University of Memphis
Department of Mathematical Sciences
MATH 4151/6151
History of Mathematics
D.P.Dwiggins, PhD
Fall 2020

Text: A Short Account of the History of Mathematics,
W. W. Rouse Ball (Trinity College, Cambridge, 1893).
(reprinted by Dover (NY) in 1960)

Class Meetings: MWF 11:30-12:25, Location TBD

This course is divided into three parts.
Part One, Early Mathematics, will be covered during Weeks # 1-5,
Part Two, Medievel Mathematics, will be covered during Weeks # 6-9, and
Part Three, Modern Mathematics, will be covered during Weeks # 10-13.
The time remaining at the end of the semester will be for completing class projects,
and also as review time for the final exam (scheduled right before Thanksgiving).
There will also be a Mid-Term Exam at the end of Week # 7 (Friday October 2),
which will cover Chapters I-VIII (and part of Chapter IX) of the textbook.

Week # 1: M-W-F = Aug 17-19-21
Chapters I, VII, and XI, Numeration and Arithmetic
(a survey of mathematics along the seven pre-historic river cultures)

Week # 2: M-W-F = Aug 24-26-28
Chapter II, Early Greek Mathematics
(from Thales to Zeno of Elea)

Week # 3: M = Aug 31, W-F = Sep 2-4
Chapter III, The Influence of Athens
(from Anaxagorus to Aristotle)

Week # 4: W-F = Sep 9-11
Chapter IV, The Library at Alexandria
(from Euclid to Proclus)

Note: Because Labor Day makes Week # 4 a short week, the material in
Chapter IV will also be discussed on Friday Sep 4 and Monday Sep 14.

Week # 5: M-W-F = Sep 14-16-18
Chapters V and VI, Mathematics during the Roman and Byzantine Empires

Week # 6: M-W-F = Sep 21-23-25
Chapter VIII, Western Europe, 600-1200
(the development of the university)

Week # 7: M-W = Sep 28-30, Friday Oct 2 = Mid-Term Exam
Chapter IX, The Rise of Arabic Mathematicians
(the invention of algebra)

Week # 8: M-W-F = Oct 5-7-9
Chapters X and XI, Arithmetic, Algorithms, and Logarithms

Week # 9: M-W-F = Oct 12-14-16
Chapters XII and XIII, Mathematics During the Renaissance
(from Fibonacci to Desargues)

Week # 10: M-W-F = Oct 19-21-23
Chapters XIV and XV, The Rise of Analytic Geometry
(from Descartes to Huygens)

Week # 11: M-W-F = Oct 26-28-30
Chapters XVI and XVII, The Calculus Revolution
(Newton, Leibnitz, and the rest of the gang)

Week # 12: M-W-F = Nov 2-4-6
Chapters XVIII and XIX, Nineteenth Century Mathematics
(Euler, Gauss, Riemann, and Non-Euclidean Geometry)

Week # 13: M-W-F = Nov 9-11-13
Instructor's Supplement, Twentieth Century Mathematics
(from Hilbert's Problems to the Millenium Prize and Beyond)

Weeks # 14-15: Review for Final Exam (date TBD).