MATH 6101: Foundations of Real Analysis
Tentative Outline of Topics

Aug. 27

Day 1

a) What is the Mathematics that we teach?

b) History and prehistory of numbers

Sept 3

Day 2

Aristotle and the Parabolic Segment(Method of Exhaustion)

Sept 10

Day 3

Fermat and his approach to tangents

Sept 17

Day 4

Newton and Calculus – Episode I

Sept 24

Day 5

Newton and Calculus – Episode II

Oct 1

Day 6

Euler and Trigonometric Functions

Oct 8

Day 7

The Real Numbers
Sequences and Limits

Oct 15

Day 8

The Cauchy Property of real numbers

Oct 22

Day 9

Series and Convergence

Oct 29

Day 10

Power Series

Nov 5

Day 11

Continuity

Nov 12

Day 12

Differentiability

Nov 19

Day 13

Uniform Convergence

Nov 26

Day 14

Thanksgiving Break

Dec 3

Day 15

Putting it all together

Dec 10

Reading Day

Dec 17

Final Exam (1830 – 2130)