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 – Euler’s 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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