# Oleg Muzician

## Expertise

Complex Analysis and Complex Dynamical Systems

## Degrees

- B.S. CUNY-Brooklyn College, Mathematics,
- B.S. CUNY-Brooklyn College, Computer Science,
- Ph.D. CUNY-Graduate Center, Mathematics,

## Courses Taught

- This course is a combination of arithmetic and elementary algebra. It includes the arithmetic of integers, fractions, decimals, and percent. In addition, such topics as signed numbers, algebraic representation, operations with polynomials, factoring, the solution of simultaneous linear equations of two variables, and graphing are covered.

Students who passed MAT 12, MAT 14, MAT 41, MAT 51, MAT 56, MAT 160, MAT 161, MAT 56.5, MAT 150.5 cannot take MAT 161.5.

Course Syllabus - This developmental course provides an alternative and accelerated pathway to the college-level liberal arts mathematics courses. The course will focus on applications of numerical reason to make sense of the world around us. Applications of arithmetic, proportional reasoning and algebra are emphasized. This course cannot be used as a prerequisite for MAT 056 and is not suited for Science, Technology, Engineering or Mathematics (STEM) students.

Students who passed MAT 12, MAT 14, MAT 41, MAT 51, MAT 56, MAT 160, MAT 161, MAT 56.5, MAT 150.5 cannot take MAT 161.5.

Course Syllabus - This course is the first algebra course offered at the College. It includes such topics as algebraic representation, signed numbers, operations with polynomials, factoring, the solution of linear equations, the coordinate system, the solution of simultaneous linear equations of two variables, and graphing. This course is designed to prepare students for the CUNY Freshman Skills Assessment Test required for transfer to the upper division of CUNY, as well as for more advanced math courses. If a student passes MAT 12, the student should not register for MAT 51, since MAT 12 combines MAT 8 and MAT 51.

Students who passed MAT 12, MAT 14, MAT 41, MAT 51, MAT 56, MAT 160, MAT 161, MAT 56.5, MAT 150.5 cannot take MAT 161.5.

Course Syllabus - This course is the second algebra course offered at the college. It is open to students who have completed elementary algebra or its equivalent. It includes such topics as: factoring, solutions of linear and quadratic equations, trigonometric relationships, exponents, logarithms, and the graphs of quadratic equations.

Students who passed MAT 12, MAT 14, MAT 41, MAT 51, MAT 56, MAT 160, MAT 161, MAT 56.5, MAT 150.5 cannot take MAT 161.5.

Course Syllabus - This course covers basic statistics, including: measures of central tendency, measures of dispersion, graphs, correlation, the regression line, confidence intervals, the significance of differences, and hypothesis testing, including z-tests, t-tests, and chi-square tests.

Prerequisites: MAT 12, MAT 14, MAT 41, MAT 51 or MAT 161.5

Course Syllabus - This course covers basic algebraic and trigonometric skills, algebraic equations, and functions. Topics include: mathematical induction, complex numbers, and the binomial theorem.

Prerequisite: MAT 56 or MAT 56.5

Course Syllabus - This course covers statistical concepts and techniques with applications. Topics include probability, random variables, the binomial distribution, the hyper-geometric distribution, measures of central tendency, the normal distribution, precision and confidence intervals, sample design and computer projects.

Prerequisite: MAT 206 or MAT 206.5

Course Syllabus - This is an integrated course in analytic geometry and calculus, applied to functions of a single variable. It covers a study of rectangular coordinates in the plane, equations of conic sections, functions, limits, continuity, related rates, differentiation of algebraic and transcendental functions, Rolle's Theorem, the Mean Value Theorem, maxima and minima, and integration.
Prerequisite: MAT 206 or MAT 206.5

Course Syllabus - This course covers the standard material comprising an introduction to group and ring theory: set theory and mappings; groups, normal subgroups, and quotient groups; Sylow's Theorem; rings, ideals, and quotient rings, Euclidean rings, polynomial rings.
Corequisite: MAT 315

Course Syllabus - This course includes the study of several mathematical systems. The role of mathematics in modern culture, the role of postulational thinking in all of mathematics, and the scientific method are discussed. The course considers topics such as: the nature of axioms, truth and validity; the concept of number; the concept of set; scales of notation; and groups and fields.

Prerequisites: MAT 12, MAT 14, MAT 41, MAT 51 or MAT 161.5

Course Syllabus - This course covers topics in intermediate algebra and emphasizes problems and applications in respiratory therapy. It includes such topics as: algebraic representation, factoring, approximate numbers, significant digits and scientific notation, first and second degree equations with applications, ratio and proportions, square roots, radicals and exponents, logarithms, graphing linear equations, vectors and the metric system.

Course Syllabus - This course covers matrices, determinants, systems of linear equations, vector spaces, eigenvalues and eigenvectors, Boolean algebra, switching circuits, Boolean functions, minimal forms, Karnaugh maps.
Prerequisite: MAT 302, or permission of the department

Course Syllabus

## Research and Projects

## Publications

- J.Hu, O.Muzician. “Cross-ratio distortion and Douady-Earle extension: I. A new upper bound on quasiconformality.”2012, Journal of London Math. Society
- J. Hu, O. Muzician “Cross-ratio distortion and Douady-Earle extension: II. Quasiconformality and asymptotic conformality are local.”2012, Journal d’Analyse Mathematique
- J.Hu, F.G. Jimenez, O. Muzician. “Rational maps with half symmetries, Julia sets, and Multibrot sets in parameter planes”2012, Contemporary Mathematics
- J. Hu, O. Muzician. “Conformally natural extensions of continuous circle maps: I. The case when the pushforward measure has no atom.”2012, Contemporary Mathematics
- J. Hu, O. Muzician. “Conformally natural extensions of continuous circle maps: II. The general case.” (accepted 2014)2017, Journal d’Analysis Mathematique
- Jun Hu, Oleg Muzician, Yingqing Xiao “Dynamics of regularly ramified rational maps: I Julia sets of maps in one parameter families”, (accepted 2017), Discrete and Continuous Dynamical Systems
- Jun Hu, Oleg Muzician “Cross-ratio distortion and Douady-Earle Extension: III. How to control the dilatation near the origin” (submitted 2017), Annales Academiae Scientiarum Fennicae Mathematica