Bilkent University

The double major program in mathematics is an option for exceptional undergraduate students enrolled in an undergraduate program to pursue a second bachelor's degree from the Mathematics Department to prepare them for interdisciplinary research. Students are closely supervised and are responsible for all courses in the mathematics undergraduate curriculum except common or equivalent courses with their host undergraduate programs.

Admission Requirements: Students with a cumulative grade point average of 3.30/4.00 and higher can start after completing two or three semesters in their host undergraduate programs.

Degree Requirements: Students must have a cumulative grade point average of 3.00/4.00 and higher in their host undergraduate programs while continuing in the double major mathematics program and finishing it within ten semesters after enrolling in their host undergraduate programs.

The minor program in mathematics is designed to give the students a short view of what constitutes modern mathematics beyond the more computational Calculus courses. The mathematics courses taken by students in other disciplines are usually geared towards using certain methods. However, one might also want to understand the reasons, mechanisms, and the axiomatic structure underlying the results. For this, one must also learn the proofs of mathematical theorems and obtain from them further mathematical results. This is what is generally considered doing mathematics.

In the minor program, students take 4 required courses, 2 from each of mathematics' two classical well-established areas, algebra and analysis. They form a well-balanced introduction to modern mathematics. They are also essential for an understanding of more advanced courses in these and other areas, two of which should be taken as electives. A good selection of electives would include courses in other areas as well so that students would have an idea of some of the newer developments in modern mathematics. The purpose is not to specialize in a narrow area, but rather to broaden one's understanding.

Prerequisite Courses:

• MATH 102 Calculus II
• MATH 106 Introduction to Calculus II
• MATH 114 Multi Variable Calculus
• MATH 116 Intermediate Calculus III

The aim of the program is to develop students into mathematicians who can pursue original and creative research. The program emphasizes research in pure and applied mathematics. At present, research in the graduate program is focused on algebra, algebraic number theory, algebraic geometry, algebraic topology, analytic number theory, complex analysis, functional analysis, non-linear differential equations and general relativity.

Degree Requirements: In addition to at least 21 credit units of course work, the M.S. degree candidate must prepare and successfully defend a thesis. Expected duration to complete the M.S. program is four semesters; the maximum duration is six semesters.

The descriptions provided here for different elective course groups are only for guidance. The complete list of courses in each elective group are given in the electronic registration system.

Graduate Elective Courses: All 5XX or higher level courses with at least 3 credits offered by Graduate School of Engineering and Science. Graduate School of Engineering and Science comprises graduate programs of the departments of Computer Engineering, Electrical and Electronics Engineering, Industrial Engineering, Mechanical Engineering, Chemistry, Mathematics, Molecular Biology and Genetics, Physics, Architecture, and the interdisciplinary graduate programs Material Science and Nanotechnology, and Neuroscience.

Degree Requirements:21 credit units of course work beyond the M.S. level or 42 credits of course work beyond the B.S. level is required. Ph.D. candidates must pass a qualifying exam and then must prepare a thesis work proposal. Preparing and defending a dissertation based on original research is the essence of the program. A paper based on the candidate's thesis must be accepted or published in a reputable journal before the dissertation can be defended. The expected duration to complete the Ph.D. program is eight semesters for students who enter the program after an M.S. degree, and ten semesters for those who enter after a B.S. degree. The maximum durations are twelve and fourteen semesters, respectively.

The descriptions provided here for different elective course groups are only for guidance. The complete list of courses in each elective group are given in the electronic registration system.

Graduate Elective Courses: All 5XX or higher level courses with at least 3 credits offered by Graduate School of Engineering and Science. Graduate School of Engineering and Science comprises graduate programs of the departments of Computer Engineering, Electrical and Electronics Engineering, Industrial Engineering, Mechanical Engineering, Chemistry, Mathematics, Molecular Biology and Genetics, Physics, Architecture, and the interdisciplinary graduate programs Material Science and Nanotechnology, and Neuroscience.