General Elective

SCIE 105 / MATERIALS AND SOCIETY**Sınıf:** **Credit:** 3**Precondition:**

Modern materials such as plastics, transistors, alloys, etc. resulted from ingenious scientific breakthroughs. This course will introduce the basic principles, in a historical perspective, that lead to breakthroughs in materials science and technology, and will discuss the impact of modern materials on our society and civilization.

SCIE 107 / ENERGY AND ENVIRONMENT**Sınıf:** **Credit:** 3**Precondition:**

Energy production from non-renewable sources such as fossil fuels, oil and natural gas. Comparative discussion of the present and future (renewable) alternative energy resources (solar, geothermal, wind, biomass, hydrogen) and technologies for their commercialization. Environmental consequences, greenhouse effect and global warming, destruction of ozone layer and water pollution. Recycling and sustainable development.

SCIE 108 / WORLD OF CHEMISTRY**Sınıf:** **Credit:** 3**Precondition:**

Chemical facts; matter and energy; nucleus, atom and periodic law; chemical bonding; chemical reactions; polymers. The impact of scientific methods and chemical discoveries on our standard of living. Understanding contemporary issues related to atmosphere, hydrosphere, air and water pollution; global warming and renewable energy; recycling.

MATH 100 / ELEMENTS OF FINITE MATHEMATICS AND CALCULUS**Sınıf:** **Credit:** 3**Precondition:**

Tools for quantitative reasoning and basic college level mathematical concepts for social science students. Mathematics of finance, linear equations and matrices, probability, game theory, derivative, integral, special functions: log, exp, trigonometric and function sketching techniques.

MATH 101 / FINITE MATHEMATICS**Sınıf:** **Credit:** 3**Precondition:**

Linear algebra and matrix theory; mathematics of finance; counting and the fundamentals of probability theory; game theory.

MATH 102 / CALCULUS**Sınıf:** **Credit:** 3**Precondition:**

Limit of a function; Continuous functions and their properties; Derivative andapplications; Extreme values; Indefinite integral; Riemann integral and fundamental theorem of calculus; Logarithmic and exponential functions; L?Hospital?s rule; Sequence and series of numbers; Power series and their properties;

MATH 103 / INTRODUCTION TO ABSTRACT MATHEMATICS**Sınıf:** **Credit:** 3**Precondition:**

Sets; logic and implications; proof techniques with examples; mathematical induction and well-ordering; equivalence relations; functions; cardinality; countable and uncountable sets.

MATH 104 / DISCRETE MATHEMATICS**Sınıf:** **Credit:** 3**Precondition:**

Counting problems; combinatorial methods; integers, divisibility and primes; graphs and trees; combinatorics in geometry; introduction to complexity and cryptography.

MATH 106 / CALCULUS I**Sınıf:** **Credit:** 3**Precondition:**

Limits and continuity; derivative and properties of differentiable functions; mean value theorems, Taylor's formula, extreme values; indefinite integral and integral rules; Riemann integral and fundamental theorem of calculus; L'Hospital's rule; improper integrals.

MATH 107 / INTRODUCTION TO LINEAR ALGEBRA**Sınıf:** **Credit:** 3**Precondition:**

Vectors; matrices and systems of linear equations; vector spaces; linear maps; orthogonality; algebra of complex numbers; eigenvalue problems.

MATH 201 / STATISTICS**Sınıf:** **Credit:** 3**Precondition:** (MATH.101 or MATH.102 or MATH.106) or consent of the instructor

Descriptive statistics; measures of association, correlation, simple regression; probability theory, conditional probability, independence; random variables and probability distributions; sampling distributions; estimation; inference (confidence intervals and hypothesis testing). Topics are supported by computer applications.

MATH 202 / STATISTICS FOR SOCIAL SCIENCES**Sınıf:** **Credit:** 3**Precondition:**

A course in basic concepts and tools of statistics for students who will study social and Behavioral sciences. Topics to be covered are representation of quantitative information in social sciences, forms of numerical data, creating and interpreting graphical and tabular summaries of data, descriptive statistics, estimation of population parameters, confidence intervals, basic hypothesis testing, t-statistics, chi-squared tests and analysis of variance.

MATH 203 / MULTIVARIABLE CALCULUS**Sınıf:** **Credit:** 3**Precondition:** MATH. 106 or consent of the instructor

Functions of several variables; partial differentiation; directional derivatives; exact differentials; multiple integrals and their applications; vector analysis; line and surface integrals; Green?s, Divergence and Stoke?s theorems.

MATH 204 / DIFFERENTIAL EQUATIONS**Sınıf:** **Credit:** 3**Precondition:** MATH. 107 or consent of the instructor

First order differential equations. Second order linear equations. Series solutions of ODE?s. The Laplace transform and applications. Systems of first order linear equations. Nonlinear equations and systems:existence, uniqueness and stability of solutions. Fourier series and partial differential equations.

MATH 205 / ALGEBRA I**Sınıf:** **Credit:** 3**Precondition:** MATH. 103 or consent of the instructor

Natural numbers; modular arithmetic; introduction to groups; cyclic and permutation groups; homomorphisms and isomorphisms; normal; factor, simple and free groups; introduction to rings, integral domains, and fields; factor rings and ideals; extension fields; outline of Galois theory.

MATH 206 / ALGEBRA II**Sınıf:** **Credit:** 3**Precondition:** MATH. 205 or consent of the instructor

Natural numbers; modular arithmetic; introduction to groups; cyclic and permutation groups; homomorphisms and isomorphisms; normal; factor, simple and free groups; introduction to rings, integral domains, and fields; factor rings and ideals; extension fields; outline of Galois theory.

MATH 207 / COMMUTATIVE ALGEBRA**Sınıf:** **Credit:** 3**Precondition:** MATH 205 or Consent of the Instructor

Review of Unique Factorization Domains and Principal IdeaI Domains, Maximal and prime ideals, Nilradical, Local rings, Modules, Cayley-Hamilton theorem, Nakayama's lemma, Exact and split exact sequences, Noetherian rings, Noetherian modules, Hilbert basis theorem, Integral extensions, Integral closure, Non-singularity, Normal rings, Noether normalization, Hilbert nullstellensatz, Spec(A), Localization, Support of a module and the associated primes, Discrete valuation rings, Trace and separability, Completion, Artin-Rees Lemma, An overview of further topics: Dimension theory, Regular rings, Connections with geometric notions.

MATH 208 / ADVANCED CALCULUS**Sınıf:** **Credit:** 3**Precondition:** MATH. 103 and MATH 107 or consent of the instructor

Completeness axiom for real numbers; convergent sequences; compactness; continuous functions; differentiation; linear and topological structure of Euclidean spaces; limit, compactness and connectedness in a Euclidean space; continuity and differentiation of functions of several variables; inverse and implicit function theorems.

MATH 211 / STATISTICS FOR SCIENCES**Sınıf:** **Credit:** 3**Precondition:** MATH. 106 or consent of the instructor

Descriptive statistics; Probability; Random variables; Special distributions; Estimation; Hypothesis testing; Normal distribution; Two-Sample Inference; Regression.

MATH 301 / REAL ANALYSIS I**Sınıf:** **Credit:** 3**Precondition:** MATH. 208 or consent of the instructor

Metric spaces and their topology; continuity, compactness and connectedness in a metric space; completion of a metric space; differentiation and Riemann integration; sequences and series of functions; uniform convergence; Ascoli-Arzela theorem; Stone-Weierstrass theorem; Banach fixed-point theorem and its applications.

MATH 302 / ELEMENTS OF FUNCTIONAL ANALYSIS**Sınıf:** **Credit:** 3**Precondition:** MATH. 301 and MATH 320 or consent of the instructor

Normed and Banach spaces; linear operators; duality; inner product and Hilbert spaces; Riesz representation theorem; Hahn-Banach theorem; uniform boundedness principle; open mapping theorem; strong, weak and weak* convergence.

MATH 303 / APPLIED MATHEMATICS**Sınıf:** **Credit:** 3**Precondition:** MATH. 204 or consent of the instructor

Review of vector calculus; Fourier series and Fourier transform; Calculus of functions of a complex variable.

MATH 305 / NUMERICAL ANALYSIS**Sınıf:** **Credit:** 3**Precondition:** MATH. 107 or consent of the instructor

Fixed point iteration and Newton’s method for nonlinear equations, direct solution of linear systems and the least squares problem, symmetric positive definite and banded matrices, systems of nonlinear equations, the QR algorithm for the symmetric eigenvalue problem, Lagrange and Hermite polynomial interpolation, polynomial approximation in the infinity norm and the Chebyshev polynomials, approximation in the 2 norm and the orthogonal polynomials, numerical differentiation, Newton-Cotes and Gaussian quadratures for numerical integration.

MATH 309 / PARTIAL DIFFERENTIAL EQUATIONS**Sınıf:** **Credit:** 3**Precondition:** MATH. 204 or consent of the instructor

Classification of second order partial equations; well posed problems; method of separation of variables and applications; wave equation: D?Alambert?s solution; Laplace equation: Poisson?s formula, maximum principle, boundary value and eigenvalue problems; heat equation: Cauchy problem, maximum principle.