MATH 6101 – 090
Foundations of Real Analysis
FALL 2008

Dr. David C. Royster

General Class Information

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

Class Worksheets and Lecture Notes (PDF files)

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

Chapter 2 – NUMB3RS and what they have wrought - Lecture Outline

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 – Series and Convergence - Lecture Notes (pdf, handouts, color handouts)

                                                             Lecture Notes with answers (pdf, handouts) 52 slides

Chapter 12 – Series of Functions – Power Series - Lecture Notes (pdf, handouts, color handouts)

                                                             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

Assignments

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

Solutions

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

Solutions

Assignment for September 17, 2008 — No homework assignment

Solutions

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

Solutions

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

Solutions

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

Solutions

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.

Solutions

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

Final Exam December 17 from 6:30 - 9:30 PM in the same room.

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Last updated 08/19/2009 by David Royster

© 2008 David Royster, Purple Bear NC, Inc.