American University of Central Asia - AUCA

Mathematics Course Descriptions

MAT 020: College Mathematics I

6 credits

Prerequisites: none

The course College Mathematics I, II will cover themes from elementary mathematics dealing with secondary school requirements. This class will develop the student’s ability to solve problems of various levels of complexity. The course is recommended specially for Preparatory Program students

MAT 021: College Mathematics II

6 credits

Prerequisites: MAT 020

The course is continuation of the College Mathematics 1 and recommended specially for Preparatory Program students.

MAT 103: Linear Algebra and Analytic Geometry

3 credits

Prerequisites: none

This course will introduce to the basics of linear algebra, analytic geometry and linear programming models 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. The course is recommended for BA, ECO and SFW students.

MAT 118: Finance Mathematics

3 credits

Prerequisites: none

Students will focus on the basic sections of finance mathematics. The following issues will be considered: simple interest and discount, compound interest, annuities, leasing, bonds and shares. Students should understand the concept of time value of money. They will have enough knowledge to make decision in finance and investment areas. The course is recommended for BA students.

MAT 128: An Introduction to Contemporary Mathematics I

3 credits

Prerequisites: none

This course introduces you to a variety of mathematical subjects and makes you think about the nature of mathematics itself. You will study a number of approaches to contemporary mathematics- linear algebra, analytic geometry, linear programming. We introduce the concept of a set. You will learn to think like a mathematician and to apply mathematical principles to everyday life and scientific study. You will come to see how the numbers and shapes that are such an organic part of our everyday lives can be used to design elegant models that alter the way we think and enable the development of new knowledge. The course is recommended for AS, ANTH, ICP, ES, LAW, JOUR, PSY, SOC students.

MAT 227: Mathematical Analysis I

3 credits

Prerequisites: MAT 103 or MAT 128

This course will introduce to the basics of Mathematical Analysis, following topics will be presented. Functions: limit of the functions and basics of differential calculus and its applications. Derivative: first derivative test; concavity, second derivative test. Relative maxima and relative minima; optimization problems. Functions of two variables: local extremum, partial derivatives. Conditional extremum; Lagrange Multiplier method. Indefinite and definite integrals: integration by substitution, integration by parts. Applications of a definite integral. Basics of differential equations. The course is recommended for BA, ECO and SFW students.

MAT 228: An Introduction to Contemporary Mathematics II

3 credits

Prerequisites: MAT 128 or MAT 103

This course will introduce you to basic theory of probability and statistics with applications in the social sciences and business. The course consists of the following themes: counting techniques; basic probability concepts and theorems; discrete and continuous probability distributions; statistical inference and sampling, statistical conclusions for the normal distribution. Additionally, you will familiarize with elements of mathematical logic: propositions and proof methods. The course is recommended for AS, ANTH, ICP, ES, LAW, JOUR, PSY, SOC students.

MAT 306: The Theory of Probabilities and Mathematical Statistics

3 credits

Prerequisites: MAT 103 or MAT 128

This course will introduce you to the basic tools of theory of probability and statistics with applications to social sciences and business. The course consists of the following themes: 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. The course is recommended for BA, ECO, SFW, PSY and SOC students.

MAT 316: Mathematical Analysis II

3 credits

Prerequisites: MAT 227

Course will focus on advanced sections of mathematical analysis, such as: Infinite Series with constant and variable terms and Introduction to the theory of the Ordinary Differential Equations with discussion of techniques for relevant problem solving. The course is recommended specially for SFW students.

MAT 406: Numerical Methods

3 credits

Prerequisites: MAT 316; additionally, skills of programming on one of a high level programming language are necessary.

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, and numerical methods for solving ordinary differential equations. The course is recommended specially for SFW students.

Natural Sciences Course Descriptions

ECL 102: Environmental Protection

3 credits

Prerequisites: none

The course on Environmental Protection is divided into three parts: a basis element taught during the first 2-3 weeks that provides students with a basic knowledge on ecosystem and its functioning, an intermediate element lasting approximately for 7 to 9 weeks that gives an understanding of global environmental problems, their interdependence and segregated effect they have on each other and the ecosystem as a whole, and a final element (4-5 weeks) providing an overview of measures applied and policies developed to address these problems. Due to the varied interests of the students, the first aim of the course is to introduce to all students the basic principles required for a full understanding of the various subject areas. These basic skills are built upon focusing on issues of prime importance in the Kyrgyz Republic and all over the world, and relating them to global problems and solutions. The course intends to emphasize a multi- and inter-disciplinary nature of the discipline relating environmental issues to legal, economic, and political aspects that will be provided during the final element of the course.

ECL 103: Basics of Ecology and International Environmental Protection

3 credits

Prerequisites: none

The course serves as an introduction to environmental science and is designed to provide students with theoretical knowledge of environmental science as well as practical skills on case studies. The course covers a number of issues including: earth science and ecology, environmental degradation issues, energy production, environmental impact assessment, environmental law and policy, environmental monitoring, environmental education issues, and includes extensive project work and case studies.

ECL 112: The Nature of the Earth: Preservation of the Environment in the Countries of the World

3 credits

Prerequisites: none

The key subjects of this academic course include a description of modern stage of development of Environment Protection State on both regional and world levels, which are based on studying the correlation of nature and basic laws of nature systems' functioning.

ECL 113: Clean Development Policy and Practice

3 credits

Prerequisites: none

The course introduces students of all majors to the field of environment and development, its multi-disciplinary character and its policy focus. It is not a listing of facts and figures, but in interactive ways it explores the causes of unsustainable development in economy, technology and human behavior. Using past experience as well as critical thinking and problem-solving skills we will unveil directions for a more sustainable future, so that you are equipped to play your part in it, either in business or in the public sector. This is one of the ways in which the course prepares AUCA graduates for a world in which environmental literacy is a must for change agents.

GEO 109: Geography of the USA

3 credits

Prerequisites: none

The systematic studying of particularities of using natural resources, distribution of population, structure of national economy, and international economic relations will be provided within'this academic course, as a completed situation of the contemporary international integration and cooperation of the United States of America with other countries worldwide. The complex evaluation of development of the U.S. A will be based on analysis of existing political situation in a global economy and related role of the United States of America in global development.

GEO 111: Geography of the Kyrgyz Republic

3 credits

Prerequisites: none

A modern picture of international integration relationships and cooperation of the Kyrgyz Republic with countries of the world is considered in this course. Studying particularities of the natural resources' using settling of population, structure of national economy and international relations has taken a new importance for students specializing not only in Natural Sciences field, but Business Administration and Comparative Politics also, especially on an international level.

NTR 104: The History and Philosophy of Sciences

3 credits

Prerequisites: none

This course introduces modern scientific methods used in studying the Universe. It outlines the history of natural sciences and demonstrates their great historical impact on humanity. It makes obvious the profound interconnection between philosophy and natural sciences as essential elements of human culture. Students will have an opportunity to learn the fundamental concepts about the nature of scientific endeavor within which all great scientific explorations have been undertaken. Students will also study a variety of methodologies and ideas rooted in ancient, medieval and modern natural sciences which were gradually, but surely, forming today’s contemporary world view of science – both generally and in its infinitesimal details. This study allows students to place the main ideas and theories underlying modern natural sciences in their proper cultural, historical, philosophical, and intellectual contexts. This course applies to the fulfillment of AUCA’s Liberal Arts requirements.

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