# Mathematics and Computer Science

How does the human brain work? What does the future hold for our climate? Is it possible for a computer to understand natural language? How can we most efficiently and securely transmit information over the Internet? When is it useful to distinguish between different levels of infinity?

Mathematics and computer science provide the critical foundation required to answer some of the most pivotal and complex questions of our time. Mathematicians design the models that enable us to understand and improve the structure of transportation networks, computer networks and physical processes, making them more efficient, effective, and versatile. Whether or not practical applications are foreseen, mathematicians revel in exploring the structure and beauty of abstract patterns, logical relationships, and rigorous formal proofs. Computer scientists build the invisible layer of software that drives significant advances in scientific research and improves everyday life. The newest smart phones are driven by tens of millions of lines of computer code, while a modern automobile includes over one hundred million lines of code-every aspect of which we depend upon for our productivity and safety.

To equip students with the conceptual knowledge to tackle such problems, the curriculum for the Department of Mathematics and Computer Science stresses the development of problem-solving techniques, logical reasoning, and data analysis. Special emphasis is placed on the value of abstraction: the process of simplifying a messy real-world problem to focus on the relevant details. Consistent with the university's core curriculum, the department provides a learning environment that encourages both independent thinking and group collaboration. Communication is of paramount importance; students learn to clearly articulate the nature of the problem, the analysis process, and the solution. Students who choose to study mathematics join a discipline that has been an important part of society for at least four thousand years. The foundation for a major in mathematics is formed by completing a sequence of three courses in calculus, and a course in linear algebra. Of calculus, Morris Kline wrote, "Following hard on the adoption of the function concept came the calculus, which, next to Euclidean geometry, is the greatest creation of all of mathematics." Linear algebra shares in the beauty, power and applicability of the calculus by providing a rich theory for modeling real-world phenomena by means of systems of linear equations. Building upon this foundation, students can select from a number of upper-division mathematics courses that broaden and deepen their understanding of mathematics, exploring areas such as abstract algebra, real and complex analysis, probability and statistics, mathematical modeling, and optimization.

Students studying computer science begin by learning how to write computer programs, but computer science is far more than just programming. Among other pursuits, computer scientists design and study algorithms (computational problem solving strategies) to solve difficult real-world problems, learn software engineering patterns to break down large projects into manageable pieces, and study the design of programming languages themselves. Those choosing to major or minor in computer science will have the opportunity to explore a rich set of elective courses, including artificial intelligence, computer graphics, database management systems, networks, and operating systems. For students with an interest in business, there is also an option to pursue an interdisciplinary Bachelor of Science degree in Computer Science and Business.

Students majoring in either mathematics or computer science will have the opportunity to join a strong community, through participation in a variety of student-initiated and faculty-sponsored groups. The department hosts a student-run Mathematics Club (first begun in 1927), and offers two faculty-guided problem-solving seminars preparing students to compete in the annual Mathematical Contest in Modeling (MCM) and Putnam contests. The department also features a local chapter of the Association of Computing Machinery (ACM) and a computer game development club, in which artists and computer science students are teaming up to create a new computer game.

The study of mathematics and computer science prepares students to enter a world in which computational and mathematical literacy are crucial. Many of our students move on to graduate study, and ultimately pursue careers in business, research, industry, education, government, and actuarial work, among others. Whether considering a major in mathematics or computer science, building the foundation for another discipline, or simply developing the quantitative literacy required to interact in an increasingly quantitative world, the Department of Mathematics and Computer Science provides the strategies and conceptual understanding to help students reach these goals.

Students who graduate from the Department of Mathematics and Computer Science will be able to communicate precisely in the formal language of mathematics or computer science, both verbally and in written form, work effectively individually and as part of a team, and leverage the power of abstraction to transform complex problems into simpler but conceptually relevant ones.

Additionally, students completing a degree in mathematics will be able to:

• Demonstrate an understanding of the core ideas in calculus and linear algebra, as well as a breadth or depth of understanding in other mathematical subject areas;
• Write clear and correct mathematical proofs;
• Successfully transition to advanced study in any of a range of pure or applied mathematical subject areas.