Dr. Gohar Marikyan's website




 

Gohar Marikyan, Ph.D.
Course Created and Taught
Mathematical Sciences Courses
 Abstract Algebra
 Analytic Geometry
 Calculus I
 Calculus II
 Calculus III
 College Algebra II
 College Geometry
 College Mathematics
 Differential Equations
 Discrete Mathematics
 Game Theory
 Geometry and Its Applications
 Graph Theory
 Introduction to College Algebra
 Linear Algebra
 Mathematical Analysis
 Mathematical Logic
 Mathematical Proofs
 Mathematical Statistics
 Mathematics for Business
 Mathematics for Game Programmers
 Mathematics for Practical Applications Workshop
 Number Theory
 Mathematics in Native American Civilization
 Optimization
 Precalculus
 Recursion Theory
 Secondary Mathematics from an Advanced Viewpoint
 Set Theory
 Statistics
 Technology in Mathematics Education
 Theory of Algorithms
 Theory of Computation
 Theory of Probability
 Trigonometry
Abstract Algebra
Advanced, Liberal
4 credits
Abstract Algebra study offers basic knowledge of sets, groups, rings, and fields. It provides a
deeper understanding of the structure of mathematical systems. During the study a wide variety
of methods of proof essential to this branch of mathematics is developed and used. This study
strengthens the student's background for advanced work in mathematics. The study covers mapping
and operations, introduction to groupspermutation and symmetry group, equivalence relations,
congruence and divisibility, groupselementary properties, generators, cosets, isomorphisms,
introduction to rings, integral domains, and fields.
Prerequisite: Linear Algebra.
Analytic Geometry
Advanced, Liberal
4 credits
This study is designed for students who wish to expand their knowledge in analytic geometry. It includes
such topics as plane analytic geometry, vectors, lines, circle, and conic sections in the plane, the,
transformation of coordinates, curve sketching, polar coordinates and parametric equations, and topics
in solid analytic geometry.
Prerequisites: Trigonometry or Precalculus.
Calculus I
Introductory, Liberal
4 credits
Using an online tutorial and course management system for assignments, this study is designed for
students who wish to examine and apply the fundamental concepts and methods of calculus I. It
includes such topics as functions and models, four ways to represent a function, graphing
calculators and computers, limits and rates of change, continuity, derivatives, differentiation
formulas, derivatives of trigonometric functions, applications of differentiation, maximum and
minimum values, how derivatives affect the shape of a graph, limits at infinity. During the study
the student will learn the principles of problem solving, do applied projects, and do graphing
with calculus and calculators.
Prerequisite: Precalculus.
Calculus II
Advanced, Liberal
4 credits
Using an online tutorial and course management system for assignments, this study is designed
for students who wish to examine and apply the fundamental concepts and methods of calculus II.
It includes such topics as integral and their applications, inverse functions, exponential and
logarithmic functions, inverse trigonometric functions, techniques of integration, trigonometric
and improper integrals, and infinite series.
Prerequisite: Calculus I.
Calculus III
Advanced, Liberal
4 credits
This study is designed for students who wish to examine and apply the fundamental concepts and
methods of calculus III. It includes such topics as parametric equations, polar coordinates,
sequences, series, vectors, partial derivatives, multiple integrals and secondorder differential
equations.
Prerequisite: Calculus II.
College Algebra II
Introductory, Liberal
4 credits
Using an online tutorial and course management system for assignments, this study is designed
for students who wish to develop their decision making skills, to improve their logical and
critical thinking, and to expand their algebraic skills. It includes such topics as systems of
linear equations in two and three variables, matrices, linear programming, exponents and
polynomials, scientific notation, rational expressions and functions, radicals and rational
exponents, quadratic equations and inequalities, exponential and logarithmic functions,
sequences and series, counting and probability. Students will use an online tutorial and course
management system for assignments.
Meets General Education requirements in Mathematics.
Prerequisite: Introduction to College Algebra.
College Geometry
Introductory, Liberal
4 credits
This study is designed for students who wish to expand their skills in geometry. It covers the
important principles and realworld applications of geometry. Through integrated activities and
tools this study promotes handson application and discovery. The study includes such topics as
line and angle relationships, parallel lines, triangles, quadrilaterals, similar triangles,
circles, locus and concurrence, areas of polygons and circles, surfaces and solids, and
introduction to analytic geometry.
College Mathematics
Introductory, Liberal
4 credits
Using an online tutorial and course management system for assignments, this study is designed
for students who wish to learn the use of mathematics as an everyday tool, and to get better
prepared for their individual career. Principles and applications of mathematical topics around
us will be covered through discussions and problem solving. This study is beneficial for students
majoring in community and human services, social theory, business, labor, cultural, historical
and educational studies, as well as in arts, human development, science, mathematics, technology
and other concentrations.
Differential Equations
Advanced, Liberal
4 credits
This study offers basic knowledge of differential equations, and Laplace transforms. It
includes such topics as firstorder differential equations, secondorder and higherorder
linear differential equations, variable coefficents, systems of linear differential equations,
scalar approach and matrix approach, Laplace transforms, and numerical solution of
differential equations.
Meets General Education requirements in Mathematics.
Prerequisite: Calculus III.
Discrete Mathematics
Advanced, Liberal
4 credits
This study is designed for students who wish to expand their knowledge in computer science. It
includes such topics as number systems, sets and logic, combinatorics, probability, relations
and functions, vectors and matrices, Boolean algebra, graph theory.
Meets General Education requirements in Mathematics.
Prerequisite: Precalculus.
Geometry and Its Applications
Advanced, Liberal
4 credits
This study is designed for students who wish to major in mathematics and/or are prospective
teachers. It covers Euclidean and nonEuclidean geometry. Discovery approach guides students
to their own conclusions. The study includes such topics as points, lines, segments, and angles,
triangles, quadrilaterals, and circles, trigonometry, coordinates, and vectors, transformations
in geometry, nonEuclidean geometry, an introduction to three dimensional geometry, parallelism
in space, spherical geometry.
Introduction to College Algebra
Introductory, Liberal
4 credits
Using an online tutorial and course management system for assignments, this study is designed for
students who wish to develop their decision making skills, to improve their logical and critical
thinking, and to reinforce and expand their algebraic skills. The course serves as a good
foundation to study statistics, economics, accounting, science, and to master quantitative
methods. It includes such topics as properties of numbers, first and second degree equations and
inequalities, systems of linear equations and inequalities, exponents and polynomials, rational
expressions, exponential and logarithmic functions, graphing and curve sketching.
Meets General Education requirements in Mathematics.
Linear Algebra
Advanced, Liberal
4 credits
The Linear Algebra study covers linear equations in linear algebra, matrix algebra, determinants,
vector spaces, eigenvalues and eigenvectors, orthogonality and least squares, symmetric matrices
and quadratic forms. During this study the following real life examples will be covered:
determinants in analytic geometry, space flight and control systems, dynamical systems and
spotted owls, readjusting the North American datum, multichannel image processing, the platonic
solids, and the Berlin airlift.
Mathematical Proofs
Advanced, Liberal
4 credits
As a bridge from introductory to advanced level course in mathematics, students will learn what constitutes a rigorous mathematical proof, how to evaluate the soundness of a proof, and how to write a new proof. Specifically, students will review the basics of logic, will develop ability to understand mathematical systems expressed as systems of axioms and definitions, and will learn the techniques of direct proof, proof by contradiction, finding counterexamples, and mathematical induction. Students will also develop ability to express mathematical ideas clearly in writing, and will comprehend material in which mathematical symbols are used freely using ideas drawn from calculus and other elementary mathematical subjects.
Mathematical Statistics
Advanced, Liberal
4 credits
In this upper level calculusbased probability and statistics course, students will study topics including descriptive statistics, probability models and related concepts and applications, statistical estimation, and hypothesis testing.
Mathematics for Business
Introductory, Liberal
4 credits
Mathematics for Business presents math skills and knowledge that can be applied in solving financial
problems. The core topics include business finance, trade and cash discounts, markup and markdown,
business statistics, wages and payroll, simple interest and simple discount, compound interest,
future value, and present value, mortgages, sinking funds, and amortization, depreciation,
inventory, insurance, business insurance, life insurance, annuities, taxes, stocks and bonds.
Students will also gain an understanding of financial instruments and terminology used in
business finance. This serves as a foundation for further studies in business, management,
accounting, and finance. Students will gain skills to manage personal finance.
Meets General Education requirements in Mathematics.
Mathematics for Game Programmers
Introductory, Liberal
4 credits
Mathematics for Game Programmers presents math skills and knowledge that can be applied in game
programmers. The core topics include points and lines, parabolas, circles and spheres, degrees
versus radians, trigonometric functions, vector operations, matrix operations, and
transformations. The study serves as a good foundation for further study in computer
programming and computer graphics.
Meets General Education requirements in Mathematics.
Prerequisite: Introduction to College Algebra.
Mathematics for Practical Applications Workshop
Introductory, Liberal
4 credits
This workshop is designed for students who wish to learn the use of mathematics as an everyday
tool, and to get better prepared for their career. Principles and practical applications of
mathematics will be covered through discussions and problem solving. This workshop is beneficial
for students majoring in science, community and human services, social theory, business, labor,
cultural, historical and educational studies, as well as in arts, human development, mathematics,
technology and other concentrations.
Meets General Education requirements in Mathematics.
Number Theory
Advanced, Liberal
4 credits
The Number Theory study provides a simple account of classical number theory plus the historical
background to show the subject's evolution from antiquity to the present. It covers the following
topics: Mathematical Induction, the Binomial Theorem, Divisibility Theory in the integers, the
Euclidean Algorithm, the Diophantine Equation ax + by = c, primes and their distribution, the
Theory of Congruences, Fermat's Theorem, numbertheoretic functions, Euler's generalization of
Fermat's Theorem, primitive roots and indices, and the Quadratic Reciprocity Law.
Meets General Education requirements in Mathematics.
Mathematics in Native American Civilization
Introductory, Liberal
4 credits
This study is designed for students who wish to learn the use of mathematics as an everyday tool,
and to get better prepared for their career. Students will explore how Native Americans, such as
the Iroquois, Algonquians, Mayas, Aztecs and Incas used mathematics across centuries in the diverse
aspects of their civilization, art, architecture, construction, and everyday life. The discovery
will lead the student to develop interest in the universal application of mathematics. This study
is equally beneficial to students majoring in community and human services, social theory, business,
labor, cultural, historical and educational studies, as well as in arts, human development, science,
mathematics, technology and other concentrations. The topics will include real numbers and variables,
ratio and proportion, measurements, geometry, topics in algebra, and problem solving.
Meets General Education requirements in Mathematics.
Precalculus
Introductory, Liberal
4 credits
Using an online tutorial and course management system for assignments, this study is designed
for students who wish to examine and apply the fundamental concepts and methods of precalculus.
It includes such topics as functions and their graphs, polynomial and rational functions,
exponential and logarithmic functions, trigonometric functions, applications of trigonometry,
relations and conic sections, systems of equations and inequalities, integer functions and
probability.
Prerequisite: College Algebra II.
Secondary Mathematics from an Advanced Viewpoint
Advanced, Liberal
4 credits
This study is designed for those students who wished to explore secondary school mathematics from a deeper viewpoint in order to become an effective teacher. The study reviews current methods of teaching mathematics, relationships of basic concepts, role of technology in teaching secondary mathematics. The study covers the following topics: the challenge of teaching, planning for instruction, teaching more effectively, the role of problemsolving, using technology to enhance mathematics instruction, the scientific calculator, the graphing calculator, dynamic geometry using the geometer's sketchpad, assessing the understanding of mathematics, developing number concepts, and developing understanding of numeration.
Statistics
Advanced, Liberal
4 credits
This study is designed for students who wish to examine and apply the fundamental concepts and
methods of both descriptive and inferential statistics. It includes such topics as data
collection, organizing and summarizing data, describing the relation between two variables,
probability, the binomial probability distribution, the normal probability distribution, “t”
distribution, confidence intervals, hypothesis testing. Computers and related software will be
used throughout the course.
Prerequisite: College Algebra II.
Theory of Computation
Advanced, Liberal
4 credits
Theory of Computation is a capstone course for computer science. It is concerned with theoretical aspects
such as regular languages, finite automata, contextfree languages, pushdown automata, the ChurchTuring
thesis, Turing machines, decidability, the halting problem, time complexity, and P and NP classes.
Students will improve their ability to learn mathematics independently and improve their ability to create
proofs. Prerequisite (must complete before registering): Discrete Mathematics Assumptions about surrounding
courses: It is essential to know general methods of proof and have some prior experience with proving theorems.
To achieve this, the contents of Discrete Math taken at the advanced level are essential. A course in proofs
is recommended. Notes: Theory of Computation is usually a requirement for graduate school in Computer Science.
Technology in Mathematics Education
Advanced, NonLiberal
4 credits
This study is designed to gain competence in selection, evaluation, and utilization of various
instructional technologies in mathematics education. Application of new technologies to teaching
and learning will be emphasized along with performancebased activities in instructional design.
This study will provide the student with an understanding of learning models and the impact technology
can have toward enhancing and enriching the learning process. The use of technology tools for solving
a variety of problems, evaluating student performance, and implementing blended learning systems will
also be explored.
Trigonometry
Introductory, Liberal
4 credits
This study is designed to prepare students for studying calculus and other upper level
mathematics studies. It includes such topics as introduction to trigonometry, trigonometric
graphs, transformations and applications of trigonometric graphs, trigonometric models, trig
identities and their application, trigonometric equations, applications of trigonometry, and
conic sections and polar coordinates.
Meets General Education requirements in Mathematics.
Prerequisite: College Algebra II.
Courses created and taught
Mathematical Sciences Courses
Computers Sciences Courses
Other courses
