## Mathematics

## What is Math?

Mathematics is a logical system, based on a few simple assumptions, from which all facts (theorems) can be derived using an agreed-upon system of logical deduction. Once a theorem is proved, everyone agrees that it is unequivocally true. Math is unique in this respect. Mathematics can be extremely creative, as it is based on problem solving and insight. It is also very rigorous – based on critical thinking and symbolic reasoning – and rigidly structured.

In some ways, it is easier to answer the question of what math is not. First, math is not simply number crunching; in fact, many math professors rarely encounter numbers in their research. Generally what mathematicians seek is a much deeper understanding of the nature of the world. Math is not only evidence-based calculation; it is also proof-based. To understand what a proof is, we have to uncover the fundamental nature of mathematics.

Mathematics has been around since antiquity, and has fascinated and stimulated creative and logical thought for millennia. It is ubiquitous in nature and science, and is rich in applications to the real world. Many mathematicians speak of the beauty of mathematics as a language for describing the universe. However, mathematics is not only a science; it is also an art. Although mathematicians are perceived as straight-laced, we all feel emotion when we think of math in terms of its fundamental nature, its omniscience, its art, and its science. To do pure math – math with no proposed application to any other field – is to get to the very heart of things. Math research is the discovery of new mathematical ideas, definitions, and theorems. Boolean algebra (George Boole, 1854) was thought to be of no value at the time of its discovery. It was rediscovered a hundred years later and now serves as the basis of modern computation and digital logic. Calculus, now a common mathematical system, did not exist four hundred years ago. And although it was discovered four centuries earlier, we still find new uses for it today!

## What can I do with a Math degree?

The job of mathematician has been hailed as one of the best, and well-paid, in the world. What could be better for a math lover than to sit around and solve math problems all day? Even if you don't want to be a professional mathematician, the study of math can be quite lucrative. A math degree not only guarantees skill in logical thinking and creative problem solving, but it also prepares graduates to excel in whatever job they choose. Students of mathematics are also suited for law school, medical school, business school, and further studies in computer science. A math degree is infinitely useful and applicable to most career fields. Due to the variety of careers available to math majors, HPU offers four concentrations within the Mathematics major.

### Pure and Educational Math

The Pure Math concentration lends itself to the advanced study of mathematics in graduate school. Students attending graduate school in math may become professors, researchers in national labs, or consultants. This concentration focuses more heavily on abstract mathematical thought and logic, and produces students who are not only proficient in reading and writing proofs, but are strong critical thinkers and problem solvers as well.

Teaching mathematics and sharing its beauty and wealth of applications with future generations can be a very rewarding way to use a math degree, too. To this end, the Math Education specialization prepares our graduates for a job as an educator in the K-12 system.

### Applied Math and Engineering

The Applied Math concentration focuses on applying mathematical ideas to specific problems in the sciences. Students graduating with an applied math concentration are prepared to go to school for engineering, to work for the government, or to train as actuaries.

Students who are particularly interested in applying their math skills to a career in engineering may wish to consider our Math-Engineering Dual Degree Program.

## Why study Math at HPU?

HPU offers more individualized attention - our upper division class sizes range from 8-15 students. Our faculty are dedicated to teaching. They come from top mathematics programs across the country and have been actively engaged in world-class mathematics research.We implement a variety of teaching techniques that are innovative and student-centered, promoting creativity and critical thinking skills rather than being rigidly structured to the lecture hall paradigm. As a student, you will not only be exposed to different instructional styles, but will also be able to interact with a diverse set of peers in our mathematics clubs and study groups. In your final year, you may have the opportunity to work closely with a faculty mentor on advanced material catered specifically to your personal interests.