# Mathematics

The mission of the Mathematics Program at Fairfield University is two-fold:

We strive, as mentors and teachers, to graduate majors with broad knowledge of the principal content of Mathematics and its applications, who are aware of the historical and, when appropriate, cross-cultural development of Mathematics and the manifold connections among its subject areas, who have seen some of the connections of Mathematics to other disciplines, and who can think quantitatively and analytically. We want our majors to possess technical problem-solving skills, to have a deep appreciation for mathematical beauty and the power of abstraction, and to be able to understand and build complex logical arguments and communicate these arguments through written, visual, and oral means.

We strive to serve the mission of the Fairfield University Core by ensuring that the student body possesses the ability to reason quantitatively and analytically, and understands not only the power of Mathematics (and especially the calculus) as the language of the sciences, but also the pervasive role of Mathematics in the arts, sciences, and other disciplines.

## Mathematics in the Major: Learning Goals and Objectives

We would like mathematics majors to come away with the following:

- Knowledge of:
- The fundamental concepts underlying the major areas of undergraduate Mathematics, including calculus, discrete mathematics, real analysis, linear algebra, and abstract algebra
- Applications of Mathematics to other disciplines
- Mathematical content and skills needed to support graduate study and/or professions that require mathematical proficiency

- Awareness of:
- The beauty and power of Mathematics
- Connections between different fields of Mathematics
- The historical development of Mathematics across cultures

- Ability to:
- Think quantitatively, analytically, and abstractly
- Understand and create logical arguments and proofs
- Read mathematics with comprehension
- Write and communicate mathematics clearly and effectively
- Demonstrate proficiency in symbolic representation and manipulation
- Use technology as a tool to solve problems

For the student of the humanities, the social sciences, or business, mathematics at Fairfield University offers training in basic mathematical skills and their application to real world problems. However, more importantly, it attempts to make the student aware of the relationships between mathematics and other branches of knowledge, while imparting a sense of its historical and cultural value.

The mathematics major offers students a strong and broad background in undergraduate mathematics, providing the foundation for further graduate studies in theoretical or applied fields of mathematics, for advanced study in fields where strong quantitative skills are needed, or for employment in mathematics-related fields in industry or in teaching. The mathematics minor offers students an opportunity to strengthen their mathematical backgrounds.

## Mathematics in the Magis Core Curriculum: Learning Objectives

Beginning with the Class of 2023, all undergraduate students will be required to complete the Magis Core Curriculum. Please refer to the Curricula section of this undergraduate catalog for a detailed explanation of the Magis Core.

- Develop a Depth of Understanding of Mathematical Concepts, Context and Theories
- Understand sophisticated mathematical ideas when expressed abstractly and generally
- Critically analyze mathematical statements, arguments and solutions for correctness
- Be aware of the development and impact of mathematics in the context of human progress

- Engage in Sophisticated Mathematical Problem Solving
- Solve multi-step problems by creatively combining a variety of mathematical techniques and reasoning, including graphical, symbolic, computational (including the use of technology), and algorithmic
- Solve problems arising from a broad array of disciplines and see the common mathematical threads that unite them

- Effectively Model Situations Mathematically and Abstractly
- Translate word descriptions and real situations into mathematical language, recognizing unknown quantities and relationships, and identifying tools to help solve the problem
- Understand how mathematics describes problems in the real world and a wide variety of disciplines

- Communicate in the Language of Mathematics
- Express ideas precisely, rigorously, abstractly and generally
- Communicate and demonstrate an understanding of mathematical concepts through projects, reports, problem sets and presentations