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.

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.

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.

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.

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.

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

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.

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

Quadratic Reciprocity, Quadratic Forms, Gauss' Composition Law and Genus Theory, Cubic and Biquadratic Reciprocity, Number Fields, Hilbert Class Field, Orders in Imaginary Quadratic Fields, The Class Number, Class Field Theory and Cebatorev Density Theorem, Norms and Ideles, Elliptic Functions and Theory of Complex Multiplication. Divisibility, Primes, Congruences, Prime Modules and Primitive Roots, Groups, a review of Rings and Fields, Arithmetic Functions, Diophantine Problems, Farey Fractions ad Geometry of Numbers, Continued Fractions, Multiplicative Number Theory and Dirichlet Series.

Finite-dimensional real and complex vector spaces, bases of a vector space, linear maps, dual spaces, quadratic forms, self-adjoint and unitary transformations, eigenvalue problem, canonical form of a linear transformation, tensors, and applications.

Fundamental concepts in graph theory; trees; matchings in graphs; connectivity and planarity; the colorings of graphs and diagraphs; Hamilton cycles; matroids.

Linear algebra: Vector and inner product spaces, linear operators, eigenvalue problems; Vector calculus: Review of differential and integral calculus, divergence and Stokes' theorems. Ordinary differential equations: Linear equations, Sturm-Liouville theory and orthogonal functions, system of linear equations; Methods of mathematics for science and engineering students.

Free groups, group actions, group with operators, Sylow theorems, Jordan-Hölder theorem, nilpotent and solvable groups. Polynomial and power series rings, Gauss?s lemma, PID and UFD, localization and local rings, chain conditions, Jacobson radical.

Lebesgue measure and Lebesgue integration on Rn, general measure and integration, decomposition of measures, Radon-Nikodym theorem, extension of measures, Fubini's theorem.

Matchings, edge colorings and vertex colorings of graphs. Connectivity, spanning trees, and disjoint paths in graphs. Cycles in graphs, embeddings. Planar graphs, directed graphs. Ramsey Theory, matroids, random graphs.

Introductory overview of contemporary mass media systems and an examination of the various factors -historical, economic, political, and cultural- that have shaped their development. Components of culture industries such as the Internet, radio, television, cinema, newspapers and journalism, advertising, and public relations. Investigation of theories and research related to media effects.

Foundations of visual language. Introduction to the principles and elements of design. Control of line, shape, space, texture, color, composition and sequence to convey a message. Strategic exercises to channel design to an interdisciplinary level. Studio practice, theory, critique, exhibition.

Foundations of visual language. Introduction to the principles and elements of design. Control of line, shape, space, texture, color, composition and sequence to convey a message. Strategic exercises to channel design to an interdisciplinary level. Studio practice, theory, critique, exhibition.

Studio practice in classical and contemporary drawing. Learning to look and sketch. Convey the illusion of light, depth and texture on paper. Building skills for composition, expression and abstraction. Experimenting with various materials.

Introduction to visual communication design in an interactive media environment: visualizing a catchword, visualizing actions referring to interface design, making a visual design by creating clever remark between object and a concept, creating interest on a point using non-textual visual metaphors, visualizing the relation between linear and non-linear structures.

Introduction to visual communication design in an interactive media environment: visualizing a catchword, visualizing actions referring to interface design, making a visual design by creating clever remark between object and a concept, creating interest on a point using non-textual visual metaphors, visualizing the relation between linear and non-linear structures.

Intensive writing practice for a variety of media formats. Different conventions of writing for print media, radio, and television. Class structure, assignments, and timed writing exercises are designed to simulate a working media environment.

Graphic design and image editing skills through the use of creative software. Use of design principles and techniques as well as visual and graphic design software.