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Computer Science

1. Create and demonstrate software that correctly solves realistic problems with open-ended scope.
2. Use empirical methods to analyze computational systems and models.
3. Employ multiple levels of algorithmic and data abstraction to manage system complexity.
4. Employ mathematical ideas in a computing context.
5. Create, implement, and evaluate software abstractions that model complex phenomena.
6. Create, apply, and understand the software abstractions that manage interaction with hardware.
7. As part of a team, develop robust software artifacts that successfully enable their users to achieve their goals.
8. Employ written and oral communication in both technical and nontechnical settings.
9. Understand the social and ethical context of computing.

Mathematics

1. Employ the methodologies used in mathematics, including calculation, proof, discovery of new mathematics, and application.
2. Understand basic content and principles in each of the broad divisions within mathematics: discrete (algebra and combinatorics), continuous (calculus and analysis), and geometric (linear algebra and topology).
3. Master at least one field of mathematics to a depth beyond that typical of a single advanced undergraduate course in the topic.
4. Understand the motivation and aesthetics underlying mathematics, including the historical and cultural context in which it was developed.
5. Communicate mathematical ideas in written papers, oral presentations, and group discussions. Possess the ability to argue mathematical proof validity in both written and oral work.