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The lectures are at a beginning graduate level and assume only basic familiarity with Functional Analysis and Probability Theory. Topics covered include: Random variables in Banach spaces: Gaussian random variables, contraction principles, KahaneKhintchine inequality, Anderson’s inequality. Stochastic integration in Banach spaces I: γRadonifying operators, γboundedness, Brownian motion, Wiener stochastic integral. Stochastic evolution equations I: Linear stochastic evolution equations: existence and uniqueness, Hölder regularity. Stochastic integral in Banach spaces II: UMD spaces, decoupling inequalities, Itô stochastic integral. Stochastic evolution equations II: Nonlinear stochastic evolution equations: existence and uniqueness, Hölder regularity.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Stochastic partial differential equations Evolution equations
 Resource Type:
 Courseware

Courseware
How do populations grow? How do viruses spread? What is the trajectory of a glider? Many reallife problems can be described and solved by mathematical models. In this course, you will form a team with another student and work in a project to solve a reallife problem. You will learn to analyze your chosen problem, formulate it as a mathematical model (containing ordinary differential equations), solve the equations in the model, and validate your results. You will learn how to implement Euler’s method in a Python program. If needed, you can refine or improve your model, based on your first results. Finally, you will learn how to report your findings in a scientific way. This course is mainly aimed at Bachelor students from Mathematics, Engineering and Science disciplines. However it will suit anyone who would like to learn how mathematical modeling can solve realworld problems.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematical models
 Resource Type:
 Courseware

Courseware
Statistics is the science that turns data into information and information into knowledge. This class covers applied statistical methodology from an analysisofdata viewpoint. Topics covered include frequency distributions; measures of location; mean, median, mode; measures of dispersion; variance; graphic presentation; elementary probability; populations and samples; sampling distributions; one sample univariate inference problems, and two sample problems; categorical data; regression and correlation; and analysis of variance. Use of computers in data analysis is also explored.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Statistics
 Resource Type:
 Courseware

Courseware
Mathematica and its applications to linear algebra, differential equations, and complex functions. Fourier series and Fourier transforms. Other topics in integral transforms.
 Subjects:
 Physics and Mathematics and Statistics
 Keywords:
 Physics Mathematical physics
 Resource Type:
 Courseware

Courseware
In this course, students will learn basic linear algebra necessary to understand the operations regarding derivatives of functions with more than one variable to investigate maximum and minimum values of those functions with economics applications in mind. Students will also see how to solve linear systems and then how to turn them into problems involving matrices, then learn some of the important properties of matrices. This course will focus on topics in linear algebra and multivariable differential calculus suitable for economic applications. Recorded Summer 2013
 Subjects:
 economic applications, matrices, Economics, and Mathematics and Statistics
 Keywords:
 Economics Mathematical
 Resource Type:
 Courseware

Courseware
Math 2B is the second quarter of SingleVariable Calculus and covers the following topics: Definite integrals; the fundamental theorem of calculus. Applications of integration including finding areas and volumes. Techniques of integration. Infinite sequences and series. Parametric and polar equations.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Calculus
 Resource Type:
 Courseware

Courseware
UCI Math 2A is the first quarter in SingleVariable Calculus and covers the following topics: Introduction to derivatives, calculation of derivatives of algebraic and trigonometric functions; applications including curve sketching, related rates, and optimization. Exponential and logarithm functions.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Calculus
 Resource Type:
 Courseware

Courseware
This PreCalculus course is designed to prepare students for a calculus course. This course is taught so that students will acquire a solid foundation in algebra and trigonometry. The course concentrates on the various functions that are important to the study of the calculus.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Precalculus Trigonometry Algebra
 Resource Type:
 Courseware

Courseware
After reviewing tools from probability, statistics, and elementary differential and partial differential equations, concepts such as hedging, arbitrage, Puts, Calls, the design of portfolios, the derivation and solution of the BlacScholes, and other equations are discussed.
 Subjects:
 Finance and Mathematics and Statistics
 Keywords:
 Business mathematics
 Resource Type:
 Courseware

Courseware
Second introductory course covering basic principles of probability and statistical inference. Topics: Point estimation, interval estimating, and testing hypotheses, Bayesian approaches to inference.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Probabilities Mathematical statistics
 Resource Type:
 Courseware