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Advanced Stochastic Processes, Fall 2013
Conditions of Use:
Remix and Share
Rating

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.

Subject:
Business and Communication
Finance
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Gamarnik, David
Date Added:
01/01/2013
Alphabet with Nan and Lyly
Rating

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.

Subject:
Arts and Humanities
Languages
Material Type:
Interactive
Provider:
Baraem TV
Date Added:
10/14/2013
Applied Probability
Conditions of Use:
Remix and Share
Rating

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.

Subject:
Statistics and Probability
Material Type:
Full Course
Homework/Assignment
Lecture
Lecture Notes
Reading
Provider:
ArsDigita University
Provider Set:
ArsDigita University
Author:
Rajeev Surati
Tina Kapur
Date Added:
02/16/2011
Beginning Algebra (BPCC Open Campus: Math 098)
Rating

In this beginning algebra course, you'll learn about
fundamental operations on real numbers
exponents
solving linear equations and inequalities
applications
functions
graphing linear equations
slope
systems of linear equations

Subject:
Algebra
Material Type:
Full Course
Lecture
Lesson
Module
Provider:
Bossier Parish Community College
Author:
Gail Hendrix
Date Added:
10/16/2017
A Computational Introduction to Number Theory and Algebra
Rating

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.

Subject:
Mathematics
Algebra
Material Type:
Textbook
Author:
Victor Shoup
Date Added:
01/01/2008
Forces in 1 Dimension
Conditions of Use:
No Strings Attached
Rating

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).

Subject:
Physics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Danielle Harlow
Kathy Perkins
Sam Reid
Trish Loeblein
Date Added:
10/03/2006
Fuel Cells: Driving the Future
Rating

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.

Subject:
Automotive Technology and Repair
Education
Chemistry
Material Type:
Activity/Lab
Lesson Plan
Unit of Study
Provider:
Center for Automotive Technology - Macomb
Provider Set:
Center for Advanced Automotive Technology
Author:
General Motors
Date Added:
10/15/2007
Gas Properties
Conditions of Use:
No Strings Attached
Rating

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.

Subject:
Physics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Carl Wieman
Danielle Harlow
Jack Barbera
Kathy Perkins
Linda Koch
Michael Dubson
Ron LeMaster
Date Added:
10/05/2006
Gas Properties (AR)
Conditions of Use:
Read the Fine Print
Rating

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.

Subject:
Physics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Carl Wieman
Danielle Harlow
Jack Barbera
Kathy Perkins
Linda Koch
Michael Dubson
Ron LeMaster
Date Added:
07/02/2009
Geometry - Pythagoreom Theorem (Student's Edition)
Conditions of Use:
Remix and Share
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This stand-alone module examines the history, applications, and various proofs of the Pythagorean Theorem. The module also includes student activities and exercise problems. The module assumes the reader has a basic geometry background.

Subject:
Geometry
Material Type:
Textbook
Provider:
CK-12 Foundation
Provider Set:
CK-12 FlexBook
Author:
Sheng, Joy (Editor)
Swenson, Laura
Date Added:
11/08/2010
Ladybug Revolution
Conditions of Use:
No Strings Attached
Rating

Join the ladybug in an exploration of rotational motion. Rotate the merry-go-round to change its angle, or choose a constant angular velocity or angular acceleration. Explore how circular motion relates to the bug's x,y position, velocity, and acceleration using vectors or graphs.

Subject:
Physics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Kathy Perkins
Mindy Gratny
Sam Reid
Wendy Adams
Date Added:
10/28/2008
Ladybug Revolution (AR)
Conditions of Use:
Read the Fine Print
Rating

Join the ladybug in an exploration of rotational motion. Rotate the merry-go-round to change its angle, or choose a constant angular velocity or angular acceleration. Explore how circular motion relates to the bug's x,y position, velocity, and acceleration using vectors or graphs.

Subject:
Physics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Kathy Perkins
Mindy Gratny
Sam Reid
Wendy Adams
Date Added:
08/02/2011
Linear Algebra II
Conditions of Use:
Read the Fine Print
Rating

Linear Algebra is both rich in theory and full of interesting applications; in this course the student will try to balance both. This course includes a review of topics learned in Linear Algebra I. Upon successful completion of this course, the student will be able to: Solve systems of linear equations; Define the abstract notions of vector space and inner product space; State examples of vector spaces; Diagonalize a matrix; Formulate what a system of linear equations is in terms of matrices; Give an example of a space that has the Archimedian property; Use the Euclidean algorithm to find the greatest common divisor; Understand polar form and geometric interpretation of the complex numbers; Explain what the fundamental theorem of algebra states; Determine when two matrices are row equivalent; State the Fredholm alternative; Identify matrices that are in row reduced echelon form; Find a LU factorization for a given matrix; Find a PLU factorization for a given matrix; Find a QR factorization for a given matrix; Use the simplex algorithm; Compute eigenvalues and eigenvectors; State Shur's Theorem; Define normal matrices; Explain the composition and the inversion of permutations; Define and compute the determinant; Explain when eigenvalues exist for a given operator; Normal form of a nilpotent operator; Understand the idea of Jordan blocks, Jordan matrices, and the Jordan form of a matrix; Define quadratic forms; State the second derivative test; Define eigenvectors and eigenvalues; Define a vector space and state its properties; State the notions of linear span, linear independence, and the basis of a vector space; Understand the ideas of linear independence, spanning set, basis, and dimension; Define a linear transformation; State the properties of linear transformations; Define the characteristic polynomial of a matrix; Define a Markov matrix; State what it means to have the property of being a stochastic matrix; Define a normed vector space; Apply the Cauchy Schwarz inequality; State the Riesz representation theorem; State what it means for a nxn matrix to be diagonalizable; Define Hermitian operators; Define a Hilbert space; Prove the Cayley Hamilton theorem; Define the adjoint of an operator; Define normal operators; State the spectral theorem; Understand how to find the singular-value decomposition of an operator; Define the notion of length for abstract vectors in abstract vector spaces; Define orthogonal vectors; Define orthogonal and orthonormal subsets of R^n; Use the Gram-Schmidt process; Find the eigenvalues and the eigenvectors of a given matrix numerically; Provide an explicit description of the Power Method. (Mathematics 212)

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
11/11/2011
Linear Algebra with Applications
Conditions of Use:
Remix and Share
Rating

After being traditionally published for many years, this formidable text by W. Keith Nicholson is now being released as an open educational resource and part of Lyryx with Open Texts! Supporting today’s students and instructors requires much more than a textbook, which is why Dr. Nicholson opted to work with Lyryx Learning.

Overall, the aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work.

The contents have enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners whereas Chapters 5–9 contain a second semester course. The text is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix A).

Subject:
Algebra
Material Type:
Textbook
Provider:
Lyryx Learning
Author:
W. Keith Nicholson
Date Added:
01/17/2018
Masses & Springs
Conditions of Use:
No Strings Attached
Rating

A realistic mass and spring laboratory. Hang masses from springs and adjust the spring stiffness and damping. You can even slow time. Transport the lab to different planets. A chart shows the kinetic, potential, and thermal energy for each spring.

Subject:
Physics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Kathy Perkins
Michael Dubson
The Mortenson Family Foundation
Wendy Adams
Date Added:
04/26/2006
Masses & Springs (AR)
Conditions of Use:
Read the Fine Print
Rating

A realistic mass and spring laboratory. Hang masses from springs and adjust the spring stiffness and damping. You can even slow time. Transport the lab to different planets. A chart shows the kinetic, potential, and thermal energy for each spring.

Subject:
Physics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Kathy Perkins
Michael Dubson
Wendy Adams
Date Added:
08/02/2009
Maze Game
Conditions of Use:
No Strings Attached
Rating

Learn about position, velocity, and acceleration in the "Arena of Pain". Use the green arrow to move the ball. Add more walls to the arena to make the game more difficult. Try to make a goal as fast as you can.

Subject:
Physical Science
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Michael Dubson
Mindy Gratny
Sam Reid
Wendy Adams
Date Added:
10/30/2006
Motion in 2D
Conditions of Use:
No Strings Attached
Rating

Try the new "Ladybug Motion 2D" simulation for the latest updated version. Learn about position, velocity, and acceleration vectors. Move the ball with the mouse or let the simulation move the ball in four types of motion (2 types of linear, simple harmonic, circle).

Subject:
Mathematics
Physics
Material Type:
Activity/Lab
Interactive
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Michael Dubson
Sam Reid
Date Added:
11/15/2007
Motion in 2D (AR)
Conditions of Use:
Read the Fine Print
Rating

Try the new "Ladybug Motion 2D" simulation for the latest updated version. Learn about position, velocity, and acceleration vectors. Move the ball with the mouse or let the simulation move the ball in four types of motion (2 types of linear, simple harmonic, circle).

Subject:
Physics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Michael Dubson
Sam Reid
Date Added:
07/02/2009