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.

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.

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.

Review of elementary probability; multivariate random variables and their functions; conditional distribution and expectation; generating functions and transforms; order statistics; multivariate normal distribution; types of convergence; laws of large numbers; central limit theorem.

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.

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.

Hands-on introductory class for students to learn proper treatment and use of audiovisual tools and equipment. Learning objectives: correctly operating camera, photography, lighting and sound equipment with in-class exercises and demonstrations. Access to equipment checkout from MAVA CAGE upon successful completion.

Hands-on introductory class for students to learn proper treatment and use of audiovisual tools and equipment. Learning objectives: correctly operating camera, photography, lighting and sound equipment with in-class exercises and demonstrations. Access to equipment checkout from MAVA CAGE upon successful completion.

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.

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.

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.

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.

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.

Fundamentals of digital video camera skills such as framing and exposure as well as guidelines of non-linear digital editing, such as montage, parallel editing, transitions, editing to sound and exporting for various platforms. Multiple hands on exercises with camera and final short video production.

Fundamentals of digital video camera skills such as framing and exposure as well as guidelines of non-linear digital editing, such as montage, parallel editing, transitions, editing to sound and exporting for various platforms. Multiple hands on exercises with camera and final short video production.

Fundamentals of digital video camera skills such as framing and exposure as well as guidelines of non-linear digital editing, such as montage, parallel editing, transitions, editing to sound and exporting for various platforms. Multiple hands on exercises with camera and final short video production.

Fundamentals of digital video camera skills such as framing and exposure as well as guidelines of non-linear digital editing, such as montage, parallel editing, transitions, editing to sound and exporting for various platforms. Multiple hands on exercises with camera and final short video production.

Brief history of photography from 1839 to the present. Fundamentals of photography from conventional to digital. Methods of image capturing by using correct exposure, lighting and composition techniques. Basic photographic variables such as; aperture, shutter speed and ISO. Introduction to the photographic equipment, materials, processes and philosophy. Ways of seeing are discussed throughout the course.