Geremías Polanco Encarnación

Geremías Polanco Encarnación, assistant professor of mathematics, holds a Ph.D. in mathematics and an M.S. in actuarial science. Prior to Hampshire, he was a visiting assistant professor at Illinois Wesleyan University, and is a graduate of the University of Illinois at Urbana-Champaign.

His passion is to understand and communicate mathematics. His primary interest is analytic number theory, but this has led him also into the kindred area of algebraic combinatorics. The topics he is most involved with so far are related to Sturmian and Beatty sequences, uniform distribution, spectra in general, continued fractions, combinatorial sequences, and L-functions. He is interested in expanding his research work to other areas of mathematics and to interdisciplinary collaborative research.

Recent and Upcoming Courses

Math to Survive in the World
Many factors determine whether or not you get a job, succeed or fail in a project, and loose or make money on an investment. Your problem-solving ability is one of them, but understanding the principles behind the situation you face (in practice or in theory) is one of the most fundamental. To survive in the world, people need to apply countless mathematical principles, consciously or unconsciously. In this course you will understand some of the mathematical principles that you already use, and will learn some other new ones. Topics will include minimizing time required to complete certain tasks; scheduling and critical path analysis; fair division; voting theory; coding theory; mathematics of investment and credit; art, beauty and math; and other topics at our discretion
Probability Theory
We will move from Wall Street to the North Pole, with a stop at the Hospital and a little break at the Casinos. Because from financial markets to meteorology, sports projections to medical testing, and scientific studies to gambling, probability and statistics are fundamental to analyzing data and making predictions that are scientifically sound. They are invaluable tools for any subject of study in any of the sciences. In this introductory course to probability we will cover topics that include the calculus of probability, combinatorial analysis, random variables, expectation, distribution functions, moment-generating functions, central limit theorem and joint distributions. Computers will be used throughout. Problem sets will be assigned for almost every class.
Linear Algebra
Linear algebra is valuable for explaining fundamental principles and simplifying calculations in Mathematics, Statistics, Computer Science, Engineering, Physics, Biology, and Economics. In this course, we will focus on different applications based on course design and student preferences. These will include applications to chemistry, cryptography, economics, genetics, geometry, geology, heat distributions, marketing, image compression, Markov chains and networks. They will be based on the study of linear equations, matrices, vector spaces, linear transformations, eigenvalues and eigenspaces, as well as others as time permits. Pre-requisite: Calculus or Send an email to consult with the instructor.
Numbers,Patterns and Experiments
This course is for any science and related studies concentrators who wishes to further develop their quantitative skills. Focusing on skills rather than content, students in the course will focus on the following: using computers to gain insight and develop intuition and to discover new patterns and relationships; using graphical display to suggest mathematical principles; testing and falsifying conjectures; Finding real world applications for mathematical concepts, exploring a possible result to see if it is worth a formal proof; suggesting approaches for formal proof; learning how to construct formal proofs; replacing lengthy hand-derivations with computer-based derivations; and confirming analytically-derived results. The topics studied will simply be the means to our desired end: obtaining the skills described above. Pre-requisite: Calculus or Send an email to consult with the instructor.
Mathematical Experiments and Reasoning I
This course focuses on skills rather than content. The skills emphasized are the essential ones you need to work in any area in which a quantitative background is required. We will focus on the following: using computers to gain insight and develop intuition and to discover new patterns and relationships; using graphical display to suggest mathematical principles; testing and falsifying conjectures; exploring a possible result to see if it is worth a formal proof; suggesting approaches for formal proof; learning how to construct formal proofs; replacing lengthy hand-derivations with computer-based derivations; and confirming analytically-derived results. The topics studied will simply be the means to our desired end: obtaining the skills described above. They will come mostly from Number Theory.