Linear Algebra for Beginners: Open Doors to Great Careers 2

Learn the core topics of Linear Algebra to open doors to Computer Science, Data Science, Actuarial Science, and more!
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  • Lectures 87
  • Length 11.5 hours
  • 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 1/2016 English

Course Description

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

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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:

  • Inner Product Spaces
  • Linear Transformations
  • Eigenvalues and Eigenvectors
  • Symmetric Matrices and Orthogonal Diagonalization
  • Quadratic Forms
  • Singular Value Decomposition

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?

  • The Udemy Course "Linear Algebra for Beginners; Open Doors to Great Careers"

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
Preview
04:00
Section 2: Inner Product Spaces
17:01

The notion of a norm is introduced.

Students will learn how to find the norm of a vector and how to find the unit vector in the direction of a given vector.

09:20

The notion of the distance between two vectors is introduced.

Students will learn how to find the distance between two vectors.

19:57

The notion of the angle between two vectors is introduced. The notions of dot product and orthogonality are introduced as well.

Students will learn how to find the angle between two vectors and how to find the dot product of two vectors.

1 page

Practice problems for norms and dot product for Rn.

2 pages

Solutions to Problem Set: Norms and Dot Product for Rn

11:08

The definitions of inner product and of inner product spaces are provided.

12:34

Students will learn about some examples of inner product and of inner product spaces.

18:56

The definitions of norm, distance, and angle between two vectors in an inner product space are provided.

08:06

An additional example of norm, distance, and angle for inner product spaces is provided.

12:51

Students will learn how to find the orthogonal projection of one vector onto another vector.

2 pages

Practice problems for inner product spaces.

2 pages

Solutions to Problem Set: Inner Product Spaces

10:55

The definitions of orthogonal basis and of orthonormal basis are provided.

15:15

Students will learn how to find the coordinates of a vector relative to a given orthonormal basis.

08:09

Students will learn what the Gram-Schmidt process is.

12:45

Students will learn how to apply the Gram-Schmidt process.

15:42

An additional example of applying the Gram-Schmidt process is provided.

1 page

Practice problems for orthonormal bases.

4 pages

Solutions to Problem Set: Orthonormal Bases

09:12

The least-squares problem is introduced.

13:59

Students will learn how to solve least-squares problems.

1 page

Practice problems for least squares problems.

5 pages

Solutions to Problem Set: Least Squares Problems

Section 3: Linear Transformations
14:09

The definition of linear transformation is provided.

06:55

Students will learn about linear transformations represented by matrices.

1 page

Practice problems for linear transformations.

2 pages

Solutions to Problem Set: Linear Transformations

13:05

The definition of the kernel of a linear transformation is provided.

Students will learn how to find the kernel of a linear transformation.

08:23

Students will learn how to find a basis for the kernel of a linear transformation.

05:41

The definition of the range of a linear transformation is provided.

04:58

Students will learn how to find a basis for the range of a linear transformation.

09:47

The definitions of rank and nullity of a linear transformation are provided.

Students will learn how the rank and nullity of a linear transformation are related.

14:34

The definitions of the one-to-one and onto properties are provided.

Students will learn how to show that a given linear transformation is one-to-one and how to show that a given linear transformation is onto.

03:52

The definition of isomorphism is provided.

2 pages

Practice problems for the kernel and range of a linear transformation.

7 pages

Solutions to Problem Set: The Kernel and Range of a Linear Transformation

14:52

Students will learn how to find the standard matrix for a linear transformation and how to find the matrix of a linear transformation relative to the bases B and B'.

17:11

Students will learn how to find the matrix of a linear transformation relative to the bases B and B'.

12:25

Additional examples of finding the matrix of T relative to the bases B and B' are provided.

1 page

Practice problems for matrix representation of linear transformations.

4 pages

Solutions to Problem Set: Matrix Representation of Linear Transformations

08:04

Students will learn about reflections and rotations in the plane.

05:48

Students will learn how to apply compositions of linear transformations.

15:33

Students will learn how to apply rotations in 3-dimensional space.

1 page

Practice problems for applications of linear transformations.

2 pages

Solutions to Problem Set: Applications of Linear Transformations

Review Request
1 page
Section 4: Eigenvalues and Eigenvectors
14:37

The definitions of eigenvalue, eigenvector, and eigenspace are provided.

Students will learn the geometric interpretation of eigenvalues and eigenvectors.

07:15

Students will learn how to find the eigenvalues and eigenvectors of a matrix.

10:13

An example of finding eigenvalues and eigenvectors of a matrix is provided.

14:36

An additional example of finding eigenvalues and eigenvectors is provided. The notion of multiplicity of an eigenvalue is also introduced.

1 page

Practice problems for eigenvalues and eigenvectors.

4 pages

Solutions to Problem Set: Eigenvalues and Eigenvectors

13:01

The notion of diagonalizability is introduced.

15:30

Students will learn about a necessary and sufficient condition for diagonalizability.

05:15

Students will learn about a necessary and sufficient condition for diagonalizability.

04:43

Students will learn how to diagonalize a matrix.

1 page

Practice problems for diagonalization.

5 pages

Solutions to Problem Set: Diagonalization

14:19

Students will learn how to apply diagonalization to solving a system of linear differential equations.

13:38

An example of solving a system of linear differential equations is provided.

1 page

Practice problems for applications to differential equations.

3 pages

Solutions to Problem Set: Applications to Differential Equations

Section 5: Symmetric Matrices and Orthogonal Diagonalization
03:17

Students will learn about the properties of symmetric matrices.

17:52

An example of verifying the properties of symmetric matrices is provided.

19:54

The definition of orthogonal diagonalization is provided.

Students will learn how to orthogonally diagonalize a matrix.

06:45

The steps of orthogonal diagonalization are summarized.

03:31

The properties of symmetric matrices are summarized in the Spectral Theorem for Symmetric Matrices.

1 page

Practice problems for symmetric matrices and orthogonal diagonalization.

5 pages

Solutions to Problem Set: Symmetric Matrices and Orthogonal Diagonalization

13:07

Quadratic forms are introduced, and several examples are provided.

06:30

Students will learn how to apply orthogonal diagonalization to eliminating cross-product terms in quadratic forms.

13:42

An example of eliminating cross-product terms in a quadratic form is provided.

05:38

Students will learn about the Principal Axes Theorem.

1 page

Practice problems for quadratic forms.

2 pages

Solutions to Problem Set: Quadratic Forms

08:44

Students will learn what a singular value decomposition of a matrix is.

14:05

An example of finding a singular value decomposition of a matrix is provided.

Students will learn how to find a singular value decomposition of a matrix.

13:50

An example of finding a singular value decomposition of a matrix is provided.

Students will learn how to find a singular value decomposition of a matrix.

1 page

Practice problems for singular value decomposition.

6 pages

Solutions to Problem Set: Singular Value Decomposition

Section 6: Application of SVD to Statistics: Principal Component Analysis
09:35

Students will learn what mean-deviation form is and what a covariance matrix is.

09:21

Students will see an illustration of mean-deviation form and covariance matrix. Students will also learn what variance is.

10:16

The notion of principal component is introduced.

Students will learn how singular value decomposition is useful for finding principal components.

Section 7: Conclusion
Concluding Letter
1 page
Bonus Lecture
2 pages

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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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