# Mathematics

Do the angles of all triangles add to 180**°**? How do we know? Has someone actually measured the angles of every possible triangle?

The area of a circle is πr^{2}. How can an area be a decimal number that goes on forever? Can anyone measure an area *that* accurately? If not, how do we know this formula is correct?

Rate equals distance divided by time. That is what we mean by miles per hour. But what do I mean when I say that I am driving 60 mph *right now*? For instantaneous velocity, no time elapses and my car hasn't moved. So, what is my speedometer telling me?

In studying math at Commonwealth, you will learn the answers to these problems and many others. You will learn to translate real-life situations into mathematical equations and how to construct logical proofs, starting from basic assumptions and arriving at expected *and* surprising results.

You will learn how to picture equations with graphs and tables of values and develop intuition about their behaviors. You can study calculus and learn about limits, instantaneous velocity, and precise areas—vital to the study of physics and other sciences. You can also study statistics, which has real-world applications in the sciences, the social sciences, political discourse—and everyday life. If you enjoy challenging your creativity in a competitive environment, you can join our math team as it faces off against groups throughout New England. Regardless of the path you take through our math program, you will learn to think logically, to calculate accurately, and to solve challenging problems.

When I came to Commonwealth, I was not a math person. After four years of intensive math training and application in other classes, though, I have come to have a rich and abiding love for math and all of its applications.

## Courses

## Electives

Please note: electives may change from year to year.

- Abstract Algebra: Groups, Rings, Fields
- Axiomatic Set Theory
- Calculus 2
- Category Theory
- Differential Equations
- Differential Geometry
- The Geometry of Conic Sections
- Linear Algebra
- Mathematical Logic
- Medieval Islamic Mathematics
- Multivariable Calculus
- Problem Solving
- Statistics
- Theoretical Calculus
- Topology

## Abstract Algebra: Groups, Rings, Fields

## Axiomatic Set Theory

## Calculus 2

## Category Theory

## Differential Equations

## Differential Geometry

## The Geometry of Conic Sections

## Linear Algebra

## Mathematical Logic

## Medieval Islamic Mathematics

## Multivariable Calculus

## Problem Solving

## Statistics

## Theoretical Calculus

## Topology

## Meet the Math Faculty

### Alan Letarte

M.A., University of Wisconsin–Madison

Ph.D., University of Wisconsin–Madison