This seminar is designed to have faculty do small lectures to start conversations on advanced mathematics. These talks will be accessible to undergraduate students and cover a wide range of topics. For the Fall 2016 semester, we will meet in NAC 4/148 from 1:00PM-2:00PM on Thursdays.
Thursday, October 27, 2016, 01:00PM, NAC 4/148Prof. Ethan Akin (CCNY Math Department), What is Dynamics?
We describe what is a dynamical system, with examples from Nietzsche, Collatz and Edward Lorenz
Thursday, November 03, 2016, 01:15PM, NAC 4/148Prof. Alice Medvedev (CCNY Math Department), 10-adics and 2-adics: decimals with dot-dot-dot on the wrong side
What if decimal expansions had to be finite to the right of the decimal point, but were allowed to be infinite on the left? Certainly, we can still express integers; but what fractions can we express? What numbers have square roots? What familiar properties of addition and multiplication do we lose? Is it better to use base 2, that is binary exapansion, like 1011 for eleven? That's all algebra; what is analysis like in this strange world?
Thursday, December 01, 2016, 01:15PM, NAC 4/148Dr. Ruthi Hortsch (Bridge to Enter Advanced Mathemtics), Triangles, Congruent numbers, and Elliptic Curves
We are all familiar with the Pythagorean Theorem, and perhaps with methods of constructing right triangles with all rational sides. While a right triangle with rational sides will always have rational area, does this work the other way round? For a given rational number n, can we find a right triangle with all sides rational that has area n? Not always---but this isn't obvious! If we can find such a triangle, we call the number n "congruent”. In the quest to discover which n are congruent, we will encounter elliptic curves and their group structure, and maybe even mention the elusive Birch and Swinnerton-Dyer Conjecture.
Thursday, December 08, 2016, 01:15PM, NAC 4/148Prof. Samuel Van Gool (CCNY Math Department), A Taste of Logic
I will discuss a few logic puzzles (easy to state, not so easy to solve), and show how these are related to current research in math and computer science.