Matrix Algebra with Computational Applications is a collection of Open Educational Resource …
Matrix Algebra with Computational Applications is a collection of Open Educational Resource (OER) materials designed to introduce students to the use of Linear Algebra to solve real-world problems. These materials were developed specifically for students and instructors working in a "flipped classroom" model that emphasizes hands-on problem-solving activities during class meetings, with students watching lectures and completing readings and assignments outside of the classroom. To access the Matrix Algebra with Computational Applications website, please go to http://colbrydi.github.io/MatrixAlgebra
We all know that calculus courses such as 18.01 Single Variable Calculus …
We all know that calculus courses such as 18.01 Single Variable Calculus and 18.02 Multivariable Calculus cover univariate and vector calculus, respectively. Modern applications such as machine learning and large-scale optimization require the next big step, “matrix calculus” and calculus on arbitrary vector spaces. This class covers a coherent approach to matrix calculus showing techniques that allow you to think of a matrix holistically (not just as an array of scalars), generalize and compute derivatives of important matrix factorizations and many other complicated-looking operations, and understand how differentiation formulas must be reimagined in large-scale computing.
Linear algebra concepts are key for understanding and creating machine learning algorithms, …
Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization–and above all a full explanation of deep learning.
Students obtain a basic understanding of microfluidic devices, how they are developed …
Students obtain a basic understanding of microfluidic devices, how they are developed and their uses in the medical field. After conducting the associated activity, they watch a video clip and learn about flow rate and how this relates to the speed at which medicine takes effect in the body. What they learn contributes to their ongoing objective to answer the challenge question presented in lesson 1 of this unit. They conclude by solving flow rate problems provided on a worksheet.
A work in progress, CK-12's Math 7 explores foundational math concepts that …
A work in progress, CK-12's Math 7 explores foundational math concepts that will prepare students for Algebra and more advanced subjects. Material includes decimals, fractions, exponents, integers, percents, inequalities, and some basic geometry.
In this task students are asked to write two expressions from verbal …
In this task students are asked to write two expressions from verbal descriptions and determine if they are equivalent. The expressions involve both percent and fractions. This task is most appropriate for a classroom discussion since the statement of the problem has some ambiguity.
The purpose of this task is to emphasize the use of the …
The purpose of this task is to emphasize the use of the Remainder Theorem (a discussion of which should obviously be considered as a prerequisite for the task) as a method for determining structure in polynomial in equations, and in this particular instance, as a replacement for division of polynomials.
This task assumes students are familiar with mixing problems. This approach brings …
This task assumes students are familiar with mixing problems. This approach brings out different issues than simply asking students to solve a mixing problem, which they can often set up using patterns rather than thinking about the meaning of each part of the equations.
The problem deals with a rational expression which is built up from …
The problem deals with a rational expression which is built up from operations arising naturally in a context: adding the volumes of the fertilizer and the water, and dividing the volume of the fertilizer by the resulting sum. Thus it encourages students to see the expression as having meaning in terms of numbers and operations, rather than as an abstract arrangement of symbols.
This lesson unit is intended to help you assess how well students …
This lesson unit is intended to help you assess how well students use algebra in context, and in particular, how well students: explore relationships between variables in everyday situations; find unknown values from known values; find relationships between pairs of unknowns, and express these as tables and graphs; and find general relationships between several variables, and express these in different ways by rearranging formulae.
This undergraduate course focuses on traditional algebra topics that have found greatest …
This undergraduate course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics.
Students will breed fruit flies through several generations and record their data …
Students will breed fruit flies through several generations and record their data using mathematical models in order to demonstrate the inheritance of trait variations.
In this seminar you will learn how to complete multiple step equations. …
In this seminar you will learn how to complete multiple step equations. You will apply techniques you have learned about inverse operations to solve for a missing variable. You will use the techniques learned in this seminar to verify solutions to various other types of problems as you move forward. When solving multiple step equations, you will identify which operation to address first, which second, and so on, until you have the variable all alone and a solution for it. The best part? You can always substitute your answer into the original problem to make sure your answer is correct.StandardsCC.2.2.HS.D.8Apply inverse operations to solve equations or formulas for a given variable.
In the world of mathematics you can always count on encountering problems …
In the world of mathematics you can always count on encountering problems involving multiplication. With polynomials, things are no different. It is imperative to look at various types of multiplication problems since there are many different polynomials such as: monomials, binomials, trinomials, and more. This seminar covers the various forms of multiplication with these different types of polynomials.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomials.
In this seminar you will learn what rational expressions are and how …
In this seminar you will learn what rational expressions are and how to work with them. You will also be able to recognize real-world situations that involve rational expressions and how to apply the use of rational expressions to a variety of day-to-day situations. You will come to understand strategies for taking complex situations and simplifying them in order to find solutions for them.StandardsCCSI: HS: Algebra: HSA-SSE.A. Interpret the structure of expressions.CCSI: HS: Algebra: HSA-SSE.B. Write expressions in equivalent forms to solve problems.
This course covers vector and multi-variable calculus. It is the second semester …
This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include Vectors and Matrices, Partial Derivatives, Double and Triple Integrals, and Vector Calculus in 2 and 3-space.
This course covers vector and multi-variable calculus. It is the second semester …
This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates.
No restrictions on your remixing, redistributing, or making derivative works. Give credit to the author, as required.
Your remixing, redistributing, or making derivatives works comes with some restrictions, including how it is shared.
Your redistributing comes with some restrictions. Do not remix or make derivative works.
Most restrictive license type. Prohibits most uses, sharing, and any changes.
Copyrighted materials, available under Fair Use and the TEACH Act for US-based educators, or other custom arrangements. Go to the resource provider to see their individual restrictions.
