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Mat Leonard,
Andrew Paster,
Jennifer Staab,
Luis Serrano,
Juan Delgado,
Juno Lee,
Mike Yi,
Grant Sanderson,
and
Ortal Arel
Learn the basics of the beautiful world of Linear Algebra and
why it is such an important mathematical tool in the world of AI.
Register for this course and see more details by visiting:
OpenCourser.com/course/6b00ma/linear
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UDACITY40
What's inside
Syllabus
Take a sneak peek into the beautiful world of Linear Algebra and learn why it is such an important mathematical tool.
Learn about vectors, the basic building block of Linear Algebra.
Read more
Syllabus
Take a sneak peek into the beautiful world of Linear Algebra and learn why it is such an important mathematical tool.
Learn about vectors, the basic building block of Linear Algebra.
Read more
Learn how to scale and add vectors and how to visualize the process.
What is a linear transformation and how is it directly related to matrices? Learn how to apply the math and visualize the concept.
Learn how to graph 2D vectors.
Learn how to computationally determine a vector's span and solve a simple system of equations.
Learn how to solve some problems computationally using vectors and matrices.
Take a peek into the world of Neural Networks and see how it related directly to Linear Algebra!
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Ideal for those unfamiliar with this math
Enhances a basis for those familiar with linear algebra
Instructors are industry professionals
Save this course
Save Linear Algebra Essentials to your list so you can find it easily later:
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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 Essentials with these
activities:
Review Matrix Algebra
Show steps
Review the basics of Matrix Algebra to ensure a solid foundation before beginning this course.
Browse courses on
Matrix Algebra
Show steps
-
Revisit theorems and proofs about matrix properties.
-
Practice matrix transformation and inversion.
-
Solve systems of equations using matrices.
Review 'Linear Algebra and its Applications' by David C. Lay
Show steps
Read or revisit key chapters from this classic textbook to solidify your understanding of linear algebra concepts.
View
Linear Algebra and Its Applications, Global...
on Amazon
Show steps
-
Review the chapter on vector spaces and subspaces.
-
Study the chapter on linear transformations and their applications.
Interactive Linear Algebra Simulations
Show steps
Explore interactive simulations to visualize concepts like vector spaces and transformations.
Browse courses on
Linear Algebra
Show steps
-
Use simulations to understand vector addition and scalar multiplication.
-
Visualize the effects of linear transformations on vectors.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Matrix Operations Drills
Show steps
Sharpen your skills in performing matrix operations and solving matrix equations.
Browse courses on
Matrix Operations
Show steps
-
Practice finding determinants and inverses of matrices.
-
Solve systems of linear equations using matrices.
Explain Linear Transformations to a Classmate
Show steps
Deepen your understanding by explaining the concept of linear transformations to someone else.
Browse courses on
Linear Transformations
Show steps
-
Prepare a clear and concise explanation of linear transformations.
-
Find a classmate and present your explanation to them.
-
Answer any questions and engage in a discussion about linear transformations.
Collaborative Problem-Solving Session
Show steps
Team up with peers to solve challenging linear algebra problems together.
Browse courses on
Problem Solving
Show steps
-
Form a study group with classmates who have similar interests in linear algebra.
-
Choose a set of problems from the course or a textbook.
-
Work together to solve the problems, discussing different approaches and strategies.
Develop a Linear Algebra Toolkit
Show steps
Create a comprehensive resource that summarizes key concepts and provides practical tools for applying linear algebra.
Browse courses on
Linear Algebra
Show steps
-
Gather notes, resources, and examples related to linear algebra.
-
Organize and structure the material into a cohesive toolkit.
-
Include clear explanations, step-by-step examples, and useful formulas.
Review Matrix Algebra
Show steps
Review the basics of Matrix Algebra to ensure a solid foundation before beginning this course.
Browse courses on
Matrix Algebra
Show steps
Show steps
Show steps
- Revisit theorems and proofs about matrix properties.
- Practice matrix transformation and inversion.
- Solve systems of equations using matrices.
Review 'Linear Algebra and its Applications' by David C. Lay
Show steps
Read or revisit key chapters from this classic textbook to solidify your understanding of linear algebra concepts.
View
Linear Algebra and Its Applications, Global...
on Amazon
Show steps
Show steps
Show steps
- Review the chapter on vector spaces and subspaces.
- Study the chapter on linear transformations and their applications.
Interactive Linear Algebra Simulations
Show steps
Explore interactive simulations to visualize concepts like vector spaces and transformations.
Browse courses on
Linear Algebra
Show steps
Show steps
Show steps
- Use simulations to understand vector addition and scalar multiplication.
- Visualize the effects of linear transformations on vectors.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Matrix Operations Drills
Show steps
Sharpen your skills in performing matrix operations and solving matrix equations.
Browse courses on
Matrix Operations
Show steps
Show steps
Show steps
- Practice finding determinants and inverses of matrices.
- Solve systems of linear equations using matrices.
Explain Linear Transformations to a Classmate
Show steps
Deepen your understanding by explaining the concept of linear transformations to someone else.
Browse courses on
Linear Transformations
Show steps
Show steps
Show steps
- Prepare a clear and concise explanation of linear transformations.
- Find a classmate and present your explanation to them.
- Answer any questions and engage in a discussion about linear transformations.
Collaborative Problem-Solving Session
Show steps
Team up with peers to solve challenging linear algebra problems together.
Browse courses on
Problem Solving
Show steps
Show steps
Show steps
- Form a study group with classmates who have similar interests in linear algebra.
- Choose a set of problems from the course or a textbook.
- Work together to solve the problems, discussing different approaches and strategies.
Develop a Linear Algebra Toolkit
Show steps
Create a comprehensive resource that summarizes key concepts and provides practical tools for applying linear algebra.
Browse courses on
Linear Algebra
Show steps
Show steps
Show steps
- Gather notes, resources, and examples related to linear algebra.
- Organize and structure the material into a cohesive toolkit.
- Include clear explanations, step-by-step examples, and useful formulas.
Career center
Learners who complete Linear Algebra Essentials will develop knowledge and skills
that may be useful to these careers:
Data Scientist
Data Scientist
Data Scientists explore large sets of data to draw meaningful conclusions that drive business decisions. To do so, they use mathematical tools like Linear Algebra to process, analyze, and visualize data. This course helps build a foundation in Linear Algebra, which is essential for Data Scientists to effectively perform their job duties. The course covers concepts like vectors, matrices, and linear transformations, which are all fundamental to data science.
Machine Learning Engineer
Machine Learning Engineer
Machine Learning Engineers work at the intersection of computer science and mathematics to develop and implement machine learning models. Linear Algebra is a critical component of machine learning, as it provides the mathematical framework for understanding and manipulating data. This course provides a strong foundation in Linear Algebra, which is essential for Machine Learning Engineers to succeed in their roles. The course covers concepts like vectors, matrices, and linear transformations, which are all used extensively in machine learning.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software applications. Linear Algebra is becoming increasingly important in software engineering, as it provides a mathematical framework for understanding and manipulating data. This course provides a strong foundation in Linear Algebra, which is beneficial for Software Engineers working with data-intensive applications. The course covers concepts like vectors, matrices, and linear transformations, which are all used in software engineering.
Statistician
Statistician
Statisticians collect, analyze, interpret, and present data. Linear Algebra is a fundamental tool for Statisticians, as it provides the mathematical framework for understanding and manipulating data. This course provides a strong foundation in Linear Algebra, which is essential for Statisticians to succeed in their roles. The course covers concepts like vectors, matrices, and linear transformations, which are all used extensively in statistics.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical methods to analyze financial data and make investment decisions. Linear Algebra is a core component of quantitative finance, as it provides the mathematical framework for understanding and manipulating data. This course provides a strong foundation in Linear Algebra, which is essential for Quantitative Analysts to succeed in their roles. The course covers concepts like vectors, matrices, and linear transformations, which are all used extensively in quantitative finance.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and analytical methods to solve complex business problems. Linear Algebra is a fundamental tool for Operations Research Analysts, as it provides the mathematical framework for understanding and manipulating data. This course provides a strong foundation in Linear Algebra, which is essential for Operations Research Analysts to succeed in their roles. The course covers concepts like vectors, matrices, and linear transformations, which are all used extensively in operations research.
Actuary
Actuary
Actuaries use mathematical and statistical methods to assess risk and uncertainty. Linear Algebra is a fundamental tool for Actuaries, as it provides the mathematical framework for understanding and manipulating data. This course provides a strong foundation in Linear Algebra, which is essential for Actuaries to succeed in their roles. The course covers concepts like vectors, matrices, and linear transformations, which are all used extensively in actuarial science.
Financial Analyst
Financial Analyst
Financial Analysts use financial data to make investment recommendations. Linear Algebra is becoming increasingly important in financial analysis, as it provides the mathematical framework for understanding and manipulating data. This course provides a strong foundation in Linear Algebra, which is beneficial for Financial Analysts working with complex financial models. The course covers concepts like vectors, matrices, and linear transformations, which are all used in financial analysis.
Business Analyst
Business Analyst
Business Analysts use data and analysis to solve business problems. Linear Algebra is a valuable tool for Business Analysts, as it provides the mathematical framework for understanding and manipulating data. This course provides a strong foundation in Linear Algebra, which is beneficial for Business Analysts working with complex data-driven projects. The course covers concepts like vectors, matrices, and linear transformations, which are all used in business analysis.
Data Analyst
Data Analyst
Data Analysts collect, clean, and analyze data to identify trends and patterns. Linear Algebra is a valuable tool for Data Analysts, as it provides the mathematical framework for understanding and manipulating data. This course provides a strong foundation in Linear Algebra, which is beneficial for Data Analysts working with complex datasets. The course covers concepts like vectors, matrices, and linear transformations, which are all used in data analysis.
Risk Analyst
Risk Analyst
Risk Analysts use mathematical and statistical methods to assess risk and uncertainty. Linear Algebra is a fundamental tool for Risk Analysts, as it provides the mathematical framework for understanding and manipulating data. This course provides a strong foundation in Linear Algebra, which is essential for Risk Analysts to succeed in their roles. The course covers concepts like vectors, matrices, and linear transformations, which are all used extensively in risk analysis.
Market Researcher
Market Researcher
Market Researchers collect and analyze data to understand consumer behavior. Linear Algebra is a valuable tool for Market Researchers, as it provides the mathematical framework for understanding and manipulating data. This course provides a strong foundation in Linear Algebra, which is beneficial for Market Researchers working with complex datasets. The course covers concepts like vectors, matrices, and linear transformations, which are all used in market research.
Researcher
Researcher
Researchers conduct original research in a variety of fields. Linear Algebra is a valuable tool for Researchers, as it provides a mathematical framework for understanding and analyzing data. This course provides a strong foundation in Linear Algebra, which is beneficial for Researchers working with complex datasets. The course covers concepts like vectors, matrices, and linear transformations, which are all used in research.
Teacher
Teacher
Teachers educate and inspire students. Linear Algebra is a valuable tool for Teachers, as it provides a mathematical framework for understanding and presenting complex concepts. This course provides a strong foundation in Linear Algebra, which is beneficial for Teachers working with students in STEM fields. The course covers concepts like vectors, matrices, and linear transformations, which are all used in teaching mathematics and other STEM subjects.
Consultant
Consultant
Consultants advise clients on a wide range of business issues. Linear Algebra is a valuable tool for Consultants, as it provides a mathematical framework for understanding and analyzing data. This course provides a strong foundation in Linear Algebra, which is beneficial for Consultants working with data-driven projects. The course covers concepts like vectors, matrices, and linear transformations, which are all used in consulting.
For more career information including salaries, visit:
OpenCourser.com/course/6b00ma/linear
Reading list
We've selected 12 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Linear Algebra Essentials.
More advanced treatment of linear algebra that is suitable for students who have already taken a basic course in the subject. It covers a wide range of topics, including abstract vector spaces, linear transformations, and matrices.
More advanced treatment of linear algebra that is suitable for students who have already taken a basic course in the subject. It covers a wide range of topics, including matrix theory, linear equations, and eigenvalues.
Classic textbook on linear algebra that is widely used in undergraduate and graduate courses. It provides a comprehensive introduction to the subject, covering a wide range of topics from basic concepts to advanced applications.
Save
More advanced treatment of linear algebra that is suitable for students who have already taken a basic course in the subject. It covers a wide range of topics, including matrix theory, numerical linear algebra, and applications.
More specialized treatment of linear algebra that is tailored to the needs of machine learning students. It covers a wide range of topics, including vectors, matrices, and linear transformations. It also includes a number of applications to machine learning.
Modern introduction to linear algebra that is accessible to students with a variety of backgrounds. It covers a wide range of topics, including vectors, matrices, and linear transformations. It also includes a number of applications to other fields, such as computer science and economics.
Widely used textbook for undergraduate linear algebra courses. It good choice for students who are looking for a comprehensive introduction to the subject.
Comprehensive introduction to linear algebra that is suitable for students with a variety of backgrounds. It covers a wide range of topics, including vectors, matrices, and linear transformations. It also includes a number of applications to other fields, such as physics, engineering, and computer science.
More concise and accessible introduction to linear algebra than Strang's book. It good choice for students who are looking for a less challenging introduction to the subject.
More applied introduction to linear algebra than most other textbooks. It good choice for students who are looking for a more practical understanding of the subject.
Save
More concise and accessible introduction to linear algebra than Lay's book. It good choice for students who are looking for a less challenging introduction to the subject.
Save
More specialized treatment of linear algebra that is tailored to the needs of economics students. It covers a wide range of topics, including vectors, matrices, and linear transformations. It also includes a number of applications to economics.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/6b00ma/linear
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Time
540 hours
Level
Introductory
Via
Udacity
Instructors
Mat Leonard
Andrew Paster
Jennifer Staab
Luis Serrano
Juan Delgado
Juno Lee
Mike Yi
Grant Sanderson
Ortal Arel
Language
English
Good to know
Ideal for those unfamiliar with this math
Enhances a basis for those familiar with linear algebra
Instructors are industry professionals
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