Category Archives: Number Theory

125th Anniversary of Ramanujan’s Birth

Posted on 22/12/2012 by tpc

It was a privilege to be in Delhi, India to celebrate the 125th Anniversary of the birth of Ramanujan. It was a good conference with good talks by many speakers. Personally for me I didn’t get any new ideas or … Continue reading →

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Is 0 even?

Posted on 5/12/2012 by tpc

I first saw this from BBC news. The aftermath of hurricane Sandy resulted in a shortage of fuel and New York City had to implement an odd-even system. The following is taken from their press release: 1) Vehicles with license … Continue reading →

Posted in Number Theory, Probability, Teaching | Leave a comment

16 Plates

Posted on 9/8/2012 by tpc

An interesting problem from the wordplay column of the New York Times. Can you arrange plates numbered 1 to 16, in a circle so the sum of adjacent pairs is always a perfect square? The quick answer is no, since … Continue reading →

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Turing Doodle

Posted on 23/6/2012 by tpc

I was supposed to wake up early before my two year old boy so that I could get some work done, but alas, I got distracted by the neat little Turing machine puzzle put up by the guys at google. … Continue reading →

Posted in Fun Stuff, Number Theory, Quotes/People, Technology | 4 Comments

It’s Pi Day today

Posted on 14/3/2012 by tpc

A little creative tinkering yielded this mnemonic for [tex]\pi[/tex] Pi (apologies, latex died) to 15 places. “How I need a drink, alcoholic of course, after the heavy lectures involving Euclid’s algorithm” I’ve substituted “quantum mechanics” with “Euclid’s algorithm”, not exactly … Continue reading →

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Hardy on Number Theory

Posted on 14/3/2012 by tpc

The elementary theory of numbers should be one of the very best subjects for early mathematical instruction. It demands very little previous knowledge; its subject matter is tangible and familiar; the processes of reasoning which it employs are simple, general … Continue reading →

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Riemann hypothesis

Posted on 14/12/2011 by tpc

A general article on the Riemann hypothesis written by two insanely brilliant number theorists from Oz. It is part of a series explaining the millennium problems.

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Pi to two million digits

Posted on 20/11/2011 by tpc

is a book I chanced upon in the library. The book consists, as the title states, of the constant [tex]\pi[/tex] to two million digits in 296 pages. My first reaction was, what is it doing in a university library? I’m … Continue reading →

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Applications of number theory

Posted on 26/9/2011 by tpc

It can get you a job? In Mr Magorium’s Wonder Emporium, the first question the prospective accountant was asked was Name the Fibonacci series from its eleventh to its sixteenth. The accountant answered correctly and after another couple of questions … Continue reading →

Posted in Applications, Books, Number Theory | 1 Comment

An application of quadratic residues

Posted on 8/8/2011 by tpc

A certain Count had 5 daughters and 11 peasants. Upon his death he willed that the square shaped county be divided into equal square plots such that each daughter gets one plot and the remaining plots are divided evenly among … Continue reading →

Posted in Applications, Number Theory | 3 Comments

I heart* my TI-84

Posted on 14/7/2011 by tpc

my department (a.k.a academic group) loaned me a TI-84 Plus Silver Edition because students here are all supposed to be equipped with one. I just love how I’m learning new mathematics everyday with the TI-84. For example, 1) Andrew Wiles … Continue reading →

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The man who know Ramanujan

Posted on 30/6/2011 by tpc

An article from The Hindu about Professor Bruce Berndt. The title of the article is probably a play on the book The man who knew infinity.

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An AMC problem on sieveing primes

Posted on 30/6/2011 by tpc

The following is an AMC 12 problem from 2005, courtesy of the MAA Minute Math. Follow the link for an interactive version complete with hints, solutions and difficulty hosted on MAA.org. Problem: Call a number “prime-looking” if it is composite … Continue reading →

Posted in Combinatorics, Number Theory, Problems | Leave a comment

Finance and Fibonacci

Posted on 27/6/2011 by tpc

This could be an application if you believe it. Certainly it is “more scientific” than reading tea leaves. Fibonacci level. Perhaps there is some relationship, afterall both finance and fibonacci starts with the letter “f”, then again so does “fail”.

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Number Theory by

Posted on 24/5/2011 by tpc

Pommersheim, Marks and Flapan. The full subtitle of the book is “A Lively Introduction with Proofs, Applications, and Stories.” I have to admit I only browsed through a couple of pages of the book but it already lives up to … Continue reading →

Posted in Books, Number Theory | 1 Comment

Zeta(5) is irrational ?

Posted on 6/5/2011 by tpc

The answer is that it probably is but mathematicians do not yet know how to prove it. A paper has been put up in arXiv (dated 4 May) that claims to have used very elementary methods to prove that [tex]\zeta(5)[/tex] … Continue reading →

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12 Days of Christmas

Posted on 21/12/2010 by tpc

Nice problem and solution at squarecirclez about counting the total number of presents. Triangular numbers appears! It seems that this year’s Simpsons Christmas special was a live action parody/tribute to Sesame Street and the Muppets. It had them singing the … Continue reading →

Posted in Calculus/Analysis, Fun Stuff, Number Theory, Problems, Teaching, Technology | Leave a comment

703 ; Waring’s Problem

Posted on 26/10/2010 by tpc

I receive the twitter feed from MAA and one daily feed they do is the number-a-day blog. For example the entry for Oct 19. Sometimes, I wonder what do people do with these facts about a specific number? Quote them … Continue reading →

Posted in Number Theory, Technology | 1 Comment

Sch�nhage-Strassen multiplication

Posted on 27/8/2010 by tpc

Feature column on AMS website this month, using FFT to quickly multiply two large integers. Yet another useful application of Fourier transform.