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 proper bibliographic style (clear, consistent)
Overall effort (10%): General impression – was a lot of work put in, or was it written at the last minute?
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 subject areas. Avoid general descriptive overviews or reports on the literature. Although the essay may contain a synthesis of factual material, it should be focussed, analytical and issue-oriented.
Decomposition of unit fractions in Egyptian mathematics
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
Numerical methods in Ptolemy’s Almagest
The role of mathematics in the development of Greek astronomy
Contributions of Islamic mathematical science 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
Concepts of the continuum in Medieval mahematics
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