## Learning Outcomes

Upon completion of the mathematics major or mathematics major with a concentration in statistics, a student will have demonstrated a broad mastery of the fundamentals of mathematics, planned and executed a sustained research project, and clearly communicated their understanding/findings both in written and oral presentation. The student will be able to:

- Make arguments and solve problems in topics from one-variable calculus; the real and complex number systems and beginning analysis; combinatorics, probability, and number theory; linear algebra; and vector calculus.
- Execute a sustained research project:
- Choose and define a significant topic of inquiry from the major field.
- Independently execute a significant research project under the mentorship of an adviser.
- Identify, analyze, critique, and evaluate existing scholarship.
- Develop new research or systematize or explain existing research.

- Clearly communicate work done:
- Write a clear and coherent document that is substantially longer than a traditional term paper or project and in the style and format appropriate to the field.
- Present, discuss, and defend their work orally to scientific and non-scientific audiences.

The primary assessment tool for learning in the major at Reed and the level of student achievement in these areas, is the senior thesis; in addition, the junior qualifying examination offers a secondary assessment tool for student learning in the major.

For more information on the thesis and junior qualifying examination, see Requirements for the Major. Beyond these learning outcomes, mathematics majors must make arguments, solve problems, and carry out term projects in topics from real analysis, abstract algebra, and other advanced courses such as probability and statistics, geometry, and topology; mathematics majors with concentration in statistics must solve problems, analyze data, and carry out statistical investigations in topics from real analysis, probability, mathematical statistics, and a data analysis course, along with other advanced courses such as statistics practicum and stochastic processes.

### Mathematics-Physics

Upon completion of the math-physics major a student will be able to:

- Demonstrate command of the material from the 100- and 200-level Introductory Physics classes: classical mechanics; electricity, magnetism and optics; oscillations/waves; thermal physics, special relativity, and quantum mechanics; introductory electronics, computational physics, and experimental physics.
- Demonstrate command of 100- and 200-level mathematics classes, including one-variable calculus; the real and complex number systems and beginning analysis; combinatorics, probability, and number theory; linear algebra; and vector calculus.
- Apply physical models and computational/analytical techniques used by practicing physicists and mathematicians to solve problems in the foundational areas of classical mechanics, electrodynamics, quantum mechanics, and differential equations.
- Execute a significant independent research project:
- choose and define a research topic of contemporary interest from a subdiscipline of physics or applied mathematics
- design and execute current experimental or theoretical approaches appropriate to the research topic
- independently investigate that topic with the support of an advisor
- in experimental theses, design and construct an experimental station, collect experimental data or assemble data sets from appropriate sources, and evaluate the data using appropriate analytical or theoretical techniques; in theoretical theses, implement up-to-date analytical and/or computational methods to explore and increase understanding of the chosen topic
- analyze, critique, and evaluate existing scholarship

- Communicate work done:
- write a clear and coherent document that is substantially longer than a traditional term paper or project and formatted in a style appropriate to physics research literature
- present, discuss and defend research orally, couching results in the context of accepted physical models and existing research literature

The primary assessment tool for learning in the major at Reed and the level of student achievement in these areas, is the senior thesis; the junior qualifying examination serves as the secondary assessment tool, and math-physics majors take the junior qualifying examinations in both math and physics. For more information, see the pages for the physics junior qual and the math junior qual, and consult with your adviser.