MATH 528 Analytic Number Theory (4+0+0) 4 ECTS 10 Method of descent, unique factorization, basic algebraic number theory, diophantine equations, elliptic equations, p-adic numbers, Riemann zeta function, elliptic curves, modular forms, zeta and L-functions, ABC-conjecture, heights, class numbers for quadratic fields, a sketch of Wiles' proof. Valuations of a field, local fields, ramification index and degree, places of global fields, theory of divisors, ideal theory, adeles and ideles, Minkowski's theory, extensions of global fields, the Artin symbol. MATH 525 Algebraic Number Theory (4+0+0) 4 ECTS 10 Modules, direct sums, free modules, sums and products, exact sequences, morphisms, Hom and tensor functors, duality, projective, injective and flat modules, simplicity and semisimplicity, density theorem, Wedderburn-Artin theorem, finitely generated modules over a principal ideal domain, basis theorem for finite abelian groups. Galois theory, solvability of equations by radicals, separable extensions, normal basis theorem, norm and trace, cyclic and cyclotomic extensions, Kummer extensions. Polynomial and power series rings, Gauss's lemma, PID and UFD, localization and local rings, chain conditions, Jacobson radical. ** PhD students who took any of MATH 522, 532, 533 courses during their MSc studies must take other MATH courses to fulfill the corresponding credit load.įree groups, group actions, group with operators, Sylow theorems, Jordan-Hölder theorem, nilpotent and solvable groups. thesis carried out according to the regulations of the Institute. program in Mathematics is composed of 21 or more credits of course work planned under the supervision of an advisor and Ph.D. None of these courses can be a reading course nor a 400 level course. Students must take a two course sequence chosen from one topic among the list above from a) to f) such as MATH 531-532, MATH 521-522 etc. Two of these courses can be chosen from 400 level courses approved by the department. Students are expected to take at least one course from four of the topics chosen from the list below. There is a breadth requirement and a depth requirement to fulfill as follows. The elective courses are chosen from the graduate courses offered by the Program or the Institute, and are subject to the approval of the student's advisor. The total number of credits includes 9 credits of required courses. program in Mathematics comprises 22 credits or more credits of course work (minimum 7 courses), graduate seminar and a Master's thesis. ** “Elective Course”s must be either MATH courses or courses from PHYS, ECON, IE, EE, CMPE, subject to the approval of Mathematics Department. * ECTS and credit hours specified are the minimum required values. MASTER OF SCIENCE PROGRAM IN MATHEMATICS First Semester Professors : Talin Budak, Olcay Coşkun, Sadık Değer, Ahmet Feyzioğlu, Burak Gürel, Nilgün Işık, İlhan İkeda, Ferit Öztürk, Betül Tanbay, Yalçın YıldırımĪssociate Professor : Müge Taşkın Aydın, Alp Bassa, Özlem Beyarslan, Arzu Boysal, Craig Charles Van Coevering, Fatih Ecevit, Ayhan Günaydın, Çağrı Karakurt, Ekin Özman Associate Department Heads: Özlem Beyarslan, Çağrı Karakurt
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