# Mathematics and Statistics

The goal of the Mathematics and Statistics Department is to enable students to analyze and organize information using quantitative and statistical tools, to reason and argue logically, to employ appropriate problem-solving strategies, and to communicate complex ideas clearly and efficiently.

## About the Major

Ancient thinkers recognized mathematics as the language of the natural world. Today we know it drives science and social science, business and industry, even art and design. Math majors at Hamilton explore both the abstract, theoretical aspects of mathematics and its applications to a variety of topics. The curriculum delves into the many branches of math, and courses foster deductive reasoning, persuasive writing, and analytical and quantitative problem-solving. Those who love math will find themselves among like-minded peers and mentors, talking shop outside their professors' offices and producing research that they may present at a professional conference. The department also offers a minor in statistics.

### Students Will Learn To:

- Use mathematical and/or statistical tools to model real-world problems
- Construct mathematical proofs based on rules of logical inference
- Communicate complete mathematical and/or statistical arguments

## A Sampling of Courses

### Graph Theory

An introduction to the theory and applications of graph theory. Topics include: trees; connectivity; Eulerian and Hamiltonian graphs; vertex-, edge- and map-colorings; digraphs; tournaments; matching theory; planarity and Ramsey numbers.

### Explore these select courses:

This course covers statistical methods in machine learning such as decision trees, random forests and support vector machines The course will use a project-based approach to give students hands-on experience using these techniques by analyzing large and complex real-world datasets. More importantly, they will learn the statistical principles behind these procedures, such as loss functions, maximum likelihood estimation and bias-variance trade-off as well as why these principles matter in real world settings.

Number theory is the study of the properties of the positive integers. Topics include divisibility, congruences, quadratic reciprocity, numerical functions, Diophantine equations, continued fractions, distribution of primes. Applications will include cryptography, the practice of encrypting and decrypting messages, and cryptanalysis, the practice of developing secure encryption and decryption protocols and probing them for possible flaws. Speaking Intensive.

## Meet Our Faculty

graph theory, graph symmetries, geometric graph theory, combinatorics

noncommutative algebras, Lie (super)algebras, quantum (super) groups, and representation theory

uncertainty quantification, probabilistic modeling and simulation, mathematical biology, and high-performance computing

low dimensional topology; knot theory; Heegaard Floer homology; differential geometry; contact geometry

discrete mathematics, particularly graph theory and combinatorial optimization, with a secondary teaching interest in philosophy of mathematics

dynamical systems, symbolic dynamics, and ergodic theory

commutative algebra, homological algebra, and applied algebra

analysis and commutative Banach algebras

### Chinthaka Kuruwita

Associate Professor of Statistics, Director of Data Science

nonparametric density estimation and quantile regression models

dynamical systems and topological dynamics

Probabilistic geometric group theory

## Careers After Hamilton

Hamilton graduates who majored in mathematics are pursuing careers in a variety of fields, including:

- Financial Analyst,
*The New York Times* - Resident Physician, Westchester Medical Center
- Business Analyst, Federal Reserve Bank of New York
- Professor of Industrial Engineering, Northeastern University
- Software Engineer, Mitre Corp.
- Legal Analyst, Department of Justice
- Actuarial Analyst, GEICO
- Math Teacher, Midlakes High School
- Infectious Disease Epidemiologist, UNC Gillings School of Global Public Health

## Explore Hamilton Stories

While traversing the scenic peaks of the Adirondacks or canoeing through quiet backcountry streams, few first-year students are thinking about algorithms and linear optimization. But these mathematical ideas are as much a part of Hamilton orientation trips as any pack or paddle: they ensure that incoming students have the most worthwhile experience possible.

Five Faculty Retirees Reflect on their Time at Hamilton

Hamilton alumni, students, and colleagues send well-wishes and thanks to five members of the faculty who entered the world of retirement at the conclusion of the 2023-24 academic year. We asked them to reflect on their time on College Hill and whatâ€™s next.

Boutin Gives Plenary Talk at Graph Theory Workshop

Debra Boutin, the Samuel F. Pratt Professor of Mathematics, gave a plenary research talk at the New York Graph Theory Workshop at CUNY Graduate Center in May.

## Contact

Department Name

Mathematics and Statistics Department

Contact Name

Debra Boutin, Chair

Clinton, NY 13323