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

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.
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
Elementary Theory of Numbers
Number theory is the branch of mathematics that deals with the properties of whole numbers. This is an area in which simplicity and complexity meet in an astonishing way. Therefore, in this course you will be presented with problems that, in most cases, are very easy to state, but whose degrees of difficulty range from very easy to incredibly difficult. We will focus on learning the tools and techniques that are used to attack problems in the field and beyond. By following an inquisitive approach in this exploration of the theory of numbers, we will help sharpen problem-solving skills, the basic weapon of a professional mathematician. You will also learn and apply basic principles used in mathematical research. Topics include divisibility, primes and factorization, congruency, arithmetical functions, quadratic reciprocity, primitive roots, Dirichlet's series, and other topics at our discretion and as time permits.