Geremías Polanco Encarnación, assistant professor of mathematics, received his Ph.D in mathematics and his 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.
Calculus provides the language and some powerful tools for the study of change. As such, it is an essential subject for those interested in growth and decay processes, motion, and the determination of functional relationships in general. Using student-selected models from primary literature, we will investigate dynamical systems from economics, ecology, epidemiology and physics. Computers are essential tools in the exploration of such processes and will be integral to the course. No previous programming experience is required. Topics will include: 1) dynamical systems, 2) basic concepts of calculus-- rate of change, differentiation, limits, 3) differential equations, 4) computer programming, simulation, and approximation, 5) exponential and circular functions. While the course is self-contained, students are strongly urged to follow it up by taking NS 316-Linear Algebra or NS 261-Calculus II to further develop their facility with the concepts. In addition to regular substantial problem sets, each student will apply the concepts to recently published models of their choosing. This course satisfies Division I distribution requirements.
The world we live in is an ever-growing financial market, in which governments, corporations and individuals engage in a wide variety of complex transactions. To be an effective investor, saver or borrower, one needs to understand the fundamental principles upon which all financial transactions are based. Central to these principles is the concept of interest. Thus, in this course we seek to learn how to be an effective investor, saver and/or borrower by developing an understanding of the mathematics underlying interest theory and its applications to personal and/or institutional finance. Prerequisite: Calc 1 required, Probability desirable but not required.
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.
This course extends the concepts, techniques and applications of an introductory calculus course. We'll detect periodicity in noisy data, and study functions of several variables, integration, differential equations, and the approximation of functions by polynomials. We'll continue the analysis of dynamical systems taking models from student selected primary literature on ecology, economics, epidemiology, and physics. We will finish with an introduction to the theory and applications of Fourier series and harmonic analysis. Computers and numerical methods will be used throughout. In addition to regular substantial problem sets, each student will apply the concepts to recently published models of their choosing. Pre-requisite: Calculus in Context (NS 260) or another Calc I course.
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.
Geremias Polanco Encarnacion
Assistant Professor of Mathematics
Mail Code NS
Cole Science Center
893 West Street
Amherst, MA 01002