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December 13, 2014 – Dr. Jon Kane – Counting Problems

Suppose one afternoon a theater sells 10 adult tickets and 15 child tickets. In how many different orders can those tickets be sold? What if no more than two child tickets are sold between each sale of adult tickets? How about if 10 adult tickets and 10 child tickets are sold but as the tickets are sold, the number of child tickets sold is never allowed to exceed the number of adult tickets sold? We will discuss many variations of these types of problems and draw parallels to many other kinds of counting problems.

December 6, 2014 – Gabriel Dospinescu – What do powers of 2 and primes have in common?

Join us this Saturday as we journey together to discover the answer to this question, “What do powers of 2 and primes have in common?”  We will start by discussing a problem de Polignac posed in 1849 that raised the question, “Which numbers can be written as the sum of a prime and of a power of 2?”  The conjecture was refuted by Paul Erdos in 1950 with the following theorem: there is an infinite arithmetic progression of odd numbers which cannot be written as the sum of a prime and of a power of 2.  After we reflect on Erdos’ theorem, we will compare the result with Romanov’s theorem which states that a positive proportion of positive integers are the sum of a prime and of a power of 2.

Gabriel Dospinescu, co-author of Problems from the Book and Straight from the Book, is an associate professor at l’Ecole Normale Supérieure de Lyon.

**Special Note:  While our MMC students enjoy this enlightening talk, parents can learn more information about Stanford University Online High School (OHS).  The Director of Admissions for the OHS, Claire Goldsmith, will be in the area offering presentations at local private/public schools and will stop by the math circle for the benefit of our community.

Stanford Online High School serves academically gifted and talented students in grades 7 – 12 from around the world. Students partake in interactive, real-time online seminars taught by expert instructors and are placed by ability, not grade level. Students also have access to a vibrant student life with over 50 clubs and organizations as well as local and regional meet ups. Students can attend full-time and graduate from Stanford OHS or enroll part-time, choosing courses from a catalog of over 60, many of which are AP or University level. For more information visit the school’s website https://ohs.stanford.edu/; or to speak with an Admission Officer, email ohsadmissions@stanford.edu.
Claire Goldsmith is Director of Admission and Financial Aid at Stanford OHS and also oversees external relations for Stanford Pre-Collegiate Studies. She has also run student life and taught History at Stanford OHS. Previously, Claire taught English and French and coached debate at the Harvard-Westlake School in Los Angeles. She graduated magna cum laude in History and Literature from Harvard College and holds a Masters in Policy, Organization, and Leadership Studies from Stanford University Graduate School of Education.