MATH 6101 090

Foundations of Real Analysis

FALL
2008

Text: *Real
Analysis: A Historical Approach*, Saul Stahl

Class Syllabus . Click here for a PDF version for printing.

List of topics to be covered each day. Click here for a PDF version for printing.

Homework Discussion board

Chapter
1 Thoughts on Numbers, Mathematics, and How We
Got Here

Chapter
2 NUMB3RS and what they have wrought

Chapter 3 Early Attempts at Quadrature - Lecture Notes (pdf, handouts, color handouts)

Chapter 4 Fermat and Calculus - Lecture Notes (pdf, handouts, color handouts)

Chapter 5 Newton and Calculus - The Binomial Theorem - Lecture Notes (pdf, handouts, color handouts)

Chapter 6 Newton and Calculus - Differential Equations - Lecture Notes (pdf, handouts, color handouts)

Chapter 7 Euler and Analysis - Lecture Notes (pdf, handouts, color handouts)

Chapter 8 The Real Numbers - Lecture Notes ( pdf, handouts, color handouts)

Chapter 9 Sequences and Limits - Lecture Notes (pdf, handouts, color handouts)

Chapter 10 Cauchy and his Property - Lecture Notes ( pdf, handouts, color handouts)

Chapter
11

Lecture Notes with answers (pdf, handouts) 52 slides

Chapter
12

Lecture Notes with answers (handouts)

Chapter 13 Continuity - Lecture Notes (pdf, handouts, color handouts)

In Class Handouts (handouts)

Chapter 14 Differentiability - Lecture Notes (pdf, handouts, color handouts)

Chapter 15 Uniform Convergence - Lecture Notes (pdf, handouts, color handouts)

Appendix
A Babylonian Mathematics (from MacTutor)

Appendix
B Egyptian Mathematics (from MacTutor)

Appendix
C The Irrationality of *e*

Appendix
D The Irrationality of π

Appendix
E Roots of the Quartic Equation

Appendix
F Eulers Gamma Function

Appendix
G Axioms and Proof

Appendix
H Reversions of Series

Handout
1 The Galley Method of Division

Handout
2 The Egyptian Method of Multiplication

Assignment for
September 3, 2008 Due
September 10, 2008.

Assignment for September 10,
2008 Due September 17, 2008.

Assignment for September 17, 2008 No homework assignment

Assignment for September 24,
2008 Due October 1, 2008.

Assignment for October 1,
2008 Due October 8, 2008.

Assignment for October 8,
2008 Due October 15, 2008.

Assignment for October 15,
2008 Due October 22, 2008.

Solutions

Assignment for October 22,
2008 Due October 29, 2008.

Solutions - In-class discussion notes from 10-29-08

Assignment for October 29,
2008 Due November 5, 2008.

Assignment for November 5, 2008 No homework assignment

Assignment for November 12,
2008 Due November 19, 2008.

Final Questions to be done by December
3, 2008 to prepare for Final Exam

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Last updated 08/19/2009 by David Royster

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