September 24, 2011 – Joshua Nichols-Barrer – “Modular Arithmetic in Contest Mathematics”

We look forward to seeing old and new friends today at the September 17  session of Metroplex Math Circle.  Next week we look forward to a lecture from Joshua Nichols-Barrer.   Dr. Nichols-Barrer earned his PhD at MIT and is the AwesomeMath Academic Director, a two time IMO silver medalist and a multiple winner of the USAMO.

Here is a description of the session in Dr. Nichols-Barrer’s own words:

Modular arithmetic is an essential tool for properly treating number theory problems in contest mathematics.  While there is far more to talk about than we have time for today, we will extensively cover the foundations of arithmetic mod an integer $m$, looking to differences between mod $m$ arithmetic and that which we are all familiar with, as well as those things which distinguish arithmetics mod $m$ for distinct values of $m$.  We will also begin to think about algebra mod $m$ should we have the time.

Modular arithmetic is one of the many fields ignored by standard math curricula but critical for success in math competitions or a career in mathematics or sciences.

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October 9 – Number Theory Done Right

Number Theory is one of the cornerstones of math competitions and a vast field explored by professional mathematicians.  We are very fortunate to have Dr. Josh Nichols-Barrer present to us next week.  Dr. Nichols-Barrer was a very accomplished teenage competitive problem solver who has earned his doctorate at MIT.  In addition to Number Theory our students can learn a great deal from his personal experiences.  Here is a description of the session in Dr. Nichols-Barrer’s own words:

As you know, each positive integer may be factored uniquely into a product of powers of primes.  Do you know why?   In this class we will look at the structure of the integers in the simplest terms, and use that for a foundation from which we might actually prove that what we know to be true actually is.  In the first half we will recall some things about arithmetic that we know intuitively and can name (with maybe a surprise or two), and in the second half we will proceed to prove (along with some other things which are no less key) unique prime factorization in the integers.

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