 # Linear Algebra & Analytic Geometry (for AMI), MAT-131.2, 6 cr    Prerequisite: none

This course will introduce to the elements of linear algebra and analytic geometry with examples from real life and various sciences. In selecting such problems for our examples and exercises we highlighted this motivation by references to applications in the social, business, and life sciences.

The course was prepared with three related objectives: concreteness, motivation and applicability.

# Mathematical Analysis I (for AMI), MAT-233.2, 6 cr     Prerequisite: MAT-131.2

This course is the introduction to the basics of linear algebra and analytic geometry models. These models describe real life problems related to economics and business. The course was prepared with three related objectives: concreteness, motivation and applicability.

# Physics. Computer Modeling., MAT-202.1, 6 cr     Prerequisite: MAT-131.2

Computer modeling of physical phenomenon characterized by involving all fundamental physical laws describing nature events under consideration. The main aim of computer modeling is “understanding, not numbers”. Computer modeling suggests investigative nature of learning physics.

Computer modeling became very important in contemporary science because classical calculus more appropriate for linear problems, but nature phenomena usually have nonlinear behavior. Nonlinear problems can be solved by classical calculus only in very rare cases, and computer modeling gives powerful tool for research.

The question “How physical problem can be formulated on computer language?” rises new insight in understanding physical phenomena. This understanding reached in several steps.

Computer modeling starts with design of idealized model of physical system, including corresponding simplifications. On the next step, it is necessary to develop algorithm for realization of the model. After generic model is created it should be investigated for wide spectrum of parameters. Such investigation is called computational experiment.

In course “Physics. Computer modeling” students should learn all described steps of investigation gradually moving from the simplest models toward more and more sophisticated models.

# Discrete Mathematics and Mathematical Logic I, COM-227,  6 cr       Prerequisite: none

Course is focus on a base concepts and techniques of discrete mathematics; first part of this course contains the following topics: mathematical induction, set theory, relations and functions, recurrence relations, fundamentals of logic.

Course has more than one purpose. It provides the mathematical foundations for many computer science courses, including data structure, algorithms, database theory, formal languages, compiler theory, computer security, and operating systems. More importantly, course should teach students how to think mathematically, that is, to develop ability to understand and create mathematical arguments.

# Discrete Mathematics and Mathematical Logic II, COM-228,  6 cr    Prerequisite: COM-227

Course is focus on a base concepts and techniques of discrete mathematics; second part of this course contains the following topics: fundamentals of logic, principles of counting, graph theory and Boolean algebra.

Course has more than one purpose. It provides the mathematical foundations for many computer science courses, including data structure, algorithms, database theory, formal languages, compiler theory, computer security, and operating systems. More importantly, course should teach students how to think mathematically, that is, to develop ability to understand and create mathematical arguments.

# Mathematical Analysis II,  MAT-316.2 , 6 cr      Prerequisite: MAT-233

This course will focus on advanced sections of mathematical analysis. The course consists of the following topics: functions of several variables; differential calculus of functions of several variables; multiple integrals; infinite series with constant and variable terms.

In this course, you will:

• develop abstract and logical (probative) thinking;
• understand the relationship between a question that arises in the natural, computer, economic, and social sciences and the data required to provide an answer to the question;
• go into advanced study of mathematical analysis and calculus techniques;
• use the tools of calculus for the real-life problems solving.

# The Theory of Probabilities and Mathematical Statistics, MAT-307, 6 cr   Prerequisite: MAT-131

This course will introduce the basic tools of theory of probability and statistics with applications to natural and social sciences, business. The course consists of the following topics: counting techniques; basic probability concepts and theorems; discrete and continuous probability distributions; statistical inference and sampling, the central limit theorem, confidence intervals for the mean of a normal population, hypothesis testing for the mean of a normal population.

Objectives:

• to develop abstract and logical (probative) thinking,
• understanding how to set and solve problems,
• acquiring as basic knowledge of probability and statistical analysis techniques,
• to use the knowledge of probability and statistics for the problems solving in majors.

# Ordinary Differential Equations    MAT-332   6 cr   Prerequisite: MAT-233.2

This is a one-term introduction to ordinary differential equations with applications. Topics include classification of, and what is meant by the solution of a differential equation, first-order equations for which exact solutions are obtainable, explicit methods of solving higher-order linear differential equations, an introduction to systems of differential equations, and the Laplace transform. Applications of first-order linear differential equations and second-order linear differential equations with constant coefficients will be studied.

The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. The course will demonstrate the usefulness of ordinary differential equations for modeling physical and other phenomena. Complementary mathematical approaches for their solution will be presented, including analytical methods and graphical analysis.

# Equations of Mathematical Physics, MAT-360,  6 cr          Prerequisite: MAT-316.2, MAT-332

Differential equation models describe a wide range of complex problems in biology, engineering, physical sciences, economics and finance. This course focusses on partial differential equation (PDE) models, which will be developed in the context of modelling heat and mass transport and, in particular, wave phenomena, such as sound and water waves.

This course develops students' skills in the formulation, solution, understanding and interpretation of PDE models. As well as developing analytic solutions, this course establishes general structures, characterizations, and numerical solutions of PDEs. In particular, computational methods using finite differences are implemented and analyzed.

Topics covered are: Formulation of PDEs using conservation laws: heat/mass/ wave energy transport; waves on strings and membranes; sound waves; Euler equations and velocity potential for water waves. The structure of solutions to PDEs: separation of variables (space/space, space/time); boundary value problems; SturmLouiville theory; method of characteristics; and classification of PDEs via coordinate transformation. Complex-variable form of waves. Wave dispersion. Group velocity. Finite difference solution of PDEs and BVPs: implicit and explicit methods; programming; consistency, stability and convergence; numerical differentiation.

# Numerical Methods, MAT-407, 6 cr   Prerequisite: MAT-233.2, COM-118 MAT-332-desirable

This course will focus on a base material of two classical sections of numerical mathematics: numerical methods of Algebra, Analysis and methods for solving of Ordinary Differential Equations. Students will familiarize with following topics: characteristics of computer arithmetic, polynomial and spline interpolation, direct and iterative methods for solving linear and nonlinear systems of equations, numerical integration, numerical methods for solving ordinary differential equations.

# Numerical Methods for Equations of Mathematical Physics Physics, MAT-410, 6 cr Prerequisite: MAT-407, MAT-360

Course will focus on the study of both classical and modern numerical methods for solving the equations of mathematical physics. We will consider boundary-value and initial-boundary-value problems for the advection-diffusion, Poisson and non-stationary heat equations.

There are several distinct goals of the course. One definite goal is to prepare the students to be competent practitioners, capable of solving a large range of problems, evaluating numerical results and understanding how and why results might be bad. Another goal is to prepare the applied mathematics students to take additional courses (such as courses of mathematical modeling in geophysics or fluid dynamics) and to write theses in applied mathematics.

# Functional Analysis, MAT-341, 6 cr         Prerequisite: MAT-316.2, MAT-326

This course covers major theorems of Functional Analysis that have applications in Ordinary and Partial Differential Equations, Integral equations. This course is a natural follow on of the course Linear Analysis. The Hahn-Banach fixed point Theorem is used for ODE’s and Volterra integral equations, and Fredholm integral equations.

Second part of the course is devoted to Laplace transform. The following topics are covered: Linearity. First Shifting Theorem (s-Shifting), Transforms of Derivatives and Integrals. ODEs, Unit Step Function (Heaviside Function).

Second Shifting Theorem (t-Shifting), Short Impulses. Dirac’s Delta Function.

Partial Fractions, Convolution. Integral Equations, Differentiation and

Integration of Transforms, ODEs with Variable Coefficients, Systems of ODEs,

Laplace Transform: General Formulas, Table of Laplace Transforms

# Complex Variables      MAT-326   6 cr   Prerequisite: MAT-316.2

Complex analysis is a core subject in pure and applied mathematics, as well as the physical and engineering sciences. While it is true that physical phenomena are given in terms of real numbers and real variables, it is often too difficult and sometimes not possible, to solve the algebraic and differential equations used to model these phenomena without introducing complex numbers and complex variables and applying the powerful techniques of complex analysis.

Complex variables is a beautiful area from a purely mathematical point of view, as well as a powerful tool for solving a wide array of applied problems. It is related to many mathematical disciplines, including in particular real analysis, differential equations, algebra and topology. The numerous applications include all kinds of wave propagation phenomena such as those occurring in electrodynamics, optics, fluid mechanics and quantum mechanics, diffusion problems such as heat and contaminant diffusion, engineering tasks such as the computation of buoyancy and resistance of wings, the flows in turbines and the design of optimal car bodies, and signal processing and communication theory.

# Optimization Methods, MAT-435, 6 cr             Prerequisite: MAT-233.2

This course focuses on the connection between real life problems and mathematical optimization. Students will learn how to model real life problems, formulate real life problems as optimization problems, and how to solve and analyze these optimization problems.

Our primary goal is to study the methods of optimization. We mainly focus on problems arising in economics and business, although general problems will be considered with applications to other fields.

The following mathematical techniques will be covered: Lagrange Multipliers, Nonlinear optimization methods, Simplex method, The Big M Method, Stepping Stone method, Modified Distribution method.

# Introduction to Software Engineering and Informatics, COM-108, 6 cr    Prerequisite: none

The IT Essentials course covers the fundamentals of computer hardware and software and advanced concepts such as security, networking, and the responsibilities of an IT professional. It is designed for students who want to pursue careers in ICT and students who want to gain practical knowledge of how a computer works. Students who complete COM-108 will be able to describe the internal components of a computer, assemble a computer system, install an operating system, and troubleshoot using system tools and diagnostic software. Students will also be able to connect to the Internet and share resources in a networked environment. New topics in this version include mobile devices such as tablets and smartphones and client-side virtualization. Expanded topics include security, networking, and troubleshooting. Hands-on lab activities are essential elements that are integrated into the curriculum.

The inclusion of Packet Tracer supports alignment with the new CompTIA A+ certification objectives. This course helps students prepare for the CompTIA’s A+ certification, most importantly the Essentials exam.

# Structural programming, COM-118, 6 cr                   Prerequisite: none

This course helps to equip students with basic skills needed for structural and object-oriented programming. At the completion of the course students should understand fundamental programming concepts such as ow control, objects, classes, methods, procedural decomposition, inheritance and polymorphism; be able to write simple applications using most of the capabilities of the Java programming language and apply principles of good programming practices throughout the process. This course is designed for Software Engineering majors and minors.

# Object Oriented Programming, COM-119,  6 cr        Prerequisite: COM-118

This course helps to equip students with essential skills needed for structured and object-oriented programming. At the completion of the course, students should understand fundamental programming concepts such as ow control, objects, classes, methods, procedural decomposition, inheritance, and polymorphism; be able to write simple applications using most of the capabilities of the Java programming language and apply principles of good programming practices throughout the process.

At the end of the course student should be able to research, analyze, design, develop, and maintain functioning software systems in accord to the goals of the AUCA Software Engineering Department and the 510300 IT competency standard (OK 17, 17, 115).

# Computer Architecture, COM-410.1, 6 cr                      Prerequisite: COM-223.1

This course is a course on computer architecture with an emphasis on a quantitative approach to cost/performance design tradeoffs. The course covers the fundamentals of classical and modern processor design: performance and cost issues, instruction sets, pipelining, caches, physical memory, virtual memory, I/O superscalar and out-of-order instruction execution, speculative execution, long (SIMD) and short (multimedia) vector execution, multithreading, and an introduction to shared memory multiprocessors.

# Operating Systems, COM-341.1, 6 cr              Prerequisite: COM-410.1

OS in Computer System. History of operating systems. Operating System Environments. Operating System Components and Goals. Multiprogramming, time sharing, multi-user mode. Processor Management. Process concepts, process states. Interprocess communication. Concurrent processes, process intercommunication and synchronization, Semaphore, mutex, monitor. Virtual memory, organization of memory: pages, segments. Input-output control.

# Database, COM-213, 6 cr                                  Prerequisite: COM-119

By the end of the course, the students would have the knowledge and practical skills of database principals, querying, design and implementation. Topics include advanced information on database querying, models and systems, data modeling and database systems, normalization. In case of lab works, learners will get familiar with SQL, Microsoft SQL Server and its tools.

The learners will understand practically basics and advanced techniques of SQL querying language, the database lifecycle from the collecting requirements to the implementation and performance optimization. Course includes a number of short 3D-parties courses.

# Computer Graphics,  COM-391,  6 cr                   Prerequisite: COM-223.1

The course teaches students fundamentals of computer graphics through a process of developing a 3-D engine in a series of laboratory tasks throughout the course.

Students will study on how to work with graphics accelerators with the help of the OpenGL ES API to deliver rich 3-D computer-generated images, animations, or interactive applications.

As a result, students should be able to research and analyze the functioning of a complex real-time computational system, improve their skills using programming languages for software design and development in accord to the goals of the AUCA Software Engineering Department and the 510300 IT competency standard (including competency elements OK 1{7, 1{7, 1{15).

# Research Methods in Applied Mathematics, MAT-370, 6 cr          Prerequisite: MAT-131.2

Students will develop skills required for mathematical research. The Main research methods will be introduced and applied in mathematical modeling of real-life problems. This course will focus on communication in both written and oral form. Students will write documents and prepare presentations in a variety of formats for academic and non-academic purposes. The LaTeX document preparation system will be used. Since junior and senior level students may also think about applying for graduate school/internships/jobs there will be a block on "how to write a resume and cover letter".

This module is an introduction to methods often used in research in general, which will

provide preparation for the BSc project. You will learn how to review critically and evaluate scientific writing, from books to research papers. You will receive training in writing academic reports in an appropriate style and structure, and will learn how to make and deliver oral presentations. Additional topics will be included so that you are prepared for project work at an advanced level. These will include literature search, computational mathematics tools and analysis packages, scientific word processing, publishing original results, research careers, project planning and teamwork.

# Internship I (Educational Tasks), MAT-380, 3 cr and Internship II (Research Project), MAT-479, 3 cr          Prerequisite: none

These courses are related to student independent working (but under supervising of course instructor) in the framework of individually given to him problem: searching of correspondent informational resources and any possible approaches for this problem solving. During this course students receive such skills on working with big datasets (e.g. GPS, electromagnetic, mechanics, and so on) like processing, analyzing, visualizing.

 understanding of scientific research activity aim,

 understanding of the applied mathematics role in modern scientific and technical researches,

 searching and analyzing of scientific literature related to description of the given problem,

 formulating conclusions on studied materials,

 working with big datasets in accordance with the task;

 development of software in accordance with the task;

 formulating conclusions on results of scientific experiments;

 drawing up of progress report.

# Safety Management and Economics, COM-120, 3 cr          Prerequisite: none

This course is provided to ensure students are generally prepared for emergency situations, and to address security and management strategies for lives and careers. The course considers the skills and defenses needed to succeed in college, in day-to-day life, and in careers. Specific topics depend on student backgrounds and interests, and may include physical self-defense, situational preparedness, bullying, stress coping behaviors and strategies, immigration and culture shock, intellectual property, time-management, pollution and the environment, cyber security, social media, budgeting and accounting, corruption, managing people, recognizing and dealing with bad bosses, and more. The course will mostly involve teamwork and team presentations on student-selected topics relating to safety, management, and economics. A result of the course is that students will develop peer connections to help with their success in and after college, provide practice at teamwork, and experience with public speaking and public presentations in English.

# Senior project preparation II, MAT-481, 3 cr        Prerequisite: MAT-480

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