Prof. Vann McGee
MIT Course Number:
Peano Arithmetic is one of the lectures.
The lecture notes are too fast paced for many people. My books on Peano Axioms and Geometry of Addition go through this more slowly. They also build more intuition, especially in the Geometry of Addition, which is completely new over prior approaches to Peano Arithmetic.
The Peano Arithmetic assignments are as hard as the theorems. In my text, I have many easy ones as examples and exercises to build up ability.
Even the solutions at the MIT OCW course are hard to understand.
=On my two volumes so far on Peano Arithmetic.
Entire book Geometry of Addition is approximately 240 pages of material when formatted as a pdf. The entire book contains a total of 270 exercises, 119 lemmas, 30 note fields, 6 web url note fields, 161 examples, and 54 definitions. This is a total of 640 fields. This is in addition to the text. It is organized into 33 chapters. Fields and chapters are renumbered within each part of the overall work.
The first volume Peano Axioms has 178 Examples, 463 Exercises, 98 definitions, 45 Lemmas with proofs, references to over 96 web pages, 58 chapters, and is 391 pages when formatted as pdf with Latex. 178 examples + 463 exercises + 98 definitions + 45 lemmas + 96 webpages equals 880. Added to the 640 fields above is 1520 fields. This is in addition to the text not in such fields.
Total examples is 178 + 161 = 339 examples. 463 + 270 = 733 Exercises. 54 + 98 = 152 definitions. 119+45 = 164 lemmas. 96+6 = 102 web page references. 58+33 = 91 chapters. 391 + 240 = 631 pages.
There are no quadratic or higher algebra formulas. Students complain about complicated algebra in learning how to do proofs by mathematical induction. This material is thus the ideal for learning mathematical induction proofs.
Not all of Geometry of Addition is posted yet as of this Saturday morning.
Students taking Devlin’s Introduction to Mathematical Thinking at Coursera or the other Cousera course on logic starting in September 2012, will find my e-books very useful to get easy to do problems to get started instead of hard problems right away.