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Algebra II, Spring 2011
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This undergraduate level course follows Algebra I. Topics include group representations, rings, ...

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

Subject:
Algebra
Material Type:
Full Course
Textbook
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Artin, Michael
Chairs Around The Table
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In this lesson from Illuminations, students explore and discover linear relationships. Linear ...

In this lesson from Illuminations, students explore and discover linear relationships. Linear patterns are identified, extended and described verbally, numerically and algebraically through three investigations. Using manipulatives and the linked applet, "Chairs", learners determine the number of chairs needed when the number of tables is known, and vice versa. Instructional plan, questions for the students, assessment options, extensions and teacher reflections are provided.

Subject:
Mathematics
Algebra
Functions
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Samuel E. Zordak
Pan Balance-Shapes
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This Java applet allows children to explore a balancing tool and thus ...

This Java applet allows children to explore a balancing tool and thus build their algebraic thinking about equivalency. By placing shapes on each side of the balance and finding equivalent sets of weights, students discover the weight of each shape in one of six built-in sets or a random set.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Everything Balances Out in the End
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In this unit, students use online pan balances to study equality, order ...

In this unit, students use online pan balances to study equality, order of operations, numerical and variable expressions, and other key algebraic concepts. Lessons focus on balancing shapes to study equality and equivalence; balancing algebraic understanding, to explore simplifying expressions; and balancing algebra, to determine if algebraic expressions are equal.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Marcy Cook
Pan Balance-Expressions
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This interactive pan balance allows students to enter numeric or algebraic expressions ...

This interactive pan balance allows students to enter numeric or algebraic expressions and investigate the important concept of equivalence as well as practice arithmetic and algebraic skills. Users place an expression in each of the red and blue pans. These expressions may or may not include the variable x. If the expression is algebraic, a value for x is entered or adjusted by moving the slider. As the value of x changes, the results will be weighed and graphed. Instructions and exploration directions and questions are included.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
The Variable Machine
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This lesson from Illuminations provides an introduction to the use of variables, ...

This lesson from Illuminations provides an introduction to the use of variables, and develops students' algebraic thinking. Students create variable machines to discover the value of words by assigning each letter of the alphabet a unique number value. Learning objectives, a materials list, a pdf file of the student worksheet, an instructional plan, questions for the students, assessment options, extensions, and teacher reflections are provided.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Gilbert Cuevas and Karol Yeatts
As People Get Older, They Get Taller
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This two-lesson unit from Illuminations, exposes students to algebra, measurement, and data ...

This two-lesson unit from Illuminations, exposes students to algebra, measurement, and data analysis concepts and the major theme of analyzing change. In the first lesson, students measure the heights of classmates and older students and construct a table of height and age data to compare them. The second lesson's instructional goal is to understand how change in one variable, age, can relate to change in a second variable, height. Instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given.

Subject:
Mathematics
Algebra
Functions
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Elana Joram and Christina Hartman
Walk the Line: A Module on Linear Functions
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Prepared with pre-algebra or algebra 1 classes in mind, this module leads ...

Prepared with pre-algebra or algebra 1 classes in mind, this module leads students through the process of graphing data and finding a line of best fit while exploring the characteristics of linear equations in algebraic and graphic formats. Then, these topics are connected to real-world experiences in which people use linear functions. During the module, students use these scientific concepts to solve the following hypothetical challenge: You are a new researcher in a lab, and your boss has just given you your first task to analyze a set of data. It being your first assignment, you ask an undergraduate student working in your lab to help you figure it out. She responds that you must determine what the data represents and then find an equation that models the data. You believe that you will be able to determine what the data represents on your own, but you ask for further help modeling the data. In response, she says she is not completely sure how to do it, but gives a list of equations that may fit the data. This module is built around the legacy cycle, a format that incorporates educational research feindings on how people best learn.

Subject:
Engineering
Life Science
Mathematics
Algebra
Material Type:
Unit of Study
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Aubrey Mckelvey
TeachEngineering.org
VU Bioengineering RET Program,
Linear Algebra II
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Linear Algebra is both rich in theory and full of interesting applications; ...

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
Pan Balance-Numbers
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This Java tool is used to strengthen student understanding of equality and ...

This Java tool is used to strengthen student understanding of equality and computation of numerical expressions. The applet also helps students understand that equality is a relationship, not an operation. After entering an expression in both the red and blue pan, the pans will move up and down depending on which expression is greater. When the expressions are equivalent, the pans will balance and the full equation will be entered into the Balanced Equations table. Instructions and exploration directions and questions are included.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Block Pounds
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In this Illuminations lesson plan students explore the use of variables as ...

In this Illuminations lesson plan students explore the use of variables as they solve for the weights of objects using information presented in pictures. Learners model situations that involve adding and subtracting whole numbers, using objects, pictures, and symbols. A student activity sheet is available and downloadable (pdf).

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Links Away
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In this unit plan, primary learners explore the five models of subtraction ...

In this unit plan, primary learners explore the five models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using concrete (links), pictorial, and verbal representations to develop an understanding of symbolic notations. Students also investigate fact families, including those where one addend is 0 and where the addends are alike and also learn that the order (commutative) property) does not hold for subtraction. A brief bibliography of related books for children is provided. Instead of using hands on manipulatives and balances, links to Java applets: Pan Balance-Shapes and Pan Balance-Numbers ( both cataloged separately) are included. Instructional plan, questions for the students, assessment options, extensions,and teacher reflections are given for each lesson as well as links to down load all student resources.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Grace M. Burton
Stability in Numbers
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In this Illuminations lesson, students apply their knowledge of addition equations to ...

In this Illuminations lesson, students apply their knowledge of addition equations to investigate the equivalence of two numeric expressions using the "Pan Balance-Numbers" applet (cataloged separately). An instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given for the lesson as well as links to the applet and a student activity sheet(word format).

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Gary Martin and Brian Keller
Running Races
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In this unit of five lessons from Illuminations, learners begin with a ...

In this unit of five lessons from Illuminations, learners begin with a number-line model and extend it to investigate linear relationships with the Distance, Speed, and Time Simulation from NCTM's E-Examples. Students then progress to plotting points and graphing linear functions while continually learning and reinforcing basic multiplication facts. Instructional plan, questions for the students, assessment options, extensions,and teacher reflections are given for each lesson as well as links to download all student resources.

Subject:
Mathematics
Algebra
Functions
Geometry
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Grace M. Burton
Pick-a-Path
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This mobile app (available for both iOS and Android devices) was developed ...

This mobile app (available for both iOS and Android devices) was developed by the National Council of Teachers of Mathematics with funding from Verizon Foundation. The app is based on the Decimal Maze from the popular lesson "Too Big or Too Small". The goal is to help Okta reach the target (maximum, minimum, or a specific value) by choosing a path from the top of the maze to the bottom — adding, subtracting, multiplying and dividing as the player goes. Seven levels with seven puzzles in each level test the player's skills with operation with powers of ten, negative numbers, fractions, decimals, and exponents.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Verizon Foundation
Exploring Krypto
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This lesson plan provides the teacher with an activity for introducing the ...

This lesson plan provides the teacher with an activity for introducing the game Krypto, which helps to develop number sense, computational skill, and an understanding of the order of operations. Players are given five number cards. They combine them, using the standard arithmetic operations, to create a target number. As students investigate the game, they develop strategies for finding solutions efficiently. The plan includes learning objectives, materials needed, questions to ask students, assessment options, extensions, teacher self-reflection questions, and a link to the online version, Primary Krypto, (catalogued separately).

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Samuel E. Zordak
Pick-a-Path Instructional Guide:Using Pick-a-Path in Grades 3-7.
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This instructional guide (PDF) is for the mobile app Pick-a-Path (both iOS ...

This instructional guide (PDF) is for the mobile app Pick-a-Path (both iOS and Android platforms). The guide provides professional development by discussing the math in each level of the game, giving suggestions for classroom use, and recommending related resources from Illuminations. The Pick-a-Path app is cataloged separately and listed as a related resource.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Lisa Willman
Mathematics for Materials Scientists and Engineers, Fall 2005
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This course covers the mathematical techniques necessary for understanding of materials science ...

This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor Carter's 3.016 course Web site.

Subject:
Calculus
Material Type:
Full Course
Textbook
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Carter, W. Craig
Statistical Method in Economics, Fall 2006
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The course introduces statistical theory to prepare students for the remainder of ...

The course introduces statistical theory to prepare students for the remainder of the econometrics sequence. The emphasis of the course is to understand the basic principles of statistical theory. A brief review of probability will be given; however, this material is assumed knowledge. The course also covers basic regression analysis. Topics covered include probability, random samples, asymptotic methods, point estimation, evaluation of estimators, Cramer-Rao theorem, hypothesis tests, Neyman Pearson lemma, Likelihood Ratio test, interval estimation, best linear predictor, best linear approximation, conditional expectation function, building functional forms, regression algebra, Gauss-Markov optimality, finite-sample inference, consistency, asymptotic normality, heteroscedasticity, and autocorrelation.

Subject:
Statistics and Probability
Economics
Material Type:
Assessment
Full Course
Homework/Assignment
Lecture Notes
Syllabus
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Chernozhukov, Victor
Vector Calculus
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This is a text on elementary multivariable calculus, designed for students who ...

This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.

Subject:
Calculus
Material Type:
Activity/Lab
Homework/Assignment
Textbook
Provider:
Schoolcraft College
Author:
Michael Corral