Academic Program
First Year
1st Semester
Course Code
Course Name
Credit
ECTS
AE 101/111*/HSS/MLE*
Adv. Eng./HSS/MLE
3
5
Unrest. Elect1
3
5
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. PrerequisiteNone
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. PrerequisiteNone
4
8
Phys 101 **
Physics I
Sequences, limits and continuity, differentiation and its applications, integration and its applications, fundamental theorem of calculus, transcendental functions, improper integrals. PrerequisiteNone
4
8
2nd Semester
Course Code
Course Name
Credit
ECTS
PHYS** 102
Physics II
4
8
AE 102/112*/HSS/MLE*
Adv. Eng./HSS/MLE
3
4
Unrest. Elect2
3
5
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. PrerequisiteMath 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. PrerequisiteNone
4
8
Second Year
1st Semester
Course Code
Course Name
Credit
ECTS
PHYS** 201
Physics III
4
6
CMPE 150
Introduction to Computing
3
5
TK 221
Turkish I
2
3
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. PrerequisiteMath 111
4
8
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. PrerequisiteMath 132
4
8
2nd Semester
Course Code
Course Name
Credit
ECTS
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
3
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. PrerequisiteMath 111
4
8
HSS/MLE*
HSS/MLE
3
5
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. PrerequisiteMath 231
4
8
Third Year
1st Semester
Course Code
Course Name
Credit
ECTS
HSS
HSS Elect.
3
5
HTR 33
Hist. of Turk. Rep. I
2
3
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
5
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
0
0
2nd Semester
Course Code
Course Name
Credit
ECTS
Math
Elect.
3
6
Science Elect.
3
5
HSS
HSS Elect.
3
5
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. PrerequisiteMath 132
4
8
HTR
Hist. of Turk. Rep. II
2
3
Math
Elect.
3
6
Fourth Year
1st Semester
Course Code
Course Name
Credit
ECTS
Math
Math. Elective
3
6
Math
Math. Elective
3
6
Unrest. Elect.
3
5
Unrest. Elect.
3
5
Science Elect.
3
5
2nd Semester
Course Code
Course Name
Credit
ECTS
Math
Elect.
3
6
Math
Elect.
3
6
Math
Elect.
3
6
Unrest. Elect.
3
5
HSS
HSS Elect.
3
5