# Why Take a Math Course?

## Because math is beautiful!

**Mathematics is one of the greatest human discoveries**

Calculus revolutionized humankind’s ability to precisely describe and shape the world we live in. Linear algebra gives a common framework for understanding both elementary transformations (like rotations) and the long-term behavior of complicated systems.

**Each part of mathematics exhibits its own form of beauty**

In courses such as real and complex analysis, abstract algebra, and geometry much of the beauty arises from pristine arguments which make precise intuitive notions of infinity, continuity, symmetry, and space. The beauty showcased in these classes is similar to the beauty exhibited by a haiku or abstract piece of art.

**Mathematics is an intricate set of interlocking hierarchies**

Viewed from the outside, the language and methods of formal mathematics may seem intimidating, but the discipline, by its very nature, slowly builds on and develops basic concepts which are accessible to every person. Each of our courses takes students, with whatever mathematical knowledge and ability they bring, and moves them along on the path to greater mathematical understanding and ability. As they do so, they connect the main ideas of the course to concepts and themes found in other mathematics, statistics, and science courses.

**Mathematics has deep affinities with the arts and humanities**

It has inspired paintings (like this one, for example, as explained here.), made a profound impact on art history, provides important examples and problems for philosophy (as in the work of Immanuel Kant, for example), was responsible for a revolution in economic history and is intimately connected to the modern revolution in physics history. Even mathematics and music are intertwined in many interesting and complex ways.

## Because math is useful!

**Abstract mathematical ideas have unplanned impact on the world**

- Number theory, once thought of as the “most useless” of abstract mathematics, is now the basis of modern cryptography – every time your credit card number or password is transmitted over a secure connection, you’re using number theory.
- Google’s algorithm for ranking search results is an application of linear algebra.
- Persistent homology is a new data analysis tool arising from a branch of mathematics, formerly considered to be one of the most abstract subdisciplines of mathematics.

**Mathematics and statistics provide the quantitative language of the natural and social sciences**

- Biology: Mathematical biology is an upcoming field that uses sophisticated mathematics and statistics to understand biological systems. Indeed, biologists of all sorts will find mathematics and statistics extremely useful in the modern world. Mathematics can even explain why there are no 3-headed monsters.

Economics: From fixed point theorems (of the sort studied in topology and real analysis) to the Black-Scholes Formula, mathematics and statistics are everywhere in economics. Classes in calculus, linear algebra, real analysis, and statistics will get you off to a good start in understanding the mathematical foundations. - Physics: Calculus is the language of classical physics; modern physics makes extensive use of differential equations, topology, and geometry (among other mathematical subjects!)
- Chemistry: The mathematics of tilings (studied in geometry courses) governs the formation of crystals and quasi-crystals. Group theory (studied in our Abstract Algebra course) is the language for describing the symmetries of molecules. In concert with group theory, topology and knot theory provide techniques for understanding chirality.
- Computer Science: Data visualization relies on a web of concepts from linear algebra, statistics, and geometry. Quaternions (studied in Abstract Algebra) are fundamental to computer graphics. Turing machines (the theoretical foundation of computing) are formal mathematical constructs like those studied in Mathematical Reasoning (MA 274). Since computers have finite precision, any time real numbers are used in computing the techniques of numerical analysis become extremely important. Quantum computers will radically change the nature of computing in the 21st century — topology, geometry, and abstract algebra (in addition to the old standbys of calculus and linear algebra) are essential tools in quantum computing.
- Environmental Science: Mathematical models are the central tool for describing and predicting climate change. Population migrations and predator-prey relationships are studied with differential equations. To learn more about these (or related) topics take our courses in differential equations or mathematical modeling.
- Engineering: All disciplines of mathematics have contributed to the various engineering disciplines. Since we haven’t mentioned it yet, we should point to Fourier analysis as a beautiful and highly applicable mathematical subject. One of its many applications is in sound engineering: it explains why musical instruments sound the way they do! Fourier analysis is studied on occasion in our courses in real analysis, topics in analysis, or partial differential equations.

## Because you can be wrong! (and right!)

Mathematics is one of the few human endeavors where there is almost total agreement about what constitutes a correct argument. In our classes, you’ll learn how to construct rigorous arguments, detect flawed arguments, and spot vague and malformed statements.

## Because math is power!

Providing a solid, appropriate mathematical education to elementary and secondary school children empowers them to lead confident, productive lives. We love helping students who want to teach – it’s a noble calling. If you’re interested, talk to us about particular programs which might be relevant to your interests.

## Because they’re fun!

- Solving problems is fun. The moment of sudden enlightenment makes the struggle worth it.
- Connecting disparate mathematical ideas is fun. Topology shows up in real analysis, and real analysis in geometry, and geometry in number theory. Mathematics is one discipline, but with many rooms. Discovering which rooms adjoin to which is the adventure of a lifetime.
- Applying mathematical and statistical ideas to the real world is fun. Connecting the abstract to the concrete is what science and the liberal arts, more generally, are all about. It’s fascinating work and a great deal of fun.

Even if you are majoring in something else, taking more math classes may be worthwhile.** Math tends to open doors** that if left closed can be avoided, but when opened offer opportunities that are worth having. In almost any field, (and particularly in medicine, the sciences, and economics) more math always gives one an edge over those who have taken less.