Academics

Mathematics

 

Matt Ollis
John Arhin (Math Fellow)

In science, there are no such things as unrelated courses. One finds that a mathematical form that represents competition in an ecology course stands a good chance of being the same one that represents a chemical reaction or a knight’s move on a chess board. This is one of the beauties of mathematics and, at the same time, one of its powers. Mathematics is a field that (by its own structure) uses forms to investigate itself. This power of introspection will become more and more manifest as you move up the course ladder. Indeed, learning mathematics at Marlboro is learning to spot the reflections of one course in another and to see that there is a great unity and beauty to the subject.

The Mathematics curriculum at Marlboro has a two-fold purpose:

Mathematics courses at Marlboro are designed to serve both of these goals, though some are skewed strongly in favor of one or the other.

John Arhin (Math Fellow)

My research interests include combinatorial designs, in particular SOMAs which can be regarded as a generalisation of sudoku puzzles. I study the structure of SOMAs in terms of related geometries, and relate this structure to certain graphs. Also, I create computer algorithms that together with symmetries can be used to construct SOMAs as well as related mathematical objects.

Matt Ollis

My personal research is in the areas of combinatorics and group theory, especially in questions motivated by the design of experiments. These areas are very accessible to study at the undergraduate level, and expose students to both the problem solving and theory building sides of mathematics.

Areas of interest for plan-level work: Students are encouraged to pursue whatever topic demands their attention from across the many subfields of mathematics. Interdisciplinary plans are welcomed.

Starting Points(Basic and Introductory Courses)

Topics in Algebra, Trigonometry and Pre-Calculus (NSC556)
This course covers a wide range of math topics prerequisite for further study in mathematics and science and of interest in their own right. The course is divided into over 50 units. One credit will be earned for each group of 6 units completed. Students select units to improve their weak areas. There are also tailored streams for students who wish to go on to study calculus or statistics. Over the course of the academic year, 42 units will be offered in the timetabled sessions. Individual tutorial-style arrangements can be made to study the non-timetabled units or to study units earlier than their scheduled session. (Introductory) Offered every semester.

Calculus (NSC515)
A one semester course covering differential and integral calculus and their applications. This course provides a general background for more advanced study in mathematics and science. (Introductory) Offered every fall.

Statistics (NSC123)
Statistics is the science -- and art -- of extracting data from the world around us and organizing, summarizing and anlyzing it in order to draw conclusions or make predictions. This course provides a grounding in the principles and methods of statistics. Topics include: probability theory, collecting and describing data, hypothesis testing, correlation and regression, and analysis of variance. Two themes running through the course are the use of statistics in the natural and social sciences and the use (and abuse) of statistics by the news media. (Introductory) Offered every spring

Discrete Mathematics (NSC562)
Discrete math is the study of mathematical objects on which there is no natural notion of continuity. Examples include the integers, networks, permutations and search trees. After an introduction to the tools needed to study the subject, the emphasis will be on you *doing* mathematics. Series of problems will lead gradually to proofs of major theorems in various areas of the discipline. This course is recommended for those intending to do advanced work in math or computer science. (Introductory) Offered as needed.

A Whirlwind Tour Of Mathematics (NSC577)
Do you want a thorough understanding of the most important and deep theorems in every branch of mathematics? Do you want to achieve this in a four credit course from a standing start? Good luck with that - you won't manage it in this course. Instead, we'll look at six to ten topics, chosen for their accessibility and beauty, and drawn from a broad range of subdisciplines of math. Possibilities include: irrational and imaginary numbers, the infinite, chaos and fractals, Fermat's Last Theorem, the Platonic solids, the fourth dimension, the combinatorial explosion, P vs. NP, the Four Color Theorem, non-Euclidean geometry, logical paradoxes, and many others. No prior mathematical experience is expected. (Introductory)

Puzzled? (NSC541)
This course will give students a chance to test and develop their puzzle-solving ingenuity. We'll attack a series of puzzles, going from Lewis Carroll's logic problems via the classic "recreational math" puzzles of Lucas, Loyd and Dudeney to modern crazes such as the sudoku. Pass/Fail grading. (Introductory)

Game Theory (NSC555)
This course introduces several aspects of game theory from a mathematical point of view. We'll begin by considering the surprisingly complex children's game dots and boxes and move on from there to consider other two-player games (such as nim, the prisoner's dilemma and chicken), Nash equilibria, voting systems and the theory of auctions. We will see applications of the math we develop in other disciplines, particularly economics and political science. (Introductory)

Pursuing Interests (Intermediate and Thematic Courses)

Calculus II (NSC31)
We build on the theory and techniques developed in Calculus. Particular emphasis will be placed on power series and multivariate calculus. (Intermediate)

Statistics Workshop (NSC574)
A follow-up to Statistics (NSC123) in which students will acquire and hone the statistical skills needed for their work on Plan. Course content will be driven by the interests and requirements of those taking the class. (Intermediate)

Writing Mathematics (NSC575)
We will study the writing and presentation of mathematics. All skills needed for writing Plan-level math will be discussed, from the overall structure of a math paper down to the use of the typesetting package LaTeX. Much of the time will be spent working on writing proofs. Short papers, based on material in your other math classes, will be read and discussed as a group. May be repeated for credit. (Intermediate)

Linear Algebra (NSC164)
Linear Algebra is important for its remarkable demonstration of abstraction and idealization on the one hand, and for its applications to many branches of math and science on the other. We will focus our study on n-dimensional real space, considering notions such as spanning sets, linear independence and transformations and their matrix representations. The final two weeks will be given over to students to pursue a topic of interest further. Possibilities include connections to the Differential Equations course, the matrix representations of symmetries and consideration of complex or finite spaces. (Introductory)

Number Theory (NSC514)
Numbers have been a source of fascination since ancient times. We investigate some of the more intriguing properties numbers can have, and study the work of some of the great mathematicians, including Euclid, Fermat and Gauss. We also look at cryptography – a modern application of number theory. (Intermediate)

Advanced Calculus (NSC302)
This course picks up the study of Calculus from where Calculus II left off. The course is divided into two halves: Vector Calculus and Theory of Calculus. In Vector Calculus we extend the notions of derivative and integral to vector functions, leading to Green's Theorem, Stokes' Theorem, and the Divergence Theorem. Theory of Calculus begins the study of Real Analysis: that is, we work from a strict definition of the real numbers to more rigorous proofs of some of the results used in earlier Calculus courses. (Advanced)

Differential Equations (NSC342)
A study of ordinary differential equations and their solutions, including power series solutions and numerical techniques. We also look at many applications, from population dynamics to the detection of art forgeries. (Intermediate)

Good Foundation For Plan

All students of mathematics must search for a basic understanding in each of the three major areas: algebra, geometry, and analysis. To accomplish this in one undergraduate lifetime, it is important to get some core courses - Discrete Math, Calculus, Calculus II, and Linear Algebra - completed as soon as possible. Doing this will widen your range of options as you look for a topic on which to focus. When pursuing an interdisciplinary Plan, there is less urgency to complete these courses, since the "introspection" side of the Plan will turn towards investigating the relationships between mathematics and the chosen field.

Sample Tutorial Topics