# Mathematics

*Stephanie A. Salomone, Ph.D., chair*

*Faculty: Callender, Goldwyn, Hallstrom, Hill, James, Kotas, Lee, McCoy, McQuesten, Nordstrom, **Peterson, Salomone, Stauffer, Swinyard, Wootton*

Mathematics is a gateway to virtually every human endeavor. It lays the foundation for the study and practice of physics, chemistry, engineering, and computer science and has proven to be an essential tool not only in biology, ecology, medicine, and economics, but also in management, marketing, and politics. Our professors conduct research in pure mathematics and apply mathematics and statistics to research in biology, physics, robotics, ecology and business. Every math major can work one-on-one with professors, often on independent study or even research projects. Mathematics majors learn problem-solving and analytical skills preparing them for leadership in a wide variety of disciplines.

Since students study mathematics for a variety of reasons, the mathematics department offers both bachelor of arts (B.A.) and bachelor of science (B.S.) degrees. The B.A. degree is appropriate for those majoring in mathematics as part of a broader interdisciplinary program or for those pursuing a second major in science, engineering, business, the humanities, or education. The B.S. degree is intended for students who want an in-depth mathematical training in preparation for a professional career in mathematics or a closely related field. In particular, students planning to attend graduate school in mathematics, applied mathematics or a mathematically intensive scientific field should strongly consider the B.S. degree. As well, a large number of University of Portland engineering, physics, and chemistry students choose to obtain at least a minor in mathematics.

**Learning Outcomes For Mathematics Majors**

Mathematics graduates of the University of Portland should be able to:

- Demonstrate depth of knowledge in the core content areas of the discipline.
- Demonstrate knowledge of important definitions and results.
- Adequately construct elementary proofs using relevant definitions and foundational results.

- Apply content knowledge to solve complex mathematical problems.
- Identify the nature of the problem, organize relevant information and mathematical tools.
- Devise a strategy to develop a solution to the problem.
- Implement the strategy, performing relevant actions and computations, keeping an accurate record of work.
- Reflect on whether a strategy was successful, checking for correctness and plausibility of the solution.

- Demonstrate ability to construct rigorous logical arguments.
- Write complete, coherent, concise proofs demonstrating mathematical rigor.
- Employ a variety of proof techniques including direct proof, proof by contradiction and proof by induction.
- Write proofs involving quantified statements.

- Effectively communicate mathematics.
- Demonstrate the ability to understand professional mathematical writing.
- Adequately communicate mathematical ideas orally and/or in writing.