Linear Algebra for Beginners: Open Doors to Great Careers

Learn the core topics of Linear Algebra to open doors to Computer Science, Data Science, Actuarial Science, and more!
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  • Lectures 90
  • Contents Video: 7 hours
    Other: 1 hour
  • Skill Level All Levels
  • Languages English
  • Includes Lifetime access
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    Available on iOS and Android
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About This Course

Published 1/2015 English

Course Description

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The prerequisite to the course Linear Algebra for Beginners: Open Doors to Great Careers 2.

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Would you like to learn a mathematics subject that is crucial for many high-demand lucrative career fields such as:

  • Computer Science
  • Data Science
  • Actuarial Science
  • Financial Mathematics
  • Cryptography
  • Engineering
  • Computer Graphics
  • Economics

If you're looking to gain a solid foundation in Linear Algebra, allowing you to study on your own schedule at a fraction of the cost it would take at a traditional university, to further your career goals, this online course is for you. If you're a working professional needing a refresher on linear algebra or a complete beginner who needs to learn Linear Algebra for the first time, this online course is for you.

Why you should take this online course: You need to refresh your knowledge of linear algebra for your career to earn a higher salary. You need to learn linear algebra because it is a required mathematical subject for your chosen career field such as computer science or electrical engineering. You intend to pursue a masters degree or PhD, and linear algebra is a required or recommended subject.

Why you should choose this instructor: I earned my PhD in Mathematics from the University of California, Riverside. I have extensive teaching experience: 6 years as a teaching assistant at University of California, Riverside, over two years as a faculty member at Western Governors University, #1 in secondary education by the National Council on Teacher Quality, and as a faculty member at Trident University International.

In this course, I cover the core concepts such as:

  • Gaussian elimination
  • Vectors
  • Matrix Algebra
  • Determinants
  • Vector Spaces
  • Subspaces

After taking this course, you will feel CARE-FREE AND CONFIDENT. I will break it all down into bite-sized no-brainer chunks. I explain each definition and go through each example STEP BY STEP so that you understand each topic clearly. I will also be AVAILABLE TO ANSWER ANY QUESTIONS you might have on the lecture material or any other questions you are struggling with.

Practice problems are provided for you, and detailed solutions are also provided to check your understanding.

30 day full refund if not satisfied.

Grab a cup of coffee and start listening to the first lecture. I, and your peers, are here to help. We're waiting for your insights and questions! Enroll now!

What are the requirements?

  • Basic understanding of algebra

What am I going to get from this course?

  • Refresh your math knowledge.
  • Gain a firm foundation in Linear Algebra for furthering your career.
  • Learn one of the mathematical subjects crucial for Computer Science.
  • Learn one of the mathematical subjects crucial for engineering, computer science, physics, economics, computer animation, and cryptography among many others.
  • Learn one of the mathematical subjects needed for Data Science.
  • Learn a mathematical subject useful in becoming a Quant on Wall Street.

What is the target audience?

  • Working Professionals
  • Anyone interested in gaining mastery of the core concepts in Linear Algebra.
  • Adult Learners
  • College Students

What you get with this course?

Not for you? No problem.
30 day money back guarantee.

Forever yours.
Lifetime access.

Learn on the go.
Desktop, iOS and Android.

Get rewarded.
Certificate of completion.

Curriculum

Section 1: Introduction
Introduction Lecture
Preview
03:44
Section 2: Solving Systems of Linear Equations
11:13

In this lecture, we discuss Gaussian Elimination and examples of solving a system of linear equations.

Students will learn about the three moves in Gaussian elimination.

18:15

In this lecture, the row echelon form is introduced and many examples of Gaussian elimination are worked out.

Students will learn how to apply Gaussian elimination to solve systems of linear equations. Students will also see the three different cases in regard to solutions to systems of equations.

1 page

Practice problems for Gaussian elimination

1 page

Solutions to Problem set Gaussian elimination

3 pages

Detailed solutions are provided if needed.

11:13

The augmented matrix is introduced and the elementary row operations are defined.

Students will learn how to apply elementary row operations to an augmented matrix.

06:32

An additional example of applying row operations is provided.

1 page

Practice problems for Elementary Row Operations

1 page

Solutions to Problem set Elementary Row Operations

4 pages

Detailed solutions to the problem set Elementary Row Operations are provided, if needed.

Section 3: Vectors
18:57

The vector operations of addition, scalar multiplication, and matrix multiplication are introduced and the definition of linear combination is provided.

Students will learn how to add two vectors, multiply a vector by a scalar, and multiply a vector by a matrix. The student will understand what linear combinations are and what weights are.

2 pages

Practice problems for Vector Operations and Linear Combinations

1 page

Solutions to Problem set Vector Operations and Linear Combinations

16:16

In this lecture, the notion of span is introduced and it is shown how a system of equations can be rewritten as a matrix equation.

06:26

The notion of linear independence is introduced.

11:02

An example of determining linear independence is provided.

Students will learn how to determine when a set of vectors is linearly independent.

04:36

A second example of determining linear independence is provided.

Students will learn how to determine when a set of vectors is linearly independent.

1 page

Practice problems for Linear Independence

1 page

Solutions to Problem set Linear Independence

2 pages

Detailed solutions to problem set Linear Independence are provided, if needed.

Section 4: Matrix Operations
07:12

The matrix operations of addition and scalar multiplication are introduced.

Students will learn how to add two matrices and how to multiply a matrix by a scalar.

09:18

The matrix operation of multiplication is introduced.

Students will learn how to multiply two matrices.

1 page

Practice problems for Matrix Operations

1 page

Solutions to Problem set Matrix Operations

Review Request
1 page
Section 5: Properties of Matrix Addition and Scalar Multiplication
13:13

The properties of additive commutativity and associativity are introduced. The distributivity properties are also introduced.

Students will learn how to apply the additive commutativity, additive associativity, and distributivity properties.

14:25

The properties of additive and multiplicative identities, additive inverses, and multiplicative associativity and distributivity are introduced.

Students will learn how to apply properties of additive and multiplicative identities, additive inverses, and multiplicative associativity and distributivity.

1 page

Practice problems for Properties of Matrix Operations

1 page

Solutions to Problem Set Properties of Matrix Operations

3 pages

Detailed solutions to problem set Properties of Matrix Operations is provided, if needed.

06:42

The definition of transpose of a matrix is provided, and properties of the transpose are introduced.

Students will learn how to find the transpose of a matrix and how to apply properties of transposes.

1 page

Practice problems for Transpose of a Matrix.

1 page

Solutions to Problem Set Transpose of a Matrix

1 page

Detailed solutions to Problem Set Transpose of a Matrix are provided, if needed.

Section 6: The Inverse of a Matrix
05:30

The definition of inverse matrix is introduced and the formula for the inverse of a 2 by 2 matrix is given.

Students will learn what an inverse matrix is.

10:56

The process of Gauss-Jordan Elimination is explained.

Students will learn how to find the inverse of a matrix using Gauss-Jordan Elimination.

06:03

An additional example of Gauss-Jordan Elimination is provided.

1 page

Practice problems for Inverse of a Matrix

1 page

Solutions to Problem Set Inverse of a Matrix

5 pages

Detailed solutions to Problem set Inverse of a Matrix are provided, if needed.


Section 7: Determinants
02:34

The formula for the determinant of a 2 by 2 matrix is introduced.

Students will learn how to find the determinant of a 2 by 2 matrix.

07:18

The process of Cofactor Expansion is explained.

Students will learn how to apply cofactor expansion to find the determinant of a 3 by 3 matrix.

05:51

Additional examples of cofactor expansion are provided.

1 page

Practice problems for Determinants

1 page

Solutions to Problem Set Determinants

2 pages

Detailed solutions to Problem set Determinants are provided, if needed.

Review Request
1 page
Section 8: Properties of Determinants
11:07

The determinant of a product of two matrices and the determinant of a scalar multiple of a matrix are discussed.

Students will be able to find the determinant of a product of matrices and the determinant of a scalar multiple of a matrix.

07:26

The relationship between determinants and invertibility is explained.

Students will be able to determine when a matrix is invertible by examining the determinant.

03:35

The determinant of the transpose of a matrix is discussed.

Students will learn how to find the determinant of the transpose of a matrix.

1 page

Practice problems for Properties of Determinants

1 page

Solutions to Problem set Properties of Determinants

2 pages

Detailed solutions to Problem set Properties of Determinants are provided, if needed.

Section 9: Vector Spaces
07:22

The definition of vector space is explained.

Students will learn what a vector space is.

13:43

A proof is given to show that R2 is a vector space.

Students will learn how to prove a set is a vector space.

12:18

The proof of the claim that R2 is a vector space is continued.

16:46

An additional example of a vector space is provided.

04:03

The proof of the first five properties of a vector space applied to P2 is continued.

1 page

Practice problems for Vector Spaces.

4 pages

Solutions to Problem Set Vector Spaces

06:09

Examples of sets that are not vector spaces are discussed.

Students will learn how to detect when a set is a not a vector space.

1 page

Practice problems for Sets that are not vector spaces.

2 pages

Solutions to Problem set Sets that are not vector spaces.

Section 10: Subspaces
09:55

The definition of a subspace is provided, and the three subspace properties are outlined. An example of a proof showing that a subset of R2 is a subspace is demonstrated.

Students will learn how to show that a subset of a vector space is a subspace.

03:38

The definition of a trivial subspace and of a nontrivial subspace are provided.

05:17

An example of a subspace of M(2,2), the set of all 2 by 2 matrices, is provided.

1 page

Practice problems for Subspaces

2 pages

Solutions to Problem Set Subspaces

09:13

An example of a subset of R2 that is not a subspace of R2 is discussed.

Students will learn how to show that a subset of a vector space is not a subspace of that vector space.

04:25

An additional example of a subset that is not a subspace is discussed.

1 page

Practice problems for Subsets that are not subspaces.

1 page

Solutions to Problem Set Subsets that are not subspaces.

Section 11: Span and Linear Independence
15:26

Students will learn how to show that a subset of a vector space spans the vector space and how to show that a subset of a vector space does not span the vector space.

08:24

Students will learn what the span of a subset of a vector space is.

09:35

Students will learn what it means for a subset of a vector space to be linearly independent.

13:44

Students will learn how to determine if a subset of a vector space is linearly independent or dependent.

1 page

Practice problems for span and linear independence.

3 pages

Solutions to Problem Set: Span and Linear Independence

Section 12: Basis and Dimension
16:07

Students will learn how to show that a subset of a vector space is a basis for the vector space.

09:52

Students will learn how to find the dimension of a vector space.

1 page

Practice problems for basis and dimension.

2 pages

Solutions to Problem Set: Basis and Dimension

03:26

Students will learn what the coordinates of a vector relative to a basis are and what the coordinate matrix of a vector relative to a basis is.

09:23

Students will learn what change of basis means and what a transition matrix from one basis to another is.

13:02

Students will learn how to find transition matrices from one basis to another.

1 page

Practice problems for coordinates and change of basis.

2 pages

Solutions to Problem Set: Coordinates and Change of Basis

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Instructor Biography

Richard Han, PhD in Mathematics

Hi there! My name is Richard Han. I earned my PhD in Mathematics from the University of California, Riverside. I have extensive teaching experience: 6 years as a teaching assistant at University of California, Riverside, over two years as a faculty member at Western Governors University, #1 in secondary education by the National Council on Teacher Quality, and as a faculty member at Trident University International. My expertise includes calculus and linear algebra. I am an instructor on Udemy for the courses Philosophy of Language: Solidify Critical Thinking Skills and Linear Algebra for Beginners: Open Doors to Great Careers.

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