Week 1: Monday, January 17

• 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:

• A very quick survey of ancient mathematics.
• The need for mathematics in early civilizations
• Number representation in early Egypt

Other Notes:

• Office hours resume next week

Week 2: Monday, January 24

• Topics:
• Babylon
• Thales and Pythagoras
• Alexandria
• Reading
• Burton, chapters 2 - 4
• Struik, chapters 2 - 4

Monday:

• A very quick survey of ancient mathematics.
• The early mathematics of Babylon, Egypt, China, and India.

Wednesday:

• Babylonian number representation

Friday:

• A class exercise in Babylonian cuneiform

Other Notes:

• Office Hours resume this week

Week 3: Monday, January 31

• Topics:
• The beginnings of the axiomatic method in mathematics
• Reading
• Burton, chapters 3 - 4
• Struik, chapter 3, 4

Monday:

• Arabic numerals
• Fibonacci and the transmission of Arabic mathematics to Europe.
• Assignment #1 due (in class)

Wednesday:

• Geometry before Thales
• Extended essay #1 assigned

Friday:

• A quick survey of early Greek mathematics
• Thales, Pythagoras and Eudoxes
• The beginnings of proof and the axiomatic method
• First steps to the calculus:  method of exhaustion

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 wonder that was Alexandria
• The great sleep and the re-awakening
• The rise of modern mathematics
• Reading
• Burton, chapters 4 - 6
• Struik, chapter 3 - 5

Monday:

• Pythagoras
• The wonder that was Alexandria
• Euclid
• Discussion of term paper
• Problem set #2 assigned

Wednesday:

• The wonder that was Alexandria
• Euclid and Archimedes

Friday:

• The wonder that was Alexandria
• Archimedes

Other Notes:

• Extended essay #1 will be due Friday, February 25
• Extended essay #2 will be assigned Friday, February 25, and will be due Friday, March 25
• Term paper proposals are due Monday, February 28

Week 5: Monday, February 14

• Topics:
• Alexandria
• Reading
• Burton, chapters 4 - 6
• Struik, chapter 6

Monday:

• Questions on homework
• Archimedes

Wednesday:

• The wonder that was Alexandria
• Eratosthenes and Ptolemy
• The decline of Alexandria and the transmission of mathematics through the Islamic world
• Diophantus

Friday:

• The decline of Alexandria
• Pappus
• Theon
• Hypatia

Other Notes:

• Homework #2 is due next Monday
• Extended essay #1 will be due Friday, February 25 (next Friday)
• Extended essay #2 will be assigned Friday, February 25, and will be due Friday, March 25
• Term paper proposals are due Monday, February 28

Week 6: Monday, February 21

• Topics:
• The Renaissance
• Reading
• Burton, chapters 6
• Struik, chapter 6

Monday:

• The return of Greek mathematics to Europe
• The House of Wisdom
• Homework #2 due.  Homework #3 will be assigned some time this week.

Wednesday:

• Fibonacci and the transmission of Arabic mathematics to Europe.

Friday:

• Fibonacci and the transmission of Arabic mathematics to Europe.
• Extended essay #1 due. 
• Extended essay #2 assigned.

Other Notes:

• Homework #2 is due Monday
• Extended essay #1 will be due Friday, February 25 (this Friday)
• Term paper proposals are due Monday, February 28 (next Monday)  Email is OK for this milestone only.
• Monday, February 28, is the last day to drop with an automatic 'W' (next Monday)
• There will be no class or office hours next Friday, March 4 (Columbia History of Science Conference)

Week 7: Monday, February 28

• Topics:
• The Renaissance
• On the solution of algebraic equations
• Reading
• Burton, chapters 7 - 8
• Struik, chapter 6

Monday:

• In praise of great universities
• Bologna
• Paris
• Padua
• Oxford
• Cambridge
• On the solutions to algebraic equations.
• Term paper proposals due.  Email is OK for this milestone only.

Wednesday:

• Greek solutions to linear and quadratic equations

Friday:

• Columbia History of Science Conference:  No classes or office hours

Other Notes:

• Term paper proposals are due Monday, February 28 (Monday)  Email is OK for this milestone only.
• Extended essay #2 will be assigned shortly, and will be due Friday, March 25
• Monday, February 28, is the last day to drop with an automatic 'W' (this Monday)
• There will be no class or office hours this Friday, March 4 (Columbia History of Science Conference)

Week 8: Monday, March 7

• Topics:
• The Renaissance
• The beginnings of the calculus
• Reading
• Burton, chapters 7 and 8
• Struik, chapter 6

Monday:

• al-Khwarizmi and completing the square
• Omar Khayyam and the cubic equation

Wednesday:

• Fra Luca and the Summa
• dal Ferro and Antonio Maria Fior
• Fior and Tartaglia

Friday:

• Algebra and the great Cardano - Tartaglia food-fight:  The Ars Magna

Other Notes:

• Next week is Spring Break!
• Mid-term is Friday, March 11 (not an exam day for us)
• The term paper annotated bibliography is due Wednesday 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:
• The beginnings of the calculus
• Reading
• Burton, chapter 8,
• Struik, chapter 6

Monday:

• Abel and Galois:  The early development of journals

Wednesday:

• The term paper annotated bibliography is due Wednesday, March 23.  .  An annotated bibliography, for the purposes of this class, is a list of sources you intend to use, a brief description of the source, and why the source is appropriate for your paper.  Include a short paragraph for each source.  Paper submissions in class only.
• Notation
• The development of notation:  Vieta and Recorde

Friday:

• Napier, Briggs, and Logarithms

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 beginnings of the calculus
• Reading
• Burton, chapter 8,
• Struik, chapter 6

Monday:

• The dawn of the calculus and modern mathematics
• Galileo, Kepler and Descartes

Wednesday:

• Descartes on tangents
• Isaac Barrow and the Lucasian Professorship

Friday:

• John Wallis
• Isaac Barrow and tangents

Other Notes:

• Homework #3 is due Monday, March 28
• Homework #4 is due Monday, April 11
• The term paper draft is due Friday, April 15
• Extended essay #3 is due Friday, April 22

Week 12: Monday, April  4

• Topics:
• Probability and statistics
• Number Theory
• Reading
• Burton, chapters 8 and 9
• Struik, chapters 6 and 7
• See also:
• An early textbook in the calculus
• Another early textbook
• An 1812 American Edition
• More are available through Google books

Monday:

• Isaac Newton

Wednesday:

• Fluxions

Friday:

• Newton's later years
• Gottfried Wilhelm Leibniz
• Leibniz and the history of Computer Science

Other Notes:

• Homework #4 is due Monday, April 11
• The term paper draft is due Friday, April 15
• Extended essay #3 is due Friday, April 22

Week 13: Monday, April  11

• Topics:
• The Leibniz-Newton controversy
• Reading
• Burton, chapters 8 and 9
• Struik, chapters 6 and 7

Monday:

• No class- instructor ill

Wednesday:

• The Leibniz-Newton debate
• Homework #4 due (in class)
• Homework #5 assigned, due Wednesday, April 27

Friday:

• Teaching the calculus
• Term paper draft due (in class)

Other Notes:

• Homework #4 is due Monday, April 11
• The term paper draft is due Friday, April 15
• Extended essay #3 is due Friday, April 22
• Homework #5 due Wednesday, April 27

Week 14: Monday, April  18

• Topics:
• Probability and statistics
• The revival of Number Theory (Chapter 10)
• The first foundational crisis (Chapter 11)
• Reading
• Burton, chapters 9 -  11
• Struik, chapters 6 and 7

Monday:

• Teaching the calculus
• Probability and statistics (chapter 9)
• Extended Essay #4 assigned due Wednesday, May 4 (last day of class)

Wednesday:

• Probability and statistics (chapter 9)

Friday:

• Probability and statistics (chapter 9)

Other Notes:

• We will skip chapter 10 for now.
• Extended Essay #3 is due Friday, April 22
• Homework #5 due Wednesday, April 27
• Extended Essay #4 due Wednesday, May 4 (last day of class) but will be accepted without penalty until the time that the term paper is due.
• Term paper due 2:00 Wednesday, May 11

Week 15: Monday, April  25

• Topics:
• Celestial Mechanics
• The first foundational crisis (Chapter 11)
• Reading
• Burton, chapters 11
• Struik, chapters 8 and 9

Monday:

• Five books on celestial mechanics

Wednesday:

• No class (instructor ill).  Homework #5 will be due in class Friday.

Friday:

• Five books on celestial mechanics
• The King Oscar II competition and the beginnings of chaos theory
• An interesting story on the relationship between physics and mathematics:  The Theory of Knots
• The rise of combinatorial topology

Other Notes:

• Homework #5 due Wednesday, April 27
• Extended Essay #4 due Wednesday, May 4 (last day of class) but will be accepted without penalty until the time that the term paper is due.
• Term paper due 2:00 Wednesday, May 11

Week 16: Monday, May 2

• Topics:
• The first foundational crisis (Chapter 11)
• The second foundational crisis
• Reading
• Burton, chapters 11
• Struik, chapters 8 and 9

Monday:

• An interesting story on the relationship between physics and mathematics:  The Theory of Knots
• The first foundational crisis:  The parallel postulate and hyperbolic geometry (chapter 11, skipping chapter 10)
• A song to learn

Wednesday:

• The second foundational crisis:  Set theory and proof
• All materials (except for Extended Essay #4 and the Term Paper) due by class time on Wednesday.  No late material accepted past class time on Wednesday (and then only by prior arrangement)

Friday:

• Reading period:  No classes.  Office hours to be arranged.

Other Notes:

• Extended Essay #4 due Wednesday, May 4 (last day of class) but will be accepted without penalty until the time that the term paper is due.
• Term paper due 2:00 Wednesday, May 11.  I will be in our classroom from noon until 2:00 to receive papers.  At that time I will also have records of what I have in my grade book for you to review.

Week 17: Monday, May 9

• Topics:
• Final Exam Week

Notes:

• Extended Essay #4 due Wednesday, May 4 (last day of class) but will be accepted without penalty until the time that the term paper is due.
• Term paper due 2:00 Wednesday, May 11.  I will be in our classroom from noon until 2:00 to receive papers.  At that time I will also have records of what I have in my grade book for you to review.