MATH 6101/EDCI 8101 – 090
Foundations of Real Analysis
FALL 2006

General Class Information

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.

REMINDER: No class on October 09 or on October 16

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

Chapter 3 – The Real Numbers

Chapter 4 – The Complex Numbers

Chapter 5 – Functions: An Introduction

Chapter 6 – Sequences and Series [This has changed on 09/27/2006 10:03 PM. Changes occur from Section 6.7 to the end.]

Chapter 7 – Series Examples – new on 02-October-2006 – the set of problems handed out in class and their solutions.

Chapter 8 – Rational and Transcendental Functions – Part I

Chapter 9 – Special Functions – Hyperbolic Trigonometric functions, the Lambert W function and a generalized logarithm

Chapter 10 – Continuity

Chapter 11 – Uniform Continuity

Chapter 12 – Power Series

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 August 21, 2006 — Due August 28, 2006.

Assignment for August 28, 2006 — Due September 11, 2006.

Assignment #1

Assignment for September 11, 2006 — Due September 18, 2006.

Assignment #2

Here is a document (HTML PDF) that discusses Long Division and will be helpful for #3

Assignment for September 18, 2006 — Due September 25, 2006.

Assignment #3

Assignment for September 25, 2006 — Due October 2, 2006.

Assignment #4

Assignment for October 2, 2006 — Due October 23, 2006.

Assignment #5

Assignment for October 23, 2006 — Due October 30, 2006.

Assignment #6

Assignment for October 30, 2006 — Due November 6, 2006.

Assignment #7

Assignment for November 6, 2006 — Due November 13, 2006.

Assignment #8

Assignment for November 13, 2006 — Due November 20, 2006.

Assignment #9

Assignment for November 20, 2006 — Due November 27, 2006.

Assignment #10

Final Questions to be done by December 11, 2007 to prepare for Final Exam

Assignment for November 27, 2006 — Due December 4, 2006.

Solutions

Assignment #1: Due September 11, 2006.

Assignment #2: Due September 18, 2006.

Assignment #3: Due September 25, 2006.

Assignment #4: Due October 2, 2006.

Assignment #5: Due October 23, 2006.

Assignment #6: Due October 30, 2006.

Assignment #7: Due November 6, 2006.

Assignment #8: Due November 13, 2006.

Assignment #9: Due November 20, 2006.

Assignment #10: Due November 27, 2006.

Calculus Links of Interest

· Here is a list of quotations about mathematics and mathematicians

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Last updated 12/03/2006 by David Royster