# Undergraduate

Mathematics is a way of defining and solving problems by combining logic with insight, and by finding patterns and structure. At the most basic level, we use the abstract concept of “number” to understand what we observe, and we develop the method of “counting”; at a higher level, we use the language of “calculus” to understand motion, and we develop the methods of differentiation and integration. But mathematics is more than just computations with numbers and derivatives. Math is a formal way of thinking—an art that ties together the abstract structure of reason and the framework of quantitative and qualitative models in the natural and social sciences. Mathematics further involves the discovery of new relationships between various seemingly disparate quantities as well as the development of abstract concepts that can be applied to aid our understanding of the world we live in.

Undergraduate mathematics majors and minors will study:

- The foundations of analysis, which begins with the study of functions and their derivatives and integrals
- The fundamentals of advanced algebra, which is based on axiomatic systems involving operations of addition and multiplication in general settings
- Additional subjects such as geometry, probability, and topology
- Applications of mathematics to science and/or engineering.

#### Undergraduate Learning Goals

At the time of graduation, math majors should:

- Have a good working knowledge of the language of mathematics as embodied in the basic constructs of mathematics in the fundamental areas of algebra, analysis, and geometry
- Be able to analyze the logical structure of a scientific or mathematical problem and to develop a meaningful approach to a solution
- Be able to read, understand, and construct a well-formed proof
- Develop the mathematical maturity and skills necessary to extend their knowledge through self-study and independent research
- Be able to apply mathematical methods to solve research problems arising outside of mathematics
- Be able to formulate precise mathematical statements and questions
- Be able to effectively and successfully communicate mathematics in both oral and written form to a broad mathematical and lay audience.