History of Mathematics (HM)
Dr. John Bukowski

Mathematisch Instituut

Universiteit Leiden

Voorjaar 2012

 

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)

E-mail:                bukowski@juniata.edu

 

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%).

 

Required

Reading: 


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)

Do Homework 1 -- html version

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

Do Homework 2 -- html version

23 februari Greek Mathematics – Apollonius and others

Read Struik, Chapter 3, Sections 8-15
Read Dunham, Chapter 4 (Archimedes)

Do Homework 3 -- html version

1 maart

Islamic Mathematics

Al-Khwarizmi Type 4 Equations

Abu Kamil Problem 45

 

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

Do Homework 4 (note: two pages in pdf) -- html version

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)

Do Homework 5 -- html version

Next week:  We will meet at the Demonstratiezaal of the UB.

Oude Boeken Assignment -- html version

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.

Oude Boeken Assignment -- html version

Lijst van Oude Boeken -- html version

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 Dunham, Chapter 7, pages 155-160

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]

Do Homework 7 -- html version


Finish the Oude Boeken Assignment, also due next week

Final Project Ideas -- html version

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)
and Chapter 8, pages 184-190 (Leibniz)

Do Homework 8 -- html version

Final Project Information -- html version

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
Read Dunham, Chapter 8, pages 191-206 (Bernoullis)

Do Homework 9 -- html version

Remember that you must send me a Final Project progress report e-mail by next Thursday.

Next week we will meet in Snellius 413.

26 april Euler
Class will be held in Snellius 413

Read Struik, Chapter 7, Sections 4-11

Read Dunham, Chapters 9 and 10 (Euler)

Euler links:

The Euler Archive

How Euler Did It, articles by Ed Sandifer

10 mei

Student presentations, 13.45-16.00
Presentation Schedule -- html version

 

 
24 mei

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.

 

e-Studiegids page