Mat390 Essay

The essay should be ten to fifteen pages (typed double spaced). Essays must be submitted in hard-copy form; email or electronic submissions will not be accepted.

Bibliographical References and Essay Guidelines

These books are available in Gerstein Library, as well in some of the branch libraries.

J. W. Dauben The History of Mathematics from Antiquity to the Present. A Selective Bibliography (1985).

K. O. May Bibliography and Research Manual of the History of Mathematics (1973).

C. C. Gillispie Dictionary of Scientific Biography 16 volumes (1970-).

One may also consult the references at the end of chapters in the standard histories of mathematics by Katz,  Kline, Boyer, Eves, Struik, Burton, Smith and so on. The MacTutor website for the history of mathematics contains references to the historical literature that are useful. The weekly readings may also provide the basis for your research on an essay topic.

The essay is a major component of the grade for the course. It is recommended that an essay topic be chosen by the end of February and that research and writing be well under way by the middle of March. The essay should consist of your own work, and may be run through a standard database to verify that there has been no copying from some source. In particular, do not cut and paste text from websites or Wikipedia articles into your essay. Follow standard conventions for citing and quoting from sources. References and citations should be done according to APA style.

The essay will be evaluated according to the following criteria:

Arguments (50%): The essay presents a concise, well-stated, interesting and
non-trivial thesis; and it is argued for persuasively. The student engages
with historical sources (primary and/or secondary).

Style: “proper essay” (20%): The essay has a clear introduction, body,
conclusion, transitions, thesis statement etc.

Style: writing ability (10%): Clarity, sentences, paragraphs, foot/end
notes, formal (academic) style, etc.

Sources (10%): Uses good sources (number, quality, level) and properbibliographic style (clear, consistent)

Overall effort (10%): General impression – was a lot of work put in, or was
it written at the last minute?

Essay Topics

The list below is intended as a general guide in choosing a topic. The essay itself should be fairly specific in developing some theme or exploring some issue that arises in these or any other subjects.   Avoid general descriptive overviews. Although the essay will contain a synthesis of factual material, it should be focussed, analytical and issue-oriented.

Ethnomathematics

Decomposition of unit fractions in Egyptian mathematics

Interpretations of the Babylonian tablet Plimpton 322

Babylonian mathematical astronomy

The role of the “crisis” of incommensurables in the development of pre-Euclidean Greek mathematics

Geometric algebra in Euclid’s Elements

The method of exhaustion in Euclid and Archimedes

The place of construction in Greek geometry

The role of mathematics in the development of Greek astronomy

Contributions of the Arabs to algebra and arithmetic

Mathematical astronomy in Islamic science

Trigonometry and Islamic mathematics

Foundations of geometry  in Islamic mathematics

Indian work on infinite series

The reception and transmission of Euclid’s Elements in Medieval Europe

Proportion theory in the Middle Ages

Mathematical dynamics in the Middle Ages

Oresme and the latitude of forms

The handling of imaginary numbers by Cardano and Bombelli

Viète and the invention of the analytic art

Mathematics in Copernicus’s De Revolutionibus

Linear perspective in art and the origins of projective geometry

The construction of curves in Descartes’ Géométrie

Number theory in the seventeenth century

Theory of probability in the seventeenth century

Kepler’s derivation of the elliptical orbit

Napier and the invention of logarithms

The history of the concept of analysis from Pappus to Descartes

Method of indivisibles in 17th-century mathematics

Tangent methods in the pre-calculus period

Transcendental curves in 17th-century mathematics

Optimization problems in seventeenth-century mathematics

Mathematical dynamics and the invention of calculus

The Newton-Leibniz priority dispute