This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.
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This iOS application is designed to teach users to read and write the Arabic alphabet. The app provides three different functions: demonstrating how each selected letter is pronounced, illustrating how the letter is written in different positions, and allowing users to practice writing the letter.
Focuses on modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic Resonance Imaging) is done using Matlab.
Play with objects on a teeter totter to learn about balance. Test what you've learned by trying the Balance Challenge game.
In this beginning algebra course, you'll learn about
fundamental operations on real numbers
solving linear equations and inequalities
graphing linear equations
systems of linear equations
All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.
The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures.
This lesson begins a 4 lesson review about adding whole numbers, carrying in addition, and place value. [Developmental Math playlist: Lesson 10 of 196]
This is the first lesson of a 6-part review of the division of whole numbers. [Developmental Math playlist: Lesson 26 of 196]
This lesson begins a 6-part review of multiplication of whole numbers. [Developmental Math playlist: Lesson 20 of 196]
This is the 2nd part of a 6-part review of the multiplication of whole numbers. [Developmental Math playlist: Lesson 21 of 196]
This is lesson 4 of a 6-part review of the multiplication of whole numbers. [Developmental Math playlist: Lesson 23 of 196]
Explore the forces at work when you try to push a filing cabinet. Create an applied force and see the resulting friction force and total force acting on the cabinet. Charts show the forces, position, velocity, and acceleration vs. time. View a Free Body Diagram of all the forces (including gravitational and normal forces).
This fuel cell module was created by General Motors and Weekly Reader to supplement science courses for students in grades 5-8. Its duration is 4-5 class periods and includes a teacher's guide, posters, interactive diagram, and four classroom activities. Topics discussed include automotive history, environmental and energy concerns, fundamentals of fuel cells, fuel cell technologies, and sustainable energy.
Pump gas molecules to a box and see what happens as you change the volume, add or remove heat, change gravity, and more. Measure the temperature and pressure, and discover how the properties of the gas vary in relation to each other.