Program

1st Semester
Crdts ECTS
Phys 101 ** Physics I 4
AE 111*/HSS/MLE* Adv. Eng./HSS/MLE 3
Unrest. Elect1 3
Math 111
Introduction to Mathematical Structures
Propositional logic, truth tables, equivalences, quantifiers, rules of inference, proof methods, sets, power sets, functions, sequences, countability, cardinality, divisibility, modular arithmetic, primes, mathematical induction, strong induction and wellordering principle, recursive definitions, axiomatic systems, Euclid's postulates and non-Euclidean geometries.
Prerequisite
None
4 8
Math 131
Calculus of a single variable
Sequences, limits and continuity, differentiation and its applications, integration and its applications, fundamental theorem of calculus, transcendental functions, improper integrals.
Prerequisite
None
4 8
Total:
18
Total:
16
2nd Semester
Crdts ECTS
PHYS** 102 Physics II 4
AE 112*/HSS/MLE* Adv. Eng./HSS/MLE 3
Unrest. Elect2 3
Math 132
Calculus of several variables
Vectors and geometry in space, vector-valued functions and motion in space, functions of several variables, partial derivatives, multiple integrals, vector fields.
Prerequisite
Math 131
4 8
Math 162
Discrete Mathematics
Counting, the pigeonhole principle, permutations, combinations, binomial coefficients, generalized permutations and combinations, discrete probability, linear recurrence relations, generating functions, inclusion-exclusion, relations, closures of relations, equivalence relations, construction of integers and rationals, partial orderings, graphs.
Prerequisite
None
4 8
Total:
18
Total:
16
3rd Semester
Crdts ECTS
Math 231
Advanced Calculus I
Sequences and functions, compact sets, continuity, uniform continuity, limits of functions, discontinuities, differentiation, derivatives for functions of several variables, differentiation of composite functions, Taylor's Theorem, definite integrals, substitution in multiple integrals, improper integrals.
Prerequisite
Math 132
4 8
PHYS** 201 Physics III 4
CMPE 150 Introduction to Computing 3
TK 221 Turkish I 2
Math 221
Linear Algebra
Vector spaces, bases, linear transformations, matrices, subspaces, systems of linear equations, echelon and reduced echelon forms, dimension, fundamental subspaces, rank, change of coordinates, determinants, cofactor expansion, minors, eigenvalues, eigenvectors, diagonalization, inner product spaces, orthogonality, Gram-Schmidt orthogonalization process, adjoint, unitary and orthogonal transformations, dual spaces.
Prerequisite
Math 111
4 8
Total:
17
Total:
16
4th Semester
Crdts ECTS
Math 222
Group Theory
Groups, subgroups, cyclic groups, generating sets, permutations, orbits, cycles, alternating groups, cosets, Lagrange's Theorem, direct products, finite abelian groups, homomorphisms, normal subgroups, factor groups, simple groups, group actions, isomorphism theorems, Sylow's theorems.
Prerequisite
Math 111
4 8
HSS/MLE* HSS/MLE 3
Math 234
Advanced Calculus II
Infinite series, conditionally convergent series, double series, uniform convergence, series and sequences of functions, power series, improper integrals with parameters, differentiation of transformations, linear functions, differentials and inverses of transformations, inverse and implicit function theorems.
Prerequisite
Math 231
4 8
Math 202
Differential Equations
First-order differential equations, linear equations, homogeneous and non-homogeneous, series solutions, the Laplace transform, systems of first-order linear equations, boundary value problems, Fourier series.
Prerequisite
  (Math 101 or Math 131) and (Math 201 or Math 221)
4 7
TK 222 Turkish II 2
Total:
17
Total:
23
5th Semester
Crdts ECTS
HSS HSS Elect. 3
HTR 33 Hist. of Turk. Rep. I 2
Math 323
Rings, Fields and Galois Theory
Rings, integral domains, field of fractions, polynomials, factorization, ideals, factor rings, homomorphisms, prime and maximal ideals, extension fields, algebraic extensions, finite fields, unique factorization domains, Euclidean domains, Gaussian integers, field automorphisms, splitting fields, Galois theory, insolvability of the quintic equations.
Prerequisite
 Math 222 or consent of the instructor
4 8
Unrest. Elective 3
Math 331
Metric Spaces
Topology, density, separability, convergence, compactness, connectedness, continuity, open and closed maps, equicontinuity, Arzela-Ascoli theorem, contractions and fixed point theorems, completeness, Cantor's theorem, Baire category theorem, completion.
Prerequisite
 Math 231
4 8
Total:
16
Total:
16
6th Semester
Crdts ECTS
HSS HSS Elect. 3
Math 338
Complex Analysis I
Complex numbers, exponential forms, roots of complex numbers, functions of a complex variable, limits, continuity, derivatives, Cauchy-Reimann Equations, polar coordinates, analytic functions, reflection principle, exponential and logarithmic functions, branches, trigonometric and hyperbolic functions, linear transformations, definite integrals, contour integrals, branch cuts, Cauchy-Goursat theorem, simply connected domains, Cauchy integral formula, Liouville's Theorem, maximum modulus principle, Taylor and Laurent series, residues and poles, Cauchy's residue theorem, residue at infinity.
Prerequisite
Math 132
4 8
HTR Hist. of Turk. Rep. II 2
Math Elect. 3
Math Elect. 3
Science Elect. 3
Total:
18
Total:
8
7th Semester
Crdts
Unrest. Elect. 3
Unrest. Elect. 3
Science Elect. 3
Math Math. Elective 3
Math Math. Elective 3
Total:
15
8th Semester
Crdts
Math Elect. 3
Math Elect. 3
Math Elect. 3
Unrest. Elect. 3
HSS HSS Elect. 3
Total:
15