I plan to post some thoughts about elementary mathematics. I am a student and this blog is more or less directed towards undergraduates of maths who want to read a bit about someone else’s (mine 🙂 ) ways to understand some basic mathematical proofs.
My motivation to write these posts is first of all to deepen my understanding of the basics of maths. Besides i want to learn to write about mathematics and to learn to express myself in english (it isnt my native tongue). So if someone finds mistakes in my mathematics or my english I would be glad to get some comment.
I believe the best way to understand something like a mathematical statement is not to present a clean proof but to explain the ideas of the proof – how do we get from one stage of the proof to the next and what are the key concepts that are arising.
A lot of elementery (many would say easy) proofs undergraduates of mathematics encounter, are mostly straight forward (like substituing definitions) but very often contain one lightning strike. For example, showing that f(x) = x^2 is continous (in the sense of \varepsilon - \delta…) is straight forward except at one point: you have to choose (for a given \varepsilon) a special \delta which solves the inequality.
So my motivation is to understand better where these \delta‘s, that often fall from heaven, really come from.

P.S. If you are looking for more stuff like I plan to write some day (at the level of my abilities) you could visit the following sites. Most of the articles are written by professional mathematicians, so their level is far beyond mine but nevertheless accessable by (and dedicated to) students of maths:
Tricki – a wiki-like site where you’ll find articles about mathematical problem-solving techniques
many great articles by Professor Gowers (I really like the intro at top 🙂 – I find these articles very useful)
Professor Gowers blog – even more interesting math articles


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