- Course type: Self-paced
- Available Lessons: 42
- Average Lesson Length: 8 min
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Watch a preview:chapter 1 / lesson 1Algebra Vocabulary Terms
Course SummaryThis Linear Algebra Syllabus Resource & Lesson Plans course is a fully developed resource to help you organize and teach lessons on linear algebra. You can easily adapt the video lessons, transcripts, and quizzes to take full advantage of the comprehensive and engaging material we offer. Make planning your course easier by using our syllabus as a guide.
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Course Practice TestCheck your knowledge of this course with a 50-question practice test.
- Comprehensive test covering all topics
- Detailed video explanations for wrong answers
How It Works
You can use this linear algebra course as a template for designing and implementing your course. Here are the key components of the course and how you can use them:
- Chapters - Each chapter covers a unit of linear algebra, from algebraic expressions and the distributive property to orthonormal bases and the Gram-Schmidt process. Use these chapters as mile markers as you map out your course. We recommend planning to spend a week on each chapter, but you can always allocate the chapters according to the length of your specific linear algebra course.
- Lessons - Within each chapter are video lessons that further break down topics into bite-sized chunks. These lessons cover single topics like diagonalization or eigenspaces. Each one is often appropriate for a single class.
- Key Terms - Within each lesson are key terms. These are emphasized on screen and in the transcript. As you develop your syllabus, these key terms help you focus on the most important learning objectives. For example, the lesson on algebra vocabulary terms includes key terms like variables, equations and coefficients.
As you work on your linear algebra lesson plans, save time by incorporating video lessons from this resource. Here's how:
- Introduce Topics - Your students will be in the right mindset for understanding topics like linear dependence and independence if you begin class with a short video. It can be a jumping-off point for a lecture, group activity or class discussion.
- Break Up Lectures - The video format, which often includes animation, helps students visualize topics like inverse matrices and higher-order determinants.
- Assign For Homework - Each lesson in the course, from introductory linear algebra to diagonalizing symmetric matrices can be assigned to your students as homework.
Each video lesson includes a complete transcript. You can utilize these transcripts in several ways:
- Lecture Notes - Do you need a guide as you plan a lecture, such as one on solving linear equations with literal coefficients or deriving Laplace expansions? The transcripts cover each topic in depth, with key terms highlighted for quick reference.
- Student Reading - Perhaps you'd like your students to learn about linear combinations, but you don't have class time available. Assign the transcript as extra reading.
- Study Tools - When it's time for a unit exam on matrices in linear algebra, you can point your students to the transcripts on a square matrix, equal matrices and math operations with matrices as well as related topics to help them study.
Each video lesson has a corresponding quiz. Here's how to use the quizzes:
- Homework - Assign a quiz to your students as homework. You'll receive an email with the results, which enables you to verify they've completed the assignment and that they've understood the material. Questions cover everything from understanding how to find multiplicative inverses to the correct use of Cramer's rule to solve linear systems.
- Tests - You can meld the material in the quizzes into your own student assessments, saving you valuable time. Need a few questions on the use of Gauss-Jordan elimination to solve linear equations? There are plenty!
- Discussions - Jump-start a discussion with questions like: How do I use a system of equations?
Below is a sketch of the Linear Algebra syllabus modeled on a 6-week course. This sample can be adapted based on your course schedule. Navigate the chapters and lessons for more detail.
|Week||Unit||Sample of Topics Covered|
|Week 1||Basic Algebra Review||Variables in algebra, applications in linear algebra, algebra vocabulary|
|Week 2||Linear Equations and Systems||Solving simultaneous linear equations, intercepts and standard form, and applying the distributive property|
|Week 3||Vectors in Linear Algebra||Examples of orthonormal bases, methods for orthonormalizing a set of vectors, differentiating between linear dependence and independence|
|Week 4||Matrices in Linear Algebra||Defining a matrix, writing an augmented matrix, performing matrix row operations|
|Week 5||Determinants in Linear Algebra||Using determinants to solve systems of linear equations in two and three variables, minor matrices and higher-order determinants|
|Week 6||Eigenvalue and Eigenvector in Linear Algebra||Defining eigenvalues and eigenspaces, and determining the eigenvectors of matrices|
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