Looking for a collection of entry level proofs - MathOverflow

Looking for a collection of entry level proofs

2010-10-21T15:32:15Z

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

Answer by Andrew D. King for Looking for a collection of entry level proofs

2010-10-21T16:29:50Z

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.

Answer by SandeepJ for Looking for a collection of entry level proofs

2010-10-22T01:26:31Z

You can try Aigner and Ziegler's book Proofs from the book

Answer by PamNDRome for Looking for a collection of entry level proofs

2010-10-22T03:26:51Z

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

Answer by Gerald Edgar for Looking for a collection of entry level proofs

2010-10-22T16:53:51Z

Truly "entry level" ... How to Read and Do Proofs by D. Solow.

Answer by Yuri Bakhtin for Looking for a collection of entry level proofs

2010-10-22T18:51:42Z

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?

Answer by Qingchun Ren for Looking for a collection of entry level proofs

2010-10-22T22:47:16Z

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.

Answer by Kevin O'Bryant for Looking for a collection of entry level proofs

2010-10-24T02:26:16Z

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.

Answer by none for Looking for a collection of entry level proofs

2011-05-01T20:50:08Z

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/

Answer by Shahrooz for Looking for a collection of entry level proofs

2012-01-07T21:47:21Z

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