November 16, 2013 – Ivan Borsenco – The Study of Prime Numbers: from Euclid till present days

Why do prime numbers fascinate us?

Why prime numbers are still an active area of research?

What advances have mathematicians made in this field this year?

You will find answers to these questions and many more if you come to the lecture.

See you there!

Advertisement

Read Full Post »

October 16 – Mathematical Proofs

Computing a correct answer is sufficient for most grade school work, but proving that something must be true is one of the most important skills our students can learn.  This ability has immediate benefits for such important tests as USAMTS or the USAMO as well as teaching the skills of reasoning and communication that can help in any profession.

We are very fortunate to once again have a lecture by Dr. Branislav Kisačanin.  Here is his description of the upcoming session:

Introduction to Mathematical Proofs

In this lecture we will see examples of common proof techniques: direct proofs, proofs by induction, and proofs by contradiction. The students should have their pencils ready, as they will get a hands-on experience solving and proving mathematical problems.

• As the first illustration of direct proofs we will show that angle bisectors of any triangle have a common intersection point
• As the first illustration of mathematical induction, we will prove Cassini’s identity for Fibonacci numbers
• Finally, as the first illustration of proofs by contradiction, we will look at Euclid’s proof of infinitude of primes

In addition to a few more problems of historical significance, we will work on relatively simple problems that illustrate various proof techniques. In order to make things more interesting, we will let the students figure out which technique to use for each problem.

Read Full Post »

Simion Filip – Geometry and Physics: from Euclid to Einstein

This Saturday, November 8th, Simion Filip will present the way our understanding of the physical world shaped the geometric problems that we considered throughout history.  Examples will be drawn mostly from elementary Euclidian geometry and the talk should be accessible to anyone who is familiar with angles and triangles.

Mr. Filip is a senior at Princeton University, studying mathematics with an interest in mathematical physics. After graduation, he plans to pursue a Ph. D. in mathematics.  While in high-school, Simion Filip took part in both the International Mathematics and Informatics Olympiads, where he received silver and bronze medals respectively.

Read Full Post »