Oleg Muzician
Professor
Mathematics
EMAIL: OMuzician@bmcc.cuny.edu
Office: N598H
Office Hours:
Phone: +1 (212) 346-8632
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 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 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 - This course provides an introduction to the concepts of formal integration. It covers the differentiation and integration of algebraic, trigonometric, and transcendental functions. Topics include the definite integral, the antiderivative, areas, volumes, and the improper integral.
Prerequisite: MAT 301
Course Syllabus - The course covers the usual topics of a linear algebra course (e.g., vector spaces, matrices, eigenvectors). The course also covers special topics geared toward data science (e.g., Markov chains, PCA, LDA) as well as programing in Jupyter IDE.
Prerequisite: MAT 301
Research and Projects
Publications
- J.Hu, O.Muzician. “Cross-ratio distortion and Douady-Earle extension: I. A new upper bound on quasiconformality.”, Journal of the London Mathematical Society 86.2: 387-406. (Books and Publications: Article (Peer-reviewed)) 2012
- J. Hu, O. Muzician “Cross-ratio distortion and Douady-Earle extension: II. Quasiconformality and asymptotic conformality are local.”, Journal d’Analyse Mathématique 117.1: 249-71. (Books and Publications: Article (Peer-reviewed)) 2012
- J.Hu, F.G. Jimenez, O. Muzician. “Rational maps with half symmetries, Julia sets, and Multibrot sets in parameter planes”, Contemporary Mathematics 573: 119-46. (Books and Publications: Article (Peer-reviewed)) 2012
- J. Hu, O. Muzician. “Conformally natural extensions of continuous circle maps: I. The case when the pushforward measure has no atom.”, Contemporary Mathematics 575: 171-98. (Books and Publications: Article (Peer-reviewed)) 2012
- J. Hu, O. Muzician. “Conformally natural extensions of continuous circle maps: II. The general case.” Journal d’Analyse Mathématique 132.1:81-107. (Books and Publications: Article (Peer-reviewed)) 2017
- Jun Hu, Oleg Muzician, Yingqing Xiao “Dynamics of regularly ramified rational maps: I Julia sets of maps in one parameter families”, Discrete and Continuous Dynamical Systems-Series A 38(7): 3189-3221. (Books and Publications: Article (Peer-reviewed)) 2018
- Jun Hu, Oleg Muzician “Cross-ratio distortion and Douady-Earle Extension: III. How to control the dilatation near the origin”, Annals Academiae Scientarium Fennicae Mathematica 44: 523-536. (Books and Publications: Article (Peer-reviewed)) 2019
