Matrix Algebra: Eigenvalues and Eigenvectors

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the tenth topic where we talk about the eigenvalue and eigenvectors of a square matrix. Learn how to define and find eigenvalues and eigenvector of a square matrix, and get introduced to some key theorems on eigenvalues and eigenvectors.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. Eigenvalues and Eigenvectors
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Matrix Algebra: Adequacy of Solutions

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the ninth topic where we talk about the adequacy of solutions of simultaneous linear equations. Learn how this adequacy is measured through the condition number of the coefficient matrix, and how the condition number is calculated approximately as well.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. Adequacy of Solutions
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Matrix Algebra: Gauss-Seidel Method

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the eighth topic where we talk about solving a set of simultaneous linear equations using the Gauss-Seidel method.  Learn this iterative method of solving simultaneous linear equations, and its pitfalls and advantages. Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. Gauss-Seidel Method
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Synergistic Activities on NSF Proposals

The new 2019 NSF proposal guidelines effective February 25, 2019, have a change in how synergistic activities are reported. The change is described as follows.

“Chapter II.C.2.f(i)(d), Synergistic Activities, has been revised to specify that a list should include up to five distinct examples that demonstrate the broader impact of the individual’s professional and scholarly activities that focuses on the integration and transfer of knowledge as well as its creation.”

The complete language is as follows.
“A list of up to five examples that demonstrate the broader impact of the individual’s professional and scholarly activities that focuses on the integration and transfer of knowledge as well as its creation. Examples could include, among others: innovations in teaching and training (e.g., development of curricular materials and pedagogical methods); contributions to the science of learning; development and/or refinement of research tools; computation methodologies and algorithms for problem-solving; development of databases to support research and education; broadening the participation of groups underrepresented in STEM; and service to the scientific and engineering community outside of the individual’s immediate organization.”

Well, for submission to an NSF grant due February 28, 2019, I revised my synergistic activities as follows. I want to know if this does or does not follow the guidelines. What would you change? I am having issues with the language of “list”, and “distinct”. Who can one contact at NSF for clarification? This does not seem to be a question for the program manager.

  1. Conducted four workshops on engineering education internationally during a 2018 Fulbright Specialist program at Universiti Teknologi Petronas, Malaysia.  The four topics were flipped classrooms, the scholarship of teaching and learning, massive open online courses, and improving student performance through learning strategies.
  2. Guest Editor, ASEE Advances in Engineering Education, Flipped Classrooms in STEM, 2016.  This special issue consisted of eight papers that showed how to implement and assess flipped classrooms in a variety of settings.
  3. Developed, revised, assessed and refined holistic and customized web-based resources on Numerical Methods (http://nm.mathforcollege.com) and corresponding MOOCs on Numerical Methods and Introduction to Matrix Algebra.  The OCW receives 1,000,000+ annual page views, 2,000,000+ annual views of YouTube videos on NumericalMethodsGuy channel, 100,000+ annual views on Numerical Methods Guy blog.
  4. Developed a unique textbook (adopted by 70 universities worldwide) and accompanying software PROMAL for undergraduates on the topic of Mechanics of Composite Materials published in 1997 (first edition) and 2005 (second edition) by CRC Press. This includes continued development of PROMAL – instructional software package for Mechanics of Composite Materials since 1985. More than 80 universities and many self-study students all over the world use PROMAL. The textbook has been translated to Persian and Turkish.
  5. Designed open source software MCTestAnalysis for analyzing and refining multiple-choice tests based on the analytical framework developed by Jorion, et al (2016) used for the validity of concept inventories. The open source software includes results such as item difficulty, item discrimination, Cronbach alpha, model estimation, item characteristic curves, tetrachoric, and scree plots.

Matrix Algebra: LU Decomposition Method

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the seventh topic where we talk about solving a set of simultaneous linear equations using the LU decomposition method.  First, the LU decomposition method is discussed along with its motivation.  The LU decomposition method to find the inverse of a square matrix is discussed. Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. LU Decomposition Method
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Matrix Algebra: Gaussian Elimination Method

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the sixth topic where we talk about solving a set of simultaneous linear equations using Gaussian elimination method – both Naive and partial pivoting methods are discussed. How to find determinants by using the forward elimination step of Gaussian elimination is also discussed.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. Gaussian Elimination Method
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Matrix Algebra: System of Equations

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the fifth topic where we talk about setting up simultaneous linear equations in matrix form, consistent and inconsistent system of equations, the rank of a matrix, conditions when unique, infinite number or no solutions exist, and finding the inverse of a square matrix.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. System of Equations
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Adaptive learning improves the flipped classroom

A two-year exploratory study conducted at the University of South Florida, and evaluated and assessed by the University of Pittsburgh, studied the effect of using adaptive lessons in improving pre-class learning in a flipped classroom.

Read the whole article here: https://www.smartsparrow.com/demos/numerical-methods/ 

This material is based upon work supported partially by the National Science Foundation under Grant Number 1609637. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Matrix Algebra: Unary Operations

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the fourth topic where we talk about unary operations on a matrix including transpose, symmetry, determinant, and trace of a matrix.  Methods of finding determinants along with some fundamental theorems of determinants are discussed.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. Unary Operations
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Matrix Algebra: Vectors

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra.

In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra.

Here is the second topic where we talk about vectors, binary operations on vectors, set up the concept of linear combination and linear independence of vector.  Learn how vectors are used to set up simultaneous linear equations.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation.

Vectors

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