Learning: The Journey of a Lifetime
or A Cloud Chamber of the Mind

September 2005 Mathematics Learning Log

An Example of a "Learning Process" Journal

Wednesday September 28, 2005
Learning Log Number 16

5:25 am Lethbridge, Alberta

I am pleased with my combination of hand written notes and these enotes.

What is Mathematics? (1941) Richard Courant & Herbert Robbins      

Read chap 1 The natural numbers [p. 1 - 20]

Sept 26    

Notes for chap 1.1 Calculation with integers [p. 1 - 9]

Sept 26 Sept 26 Yes

Notes for chap 1.2 The infinitude of the number system [p. 9 - 20]

Sept 26    
Read chap 1 supplement The theory of numbers [p. 21 - 51]      
Notes for chap 1 supplement 1.1 The prime numbers [p. 21 - 31]      
Notes for chap 1 supplement 1.2 Congruences [p. 31 - 40]      
Notes for chap 1 supplement 1.3 Pythagorean numbers and Fermat's Last Theorem [p. 40 - 42]      
Notes for chap 1 supplement 1.4 The Euclidean Algorithm [p. 42 - 51]      
Calculus (1994) Michael Spivak      
Read chap 1 Basic properties of numbers [p. 3 - 20]      
Notes for chap 1      
Exercises for chap 1 [p. 13 - 20]      
Prime Obsession (2003) John Derbyshire      
Reread chap 1 - 8 [p. 1 - 136]      



Section 1.2 of Courant & Robbins is titles The Infinitude of the Natural Number System. The key word is infinity. The method of proof known as mathematical induction is about infinity and how we can logically extend a formula that is true for all finite integral values.

I worked through the proof for the formula for an arithmetic progression last day, and now wish to do the same for a geometric progression. This will lead to a few special formulas as well as the binomial theorem and Pascal's triangle.

I have printed Logs 1 - 8, and hope to print the remainder when in my office later today.


I began with a couple of hand written pages, but then came online to use Mathematica to create some enotes (web, Mathematica).

The expression differs depending on whether n is odd or even, but the only real difference is the behavior as the function approaches the value of the exponent (it either tends to + or -ve infinity). I might play with this again on another day, but this was a good morning on the computer as I was able to integrate a Mathematica session with both my web page and with what I was doing manually.

Now to return to my pen and paper medium and look at the proof for the expression for a geometric expression.

A great beginning to the day. Now to see what happens later today when I print both these notes and the Mathematica notebooks. I only covered one page from Courant & Robbins, but it was time well spent. I feel that I am really understanding the material at a much deeper level than when I was an undergraduate with 4 fast-paced courses to handle.

8:00 am

Total elapsed time: 2 hr. 35 min

Total elapsed time for the day: 2 hr. 35 min