Previous Weeks in Math 420

This file will contain the week-to-week reading and lecture schedules as they actually happened.  At the end of the week the "this week" page will be modified to reflect what actually happened and will be appended to this file.

Week 1: Monday, January 21

  • Topics:
    • Introduction to the course
    • A survey of ancient mathematics
  • Reading
    • Burton, chapters 1, 2
    • Struik, chapters 1, 2

Monday:

  • Martin Luther King day - no classes or office hours

Wednesday:

  • Introduction to the course

Friday:

  • Early representation of numbers

Other Notes:

  • Office hours resume next week

Week 2: Monday, January 28

  • Topics:
    • Egypt
    • Babylon
    • Thales and Pythagoras
  • Reading
    • Burton, chapters 2 - 3
    • Struik, chapters 2 - 3

Monday:

  • Mathematics in Egypt

Wednesday:

  • Mathematics in Babylon

Friday:

  • Thales, Pythagoras and Eudoxes
  • The three classical problems of antiquity

Other Notes:

  • Office Hours resume this week

Week 3: Monday, February 4

  • Topics:
    • Greek mathematics
  • Reading
    • Burton, chapters 3 - 4
    • Struik, chapters 3 - 4

Monday:

  • Assign first extended essay (discussion)
  • The three classical problems of antiquity
  • Euclid and the elements

Wednesday:

  • Euclid and the Elements

Friday:

  • Eratosthenes
  • The Almagest of Ptolemy

Other Notes:

  • Monday is the last day to drop without record
  • Extended essay #1 was to be due next week (We slid the deadline for extended essay #1 to Friday, February 22.  The second extended essay will be assigned on that date.).

Week 4: Monday, February 11

  • Topics:
    • Later Greek Mathematics
    • Medieval Islam
  • Reading
    • Burton, chapters 4 - 5
    • Struik, chapters 4 - 5

Monday:

  • Discussion of the term paper
  • Eratosthenes and the measurement of the Earth

Wednesday:

  • Archimedes and the method
  • Ptolomy and the Almagest

Friday:

  • The Arithmetica of Diophantus

Other Notes:

  • Extended essay #1 is due next week  The second extended essay will be assigned on that date.

Week 5: Monday, February 18

Topics:
  • Islamic Mathematics and the rebirth of European Mathematics
Reading:
  • Burton, chapters 5 - 7
  • Struik, chapters 4 - 5

Monday:

  • Medieval Islamic Mathematics
  • Discussion on Arabic algorithms for addition. The first "laptop"

Wednesday:

  • Return homework - notes
  • Discussion on Arabic algorithms for multiplication

Friday

  • Abelard, Gerard, and the rediscovery of Hellenistic Mathematics
  • Fibonacci
  • Extended Essay #1 due
  • Extended Essay #2 assigned.

Other Notes:

  • Extended Essay # 1 is due this week.
  • No classes or office hours next Thursday, February 28 - Friday, February 29 (travel to and attendance at the Columbia History of Science Group seminar at Friday Harbor).  For further details on this conference, please contact Kristin Johnson of the Science, Technology, and Society Program.

Week 6: Monday, February 25

Topics:
  • Algebra and the solution to equations of the third and fourth degree.
Reading:
  • Burton, chapters 7 - 8
  • Struik, chapters 6

Monday:

  • The invention of movable type
  • The rise of the universities
  • Cardan the Gambler and Tartaglia:  The great feud over the Ars Magna

Wednesday:

  • Cardan the Gambler and Tartaglia:  The great feud over the Ars Magna

Friday

  • No classes or office hours (see note below)

Other Notes:

  • No classes or office hours this Thursday, February 28 - Friday, February 29 (travel to and attendance at the Columbia History of Science Group seminar at Friday Harbor).  For further details on this conference, please contact Kristin Johnson of the Science, Technology, and Society Program.

Week 7: Monday, March 3

Topics:
  • The beginnings of modern mathematics
Reading:
  • Burton, chapters 8 - 9
  • Struik, chapter 6

Monday:

  • No classes or office hours - Instructor ill

Wednesday:

  • No classes or office hours - Instructor ill

Friday

  • The dawn of modern mathematics
  • Gallieo
  • Napier
  • Some early dates in the history of computers
  • Term paper proposals due.

Other Notes:

  • Term paper proposal due this Wednesday
  • Monday is the last day to drop with an automatic "W"
  • The second extended essay was initially due next week  We'll slide the due date until March 28 to keep this more in line with the hour exam schedules of my other classes and to give us a bit more time on this one.  The third (and final) extended essay will be assigned when this one is due..

Week 8: Monday, March 10

Topics:
  • The beginnings of modern mathematics
Reading:
  • Burton, chapter 8
  • Struik, chapter 7

Monday:

  • Brahe, and Kepler
  • The second extended essay will be due the Friday following Spring Break.

Wednesday:

  • Descartes
  • Newton and the Principia Mathematica

Friday

  • Descartes and geometry

Other Notes:

  • The second extended essay was initially due this week  We'll slide the due date until March 28 to keep this more in line with the hour exam schedules of my other classes and to give us a bit more time on this one.  The third (and final) extended essay will probably be assigned at that time.
  • Friday is mid-term (not an exam or paper date for us)
  • Spring Break is next week!

Week 9: Monday, March 17

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. (Please note change in due date)
  • Extended essay #2 is due next Friday.  The third extended essay will probably be assigned at that point (and its due date adjusted).

Week 10: Monday, March 24

Topics:
  • The mechanical universe:  Newton and Leibniz and the beginnings of the calculus
Reading:
  • Burton, chapters 8.3
  • Struik, chapter 6

Monday:

  • A quick note on projective geometry
  • Newton and his times

Wednesday:

  • Barrow on tangents
  • Newton and the binomial theorem
  • Annotated bibliography due (Please note change in due-date)

Friday

  • Newton and the calculus
  • Third extended essay assigned

Other Notes:

  • The second extended essay was initially due this week (assuming that I get the first one back to you Monday).  We'll slide the due date until March 31 to keep this more in line with the hour exam schedules of my other classes and to give us a bit more time on this one.  The third (and final) extended essay will be assigned when this one is due.  My apologies for the delays in getting work back to you.

Week 11: Monday, March 31

Topics:
  • The mechanical universe:  Newton and Leibniz and the beginnings of the calculus
Reading:
  • Burton, chapters 8.4 - 9.1
  • Struik, chapters 6, 7

Monday:

  • Leibniz and his calculus (including some notes on the origins of computer science)
  • The great Newton-Leibniz food fight
  • A quick look ahead to the early 1800's and the Analytical Society (Hershel, Babbage, and Peacock).
  • Second extended essay due

Wednesday:

  • The origins of probability
  • Second extended essay assigned (to be due Friday, May 1.  Please note change in due date).

Friday

  • The development of probability theory (9.1)
  • Pascal's triangle
  • The development of mathematical induction

Other Notes:

Week 12: Monday, April 7

Topics:
  • The development of probability
  • The revival of number theory
Reading:
  • Burton, chapters 9, 10
  • Struik, chapter 7

Monday:

  • Huygens
  • The fantastic feuding Bernoulli family

Wednesday:

  • More on the Bernoulli family
  • A brief note on French History

Friday

  • Pierre Simon Laplace

Other Notes:

  • The term paper draft is due next Friday (April 18)
  • Extended essay #3 due Friday, May 1
  • Term paper due Monday, May 12, 6:00 PM

Week 13: Monday, April 14

Topics:
  • The development of number theory
Reading:
  • Burton, chapter 10
  • Struik, chapter 7

Monday:

  • Probability

Wednesday:

  • Final notes on probability
  • Mersenne and Fermat:  The revival of number theory

Friday

  • Fermat

Other Notes:

  • The term paper draft is due this Friday (April 18)
  • Extended essay #3 due Friday, May 1
  • Term paper due Monday, May 12, 6:00 PM

Week 14: Monday, April 21

Topics:
  • The development of modern geometry
  • The development of modern analysis
Reading:
  • Burton, chapter 11
  • Struik, chapter 8

Monday:

  • The rise of journals and learned societies
  • Euler

Wednesday:

  • Gauss
  • Differential Geometry

Friday

  • The history of the parallel postulate
  • The development of non-Euclidean geometry

Other Notes:

  • Final homework assignment due Friday, May 2
  • Extended essay #3 due Wednesday, May 7
  • Wednesday, May 7, is the last day of classes.  All course material (except for the final term paper) are due.  No other materials can be accepted past 5:00 on this date.
  • Term paper due Monday, May 12, 6:00 PM

Week 15: Monday, April 28

Topics:
  • Brief topics
Reading:
  • Burton, chapters 11-12
  • Struik, chapters 8, 9

Monday:

  • Knots, physics, and manifolds.

Wednesday:

  • Rigor in analysis:  D'Alembert and Cauchy
  • The development of modern analysis:  Weierstrass and Kovalevsky
  • Mittag-Leffler

Friday

  • The development of axiomatic systems and formalism
  • The development of set theory
  • Final homework assignment collected

Other Notes:

  • Final exercise set due Friday, May 2
  • Extended essay #3 due Wednesday, May 7
  • Term paper due Monday, May 12, 6:00 PM
  • Wednesday, May 7, is the last day of classes.  All course material (except for the final term paper) are due.  No other materials can be accepted past 5:00 on this date.

 

 

 

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