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Mathematics is the science of order, and mathematicians seek to identify instances of order and to formulate and understand concepts that enable us to perceive order in complicated situations.

Perhaps the most important concept of mathematics is that of function, which provides us with the means to study dependence and change. The study of real functions of a real variable (and later complex functions), particularly in connection with the limit concept, is called analysis. The most effective tool for this study is the infinitesimal calculus that analyzes the relation between functions and their derivatives. The study of number systems and their generalizations is called algebra. Here the primary concepts are group, ring, field, and module. The last great branch of mathematics is geometry, which now goes far beyond the classical study of the space we live in to include spaces of high dimension and topology, the abstract theory of shape.

Pure mathematics is concerned with these concepts and their interrelationships, while applied mathematics considers the relation of mathematical concepts to problems arising in other disciplines. Applied mathematics is not a single subject; rather it is almost as many different subjects as there are other disciplines. (But it would be a mistake to think that applied mathematics is organized in terms of the disciplines to which it is applied.)

The concentration in Mathematics is designed to acquaint the student with the most important general concepts underlying the three branches of modern mathematics. Concentration in mathematics will provide an adequate basis for further study in either pure or applied mathematics. Because so many disciplines now rely on the mathematical sciences, a concentration in mathematics provides a valuable background for many different careers. Concentrators who do not choose to continue in mathematics have often gone on to graduate work in other academic subjects or to professional training in law, business, or medicine.

Concentration in Mathematics requires a minimum of either twelve letter-graded half-courses or eleven letter-graded half-courses plus one freshman seminar, subject to the following conditions: Eight of the letter-graded half-courses must be listed as courses taught by the Mathematics Department while the remaining half-courses can be either mathematics courses or courses in approved, related subjects. These eight mathematics courses must include at least one course in analysis, one in algebra or group theory, and one in geometry or topology (all at the 100 level or higher). Tutorials (Math 99r) are encouraged, but not required. Ordinarily no more than one Math 99r course may count toward the concentration requirement. Reading courses, Math 91r, and Math 60r (the latter for senior thesis research only; SAT/UNS only), can be arranged, but do not ordinarily count toward concentration requirements. A Freshman Seminar can be used in lieu of one of the twelve letter-graded half-courses in mathematics or related fields if it is taught by a faculty member of the Mathematics Department and if permission to do so is obtained from the Director of Undergraduate Studies in Mathematics.

Each student is required to submit a five-page expository paper in mathematics. The paper should be an original, coherent, and correct exposition of a topic in pure or applied mathematics. The paper should be written during the sophomore or junior year under the supervision of a professor or tutor in a tutorial (Math 99r), a Math 91r reading course, or a 100- or 200-level course that the student is contemporaneously enrolled in. The paper must be accepted by both that professor or tutor and the Director of Undergraduate Studies. Ordinarily students enrolled in a tutorial automatically satisfy the expository requirement as part of the structure of the tutorial. The expository requirement must be met before the end of the Reading Period of the second term of the junior year. Extensions may only be granted by the Director of Undergraduate Studies.

A candidate for honors must, in addition to the course requirements, submit a senior thesis. The thesis may be on any topic in pure or applied mathematics not directly covered in a student’s course work. It need not be an original piece of mathematical research, but should be an original exposition of material culled from several sources.

In addition, the department offers a Mathematics and Teaching option designed for students who are enrolled in the Undergraduate Teacher Education Program (UTEP). Students who choose this option will acquire eligibility for the teaching certification required for public school teaching in many states.

The department encourages students to take the most advanced courses for which they are qualified. Nevertheless, students who enter as freshmen or Advanced Standing sophomores will not ordinarily be permitted to count courses taken elsewhere toward the twelve half-course requirement. Transfer students wishing to concentrate in Mathematics should consult the Director of Undergraduate Studies, who will review their transcripts and arrange their concentration requirements.

The department welcomes students who want to change their concentration to Mathematics as long as it is plausible that they can fulfill the requirements within the time remaining. Students considering Mathematics may also wish to consider Applied Mathematics, Computer Science, or Statistics. Joint concentrations with Computer Science, Philosophy, Physics, or other fields can be arranged.