Library Assignment #2: Periodical Literature

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1 Library Assignment #2: Periodical Literature Provide research summaries of ten papers on the history of mathematics (both words are crucial) that you have looked up and read. One purpose for doing this is that it will provide everyone with lots of ideas for their major paper. The most interesting of these will be edited and posted on the web, so write your synopses with an eye towards encouraging your peers to read the paper. But be honest, if the paper is uninteresting, boring, or not well written, say so. A typical summary (for a journal article) is as follows: Hogan, Edward Robert Adrain: American mathematician, Historia Mathematica, vol. 4 (1971), pp A very good, interesting biographical sketch concentrating on Adrain s publication of two journals, his teaching, and his mathematics. Very easy to read. There are three ways to do this assignment and I encourage you to try them all: 1. Pick up one of the journals listed in the bibliography (to be distributed) and browse until you find a historical paper that interests you. 2. Pick a topic that interests you, look it up in Kenneth O. May s Bibliography and Research Manual of the History of Mathematics and then go find the paper. 3. Use one of the databases available through the library computer. I will discuss how to do this in class. The last two techniques will be the ones you will have to use when writing your research paper, so I encourage you to do some of this. Another possibility is to follow up references that you encounter in your reading. Be sure to look in some old journals as they can be lots of fun. The ten articles are to come from at least four different periodicals (books are not permitted), and deal with at least four different mathematical topics. You should strive to avoid choosing the same articles as your classmates. To much duplication will require repeating the assignment. General Library Comment: Kathy Wheeler at the USA Library has very kindly set up a webpage specifically for MA 410 students to begin exploring the resources offered here on campus. The website is

2 Journals Containing History of Mathematics The following periodicals are good sources of historical material on mathematics. I would advise you to look at a volume or two of each while doing your second library assignment. At the same time think about topics for your research paper. Historia Mathematica Devoted entirely to the history of mathematics. Included are papers, reviews of books, and short abstracts of new books and articles. The latter provide hints as to where else to look for information. Scripta Mathematica Devoted to the philosophy, history, and expository treatment of mathematics. The early volumes make very interesting browsing. The Mathematics Teacher A journal specifically devoted to the high school curriculum, which is published by NCTM, an organization prospective teachers should join. Numerous historical articles have appeared over the years. See especially the Historically Speaking column that appeared in the fifties. The American Mathematical Monthly devoted mainly to the unversity curriculum. Isis The most important journal devoted to the history of the sciences. A noteworthy feature is the critical bibliography that appears at the end of each volume. Consortium: The Newsletter of the Consortium for Mathematics and its Applications Each issue contains a column specifically designed for high school students and teacher. The following are research journals. It is worthwhile to look at them and to note the difference in the level of exposition from those in the list above. The British Journal for the History of Science Annals of Science Archives Internationales d Histoire des Sciences History of Science Archive for History of Exact Sciences These last two do not contain papers, but rather abstracts of papers. Look in the section on the history of mathematics to get some idea of the wealth of material that is being published today. Sometimes there are links to the original articles themselves; otherwise, if you are interested in seeing an article you ll need to see if you can find it in the library.

3 Mathematical Reviews (aka MathSciNet) Zeitschrift für Mathematik und ihre Grensegebeite For off campus access to many of these websites: go to and click one of the links under the title Find Articles. For example, to get to Mathematical Reviews, click Articles, Indexes, and Databases, then scroll down and click MathSciNet. You will then have to log in. Pay careful attention to the instructions regarding login name and password. Suggestion for writing your research papers You are to write a paper on a topic of your choice. Please choose a topic with care. You may prefer to write about a mathematician, or you may prefer the history of some mathematical topic. Some suggestions for topics are below, but you are encouraged to choose your own topic, and to talk with me (during office hours or via ) about possible topics before making your final decision. The only true restriction is that you cannot write a biographical paper about your mathematician from library assignment #1. Each paper must meet the following requirements: 1. The papers are to be on the history of mathematics. They can be neither all history not all mathematics. Each should contain a reasonably non-trivial piece of mathematics as well as the history and background of that mathematics. 2. Enough expository material should be included so as to make the paper self-contained. If you have doubts, ask a friend to read it. Having someone else read your paper critically is the best way to improve the exposition. 3. You should use a variety of research materials and must give careful references to your sources. You will want to use books and encyclopedias, but I especially encourage you to use the journals. Your paper should include a bibliography listing your sources, and they should be cited in the body of your paper when appropriate. The best sources to use are original sources, but, admittedly, that is hard to do (as many of you discovered in library assignment #1). 4. The paper must be typed. You may leave spaces to hand-write any symbols that your wordprocessing prgram seems unable to handle. Other issues such as length, format, etc., are up to you. Papers have a natural length. You are telling a story which needs certain background, exposition, and detail. When that is successfully done, stop; you have finished. The grading of your paper will be based on a number of factors, including: the historical and mathematical content; the significance, accuracy, and completeness of the material; the accuracy, scope, and significance of your references, and the sensitivity with which they are used and cited; and finally, the style in which it is written.

4 You are not required to turn in any preliminary version of your paper before the final due date (other than a choice of topic), but you are welcome to do so. This could be a brief summary of the major points, a formal outline, or a substantial rough draft. The more details you include, the more feedback you will get from me. Feel free to ask questions and to indicate the problems you are having. You are writing a paper on the history of mathematics. Because it is history you must document all the facts you use except those which are general knowledge. Your opinions are irrelevant. You can draw conclusions at the end of the paper (in fact, that is to be encouraged) but conjectures should be labeled as such and clearly distinguished from fact. Also be careful not to present the conjectures of others as fact. The paper that you turn in should be a polished product. Write it in your own style. Avoid stringing together a bunch of quotations. When you paraphrase the work of another you need to put it into your own words so that the paper doesn t read funny (you also need a reference). You should rewrite your paper until it reads well. Pay attention to the connecting material between sections. Don t jump from topic to topic. Respect both the historical and logical connections between the points you are trying to make. Have a friend read your paper and make suggestions on writing style, typos, sufficient detail. Don t neglect to use your dictionary and style manual (The Elements of Style, by Strunk and White is a good one). Useful tips from William Safire: If you reread your work, you will find on rereading that a great deal of repetition can be avoided by rereading and editing Proofread carefully to see if you any words out. To avoid unnecessary footnotes, references should be incorporated parenthetically into your text by citing the author and page number (and date if you cite more than one work by this author). Footnotes can be used to include interesting material that is peripheral to your main theme or to point out errors or conflicts in your sources. For ease in typing these can be grouped together at the end of your paper. A bibliography of the sources you cite should be listed on a separate sheet at the end of your paper. The items in each reference should include: author, title, journal, volume, year, pages (starred items are for journals only). Book and journal titles should be italicized; the titles of articles in journals should be in quotation marks. For reprints of books give both the original and the reprint date. Here are some more tips: When unusual mathematical terms come up, add a few words of explanation. Remember that your paper is to be self contained. Be sure to use the periodical literature. Don t just rely on one source. Include biographical details; they make your paper more interesting.

5 Foreign titles of books should be translated parenthetically. Include source of illustrations; not just where you got them, but where they came from originally. Be careful with verb tenses. History happened in the past. Don t refer to people by their first names. Long quotations (3 lines or more) should be indented as block quotes. Please double-space. Here are some comments that are typical for papers that receive a grade of A or B. Good use of journal sources. Nice combination of mathematics and history. A good summary of his life. Nice fluid writing style. Excellent explanation of the mathematical ideas. Good job of setting the historical scene. Here are comments on C and D papers: Choppy writing style; writing needs work. Stilted language. Too many quotes, especially long ones. Lacked references. Not very detailed. Mentions lots of mathematics, but no details. Technical terms not explained. Old, dated references. Mostly speculation, not history. Lots of ideas here which should have been developed. A catalog without any historical sense. Lacks detail. Too brief. Good references, but not cited in the text. Sample Paper Topics Feel free to choose from this list, or to come up with your own topic. Just remember that you cannot write a biographical paper about your mathematician from library assignment #1. History of perfect numbers from Euclid to the day before yesterday The influence of social needs on the uses of mathematics History of the binomial theorem The quadratic equation

6 An insight into Islamic mathematics Goldbach and his famous conjecture The history of logarithms and logarithm tables Geometrical mathematical recreations Prime numbers The history of trigonometry Charles Babbage and his engines Some revolutionary curves Angle trisection Relationship of mathematics to music Comparison of algebra texts from 1900 to today American mathematics prior to 1875 How our view of the early history of mathematics has changed in the last 100 years The dark ages were dark for mathematics, too Is mathematics discovered or invented? How new was the new math? Female mathematicians in history The books that most changed our present geometry texts The remarkable Bernoulli family The rise of periodical literature and how it affected mathematics The changing nature of function The calculus priority dispute The history of linear programming Quality control, with emphasis on control charts The role of cryptology in World War II Navigation and mathematics The Platonic solids Mathematics and the early Rabbis History of Hindu mathematics The history of π