92.521 Algebraic Structures Properties of rings, groups, fields, polynomials over fields, extension rings and fields, vector spaces, codes, and additional applications. 92.523 Linear Algebra Sets and maps. Vector spaces and linear maps, the matrix of a linear map, solving systems of equations, scalar products and orthogonality, eigenvalues and applications. 92.535 History of Mathematics Ancient numeral systems, Babylonian and Egyptian Mathematics, Pythagorean Mathematics, Duplication, Trisection and Quadrature, Euclid's Elements and Greek Mathematics after Euclid, Hindu and Arabian Mathematics, European Mathematics from 500 to 1600, Origins of modern Mathematics, Analytic Geometry, History of Calculus, Transition to the 20th Century, Contemporary Perspectives. This course is devoted to studying the application of mathematics to real-life problems from the physical, biological, social, and behavioral sciences.
Experience is provided with a wide variety of deterministic models.
92.570 Probability and Statistics Overview of descriptive statistics, data analysis, probability of events, discrete random variables, continuous random variables, normal, binomial and other probability distributions, central limit theorem, survey sampling, estimation, hypothesis testing, regression, experimental design, analysis of categorical data, nonparametric statistics. The course addresses the practical concerns of the math teachers who will deepen their knowledge about the curriculum and teaching strategies in secondary school mathematics. Participants are expected to gain knowledge of how to assist their students to be able to think deeply and flexibly about the relationships among facts, concepts, and procedures that constitute the structure of knowledge of mathematics. To teach mathematics effectively individuals must have knowledge of mathematics characterized by an explicit conceptual understanding of the principles and meaning underlying mathematical procedures and by connectedness of mathematical topics, rules and definitions. The topics will include the development of number and number sense, algebra, geometry, analytic geometry, trigonometry and pre-calculus.