History of Mathematics, Math 3010-1, University of Utah, Summer 2010

Due dates

Monday 6/21 for the Outline
Wednesday 7/07 for the Draft
Wednesday 7/14 for the paper

This first [long] paper should be typewritten, one-sided, and double-spaced, typed in a standard-sized font. Your paper must adhere to the following writing standards:

Your paper must have a title page that contains a title, your name, course name and number, and a date. Please do not write your social-security number on this titlepage, or anywhere else for that matter.
The main body of the paper must be 6-8 pages long. More is expected if there are inserted equations, pictures, and/or diagrams that occupy significant space.
Your paper must have a bibliography of all the references there have been used and/or cited.
Throughout the paper, you must make careful references that include page numbers [and/or other very clearly-identified pointers] that lead the reader to sources in the bibliography.
The Outline and Draft are mandatory. You can write the final version of your paper only after the Outline and Draft have been returned to you. [I will make remarks, suggestion, and corrections to those that you can use to write the final version.]

Topic: Choose a topic related to early mathematics such as that of Babylonia, Egypt, Greece, China, India, etc. Your paper should either focus on something not discussed in class, or contain a significant extension of ideas introduced in class. You can find some ideas for potential topics at the bottom of this page, as well.
Your paper must have both historical and mathematical content. For example, if your paper is primarily a biographical sketch of a certain person, then be sure that it does more than merely provide a list of mathematical achievements of that individual. Your assigned and recommended reading sources provide good examples that show how biographical, historical, and mathematical materials can be intertwined.
Outline (20 points): The process begins with a one-page outline. That outline should include a brief statement of your thesis topic (1-3 sentences), followed by a partition of the topic into three or more categories with further subdivisions if needed. Your outline will be returned to you with comments that you can use to write the draft [next stage].
The outline is worth a total of 20 points, 10 of them are for mathematical/historical context, and 10 for written correctness.
Draft (20 points): The draft should be 4-5 pages long. The writing standards mentioned above all apply to the draft. Your bibliography must be included. And your draft will be critiqued for mathematical and historical content, as well as for written correctness. The bibliography must contain at least three sources. Your textbook can be [and likely will be] one of the three. At most one of the references may be an internet address. [Wikepedia is as yet an unreliable resource, and therefore not accepted.] You may use either books, and/or journals. They can be borrowed from the main library as well as the interlibrary loan office within the main library. Useful hint: You might find the references in your textbook a helpful starting point. And you can learn how to format a bibliography from any academic book, including your textbook for this course.
The draft is worth a total of 20 points, 10 of them are for mathematical/historical context, and 10 for written correctness.
Final Version (60 points): The final version of your paper must reflect recommendations provided to you in the returned outline and draft papers. Your paper must be well written, and it should present an organized development of the topic.
The final [formal] version of your paper is worth a total of 60 points, 30 of them are for mathematical/historical context, and 30 for written correctness.

Grading (rubric)

Written Correctness (30 points of the formal paper score): Because this course satisfies the upper-level Communication/Writing Requirement (CW), your paper must be written in a formal manner. Have an effective opening paragraph that introduces your thesis topic, and a summary paragraph at the end of the paper as a conclusion.
Use proper mathematical symbols that are commonly available on word processors. For example, write x² instead of x^2 or x**2. And, of course, avoid misspellings, grammatical errors, and incomplete sentences. Deductions will be made for these, and they will be severe if your paper is submitted later than is scheduled.
Avoid contractions such as "can't," "won't," etc. Use formal, rather than conversational, language. Do not use informal phrases such as " it was cool," or other similar conversational jargon. At the same time, remember that "formal" is not the same as "convoluted." It is best to write simply, and very clearly.
It helps a great deal if you frequently use paragraphs to break up your ideas in a clearly-defined manner. Avoid very long or very short paragraphs; similar remarks apply to sentences.
Avoid self-referential sentences such as "I liked it," or "I was amazed." [That is, unless you are the topic.]
When you use a resource, site it carefully and properly. Plagiarism is taken very seriously at the University of Utah. For detailed information on what constitutes plagiarism, see Policy 6-400 of the Student Code at www.regulations.utah.edu/academics/6-400.html
Mathematical and Historical Content (30 points of the formal paper score): Your paper must have a blend of historical and mathematical content. Mathematical content refers to proofs, complete descriptions of the solution to a mathematical problem, formal definitions, a detailed computer code, together with output, that runs a certain algorithm, etc. For instance, if you wish to discuss someone's theorem, then discuss the theorem in depth, together with what he or she did in order to prove the theorem. In other words, write the way textbooks, journals, experts, etc. write. [A research paper is not a newspaper article.] If you are describing a chronological history of π, then make sure that you verify at least some of the facts that you state about π.

Some Previously-Studied Topics

Exodus and the method of exhaustion.
Advanced Greek constructions that use a compass and a ruler.
The mathematics of the Golden Ratio with applications to art and architecture.
Problems posed in the Rhind papyrus: The methods of false position and double-false position.
One or more of the three classical problems of Antiquity, and some of the efforts to solve them using something other than a compass and a ruler.
The history of π, or the imaginary number i, from ancient to modern times.
The Greek notion of a "datum" and related constructions.
A history of the parallel postulate from ancient to modern times.
Discoveries by Archimedes, or another mathematician of ancient times, that are not discussed in class.
Diophantus and Diophatine equations.
The mathematics of Pappus of Alexandria.