The Mathematics Department offers an extensive honors program, spanning all four years of the undergraduate experience. The courses at the freshman and sophomore level are offered in cooperation with the University Honors Program; they can be applied toward earning a University Honors Citation. Lower level course offerings include Honors Seminars offered by the Honors College, enhanced H-versions of the standard mathematics sequence MATH 140-141-240-241-246, as well as the special honors sequences, Math 340-341. Visit Testudo for the current class schedules, and visit our Undergraduate Courses for syllabi and other course information.

At the junior-senior level, the department offers a program leading to a degree with Honors (or High Honors) in Mathematics. Participation in the upper level program is *independent *of participation in the lower level program; however, many students who complete the requirements for a University Honors Citation also enter a Departmental Honors Program. Successful completion of the Departmental Honors Program in Mathematics results in a citation on the transcript for Honors in Mathematics; it need not imply that the student majored in Mathematics.

For more information contact

- Honors Director: Professor Larry Washington, .
- Mathematics Coordinator of Undergraduate Advising, Ida Chan, Office: Math 1115, 301-405-7582. Email:

### Freshman and Sophomore Honors Courses in Mathematics

The Mathematics Department offers honors courses at various levels of sophistication. Our goal is to allow every honors student (who is interested in mathematics) to find a course that provides challenging stimulation at a level that is appropriate for his or her background.

#### H-versions of Standard Mathematics Courses

The mathematics department offers H-versions of the standard introductory mathematics sequence for honors credit. These courses are: Math 140H, Math 141H, Math 241H, Math 246H, and Math 240H. The H-versions should be accessible to most honors students in the university. H-classes are open to students who have taken earlier H-classes, or are in the University Honors Program, or have the instructor's permission. The basic subject matter of these courses is constrained, because each course is a prerequisite for other mathematics courses. However, instructors have considerable freedom to enrich the courses. In general, enrichment means that the instructor will present more realistic applications in greater detail, or will discuss connections with other branches of mathematics or the sciences.

The freshman calculus courses (Math 140H and Math 141H) are designed for the general honors students with solid background in high school mathematics. The sophomore mathematics courses (Math 240H, Math 241H, and Math 246H) are designed primarily for honors students who intend to major in engineering or the sciences. (Naturally, students in other disciplines with an interest in mathematics are still welcome.) These latter courses are often taken by honors students who enter the university with two semesters of advanced placement credit for calculus.

#### The Honors Analysis Sequence

The primary introductory sequence of mathematics courses for freshman who have a special talent amd advanced background in mathematics consists of the honors analysis sequence Math 340 and Math 341. These courses will cover the standard material of Multi-valued Calculus, Linear Algebra and Ordinary Differential Equations at a more advanced level. The department continually strives to identify and recruit talented freshmen into these courses. Any student with an interest in these courses should contact the Honors Committee of the Department of Mathematics.

#### Freshman Honors Seminars

There are freshman honors courses in mathematics offered through the University Honors Program which are designed to expose the general audience to modern interesting ideas in Mathematics. Seminars that have been offered recently or are being contemplated include: Symmetry; Chaos; Cryptography; Knots; Philosophy of Mathematics. For more information see the University Honors Program page.

### The Departmental Honors Program in Mathematics

The upper level Departmental Honors Program in Mathematics is open to any student who meets the admissions requirements detailed below. Students who enter the Departmental Honors Program are not required to complete the lower level program leading to a University Honors Citation, nor must they major in mathematics. The department envisions a program populated by about fifteen of the top mathematics students, together with some outstanding students from engineering, physics, and related disciplines. Good students, regardless of their majors, can benefit from a closer association with faculty. They can also benefit from belonging to a group committed to similar intellectual pursuits. The analytic and critical skills that students learn in this program will be useful whether they continue in academics or take positions in government or industry.

#### Admission

In order to be admitted to the Departmental Honors Program in Mathematics, a student is expected to have completed either Math 410 or Math 341 with a grade of B or better. In addition, the student must have an overall GPA of at least 3.0. A student who is interested in the Departmental Honors Program in Mathematics should contact the people noted above, usually in the sophomore or junior year. A student who is interested in the program should meet with a member of the Honors Committee to work out a realistic plan for meeting the requirements detailed below.

#### Good Standing

In order to remain a member in good standing of the Departmental Honors Program in Mathematics, a student must maintain a GPA of 3.3 in his or her upper-division mathematics courses. In accordance with University Honors Program requirements, the student must maintain an overall GPA of 3.0. Finally, the student must continue to make progress toward completing the program requirements.

#### Program Requirements

The Departmental Honors Program in Mathematics requires a minimum of 12 credit hours of honors coursework. The program is available in a thesis option and a non-thesis option. The options have a common requirement for breadth in the study in mathematics. All honors students are expected to take advanced undergraduate courses in at least two different areas of mathematics. In these courses, students will study the fundamental ideas of modern mathematics. In addition, each option has a depth requirement. The options differ primarily in the method used to ensure that the student has achieved a deep understanding of one area of mathematics.

#### Honors Mathematics Courses

Any course in the following list may be applied toward the requirements of the Honors Program in Mathematics: MATH 403, MATH 404, MATH 405, MATH 414, MATH 432, MATH 436, MATH 446, AMSC 472, STAT 410 or STAT 420. From time to time, the department may offer H-versions of other upper level courses for honors credit. Finally, any graduate course (600-level or above) in Mathematics (MATH), Applied Mathematics (AMSC), or Statistics (STAT) may be substituted for courses on this list.

#### The Thesis Option

The breadth requirement for the thesis option of the Honors Program in Mathematics will be satisfied by taking two courses from among those listed above. The depth requirement will be satisfied by six credit-hours of MATH 498 (Selected Topics in Mathematics). The first three credits of MATH 498 must be used for a reading course during which the student develops a thesis topic. This requirement may be modified, at the discretion of the Honors Committee, for a student who can demonstrate equivalent independent study (such as participation in a Research Experience for Undergraduates). The second three credits of MATH 498 must be used to write an honors thesis. In order to receive the citation for Honors in Mathematics, the student must make a successful oral defense of the thesis.

#### The Non-Thesis Option

With the approval of the Honors Committee, honors students may choose not to write a thesis. The oral defense of the thesis is replaced by a two-hour written comprehensive examination. Students choosing the non-thesis option satisfy the breadth requirement by taking two courses from those listed above. The depth requirement will be satisfied by taking two additional courses. One of the additional courses must be a graduate course (600-level or above). The other course must be

- a reading course (three credit-hours of MATH 498), or
- a course listed above.