# Mathematics

*Hans Nordstrom, Ph.D., chair*

*Faculty: Basil, Goldwyn, Hallstrom, Highlander, Hill, James, Kotas, McCoy, McQuesten, Nordstrom, **Peterson, Quijano, Salomone, Sterner, 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 and applied mathematics, as well as STEM and mathematics education, 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 undergraduate 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 three degree programs: Bachelor of Arts in mathematics, Bachelor of Science in mathematics, and Bachelor of Science in applied mathematics. Students with an interest in developing a foundation in mathematics who wish to keep their options open for a variety of opportunities after college might choose the B.A. in mathematics, which allows for more flexibility to engage in a wide array of courses in other disciplines. Students who seek careers with a strong mathematical emphasis or students who are interested in furthering their education in graduate school will be best served by one of the two B.S. degrees. If they wish to pursue pure mathematics, they will be better served by the B.S. in mathematics, whereas the B.S. in applied mathematics will be more appropriate if they intend to pursue a career or graduate school in applied mathematics or a related applied field. 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.