Category: Algebra
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1988 IMO Problem 6
I found about this legendary problem from a Numberphile video and was intrigued. Go watch the video, even if you have seen the problem before. It’s fun! Here’s the problem which is can be found on The Official IMO page. 1988 IMO #6. Let $a$ and $b$ be positive integers such that $ab + 1$…
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Uniqueness of Factorization
A few days ago I came across a proof of the Fundamental Theorem of Arithmetic (aka Unique Factorization) in Courant and Robbin’s What is Mathematics that I hadn’t seen it before. I liked it enough to learn it. Then another surprise – I saw it again yesterday in Primes and Programming by Peter Giblin, a book…
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Typesetting synthetic division
I’m teaching an Algebra course that highlights the Fundamental Theorem of Algebra. So of course we’re looking closely at polynomial division, and in particular at synthetic division. My students are preparing their homework assignments using LaTeX, so this begs the question about how to typeset their computations. One of my students found the LaTeX package…
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A brief 4,000 year history of Diophantine Equations
I filled in for a NY Math Circle class over the weekend. Since the topic was Primitive Pythagorean Triples, I had a blast. I also shared the following outline with the students. Each item is full of wonderful mathematics and anecdotes! Plimpton 322, a Babylonian cuneiform tablet @ Columbia University. From 1900BCE – 1600BCE, and…
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Kevin’s Books
One of the great friends that I made in my time at Vanderbilt University was Kevin Blount. Kevin knew all the graduate students and professors, and often hosted dinners and movies at his nearby apartment. Kevin ended up writing his Ph.D. dissertation On the Structure of Residuated Lattices with Constantine Tsinakis, and moved on to…
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Singing and Dancing Mathematics
Long Division Style Recently, a Gangnam Style-inspired video came out of I.S. 285 Meyer Levin in Brooklyn. In this video, students sing and dance the procedure for long division. It’s absolutely delightful. The Quadratic Formula Song Music versions of math formulas and procedures are not new. One that came up recently in the Algebra class…