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

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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

Linear algebra foundations with unique laff approach

According to learners, this course provides a strong foundation in linear algebra, covering all standard topics and integrating theory with computation using the unique LAFF approach. Students often praise the instructor's clear and engaging lectures and the helpfulness of the MATLAB programming assignments for understanding abstract concepts. While many find it challenging and requiring a significant time commitment, particularly the assignments and exams, they also describe it as highly rewarding and effective for building a deep understanding. Some reviewers note that having some prior exposure to programming or mathematics is beneficial.

Requires significant effort and time commitment.

"This course is quite challenging and demands a serious time investment, especially the later assignments."

"Expect to spend a lot of hours grappling with the concepts and problems; it's not a light introduction."

"The difficulty ramps up quickly, particularly around matrix operations and proofs."

"I found the exams required a very thorough understanding, not just surface-level knowledge."

Useful integration with MATLAB coding.

"The integration of MATLAB assignments was fantastic; it really helped solidify the theoretical concepts."

"Using programming to implement algorithms discussed in lectures was a key part of my learning."

"Appreciated the hands-on coding experience, bridging the gap between math and computation."

"MATLAB exercises reinforced understanding better than just solving problems on paper."

Instructor is clear, engaging, & knowledgeable.

"Professor van de Geijn is an absolutely amazing instructor; his passion for the subject is infectious."

"The lectures are exceptionally clear and well-explained, breaking down complex topics effectively."

"He has a knack for making challenging material accessible and interesting."

"One of the best online instructors I've encountered; truly an expert who can teach."

Distinct method connecting theory & computation.

"The LAFF approach to linear algebra is truly unique and effective; it really changed how I think about the subject."

"I loved how the course intertwined theoretical concepts with practical computational aspects using the LAFF method."

"This approach is different from how Linear Algebra is typically taught, but once you get into the rhythm, it's incredibly insightful."

"Connecting the hand calculations with programming exercises made the abstract ideas much clearer."

Provides deep understanding of core concepts.

"I feel like I finally gained a deep and intuitive understanding of linear algebra fundamentals after taking this course."

"Excellent coverage from basic vector operations all the way through eigenvalues; it's a comprehensive foundation."

"The course doesn't just teach you *how* to do things, but *why*, which is crucial for true understanding."

"It lays a solid theoretical and practical groundwork that is invaluable for further study or applications."

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.

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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.

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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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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.

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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.

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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

Quantitative Analysts use their knowledge of mathematics and finance to develop and implement trading strategies. 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 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

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.

See salaries and explore the career path for Operations Research Analyst

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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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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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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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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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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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

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.

See salaries and explore the career path for Business Analyst

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.

See salaries and explore the career path for Investment Analyst

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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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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