Math 420 B

Advanced Topics:  History of Modern Mathematics

last modified 1/7/2011

Spring 2011 essay and paper schedule:

• Extended Essay #1 will be due Friday, February 25
• Extended Essay#2 will be due Friday, March 25
• Extended Essay #3 will be due Friday, April 22
• Extended Essay #4 will be due Wednesday, May 4 (last day of class)
• Math 420 has a final exam scheduled for Wednesday, May 11, from noon to 2:00 PM.  The term paper will be due at this time (no later than 2:00 Wednesday, May 11).  We will not have a final exam in this class

This is a tentative schedule of lectures and readings, and is likely to change as we progress through the semester.  I will try and keep paper dates fixed, but all else is subject to change.  The date and time of the final exam is, of course, set by the University and is not subject to change.  We will use the final exam period for the submission of term papers.

Lecture and reading schedule:

Please see The Official Schedule for details of the schedule for University events.  Please note that if any date in the following conflicts with the official schedule and exam schedules, the official schedules apply.

Schedule of lectures and readings:

Week 1:  Monday, January 17

• Topics: 
  • Survey of ancient mathematics
• Reading: 
• Burton  chapters 1, 2
• Struik chapters 1, 2
• Other Notes
• Monday is Martin Luther King day:  no classes or office hours.
• Office hours begin next week

Week 2:  Monday, January 24

• Topics: 
  • Survey of Greek mathematics
• Reading: 
• Burton chapters 3, 4
• Struik chapters 3, 4
• Other Notes
• Office hours resume this week

Week 3:  Monday, January 31

• Topics: 
  • The great sleep and the re-awakening
• Reading: 
• Burton  chapters 5 - 7
• Struik chapter 5
• Other Notes
• Monday, January 31 is the last day to drop without record.
• Extended essay #1 assigned (due Friday, February 25)

Week 4 :  Monday, February 7

• Topics: 
  • The rise of modern mathematics:  Descartes, Leibniz, Newton
  • Discussion of term paper (Monday)
• Reading: 
• Burton  chapter 8
• Struik chapter 6
• Other Notes
• .

Week 5:  Monday, February 14

• Topics: 
  • The development of probability
• Reading: 
• Burton  chapter 9
• Struik 7
• Other Notes

Week 6:  Monday, February 21

• Topics: 
  • Number Theory:  Fermat, Euler, and Gauss
• Reading: 
• Burton chapter 10
• Struik chapter 7
• Other Notes
• Extended essay #1 due (Friday, February 25)
• Extended essay #2 assigned (to be due Friday, March 25)

Week 7 :  Monday, February 28

• Topics: 
  • Non-Euclidean geometry and the first foundational crisis
• Reading: 
• Burton  chapter 11
• Other Notes
• Term paper proposal is due on Monday, February 28.  Email is OK for this milestone only.
• Monday, February 28, is the last day to drop with an automatic 'W'
• There will be no class or office hours on Friday, March 4 (Columbia History of Science Conference)

Week 8:  Monday, March 7

• Topics: 
  • Set theory and more foundational confusion
• Reading: 
• Burton  chapter 12
• Struik chapter 8
• Other Notes
• Mid-term is Friday, March 11 (not an exam day for us)
• The term paper annotated bibliography is due Monday following Spring break.  Early submissions cheerfully accepted.

Week 9:  Monday, March 14

• Topics:  Spring Break!  (No classes or office hours)
• Reading
• Other Notes
• The term paper annotated bibliography is due Wednesday following Spring break.  Early submissions cheerfully accepted.

Week 10:  Monday, March 21

• Topics: 
  • Analysis in the 18th and 19th centuries
• Reading: 
• Burton   TBA
• Other Notes
• The term paper annotated bibliography is due Wednesday, March 23.  Early submissions cheerfully accepted.
• Extended essay #2 due (Friday, March 25)
• Extended essay #3 assigned (to be due Friday, April 22)

Week 11:  Monday, March 28

• Topics: 
  • The rise of topology
• Reading: 
• Burton  chapter 13
• Struik chapter 9
• Other Notes

Week 12:  Monday, April 4

• Topics: 
  • Algebra
• Reading: 
• Burton   Chapter 13
• Other Notes

Week 13:  Monday, April 11

• Topics: 
  • Combinatorics
• Reading: 
• TBA
• Other Notes
• Term paper draft is due Friday, April 15
• Extended essay #4 assigned, to be due on the last day of class.  Please note that extended essay #4 will be assigned before extended essay #3 is due so that the due date for extended essay #3 does not conflict with the due date for the term paper draft.

Week 14:  Monday, April 18

• Topics: 
  • Computer Science
• Reading: 
• Burton   Chapter 13
• Other Notes
• Extended essay #3 due (Friday, April  22)

Week 15:  Monday, April 25

• Topics: 
  • More foundational confusion
• Reading: 
• TBA
• Other Notes

Week 16:  Monday, May 2

• Topics:  Review and catch-up
• Reading: 
• As needed
• Other Notes
• Wednesday, May 4, is the last day of classes.  All course material (except for the final term paper) are due.  No materials can be accepted past 5:00 on this date.
• Extended essay #4 is due Wednesday, May 4 (last day of class)

Final Exams

• The final exam for Math 420 is scheduled for Wednesday, May 11 from noon to 2:00 PM.  We will use this time for the submission of term papers (no final exam in this class)