Looking for a collection of entry level proofs Hi all,
I am looking to do some linguistic analysis of informal proofs. Therefore I am on a search for a collection of entry level proofs written in a clear, uninvolved style. I have one recommendation for Hardy and Wright's "An Introduction to the Theory of Numbers," and was wondering if there is something else you may add to this.
Many thanks in advance,
Nickolay
 A: You can try Aigner and Ziegler's book Proofs from the book 
A: Take a look at Lovász' paper, "Three short proofs in graph theory", Journal of Combinatorial Theory, Series B, vol. 19, 1975.  Maybe those proofs are a little too involved for what you want, but they are worth checking out.
A: Hello,
I cannot add a comment, so I must have to ask this as an answer.  What exactly does linguistic analysis consist of?  Are you really going to study the wording used, the vocabulary, the ontology, and the structuring of the lexical elements of the proof?
Are you going to analyze the symbols and formulae along with the textual words?  Thanks for considering my question.
Another question:  what if you did linguistic analysis on a proof that was incorrect?  Is there any relation between 


*

*what the content of the proof is

*what the correctness of the proof is

*what the linguistic content and the syntactical form of the proof is

*what the ontological underpinnings are of the vocabulary used in the proof

*what symbology and representational schema are used in the formulae in the proof
A: The classic "Foundations of Analysis" by Edmund Landau. It pedantically and very carefully derives elementary properties of integers, rationals, etc., from Peano axioms. Or is it too formal?
A: A very different class of examples are to be found at the Naproche project:
About Naproche: The Naproche project (Natural language Proof Checking) studies the semi-formal language of mathematics from a linguistic, philosophical and mathematical perspective. A central goal of Naproche is to develop a controlled natural language (CNL) for mathematical texts and adapted proof checking software which checks texts written in the CNL for syntactical and mathematical correctness.
A: M. Ganesalingam did a pretty interesting dissertation about linguistic analysis of math texts.  I thought I read about it here on MO but I can't seem to find the pointer right now.  Anyway, see:


*

*http://people.pwf.cam.ac.uk/mg262/
A: I think you have to determine some categories, as like as number theory, combinatorics, geometry and etc. But I think this book is so interesting:
"Ingenuity in Mathematics" by Ross Hansberger
A: Truly "entry level" ... How to Read and Do Proofs by D. Solow.
A: Here is a book that examines the structure of proofs in detail:
The Nuts and Bolts of Proofs, Third Edition: An Introduction to Mathematical Proofs
by Antonella Cupillari
It contains examples of entry level proofs of various types.
