# Courses

### Mathematics

**MAT 100 Introductory Mathematics **This course stresses elementary mathematics and basic quantitative knowledge at the pre-calculus level. Students understand and work effectively with real numbers, algebraic expressions, polynomials, equations, and functions. Students learn how to present a real-life problem in mathematical terms and model social and scientific phenomena. The course gives a broad-based mathematical knowledge to build upon in quantitative reasoning courses as well as applied and specialized courses in Business, Social and Natural Sciences. The requirement in Introductory Mathematics may also be satisfied upon admission by designated scores on the SAT exam or a placement examination, during the first semester at AUBG. Cr. 3 (6 ECTS Cr.). Offered every semester.

**MAT 102 Finite Mathematics **The topics covered provide students with basic knowledge and primary skills from several important mathematical areas, including Linear Algebra (linear systems and matrices), Linear Programming, Logic (truth sets and Venn diagrams), Probability theory, Counting Principles and applications to Probability. The study of Markov chains at the end becomes an attractive application of all ideas and technique considered earlier. Gen. Ed: Quantitative Reasoning. Prerequisite: MAT 100 or equivalent. Cr. 3 (6 ECTS Cr.). Offered every semester.

**MAT 103 Calculus I **The course develops (primarily on technical and intuitive level with only minor references to deeper points like completeness) the initial notions and skills of analysis in the real line like: limits and continuity; derivatives (the problem of "rates of change") and curve sketching; integrals (the "area" or "accumulation" problem) and techniques of integration, with the fundamental theorem of calculus linking the two main problems. Gen. Ed: Quantitative Reasoning. Prerequisite: MAT 100 or equivalent. Cr. 3 (6 ECTS Cr.). Offered every semester.

**MAT 104 Calculus II**The course aims to develop and extend the methods and technique of Calculus I. Topics discussed include: inverse functions - logarithmic and exponential functions, inverse trigonometric functions, L'Hospital's rule and applications, integration techniques, improper integrals, parametric curves and polar coordinates, infinite sequences and series, power series, representation of functions as sums of power series, Taylor and Maclaurin series and polynomials. Gen. Ed: Quantitative Reasoning. Prerequisite: MAT 103 or equivalent. Cr. 3 (6 ECTS Cr.). Offered in the Spring.

**MAT 105 Elementary Linear Algebra and Analytical Geometry **The course offers a general view to some important ideas and techniques in the field. Starting with a discussion of systems of linear equations (the natural source of the subject) the important technique of matrices, matrix operations and determinants is considered. An illustration of the general concepts in the plane and space geometry helps the students to cultivate their intuition and interpretative skills in the area. An elementary introduction to General vector spaces, Linear Transformations and Eigenvalue problems initiates the students into this powerful technique. Gen. Ed: Quantitative Reasoning. Prerequisite: MAT 100 or equivalent. Cr. 3 (6 ECTS Cr.). Offered every semester.

**MAT 201 Mathematical Statistics**** **The course offers a general view to some important ideas and techniques in Probability Theory and Mathematical Statistics, including: random variables and probability distribution functions, expectations, moment generating functions, limit theorems, sampling distributions, principle of estimation and hypothesis testing. Prerequisites: MAT 104, STA 105. Cr. 3 (6 ECTS Cr.). Offered in the Spring.

**MAT 205 Introduction to Abstract Algebra **The course offers an introduction to the basic algebraic structures, like groups, rings, integral domains and fields. Fundamental structure theorems for factorization are discussed. Applications are discussed of general results to some specific, but very important objects, like symmetric groups, ring of integers, polynomial rings, and matrix rings. Also included are splitting fields and roots of a polynomial, polynomials with integer, rational, real, and complex coefficients. Prerequisite: MAT 105. Cr. 3 (6 ECTS Cr.). Offered in the Fall.

**MAT 212 Calculus III **The course extends techniques of calculus in two and three dimensions. Topics covered include vectors and geometry of space, quadratic surfaces, space curves, cylindrical and spherical coordinates. Also included are partial derivatives, and extreme value problems for functions of several variables, Lagrange multipliers, double and triple integrals, iterated integrals and applications. Prerequisites: MAT 103, MAT 104. Cr. 3 (6 ECTS Cr.). Offered in the Fall.

**MAT 213 Introduction to Differential Equations **The course introduces a variety of solution methods for ordinary differential equations: first order equations, second order equations (solution space, base of solutions, Wronskian), power series method, Laplace transform, system of linear equations. Prerequisite: MAT 103. Cr. 3 (6 ECTS Cr.). Offered irregularly.

**MAT 214 Numerical Analysis**

The course introduces the students to the basic concepts, and techniques in the field including: methods for solution of equations in one variable; polynomial approximation, spline approximation and interpolation, numerical differentiation and integration, initial value problems for ordinary differential equations. Prerequisites: MAT 104. Cr. 3 (6 ECTS Cr.). Offered irregularly.

**MAT 225 Advanced Linear Algebra**

The course offers an extended view to the basic concepts of general vector spaces, fundamental structure theorems for linear maps and eigenvalue technique. It covers spectral theorems for symmetric, Hermitian and unitary maps (and matrices) and application to quadratic and Hermitian forms. Triangulation and Jordan canonical form are discussed. Prerequisites: MAT 102 or MAT 105. Cr. 3 (6 ECTS Cr.). Offered in the Spring.

**MAT 305 Topics in Abstract Algebra**** **An advanced course with an emphasis on learning to understand, construct and present proofs. Requires an accompanying weekly seminar. The following topics are included: Groups and group action, Sylow theorems, the free group, generators and relations, the Todd-Coxeter algorithm; Ring theory, Hilbert's Nullstellensatz, unique factorization domains, Noetherian rings, modules, free modules, generators and relations, Hilbert basis theorem; the structure theorem for abelian groups; Fields, algebraic and transcendental elements, algebraically closed fields, The Fundamental Theorem of Algebra. As an application the course suggests either an introduction to Galois theory , or introduction to commutative and noncommutative Groebner basis. Prerequisites: MAT 105, MAT 205. Cr. 3 (6 ECTS Cr.). Offered irregularly.

**MAT 313 Calculus IV**The course extends techniques of calculus in two and three dimension: vector functions, scalar and vector fields, line and surface integrals, Green's theorem, Stocks' theorem, Divergence theorem and their applications. Prerequisites: MAT 105 and MAT 212. Cr. 3 (6 ECTS Cr.). Offered irregularly.

**MAT 314 Complex Analysis **An introduction to analytic functions of one complex variable, their basic properties and applications. The material includes complex numbers, connectedness in the complex plane, conformal mappings, holomorphic functions and Cauchy's integral formulas, Liouville's theorem; mean value property and maximum modulus principle; Taylor and Laurent expansions; analytic functions and analytic continuation principle; residue theorem and evaluation of integrals by the method of residues. Prerequisite: MAT 105, MAT 212. Cr. 3 (6 ECTS Cr.). Offered irregularly.

**MAT 315 Real Analysis **Analysis and Geometry are at the roots of such basic areas of mathematics as general topology, geometric topology, differential geometry, functional analysis, measure theory, probability theory, dynamical systems, differential equations, to name a few. The course introduces the student to set theory, general topology, metric spaces, measure theory, Lebesgue integration, function spaces. Though the basic structure of analysis was set in the 19th and beginning 20th century we will explore such up to date applications as analysis of fractals or applications to financial calculus through some of the projects. Prerequisites: MAT 104 and MAT 105. Cr. 3 (6 ECTS Cr.). Offered irregularly.

**MAT 491/492 Senior Thesis I and II **A senior thesis may be arranged by qualifying students with a faculty advisor for ambitious research programs that cover one or two semesters. Cr. 3 (6 ECTS Cr.). Offered every semester.

### Science

**SCI 111 Principles of Classical Physics **This course introduces some of the basic laws and principles of classical mechanics, thermodynamics, electricity and magnetism with an emphasis on how they can be used to explain important natural phenomena or technological developments. Discussion of important turning moments in the history of physics. In-class physics experiments are included. Gen. Ed: Scientific Investigation. Prerequisite: MAT 100 or equivalent. Cr. 3 (6 ECTS Cr.). Offered every semester.

**SCI 113 Physics - Theory and Experiment**

The course covers a selected set of topics including those fundamental to a classical understanding of the physical world as well as special relativity and modern physics. Emphasis is placed on in-class demonstrations and experiments. Laboratory exercises are included. Gen. Ed: Scientific Investigation. Prerequisite: MAT 100 or equivalent. Cr. 4 (8 ECTS Cr.). Offered every semester.

**SCI 130 Elementary Stellar Astronomy and Cosmology **Students are exposed to the basic aspects of scientific inquiry applied to studies of stars and the entire Universe. The first part of the course (roughly half semester) focuses on: structure of stars; star properties; energy sources, classes of stars and principles for classification; star birth, star life and star death; star corpses (white dwarfs, neutron stars and black holes). The second part of the course covers our Galaxy and other galaxies, active galaxies and quasars, Hubble law of expansion, standard Big Bang model, inflation theory and accelerated expansion. The required mathematical skills include high-school algebra, geometry and trigonometry. Gen. Ed: Scientific Investigation. Prerequisite: MAT 100. Cr. 3 (6 ECTS Cr.). Offered every semester.

**SCI 150 Principles of Biology **Biology touches our lives every day. Whether we are concerned for the health of our own body or the health of the planet, an understanding of the basic principles of biology is important. This course explores some of the fundamental concepts of modern biology. Topics covered may include: cell structure and processes, genetics, evolution, biodiversity, animal and plant form and function, and ecology. The interconnections within the natural world along with biology's relevance to everyday life will be highlighted during the semester. Biology is an extremely diverse and complex discipline and an introductory course can only explore a thin slice of this diversity and complexity. Although this is an introductory course, it will provide enough depth and rigor to help equip students to make scientifically informed evaluations of biological issues confronting contemporary society. Furthermore, it is hoped that after completing this course, students will have a greater appreciation of the wonders of the natural world. Gen. Ed.: Scientific Investigation. Cr. 3 (6 ECTS Cr.). Offered every semester.

**SCI 160 Introduction to Environmental Science **The course gives students a basic understanding of the scientific aspects of environmental issues, thus enabling them to more intelligently engage in current environmental debates. More specifically, this course explores the functions and services provided by healthy ecosystems and how human populations are impacting the natural world. The course discusses some of the major threats to the world's ecosystems (such as: overpopulation, pollution, biodiversity loss, climate change, and over-exploitation) from a scientific viewpoint. Students will learn how the scientific method is applied to the study of these problems as society seeks solutions. Gen. Ed.: Scientific Investigation. Cr. 3 (6 ECTS Cr.). Offered in the Fall.

### Statistics

**STA 105 Statistics**

This course is designed to give students the ability to interpret results that can be drawn from data. It serves the student's need in Business, Economics, and other Social Sciences to be able to make sense of results of studies and surveys. At the end of the course students will gain experience to communicate effectively using statistical ideas and concepts. Both descriptive and inferential methods will be presented with sufficient theory to assure understanding of the material. Cr. 3 (6 ECTS Cr.). Offered every semester.