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- Professor Howard, Notes, August 29, 2007 (pdf)
- MthT 430 Notes Chapter 01 Basic Properties of
Numbers As pdf: chap01.pdf
- MthT 430 Notes Chapter 1a More on Basic
Properties of Numbers As pdf: chap1a.pdf
- MthT 491 Distributive Properties and Negative Numbers as pdf: 491dist.pdf
- MthT 430 Notes Chapter 2a Numbers of Various Sorts As pdf: chap2a.pdf
- MthT 430 Notes Chapter 2b Induction etc. As pdf: chap2b.pdf
- MthT 491 Distributive Properties and Negative Numbers As pdf: 491dist.pdf
- \sqrt{2} is an irrational number
- A proof of the irrationality of k^(1/2) (except for k a perfect square) is given in
Notes
What Pythagoras Could Have Done
Yoram Sagher
American Mathematical Monthly, Vol. 95, No. 2. (Feb., 1988), p. 117.
Factorization into primes is not used! The assignment for October 4, 2006 is to write a summary of this article.
- MthT 430 Apostol's Irrationality As pdf: apostol.pdf
- Irrationality of The Square Root of Two -- A Geometric Proof
Tom M. Apostol
The American Mathematical Monthly, Vol. 107, No. 9 (Nov., 2000), pp. 841-842.
Stable URL: http://links.jstor.org.proxy.cc.uic.edu/sici?sici=0002-9890%28200011%29107%3A9%3C841%3AIOTSRO%3E2.0.CO%3B2-7
- MthT 430 Apostol's Irrationality - More As pdf: apostoln.pdf
- MthT 430 Apostol's Irrationality - Still More As pdf: apostolnplus.pdf
- Other proofs that Square root of 2 is irrational. Apostol's argument is stated more directly in Proof 7.
Remarks on Proof 6 are given in MthT 430 sqrt (2) is Irrational, as pdf: 430sqrt2.pdf.
- MthT 430 Notes Chapter 3a Functions As pdf: chap3a.pdf
- MthT 430 Notes Chapter 3b More about Functions As pdf: chap3b.pdf
- MthT 430 Notes Chapter 4a Graphs As pdf: chap4a.pdf
- MthT 430 Notes Chapter 4b Binary Expansions and Graphs
As pdf: chap4b.pdf
- MthT 430 Notes Chapter 5a Limits As pdf: chap5a.pdf
- MthT 430 Notes Chapter 5b Geometric Limits As pdf: chap5b.pdf
- MthT 430 Notes Chapter 5c Graphical Binary Expansion Arguments As pdf: chap5c.pdf
- MthT 430 Notes Chapter 5d Sequences and Limits As pdf: chapter5d.pdf
- MthT 430 Notes Chapter 5 Equivalent Definitions As pdf: chap5define.pdf
- MthT 430 Chapter 5 Limits - An Equivalent Definition As pdf:
chap5equiv.pdf
- MthT 430 Notes Chapter 6 Binary Expansions and Arguments As pdf: chap6a.pdf
- MthT 430 Notes Chapter 6b Continuity As pdf: chap6b.pdf
- MthT 430 Notes Chapter 6c Binary Expansions As pdf: chap6c.pdf
- MthT 430 Notes Chapter 6d Graphical Binary Expansion Arguments As pdf: chap6d.pdf
- MthT 430 Notes Chap7a Three Hard Theorems As pdf: chap7a.pdf
- MthT 430 Notes Chap 7b Hard Theorems - Proofs by Binary Expansion As pdf: chap7b.pdf
- MthT 430 Notes Chap 7c Bounded Monotone Sequences Have Limits As pdf: chap7c.pdf
- MthT 430 Notes Chap 7d Bolzano - Weierstrass Theorem As pdf: chap7d.pdf
- MthT 430 Notes Chapter 8a Least Upper Bounds and Binary Expansions As pdf:
chap8a.pdf
- MthT 430 Notes Chapter 8b Least Upper Bounds - Equivalent Statements As pdf: chap8b.pdf
- MthT 430 Projects Chap 8b - Intermediate Value Property Remarks As pdf: chap8bprojsol.pdf
- MthT 430 Notes Chapter 8d Least Upper Bounds As pdf: chap8d.pdf
- MthT 430 Notes Chapter 8g Least Upper Bounds - Equivalent Statements of (P13) As pdf: chap8g.pdf
- MthT 430 Projects Chap 8f - limsup and liminf As pdf: chap8fproj.pdf
- MthT 430 Projects Chap 8f Note - limsup and liminf As pdf: chap8fprojnote.pdf
- MthT 430 Chapter 9 Derivatives As pdf: chap9.pdf
- MthT 430 Notes Chapter 9 Limits and Order As pdf: chap9order.pdf
- MthT 430 Notes Chapter 10 Differentiation As pdf: chap10.pdf
- For comments on Leibniz's Notation by H.A. Thurston, see JSTOR: Mathematical Gazette: Vol. 57, No. 401, p. 189
http://www.jstor.org/stable/3621137
A pdf of the article is at
http://www.jstor.org.proxy.cc.uic.edu/stable/pdfplus/3621137.pdf
- MthT 430 Notes Chapter 11 Significance of the Derivative As pdf: chap11.pdf
- MthT 430 Notes Derivatives of Convex Functions As pdf: chap11convex.pdf
- MthT 430 Notes Chapter 11b Consequences of MVT As pdf: chap11b.pdf
- Notes from MthT 430 Fall 2006
Notes from MthT 430 Fall 2005:
- MthT 430 Chapter One Projects As pdf: chap1proj.pdf
- MthT 430 Projects Chapter 1a
As pdf: chap1aproj.pdf
- MthT 430 Spivak Problem 1.21 As pdf: 430spivak1.21.pdf
- MthT 430 Projects Chapter 1a Inequalities as pdf: chap1aspivak20.pdf
- MthT 430 Chapter 2a Projects As pdf: chap2aproj.pdf
- MthT 430 Chapter 2b Projects As pdf: chap2bproj.pdf
- A proof of the irrationality of k^(1/2) (except for k a perfect square) is given in
Notes
What Pythagoras Could Have Done
Yoram Sagher
American Mathematical Monthly, Vol. 95, No. 2. (Feb., 1988), p. 117.
Factorization into primes is not used! The assignment for October 4, 2006 is to write a summary of this article.
- MthT 430 Apostol's Irrationality As pdf: apostol.pdf
- Irrationality of The Square Root of Two -- A Geometric Proof
Tom M. Apostol
The American Mathematical Monthly, Vol. 107, No. 9 (Nov., 2000), pp. 841-842.
Stable URL: http://www.jstor.org/stable/2695741
- MthT 430 Apostol's Irrationality - More As pdf: apostoln.htm
- MthT 430 Apostol's Irrationality - Still More As pdf: apostolnplus.pdf
- Other proofs that Square root of 2 is irrational. Apostol's argument is stated more directly in Proof 7.
- MthT 430 Projects Chapter 3 Functions As pdf: chap3proj.pdf
- MthT 430 Projects Chapter 4b Binary Expansions and Examples of Functions As pdf: chap4bproj.pdf
- MthT 430 Projects Chapter 5a Limits As pdf: chap5aproj.pdf
- MthT 430 Projects Chapter 5b Limits - Equivalent Definitions (sic) As pdf: chap5bproj.pdf
- MthT 430 Notes Chapter 5 Equivalent Definitions As pdf: chap5define.pdf
- A project on functions from the Shell Centre for Mathematical Education (Nottingham): http://www.mathshell.com/ will be handed out in class October 10, 2007.
- From the Shell Centre: MthT 430 Looking at Gradients As pdf: flask.pdf (in class October 10, 2007)
- MthT 430 Projects Chapter 6a Limits and Continuity As pdf: chap6aproj.pdf
- MthT 430 Projects Chapter 6a Solution As pdf: chap6aproj3.pdf
- MthT 430 Projects Chapter 7a - Three Hard Theorems As pdf: chap7aproj.pdf
- MthT 430 Projects Chap 7b - Three Doubtful Theorems if Numbers = Q As pdf: chap7bproj.pdf
-
MthT 430 Projects Chapter 7 Three Hard Theorems Turn In November 8, 2006 As pdf: chap7turnin.pdf
- MthT 430 Projects Chap8a Decimal and Binary Expansions As pdf: chap8aproj.pdf
- MthT 430 Projects Chap 8b - Intermediate Value Property As pdf: chap8bproj.pdf
- MthT 430 Projects Chap 8b - Intermediate Value Property Remarks As pdf: chap8bprojsol.pdf
- MthT 430 Projects Chapter 8d Adding sup and inf As pdf: chap8dproj.pdf
- MthT 430 Projects Chap 8e - More Adding sup and inf As pdf: chap8eproj.pdf
- MthT 430 Projects Chap 8f - limsup and liminf As pdf: chap8fproj.pdf
- MthT 430 Chapter 9a Spivak Problem Remarks As pdf: chap9aproj.pdf
- MthT 430 Chapter 10a Projects - Derivatives As pdf: chap10aproj.pdf
- Projects from MthT 430 Fall 2006
- Projects from MthT 430 Fall 2005:
Most assignments to be turned in must be typed. For suggestions on typing assignments see MthT 430 Typing Assignments -- pdf
430type.pdf.
Most assignments to be turned in must be typed. For suggestions on typing assignments see MthT 430 Typing Assignments -- pdf
430type.pdf.
- Due September 5, 2007 5 PM: MthT 430 PreTest As pdf: 430pretest.pdf No Grade Assigned!
- Due September 5, 2007 5 PM: MthT 430 Essay Assignment 1
As pdf: 430essay1.pdf
- Due September 5, 2007 5 PM: MthT 430 Problem Set 1
As pdf: 430prob01.pdf
- Due September 12, 2007, 5 PM: MthT 430 Problem Set 02 as pdf:
430prob02.pdf
- Due September 19, 2007, 5 PM :(Problem Set 03): MthT 430 Chapter 2b Projects As pdf: chap2bproj.pdf
- Due September 26, 2007 5 PM: MthT 430 Problem Set 04 as pdf: 430prob04.pdf
- Due October 3, 2007: MthT 430 Problem Set 05 As pdf: 430prob05.pdf
- Due October 10, 2007, 5 PM: The Square Root of 2 is Irrational MthT 430 Essay 2 As pdf:430essay2.pdf
- Due October 10, 2007: MthT 430 Problem Set 06 As pdf: 430prob06.pdf
- * Not turned in - Next assignment due October 31 *:MthT 430 Problem Set 07 As pdf: 430prob07a.pdf
- Due October 31, 2007: MthT 430 Problem Set 08 As pdf: 430prob08.pdf
- Due November 7, 2007: MthT 430 Problem Set 09 As pdf: 430prob09.pdf
- Due November 14, 2007: MthT 430 Problem Set 10 As pdf: 430prob10.pdf
- MthT 430 Thanksgiving Project Turn in November 14, 2007 As pdf: thanksturnin.pdf
- MthT 430 Term Project 2007 due November 28, 2007: MthT 430 Term Project 2007 As pdf: 2007project.pdf
- Due November 28, 2007: MthT 430 Problem Set 11 As pdf: 430prob11.pdf
- Due December 5, 2007: MthT 430 Problem Set 12 As pdf: 430prob12.pdf
- Assignments from Fall 2006
- Due September 20, 2006: MthT 430 Chapter 2 Projects to Turn in September 20, 2006 As pdf: chap2projturnin.pdf
-
Due September 27, 2006: MthT 430 Projects Chapter 3 Functions Turn In September 27, 2006 As pdf: chap3projturnin.pdf
- Essay 2, due October 4, 2006. A proof of the irrationality of k^(1/2) (except for k a perfect square) is given in
Notes
What Pythagoras Could Have Done
Yoram Sagher
American Mathematical Monthly, Vol. 95, No. 2. (Feb., 1988), p. 117. Factorization into primes is not used! The assignment for October 4, 2006 is to write a summary of this article.
- Due October 11, 2006: Problems 1 and 2 from MthT 430 Projects Chapter 5a Limits As pdf: chap5aproj.pdf.
Group work will be accepted and is encouraged.
- MthT 430 Term Project 2006 due November 29, 2006 MthT 430 Term Project 2006 As pdf: 2006project.pdf
- MthT 430 Thanksgiving Project Turn in November 28, 2007 As pdf: thanksturnin.pdf
-
Assignments from Fall 2005:
Please address questions or comments on the course or the web pages
to the course coordinator Jeff Lewis:
jlewis@uic.edu