### Categories

### Recent Comments

- tpc on Mathematics and poetry
- tpc on Discovery
- tpc on Dear Maurits
- Twin corrections | eon on Mathematics and Coffee
- tpc on Prime (Car) Number

### Links

### Archives

- August 2018
- July 2018
- June 2018
- December 2017
- November 2017
- August 2017
- May 2017
- April 2017
- March 2017
- October 2016
- September 2016
- August 2016
- July 2016
- December 2015
- October 2015
- September 2015
- August 2015
- June 2015
- March 2015
- February 2015
- January 2015
- August 2014
- July 2014
- June 2014
- April 2014
- March 2014
- January 2014
- November 2013
- October 2013
- September 2013
- August 2013
- July 2013
- June 2013
- May 2013
- April 2013
- February 2013
- January 2013
- December 2012
- November 2012
- October 2012
- September 2012
- August 2012
- July 2012
- June 2012
- May 2012
- March 2012
- February 2012
- January 2012
- December 2011
- November 2011
- October 2011
- September 2011
- August 2011
- July 2011
- June 2011
- May 2011
- April 2011
- March 2011
- February 2011
- January 2011
- December 2010
- November 2010
- October 2010
- September 2010
- August 2010
- July 2010
- June 2010
- May 2010
- April 2010
- March 2010
- February 2010
- January 2010
- October 2009
- September 2009
- August 2009
- July 2009
- June 2009
- May 2009
- April 2009
- March 2009
- February 2009
- January 2009
- December 2008
- November 2008
- October 2008
- September 2008
- June 2008
- May 2008
- April 2008
- March 2008
- January 2008
- December 2007
- November 2007
- August 2007
- July 2007
- June 2007
- May 2007
- April 2007
- March 2007
- February 2007
- January 2007
- December 2006
- November 2006
- October 2006
- September 2006
- August 2006
- July 2006
- June 2006
- May 2006
- April 2006
- March 2006
- February 2006
- January 2006
- December 2005
- November 2005
- September 2005
- August 2005
- July 2005
- June 2005
- May 2005
- April 2005
- March 2005
- February 2005
- January 2005
- December 2004
- November 2004

### Meta

# Monthly Archives: February 2005

## Logic and Lewis Carroll

Two quotes on logic by Lewis Carroll, author of Alice In Wonderland, British logician. ‘Contrariwise,’ continued Tweedledee, ‘if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.’ … Continue reading

Posted in Books, Quotes/People
Leave a comment

## Theta Series

[tex]\displaystyle \sum_{-\infty}^{\infty} e^{-n^2 \pi} = \Gamma(1/4) / \sqrt{2} \pi^{3/4}[/tex]. The proof of the fascinating result can be found in Peter Walker‘s Elliptic Functions – A Constructive Approach.

Posted in Books, Number Theory
1 Comment

## When In Rome …

In a local forum discussion about numb3rs, someone mentioned an old tv show called Square One TV. If you have time, download and watch the clip “Mathematics of Love”. It’s a funny skit about Roman numerals. Incidentally, I quote from … Continue reading

## Elementary Proofs

No one shall expel us from the paradise that Calculus has created. – tpc The fact that an analytic solution to number theoretical problems exist is bewildering. And often, the analytic proof is much simpler than the elementary proof. The … Continue reading

Posted in Calculus/Analysis, Number Theory, Problems
2 Comments

## Simple Problem

A little number theory problem posted by higherpi. Let [tex]n>1[/tex] be an integer such [tex]2^n + n^2[/tex] is prime. Prove that [tex]n \equiv 3 \pmod{6}[/tex].

Posted in Number Theory, Problems
5 Comments

## Two Types of Pure Mathematics

I quote verbatim from the preface in Simmons’ book. It seems to me that a worthwhile distinction can be drawn between two types of pure mathematics. The first – which unfortunately is somewhat out of style at present – centers … Continue reading

Posted in General
Leave a comment

## Cantor’s Set Theory

No one shall expel us from the paradise that Cantor has created. -David Hilbert (1862-1943). Hilbert probably wrote in German, so the above quote may not be word perfect, but the meaning is clear. I first learnt set theory from … Continue reading

Posted in General, Quotes/People
4 Comments

## Jordan Curve Theorem

I’ve never seen the proof of this theorem, although it is mentioned in every advanced calculus and geometry/topology course that I’ve taken. What I’ve learnt recently is that it cannot be generalised to higher dimensions, and the Alexander’s Horned Sphere … Continue reading

Posted in Geometry/Topology
Leave a comment

## The Simpsons

This is classic. Check out the main site simpsonsmath.com for a comprehensive list of all things mathematical that appeared in the series.

Posted in Fun Stuff
Leave a comment