**MATH 106 History of Mathematics, Lecture 1**
**Instructor:** Christian Haesemeyer
**Office: MS 6304**
**phone:** 310-825-3364
**Office hours:**M:10 W:2 F:10

**Teaching Assistants:**Beren Sanders and Neelesh Tiruviluamala

**Time and Location:**
MWF 1-1:50, MS 5200 (Lectures)*and* T 1-1:50, MS 5137 (Discussion section 1a) or R 1-1:50, MS 5137 (Discussion section 1b).

**Syllabus and assignments:**
This class will discuss:
The history of what has been called "mathematics discourse", that is, the practice and communication of mathematics broadly construed in various cultures and societies. We will investigate in particular the societal role of mathematics, from its use in daily life to its mystification and employment as a means of control.
The history of the ideas underlying the (differential and integral) calculus.

Week 1 & 2: (Ac-)counting. Links: Quipu, Meso-american calendar, Yoruba, Yolngu, Mesopotamia (this is the article from *Mathematics across cultures*).
Homework 1. Due in class, Friday January 27th. Please write you discussion section on the cover sheet.
Week 2 & 3: Classical notions and calculations of area and arc length. Readings: Method of exhaustion (wikipedia); chapters 1 and 2 of Edwards. A translation of Archimedes' works by Heath.
Homework 2. Due in class, Friday February 3rd.
Week 3 & 4: Indivisibles. Readings: Chapter 4 of Edwards. Kepler's *Nova Stereometria doliorum vinariorum* (Latin original). Cavalieri's *Geometria indivisibilibus* (Latin original.) And Wallis' *Aithmetica infinitorum* (Latin original.) An English version is available but not free.
Homework 3. Due in class, Friday February 10th.
Week 5: Tangents. Methods of Fermat and Descartes. Readings: Chapter 5 of Edwards. Fermat's method. Hudde's rules. Original text of the description of a method by Sluse in the *Transactions of the Royal Society*, 1673. The geometrical lectures of Isaac Barrow.
Homework 4. Due in class, Friday February 17th.
Week 6: Infinite series; Newton's deduction fo the binomial series. Readings: Chapter 6 of Edwards (only the final section starting page 162) and chapter 7 of Edwards. Wallis' review of Mercator's *Logarithmotechnia*.
Homework 5. Due in class, Friday February 24th.
Week 7 and 8: Calculus according to Leibniz. Readings: Chapter 9 of Edwards. Leibniz' differential calculus.
Homework 6. Due in class, Friday March 2nd.
Week 8 and 9: Calculus according to Newton. Readings: Chapter 8 of Edwards. The *Mathematical papers of Isaac Newton* are not available as ebook, but if you look them up on amazon you can use the "search inside" feature to get a feeling for them.
Homework 7. Due in class, Friday March 9th.
Week 9 and 10; The works of L. Euler. Readings: Chapter 10 of Edwards. Euler archive gives access to all works of Euler online.
Week 10: The further development of the calculus. Readings: Chapter 11 of Edwards.

**Midterm paper:** The paper will be due Wednesday, February 22 and should be submitted one, in printed form to me in class and second, online using turnitin. There should be a link on your myUCLA page allowing you to join the turnitin class page for this class. The paper should be at most 6 pages, double spaced; shorter is fine (you can do a five paragraph essay if you wish, but are not restricted to that form). You have a choice of two topics:

*1. Discuss the controversy about the meaning of Fermat's method of pseudo-equality (or adequality as it also known)* or

*2. Discuss in an example you choose how, why, and to what extend Western mathematics was integrated into or replaced the mathematics of non-Western cultures.*

**Final Exam:** Friday, March 23rd, 8-11.
Practice problems on Euler's work.
Review sheet.
The historical question on the final will be: "Compare Newton's and Leibniz's approaches to calculus."
Finals week office hours: Tuesday, 10:30-12:30.

**Literature:**
There is no required textbook. Our discussion of the history of the calculus will roughly follow C. H. Edwards, Jr.: *The historical development of the Calculus*, Springer 1979. A good collection of papers on the history of mathematics in non-Western cultures is *Mathematics across Cultures*, edited by Helaine Selin, Kluwer Academic Publishers 2000.

**Grading Policy:**

There will be 8 homework assignments, to be handed in in class on Fridays. Late homework will not be accepted; the lowest score will be dropped. The homework will be mathematical in nature. There will also be a midterm paper, and the final exam. The homework will account for 10% of the grade, the midterm paper for 40% and the final exam for 50%.

Requests for a regrading will only be considered within 14 calendar days of the due date of the original assignment, and no later than the day before the final. All such requests *must* be directed to the instructor; the TA is not allowed to make changes to grades.