Linear Algebra - Foundations to Frontiers from edX

Linear Algebra: Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets. Students appreciate our unique approach to teaching linear algebra because:

It's visual.
It connects hand calculations, mathematical abstractions, and computer programming.
It illustrates the development of mathematical theory.
It's applicable.

In this course, you will learn all the standard topics that are taught in typical undergraduate linear algebra courses all over the world, but using our unique method, you'll also get more! LAFF was developed following the syllabus of an introductory linear algebra course at The University of Texas at Austin taught by Professor Robert van de Geijn, an expert on high performance linear algebra libraries. Through short videos, exercises, visualizations, and programming assignments, you will study Vector and Matrix Operations, Linear Transformations, Solving Systems of Equations, Vector Spaces, Linear Least-Squares, and Eigenvalues and Eigenvectors. In addition, you will get a glimpse of cutting edge research on the development of linear algebra libraries, which are used throughout computational science.

MATLAB licenses will be made available to the participants free of charge for the duration of the course.

To see what former learners have to say about the course, read reviews on coursetalk.

We invite you to LAFF with us!

What's inside

Learning objectives

Connections between linear transformations, matrices, and systems of linear equations
Partitioned matrices and characteristics of special matrices
Algorithms for matrix computations and solving systems of equations

Vector spaces, subspaces, and characterizations of linear independence
Orthogonality, linear least-squares, eigenvalues and eigenvectors

Connections between linear transformations, matrices, and systems of linear equations
Partitioned matrices and characteristics of special matrices
Algorithms for matrix computations and solving systems of equations
Vector spaces, subspaces, and characterizations of linear independence
Orthogonality, linear least-squares, eigenvalues and eigenvectors

Syllabus

Week 0 Get ready, set, go!Week 1 Vectors in Linear AlgebraWeek 2 Linear Transformations and MatricesWeek 3 Matrix-Vector OperationsWeek 4 From Matrix-Vector Multiplication to Matrix-Matrix MultiplicationExam 1Week 5 Matrix-Matrix MultiplicationWeek 6 Gaussian EliminationWeek 7 More Gaussian Elimination and Matrix InversionWeek 8 More on Matrix InversionExam 2Week 9 Vector SpacesWeek 10 Vector Spaces, Orthogonality, and Linear Least SquaresWeek 11 Orthogonal Projection and Low Rank ApproximationWeek 12 Eigenvalues and EigenvectorsFinal

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Teaches connections between linear transformations, matrices, and systems of linear equations, which is common in advanced math and engineering

Examines partitioned matrices and characteristics of special matrices, which is important in computer science and data science

Provides algorithms for matrix computations and solving systems of equations, which is useful in various technical fields

Covers vector spaces, subspaces, and characterizations of linear independence, which has applications in machine learning and data analysis

Explores orthogonality, linear least-squares, eigenvalues and eigenvectors, which are fundamental concepts in linear algebra

Requires basic linear algebra knowledge, making it suitable for students with some prior exposure to the subject

Reviews summary

Challenging but rewarding intro to linear algebra

Learners say that this introductory course in linear algebra is well put together, with plenty of exercises and concepts explained well. Some reviewers found the heavy use of MATLAB and the Flame method a bit challenging, but ultimately appreciated it. Note that many students found that this course required a major time commitment and recommend it to those seeking a basic understanding of linear algebra.

Active instructors in discussion forums.

"The instructors were also active on the forums, which was nice to see."

Recommended for lifelong learners.

"If you are taking this course as a lifelong learner - this will be an excellent start."

Challenging but rewarding course.

"Great course. I found it challenging but rewarding."

"Hesitated between 4 and 5 stars, ended up putting 5 because I think the 2-stars given by some people are a bit of a stretch."

Easy-to-understand explanations of concepts.

"Everything is explained well in an easy to understand manner."

"The concepts are explained very well."

May not be sufficient for college-level coursework.

"if you are looking for the MOOC to complement your college course, this may not sufficiently cover your syllabus."

Heavy use of MATLAB and FLAME in the course.

"I was expecting a course that would make linear algebra interesting, one where I would understand what it it is used for and why it is useful. Instead, I found a course hugely dependent on Matlab and some weird "Flame" notation that seems to be unique to them."

"Many people complain about MATLAB and Flame which come up during the course, and I understand that."

Expect 5-8 hours of study time per week.

"LAFF requires a major time commitment."

"Unless you are already familiar with some of the topics, you'll probably spend 5-8 hours a week."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Linear Algebra - Foundations to Frontiers with these activities:

Review Matrices

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Reviewing matrices will help you refresh your knowledge of the basics and prepare you for the more advanced concepts in this course.

Browse courses on Matrices

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Review your notes from a previous linear algebra course
Read the relevant sections in a linear algebra textbook
Do some practice problems on matrices

Practice Matrix Operations

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Practicing matrix operations will help you refresh your skills and improve your fluency.

Browse courses on Matrix Operations

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Find practice problems online or in a textbook
Work through the problems step-by-step
Check your answers against the solutions

Review Introduction to Linear Algebra

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Reading this book provides a strong foundation for the concepts that will be covered in this course.

View Introduction to Linear Algebra (Gilbert Strang) on Amazon

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Read chapters 1-3
Do the practice problems at the end of each chapter

Six other activities

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Show all nine activities

Organize Your Course Materials

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Organizing your course materials will help you stay on top of the material and make it easier to study.

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Create a system for organizing your notes, assignments, and quizzes
Keep your materials in a central location
Review your materials regularly

Watch Video Tutorials

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Watching video tutorials can help you visualize the concepts and understand them more clearly.

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Find video tutorials online
Watch the tutorials at your own pace
Take notes on the key concepts

Study with a Peer

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Studying with a peer can help you learn from each other and reinforce the concepts.

Browse courses on Linear Algebra

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Find a peer who is also taking the course
Meet regularly to discuss the material
Work on practice problems together

Solve Linear Algebra Problems

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Practicing solving linear algebra problems will help you develop a deeper understanding of the concepts.

Browse courses on Linear Algebra

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Find practice problems online
Work through the problems step-by-step
Check your answers against the solutions

Create a Linear Algebra Cheat Sheet

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Creating a cheat sheet will help you organize the key concepts and formulas in a way that is easy to reference.

Browse courses on Linear Algebra

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Gather the key concepts and formulas from the course
Organize the information in a logical way
Create a cheat sheet that is visually appealing and easy to read

Mentor a Beginner

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Mentoring a beginner can help you solidify your understanding of the concepts and improve your communication skills.

Browse courses on Linear Algebra

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Find a beginner who is struggling with the course
Meet regularly to discuss the material
Help the beginner solve practice problems

Career center

Learners who complete Linear Algebra - Foundations to Frontiers will develop knowledge and skills that may be useful to these careers:

Machine Learning Engineer

Machine Learning Engineers use their knowledge of mathematics and computer science to design and implement algorithms that can learn from data. This course can be helpful for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for a Machine Learning Engineer.

See salaries and explore the career path for Machine Learning Engineer

Quantitative Analyst

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Data Scientist

A Data Scientist uses their knowledge of data and linear algebra to identify patterns and create models that can be used for decision-making. This course is a good foundation for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for a Data Scientist.

See salaries and explore the career path for Data Scientist

Statistician

Statisticians use their knowledge of mathematics and statistics to collect, analyze, and interpret data. This course can be helpful for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for a Statistician.

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Data Analyst

Data Analysts use their knowledge of data and mathematics to analyze data and identify trends. This course can be helpful for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for a Data Analyst.

See salaries and explore the career path for Data Analyst

Operations Research Analyst

Operations Research Analysts use their knowledge of mathematics and computer science to solve problems in business and industry. This course can be helpful for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for an Operations Research Analyst.

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Actuary

Actuaries use their knowledge of mathematics and statistics to assess risk and uncertainty in the insurance and finance industries. This course can be helpful for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for an Actuary.

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Auditor

Auditors use their knowledge of accounting and finance to examine financial records and ensure that they are accurate and compliant with regulations. This course can be helpful for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for an Auditor.

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Investment Analyst

Investment Analysts use their knowledge of finance and economics to evaluate investments and make recommendations to clients. This course can be helpful for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for an Investment Analyst.

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Business Analyst

Business Analysts use their knowledge of business and technology to analyze business processes and identify opportunities for improvement. This course can be helpful for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for a Business Analyst.

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Software Engineer

Software Engineers use their knowledge of computer science to design and implement software applications. This course can be helpful for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for a Software Engineer.

See salaries and explore the career path for Software Engineer

Financial Analyst

Financial Analysts use their knowledge of mathematics and finance to advise clients on investment decisions. This course can be helpful for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for a Financial Analyst.

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Risk Analyst

Risk Analysts use their knowledge of mathematics and finance to assess risk and uncertainty in the financial industry. This course can be helpful for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for a Risk Analyst.

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Consultant

Consultants use their knowledge of business and technology to help organizations solve problems and improve their performance. This course can be helpful for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for a Consultant.

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Teacher

Teachers use their knowledge of a subject matter to educate students. This course can be helpful for someone looking to enter this field because it will teach the fundamentals of linear algebra and programming, which are both essential for a Teacher.

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