History of Mathematics (HM)
Description: This course will provide a general overview of the history of mathematics. We will study the mathematics of the ancient Babylonians and Greeks, as well as Medieval Islamic mathematics. We will also focus on the mathematics of 16th, 17th, and 18th century Europe. We will study the lives and works of Euclid, Apollonius, Descartes, Galileo, Stevin, Huygens, Newton, Leibniz, Euler, and the Bernoullis, among others. We will read original sources (in translation) where possible.
Prerequisites: Analyse 1 en 2
Course Goals: (1) To provide a brief overview of the history of mathematics, from the mathematics of antiquity to 17th and 18th century mathematics and its applications.
(2) To read and appreciate original sources.
(3) To give life to your knowledge of mathematics. (F. Rickey)
Class Times: Thursday 13.45-15.30
Location: Snellius 312
Instructor: Dr. John Bukowski (Juniata College, USA)
Office: Snellius 213 (Note: new location as of 21/02/2012)
Office Hours: By appointment -- I will be happy to meet with you! Please send me an e-mail.
Examination: Regular homework assignments (60%), with a final paper and presentation in English (40%).
1 : D.J. Struik, Geschiedenis van de wiskunde (Het Spectrum, ook gratis on-line), or A Concise History of Mathematics (Dover)
|2 : W. Dunham, Journey Through Genius (Penguin) -- Please obtain a copy of this book as soon as possible!|
|3 : R. Descartes, The Geometry of René Descartes (Dover, or available free online in both French and English)|
Schedule (subject to change):
|Date||Subject||Homework and Reading|
|9 februari||Introduction and Mesopotamian/Babylonian Mathematics||
Read Struik, Chapters 1 and 2 (especially Sec. 4, 5)
Read Plimpton 322 web site, http://www.math.ubc.ca/~cass/courses/m446-03/pl322/pl322.html
Read "Sherlock Holmes in Babylon", R.C. Buck, The American Mathematical Monthly, Vol. 87, No. 5 (May 1980), 335-345. (UB, electronic)
Optional reading: "Dirk Jan Struik", C. Davis, et al., Notices of the AMS, Vol. 48, No. 6 (June/July 2001), 584-589. (UB, electronic)
|16 februari||Greek Mathematics – Euclid||
Read Struik, Chapter 3, Sections 1-7
Read Dunham, Chapter 1 (Hippocrates) and Chapter 2 (Euclid)
Euclid's Elements online, http://aleph0.clarku.edu/~djoyce/java/elements/toc.html
|23 februari||Greek Mathematics – Apollonius and others||
Read Struik, Chapter 3, Sections 8-15
Read Struik, Chapter 4
Read Dunham, Chapter 5 (Heron)
Read Descartes, Book I
St. Andrews Math History web site, http://www-history.mcs.st-and.ac.uk/
Go to History Topics --> Arabic Mathematics
Remember: No class next week! The homework is due in two weeks.
|8 maart||No class|
|15 maart||Early European Mathematics||
Read Struik, Chapter 5
Read Dunham, Chapter 6 (Cardano)
Read Descartes, Book II (pages 40-80), Book III (pages 152-179, 208-211, 240)
Next week: We will meet at the Demonstratiezaal of the UB.
|22 maart||Visit Universiteitsbibliotheek to view old mathematics books||
Meet at the Demonstratiezaal of the UB at 13.45. You must have your LU-card to enter the library.
Please note that the Oude Boeken Assignment is now due on 12 april.
|5 april||Zeventiende eeuw – Huygens et al.||
Read Struik, Chapter 6, Sections 1-6
Read "Christiaan Huygens and the Problem of the Hanging Chain", J. Bukowski, College Mathematics Journal, Vol. 39, No. 1 (Jan. 2008), 2-11. [Direct link]
Please note the e-mail that is required before class on 12 april.
|12 april||Early calculus – Newton en Leibniz||
Read Struik, Chapter 6, Sections 7-8
Read Dunham, Chapter 7, pages 160-183 (Newton)
Optional reading: "Touring the Calculus Gallery", W. Dunham, The American Mathematical Monthly, Vol. 112 (Jan. 2005), 1-19. [Direct link]
|19 april||The Bernoullis||
Read Struik, Chapter 7, Sections 1-3
Remember that you must send me a Final Project progress report e-mail by next Thursday.
Class will be held in Snellius 413
Read Struik, Chapter 7, Sections 4-11
Read Dunham, Chapters 9 and 10 (Euler)
How Euler Did It, articles by Ed Sandifer
Student presentations, 14.00-15.45
Collected final papers (9 MB, 111 pages)
|Final papers due at 12.00, in pdf form
Please send them to me in an e-mail. Do not submit a hardcopy.