 
            angle ACB? Give a complete proof. You can use any standard Theorems in Geometry.  (5 pts)

BONUS QUESTION #2 (Due Mar. 26th). Consider the set of points with non-negative integer
            coordinates in the plane (i.e., those in the first quadrant).  Assume that there are only horizontal
            & vertical roads which join these points together, so that to get from the origin to another point
            you can only move up or across right.    Let N(k,k)  =  number of paths of length 2k from (0,0)
            to (k,k) that do not go above the diagonal joining (0,0) and (k,k).  Find the correct  formula for
            N(k,k) by experimentation or by searching and then prove that your formula is correct.  (5 pts)