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Mathematics

About the Department of Mathematics

The discipline of mathematics is defined as much by its methodology as it is by its content. Indeed, it is this methodology which unifies the different areas of mathematics. The Department of Mathematics seeks to involve students at all levels in the thoughts and methods of mathematics in a creative, lively way.

The courses in the Department are organized around three related areas: the core curriculum, service to other disciplines and the major in mathematics.

The Core Requirement

Much of mathematics has its roots in science, but the spirit of mathematical inquiry is not bound to any specific area. Mathematics is an important discipline for every educated person.

All students at the university are therefore required to study some mathematics. The goal of the requirement is to strengthen the student’s imaginative and deductive powers through the discipline imposed by rigorous mathematical thinking. The precise use of language and logic characteristic of mathematics is developed in the courses which meet the core requirement.

There are several classes from which the student may choose, each dealing with profound ideas that play an important part in our culture. These courses can be categorized into three main types.

  • The courses in Euclidean and Non-Euclidean Geometry and Linear Point Set Theory are designed explicitly to engage the student in the precision of mathematical reasoning. There is little or no specific material that must be mastered before taking on these classes, although Linear Point Set Theory requires "mathematical maturity" which can be demonstrated through course work.
  • Introduction to Statistics provides a background in statistical reasoning and methodology that is needed for efficient citizenship, as well as for specific use in the fields of Biology, Business, Economics, Psychology and the health professions.
  • The main Calculus sequence, Calculus I, II and III, provides an exploration of one of the most useful parts of mathematics. However, these courses do require a broader background in mathematical computation, particularly in algebra and trigonometry. Some students who wish to take one of these courses will have to prepare by taking Precalculus at the college level.

Service to Other Disciplines

Mathematics and the sciences have cross-fertilized each other for centuries. Physics, biology, chemistry and economics all draw on mathematical ideas and techniques. The calculus sequence is the primary avenue for learning these ideas. The knowledge of computation learned in the computer science courses can be applied in other disciplines where the computer can be used as a powerful tool for scientific investigation. Many mathematical concepts grew out of problems in science and the content of a number of upper-level courses reflects this relationship.

The Major

The purpose of the major is to immerse students in the content and methodology of mathematics as it is practiced by active mathematicians. The basic requirements in the major introduce the central ideas of the discipline. Electives within the major permit students to pursue further areas of special interest.

The course in Linear Point Set Theory is an important bridge into the major. In it students begin the immersion into the mathematical process and the foundation is built for later work in Algebra, Analysis, Topology and other courses. Linear Point Set Theory, along with Abstract Algebra and Analysis, highlight methods of proof, raising and settling of questions, developing precise definitions of concepts and thinking and writing concisely in mathematical terms. Students who immerse themselves in these mathematical ideas are able to approach the other courses in the major with the perspective of the working mathematician.

Mathematical concepts have a profound influence on the world outside of mathematics. Equally important, the world external to mathematics has helped shape the discipline. It is important for majors to experience this interaction and to see the power and limitations of mathematics. Courses such as Calculus I, II and III, Linear Algebra, Differential Equations, Probability, Statistics, Numerical Analysis and Introduction to Computer Science as well as the Physics requirement aid in the development of this perspective.

A major in mathematics opens many doors. Majors go on to graduate work in such fields as mathematics, computer science, statistics, physics, economics, or biology. They pursue careers in business, actuarial science, linguistics, medicine, law and teaching. Most importantly, the major allows the budding mathematician to see the world in a creative, beautiful and profound way.

Advising

All students are urged to seek advice from the Department concerning selection of courses and placement. A placement exam is required of students wishing to enroll in 1000- or 2000-level courses except 1301 and 2305. Students considering a major in mathematics should consult with the Department as soon as possible. A faculty member can suggest courses that may help students make a decision.

Each major has a faculty advisor in the Department. Students and the advisors will have an introductory conference to talk about the program and to discuss aims and goals. At the beginning of the junior year, students and advisors meet to take stock of how students are doing and where they are going. Advisors assist the students in course selection and post-graduate plans. It is imperative that all those who intend to major in mathematics contact the Department for counseling at least once each semester before preregistration.

Degrees in Mathematics

Bachelor of Arts in Mathematics

Bachelor of Science in Mathematics

Applied Mathematics Concentration

Pure Mathematics Concentration

Course Information

Courses in Mathematics