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Maggie Myers
and
Robert van de Geijn
Linear algebra is one of the fundamental tools for computational and data scientists. In Advanced Linear Algebra: Foundations to Frontiers (ALAFF), you will build your knowledge, understanding, and skills in linear algebra, practical algorithms for matrix computations, and the analysis of the effects of floating-point arithmetic as performed by computers.
Read more
Linear algebra is one of the fundamental tools for computational and data scientists. In Advanced Linear Algebra: Foundations to Frontiers (ALAFF), you will build your knowledge, understanding, and skills in linear algebra, practical algorithms for matrix computations, and the analysis of the effects of floating-point arithmetic as performed by computers.
Read more
Linear algebra is one of the fundamental tools for computational and data scientists. In Advanced Linear Algebra: Foundations to Frontiers (ALAFF), you will build your knowledge, understanding, and skills in linear algebra, practical algorithms for matrix computations, and the analysis of the effects of floating-point arithmetic as performed by computers.
What you'll learn
-
Deciphering a matrix using the Singular Value Decomposition
-
Quantifying and qualifying numerical error
-
Solving linear systems and linear least-squares problems
-
Computing and employing eigenvalues and eigenvectors
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What's inside
Syllabus
Part 1: Orthogonalization
Part 2: Solving Linear Systems
Part 3: Eigenvalues and Eigenvectors
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Provides practical algorithms for matrix computations to enable efficient data analysis
Led by seasoned instructors Maggie Myers and Robert van de Geijn, recognized experts in linear algebra
Develops foundational skills in linear algebra, making it suitable for beginners and those seeking to strengthen their understanding
Focuses on the effects of floating-point arithmetic, providing valuable insights for practical applications
Save this course
Save Advanced Linear Algebra: Foundations to Frontiers 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 Advanced Linear Algebra: Foundations to Frontiers with these
activities:
Review Matrix Theory
Show steps
Review matrix theory concepts, such as determinants, inverses, and eigenvalues, to strengthen the foundation for advanced linear algebra.
Show steps
-
Go over notes or textbooks on matrix theory.
-
Practice solving problems related to matrix theory.
Explore Numerical Linear Algebra Resources
Show steps
Explore online resources and tutorials on numerical linear algebra to gain additional insights and perspectives.
Show steps
-
Search for online tutorials on numerical linear algebra.
-
Review materials and follow along with the tutorials.
Review 'Numerical Linear Algebra' by Trefethen and Bau III
Show steps
Review a comprehensive textbook on numerical linear algebra to gain in-depth knowledge and understanding of the subject.
View
Numerical Linear Algebra: Twenty-Fifth...
on Amazon
Show steps
-
Read and study the chapters relevant to the course.
-
Work through the exercises and problems.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Discuss Floating-Point Arithmetic
Show steps
Engage in discussions with peers or participate in study groups to exchange knowledge and clarify concepts related to floating-point arithmetic.
Show steps
-
Join a study group or online forum.
-
Participate in discussions and ask questions.
Attend a Workshop on Linear Algebra Applications
Show steps
Participate in a workshop that focuses on practical applications of linear algebra in various fields.
Show steps
-
Research and find a suitable workshop.
-
Register and attend the workshop.
Solve Matrix Analysis Problems
Show steps
Practice solving matrix analysis problems to improve understanding of matrix computations and linear systems.
Browse courses on
Matrix Analysis
Show steps
-
Identify the type of matrix problem.
-
Apply appropriate matrix operations and techniques.
-
Interpret the results in the context of the problem.
Develop a Visual Aid for Eigenvalues
Show steps
Create a visual representation, such as a diagram or infographic, to illustrate the concept of eigenvalues and eigenvectors.
Show steps
-
Research and understand the concept of eigenvalues and eigenvectors.
-
Design and create the visual aid.
Contribute to SciPy Library
Show steps
Contribute to the development of the SciPy library, which provides tools for scientific computing and linear algebra operations.
Show steps
-
Identify an area or feature to contribute to.
-
Read the SciPy documentation and codebase.
-
Develop and test the contribution.
Review Matrix Theory
Show steps
Review matrix theory concepts, such as determinants, inverses, and eigenvalues, to strengthen the foundation for advanced linear algebra.
Show steps
Show steps
Show steps
- Go over notes or textbooks on matrix theory.
- Practice solving problems related to matrix theory.
Explore Numerical Linear Algebra Resources
Show steps
Explore online resources and tutorials on numerical linear algebra to gain additional insights and perspectives.
Show steps
Show steps
Show steps
- Search for online tutorials on numerical linear algebra.
- Review materials and follow along with the tutorials.
Review 'Numerical Linear Algebra' by Trefethen and Bau III
Show steps
Review a comprehensive textbook on numerical linear algebra to gain in-depth knowledge and understanding of the subject.
View
Numerical Linear Algebra: Twenty-Fifth...
on Amazon
Show steps
Show steps
Show steps
- Read and study the chapters relevant to the course.
- Work through the exercises and problems.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Discuss Floating-Point Arithmetic
Show steps
Engage in discussions with peers or participate in study groups to exchange knowledge and clarify concepts related to floating-point arithmetic.
Show steps
Show steps
Show steps
- Join a study group or online forum.
- Participate in discussions and ask questions.
Attend a Workshop on Linear Algebra Applications
Show steps
Participate in a workshop that focuses on practical applications of linear algebra in various fields.
Show steps
Show steps
Show steps
- Research and find a suitable workshop.
- Register and attend the workshop.
Solve Matrix Analysis Problems
Show steps
Practice solving matrix analysis problems to improve understanding of matrix computations and linear systems.
Browse courses on
Matrix Analysis
Show steps
Show steps
Show steps
- Identify the type of matrix problem.
- Apply appropriate matrix operations and techniques.
- Interpret the results in the context of the problem.
Develop a Visual Aid for Eigenvalues
Show steps
Create a visual representation, such as a diagram or infographic, to illustrate the concept of eigenvalues and eigenvectors.
Show steps
Show steps
Show steps
- Research and understand the concept of eigenvalues and eigenvectors.
- Design and create the visual aid.
Contribute to SciPy Library
Show steps
Contribute to the development of the SciPy library, which provides tools for scientific computing and linear algebra operations.
Show steps
Show steps
Show steps
- Identify an area or feature to contribute to.
- Read the SciPy documentation and codebase.
- Develop and test the contribution.
Career center
Learners who complete Advanced Linear Algebra: Foundations to Frontiers will develop knowledge and skills
that may be useful to these careers:
Operations Research Analyst
Operations Research Analyst
An Operations Research Analyst uses available data and develops models to help organizations make better decisions. Your work may include advising companies about how to improve efficiency and increase profits, which is why an understanding of linear algebra is vital. This course will help you analyze the effects of floating-point arithmetic as performed by computers, which can help you when advising clients about how technology will impact their operations and decision-making.
Data Scientist
Data Scientist
Data Scientists use data to build machine learning models and make predictions. Understanding linear algebra will help you build a foundation in the field and assist with more advanced and specialized coursework in data science. This course can help you with the practical algorithms for matrix computations, which can also help you develop more robust data models.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts are responsible for developing and implementing mathematical and statistical models to assess the risk of financial instruments and portfolios. Your job may include advising portfolio managers about the risk-adjusted returns of different investment strategies, which can be aided by an understanding of linear algebra concepts like eigenvalues and eigenvectors. This course will also help you understand how floating-point arithmetic impacts computer models, which is imperative to understand as a Quantitative Analyst.
Actuary
Actuary
Actuaries use mathematical and statistical skills to assess risk and uncertainty. Understanding linear algebra can help you gain an understanding of insurance products (life, health, property & casualty) and how they can be priced and managed. This course will also help you understand how floating-point arithmetic impacts computer models, which is imperative to understand as an Actuary.
Financial Analyst
Financial Analyst
Financial Analysts study the performance of companies and make recommendations to investors. Your work often includes assessing the financial health of companies and making recommendations about whether to buy, sell, or hold a particular stock. Linear algebra can help you build a foundation in the field, including the mathematics behind financial models, and will assist you with more advanced and specialized coursework in finance. This course can help you with the practical algorithms for matrix computations, which can also help you develop more robust financial models and make informed investment recommendations.
Machine Learning Engineer
Machine Learning Engineer
Machine Learning Engineers develop, deploy, and maintain machine learning models. Your work may include building models to identify fraud, predict customer behavior, or automate tasks. Linear algebra is used to understand the math behind machine learning algorithms, including linear regression and support vector machines. This course will help you gain a foundation in linear algebra, as well as practical algorithms for matrix computations. It will also help you analyze the effects of floating-point arithmetic as performed by computers, which can help you develop more robust machine learning models.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software applications. Your work may include developing new features, fixing bugs, or improving the performance of existing applications. Linear algebra is used to solve problems in computer graphics, computer vision, and robotics. This course will help you gain a foundation in linear algebra, as well as practical algorithms for matrix computations. It will also help you analyze the effects of floating-point arithmetic as performed by computers, which can help you develop more robust software applications.
Data Analyst
Data Analyst
Data Analysts clean, analyze, and interpret data to help businesses make better decisions. Your work may include creating reports, dashboards, and visualizations to communicate data insights to stakeholders. Linear algebra is used to solve problems in data mining, data visualization, and statistical modeling. This course will help you gain a foundation in linear algebra, as well as practical algorithms for matrix computations. It will also help you analyze the effects of floating-point arithmetic as performed by computers, which can help you develop more robust data analysis techniques.
Statistician
Statistician
Statisticians use mathematical and statistical methods to collect, analyze, interpret, and present data. Your work may include designing surveys, conducting experiments, and developing statistical models. Linear algebra is used to solve problems in statistical modeling, data analysis, and machine learning. This course will help you gain a foundation in linear algebra, as well as practical algorithms for matrix computations. It will also help you analyze the effects of floating-point arithmetic as performed by computers, which can help you develop more robust statistical models.
Market Researcher
Market Researcher
Market Researchers conduct research to understand consumer behavior and trends. Your work may include designing surveys, conducting interviews, and analyzing data to identify opportunities for new products or services. Linear algebra is used to solve problems in market segmentation, customer profiling, and product positioning. This course will help you gain a foundation in linear algebra, as well as practical algorithms for matrix computations. It will also help you analyze the effects of floating-point arithmetic as performed by computers, which can help you develop more robust market research techniques.
Biostatistician
Biostatistician
Biostatisticians apply statistical methods to solve problems in biology and medicine. Your work may include designing clinical trials, analyzing data from medical research studies, and developing statistical models to predict the risk of disease or the effectiveness of treatment. Linear algebra is used to solve problems in bioinformatics, medical imaging, and drug discovery. This course will help you gain a foundation in linear algebra, as well as practical algorithms for matrix computations. It will also help you analyze the effects of floating-point arithmetic as performed by computers, which can help you develop more robust biostatistical models.
Computer Vision Engineer
Computer Vision Engineer
Computer Vision Engineers design, develop, and maintain computer vision systems. Your work may include developing algorithms to identify objects, track motion, and interpret images. Linear algebra is used to solve problems in computer vision, including image processing, object recognition, and scene understanding. This course will help you gain a foundation in linear algebra, as well as practical algorithms for matrix computations. It will also help you analyze the effects of floating-point arithmetic as performed by computers, which can help you develop more robust computer vision systems.
Operations Manager
Operations Manager
Operations Managers plan and oversee the day-to-day operations of an organization. Your work may include managing production, inventory, and customer service. Linear algebra is used to solve problems in operations research, logistics, and supply chain management. This course will help you gain a foundation in linear algebra, as well as practical algorithms for matrix computations. It will also help you analyze the effects of floating-point arithmetic as performed by computers, which can help you develop more robust operations management techniques.
Risk Manager
Risk Manager
Risk Managers identify, assess, and manage risks to an organization. Your work may include developing risk management plans, conducting risk assessments, and implementing risk mitigation strategies. Linear algebra is used to solve problems in risk management, including portfolio optimization, credit risk analysis, and operational risk management. This course will help you gain a foundation in linear algebra, as well as practical algorithms for matrix computations. It will also help you analyze the effects of floating-point arithmetic as performed by computers, which can help you develop more robust risk management techniques.
Financial Risk Manager
Financial Risk Manager
Financial Risk Managers identify, assess, and manage risks to financial institutions. Your work may include developing risk management plans, conducting risk assessments, and implementing risk mitigation strategies. Linear algebra is used to solve problems in financial risk management, including portfolio optimization, credit risk analysis, and operational risk management. This course will help you gain a foundation in linear algebra, as well as practical algorithms for matrix computations. It will also help you analyze the effects of floating-point arithmetic as performed by computers, which can help you develop more robust financial risk management techniques.
For more career information including salaries, visit:
OpenCourser.com/course/retjly/advanced
Reading list
We've selected 13 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
Advanced Linear Algebra: Foundations to Frontiers.
Save
Classic reference on matrix computations. It covers a wide range of topics, including matrix factorizations, eigenvalue computations, and singular value decompositions. It valuable resource for students who want to learn more about the numerical aspects of linear algebra.
Focuses on the numerical aspects of linear algebra. It covers topics such as matrix computations, error analysis, and the solution of linear systems. It valuable resource for students who want to learn how to use linear algebra to solve real-world problems.
This classic textbook on linear algebra that provides a comprehensive introduction to the subject. It covers a wide range of topics, including matrices, vectors, determinants, and eigenvalues. It valuable resource for students who want to learn more about the fundamentals of linear algebra.
Provides a modern and accessible introduction to linear algebra. It covers a wide range of topics, including matrices, vectors, determinants, and eigenvalues. It good choice for students who want to learn more about the fundamentals of linear algebra.
Provides a comprehensive introduction to linear algebra with a focus on applications. It covers a wide range of topics, including matrices, vectors, determinants, and eigenvalues. It good choice for students who want to learn more about the fundamentals of linear algebra and how to use it to solve real-world problems.
Save
Provides a comprehensive introduction to matrix analysis. It good choice for students who want to learn more about the theoretical foundations of linear algebra.
Provides a comprehensive introduction to linear algebra that is suitable for students with a strong background in mathematics. It covers a wide range of topics, including matrices, vectors, determinants, and eigenvalues. It good choice for students who want to learn more about the theoretical foundations of linear algebra.
Provides a comprehensive introduction to linear algebra that is suitable for students with a strong background in mathematics. It covers a wide range of topics, including matrices, vectors, determinants, and eigenvalues. It good choice for students who want to learn more about the theoretical foundations of linear algebra.
Provides a comprehensive introduction to algebra, including linear algebra. It good choice for students who want to learn more about the theoretical foundations of linear algebra.
Provides a comprehensive introduction to algebra, including linear algebra. It good choice for students who want to learn more about the theoretical foundations of linear algebra.
Provides a comprehensive introduction to linear algebra and geometry. It good choice for students who want to learn more about the theoretical foundations of linear algebra.
Provides a more abstract and theoretical approach to linear algebra than Strang's book. It good choice for students who want to learn more about the underlying mathematical structure of linear algebra.
Provides a comprehensive introduction to advanced linear algebra. It covers topics such as vector spaces, linear transformations, and matrices. It good choice for students who want to learn more about the theoretical foundations of linear algebra.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/retjly/advanced
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Effort
8 to 12 hours per week for 16 weeks
Level
Intermediate
Via
edX
Institution
The University of Texas at Austin
Instructors
Maggie Myers
Robert van de Geijn
Language
English
Transcript
English
Good to know
Provides practical algorithms for matrix computations to enable efficient data analysis
Led by seasoned instructors Maggie Myers and Robert van de Geijn, recognized experts in linear algebra
Develops foundational skills in linear algebra, making it suitable for beginners and those seeking to strengthen their understanding
Focuses on the effects of floating-point arithmetic, providing valuable insights for practical applications
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