Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 111: History of Mathematics
Approved: 2010-03-01 (revised 2013-07-01, )

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
A History of Mathematics, 3rd Edition by Victor Katz; Pearson Publishing; $132.00.
Search by ISBN on Amazon: 978-0321387004

Prerequisites:

Eight units of upper division Mathematics; one of the following: MAT 25, 67, 108, 114, 115A, 141 or 145.

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1

1.1

Egypt

2, 3

1.2

Mesopotamia

4

2.1, 2.2

Earliest Greek Mathematics, The Time of Plato

5

2.3

Aristotle

6, 7, 8

3.1 – 3.7

Euclid and The Elements

9, 10

4.1, 4.2

Archimedes and Physics, Numerical Calculations

11

5.1

Astronomy Before Ptolemy

12

5.2

Ptolemy and The Almagest

13

5.3

Practical Mathematics in Hellenistic Times

14

6.1, 6.2, 6.4

Nichomachus, Diophantus, and Hypatia; the End of Greek Mathematics

15

7

Mathematics of Ancient and Medieval China

16

8

Mathematics of Ancient and Medieval India

17

9.1, 9.2, 9.3

Mathematics of Islam – Decimal Arithmetic, Algebra

18

10.1, 10.2

Mathematics of Medieval Europe

19

11.1, 11.2

Mathematics Around the World at the Turn of the Fourteenth Century

20

12.1, 12.4, 13.1-13.3

Mathematical Methods in the Renaissance

21

13.4, 16.1

Logarithms, Isaac Newton

22

16.1

Isaac Newton

23

16.2

Gottfried Wilhelm Leibniz

24

17.4

The Foundations of Calculus

25

22.1

Rigor in Analysis

26

25.1

Set Theory: Problems and Paradoxes

Learning Goals:

Students will learn the basics of History of Mathematics. They study Mathematics of early civilizations including Egyptians, Babylonians, Greeks, India, china, North America and others. Students learn about development and transfer of mathematical Ideas in the world, through learning mathematics of in different historic periods including Hellenistic times, Islamic mathematics, mathematics of medieval Europe and Renaissance up to beginning of calculus.

Students also will learn about life and accomplishments of many of the great mathematicians, from Thales, Euclid, Archimedes, Al-Khowrizmi, Euler, Gauss, Newton, Leibniz and many others.

This course is an introduction to history of mathematics and designed to help mathematics majors and in particular those students interested in teaching be familiar with basic development of ideas in mathematics. Mastery of this course enhances students writing skills, analytic and problem solving skills and it enhances the communication skills of the students and their well-organized scientific thinking process.

Assessment:

Students are required to do a presentation in class, write a term paper, they have weekly homework assignments, two midterms and a cumulative final.