Program
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 nonEuclidean 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 
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, vectorvalued 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, inclusionexclusion, relations, closures of relations, equivalence relations, construction of integers and rationals, partial orderings, graphs.
Prerequisite None

4  8 
Total: 18 
Total: 16 
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, GramSchmidt orthogonalization process, adjoint, unitary and orthogonal transformations, dual spaces.
Prerequisite Math 111

4  8 
Total: 17 
Total: 16 
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
Firstorder differential equations, linear equations, homogeneous and nonhomogeneous, series solutions, the Laplace transform, systems of firstorder 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 
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, ArzelaAscoli theorem, contractions and fixed point theorems, completeness, Cantor's theorem, Baire category theorem, completion.
Prerequisite Math 231

4  8 
Total: 16 
Total: 16 
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, CauchyReimann Equations, polar coordinates, analytic functions, reflection principle, exponential and logarithmic functions, branches, trigonometric and hyperbolic functions, linear transformations, definite integrals, contour integrals, branch cuts, CauchyGoursat 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 
Crdts  

Unrest. Elect.  3  
Unrest. Elect.  3  
Science Elect.  3  
Math  Math. Elective  3 
Math  Math. Elective  3 
Total: 15 
Crdts  

Math  Elect.  3 
Math  Elect.  3 
Math  Elect.  3 
Unrest. Elect.  3  
HSS  HSS Elect.  3 
Total: 15 