Линейная алгебра: от идеи к формуле from Coursera

Основная особенность нашего онлайн-курса — геометрический подход к изложению. В каждом сюжете сначала мы рассказываем идею определения, пусть иногда и нестрого, а уже затем вводим формальное определение. В частности, линейные операторы, собственные векторы и числа появляются до матриц и определителей. Матрицы мы излагаем как способ записи линейного оператора. В силу этой особенности курс может быть интересен и тем, кто уже освоил стандартный вводный курс линейной алгебры. Основные темы курса: векторные пространства, линейные операторы и их свойства, квадратичные формы, матричные разложения, метод главных компонент. Иногда для решения численных задач мы используем Python. В курсе мы не рассматриваем оптимальные численные реализации методов. Обучение на курсе НИУ ВШЭ длится 6 недель. Для его успешного освоения достаточно знать стандартную школьную программу по математике.

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Explores linear algebra via geometric approach, making concepts highly relevant for those in advanced fields like machine learning and data science

Taught by Boris Demeshev, an accomplished professor in mathematics at the Higher School of Economics in Moscow, ensuring learners will gain knowledge from an expert

Introduces topics like vector spaces, linear operators, and their properties, expanding mathematical understanding for individuals already familiar with basic linear algebra

Incorporates practical applications with Python, catering to those seeking hands-on experience

Requires only standard high school-level math knowledge, making it accessible to a broad audience of learners

Focuses on the core principles of linear algebra rather than advanced numerical implementations, catering specifically to those seeking a conceptual understanding

Reviews summary

Understandable explanations

This course on linear algebra takes a geometrical approach to teaching the subject. It covers vector spaces, linear operators, quadratic forms, matrix decompositions, and the method of principal components. Students appreciate the clear explanations and well-structured content. Some students wish there were more visualizations and practice problems, but overall, the course is well-received.

Content is well-structured and organized.

"Очень хороший и структурированный курс"

Explanations are clear and understandable.

"Главный плюс курса это талант автора очень понятно объяснять материал."

More practice problems and visualizations would be helpful.

"хотелось бы побольше задачек"

"мб не хватило каких-то визуализаций"

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 Линейная алгебра: от идеи к формуле with these activities:

Read 'Linear Algebra and Its Applications' by Gilbert Strang

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Supplement course materials with a comprehensive and highly regarded textbook that provides a deeper understanding of linear algebra.

View Linear Algebra for Everyone on Amazon

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Read selected chapters and sections relevant to the course.
Solve practice problems and review examples from the book.
Attend class and participate in discussions to connect the book material to the course content.

Refresh vector space concepts

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Review the fundamentals of vector spaces, including vector addition, scalar multiplication, and the dot product.

Browse courses on Vector Spaces

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Review the definition of a vector space and its properties.
Practice identifying vector spaces and their subspaces.
Calculate the dot product of vectors and interpret its geometric significance.

Solve linear systems using Gaussian elimination

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Develop proficiency in solving systems of linear equations using Gaussian elimination.

Browse courses on Gaussian Elimination

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Practice reducing matrices to row echelon form.
Solve systems of linear equations using back-substitution.
Apply Gaussian elimination to solve real-world problems.

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Follow tutorials on matrix decompositions

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Expand knowledge of matrix decompositions by exploring video tutorials and online resources.

Browse courses on Matrix Decompositions

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Identify different types of matrix decompositions.
Watch tutorials on the steps involved in each decomposition.
Apply the decompositions to practical examples.

Attend a workshop on data mining techniques

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Gain practical experience with data mining techniques by attending a hands-on workshop.

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Identify a workshop on data mining techniques relevant to the course.
Attend the workshop and actively participate in the exercises.
Apply the learned techniques to a personal project or assignment.

Create a poster or infographic on linear transformations

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Demonstrate a deep understanding of linear transformations by creating a visual representation that explains their key concepts.

Browse courses on Linear Transformations

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Identify the main concepts of linear transformations.
Design a visually appealing and informative poster or infographic.
Present the poster or infographic to peers or instructors.

Host a study group on method of least squares

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Enhance understanding of the method of least squares by facilitating a collaborative learning environment.

Browse courses on Method of Least Squares

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Prepare a lesson plan on the method of least squares.
Facilitate a discussion on the principles and applications of the method.
Assign practice problems and guide the group through their solutions.

Contribute to an open-source linear algebra library

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Gain practical experience with linear algebra algorithms by contributing to open-source projects.

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Identify an open-source linear algebra library to contribute to.
Fix bugs, implement new features, or improve documentation.
Collaborate with other developers to maintain the library.

Career center

Learners who complete Линейная алгебра: от идеи к формуле will develop knowledge and skills that may be useful to these careers:

Data Analyst

Data Analysts use their knowledge of mathematics to gather and analyze data in order to extract meaningful insights and provide solutions to business problems. Linear algebra, in particular, is widely used in data analysis for tasks such as dimensionality reduction, feature extraction, and statistical modeling. Taking this course will help you build a foundation in linear algebra, enabling you to effectively solve complex data-related problems and make informed decisions.

See salaries and explore the career path for Data Analyst

Machine Learning Engineer

Machine Learning Engineers apply linear algebra concepts to develop and implement machine learning algorithms that can learn from data. They use techniques such as matrix factorization, principal component analysis, and singular value decomposition to improve the accuracy and efficiency of machine learning models.

See salaries and explore the career path for Machine Learning Engineer

Operations Research Analyst

Operations Research Analysts utilize linear algebra in optimization and simulation models to solve complex decision-making problems. They use techniques like linear programming, network flow analysis, and game theory to find optimal solutions for resource allocation, scheduling, and supply chain management.

See salaries and explore the career path for Operations Research Analyst

Actuary

Actuaries use linear algebra to evaluate financial risks and uncertainties in insurance, pension plans, and other financial products. They apply techniques such as matrix models, Markov chains, and regression analysis to assess the probability of events, calculate premiums, and recommend appropriate risk mitigation strategies.

See salaries and explore the career path for Actuary

Financial Analyst

Financial Analysts use linear algebra to model financial data, perform risk assessments, and optimize investment portfolios. They apply techniques such as matrix algebra, regression analysis, and time series analysis to identify trends, make predictions, and make sound investment decisions.

See salaries and explore the career path for Financial Analyst

Quantitative Analyst

Quantitative Analysts use linear algebra to develop and implement mathematical models for financial trading and risk management. They apply techniques such as portfolio optimization, statistical arbitrage, and Monte Carlo simulations to analyze market data, identify opportunities, and make informed trading decisions.

See salaries and explore the career path for Quantitative Analyst

Statistician

Statisticians use linear algebra to analyze large datasets, identify trends and patterns, and make inferences about populations. They apply techniques such as regression analysis, multivariate analysis, and experimental design to solve problems in various fields, including healthcare, public policy, and business.

See salaries and explore the career path for Statistician

Software Engineer

Software Engineers use linear algebra in computer graphics, computer vision, and machine learning. They apply techniques such as matrix transformations, vector operations, and linear equations to develop algorithms for rendering realistic images, processing video data, and building AI-powered systems.

See salaries and explore the career path for Software Engineer

Control Systems Engineer

Control Systems Engineers use linear algebra to design and analyze control systems for various industrial processes, autonomous vehicles, and robotic systems. They apply techniques such as state-space models, linear feedback control, and optimal control to ensure stability, performance, and safety in complex dynamic systems.

See salaries and explore the career path for Control Systems Engineer

Aerospace Engineer

Aerospace Engineers use linear algebra in aircraft design, flight dynamics, and navigation systems. They apply techniques such as matrix algebra, vector calculus, and differential equations to model and analyze the behavior of aircraft in flight, optimize flight paths, and design control systems.

See salaries and explore the career path for Aerospace Engineer

Mechanical Engineer

Mechanical Engineers use linear algebra in structural analysis, fluid dynamics, and robotics. They apply techniques such as stress analysis, finite element analysis, and motion planning to design and optimize mechanical systems, ensuring their strength, durability, and performance.

See salaries and explore the career path for Mechanical Engineer

Chemical Engineer

Chemical Engineers use linear algebra in process modeling, optimization, and control. They apply techniques such as matrix algebra, differential equations, and numerical methods to simulate chemical processes, optimize reactor designs, and develop control strategies for efficient and safe operation.

See salaries and explore the career path for Chemical Engineer

Electrical Engineer

Electrical Engineers use linear algebra in circuit analysis, signal processing, and power systems. They apply techniques such as matrix representations of circuits, Laplace transforms, and Fourier analysis to design and optimize electrical systems, ensuring their reliability, efficiency, and performance.

See salaries and explore the career path for Electrical Engineer

Civil Engineer

Civil Engineers use linear algebra in structural analysis, geotechnical engineering, and transportation planning. They apply techniques such as matrix methods, finite element analysis, and traffic flow modeling to design and optimize infrastructure systems, ensuring their safety, durability, and efficiency.

See salaries and explore the career path for Civil Engineer

Materials Scientist

Materials Scientists use linear algebra in crystallography and materials characterization. They apply techniques such as vector analysis, matrix representations of crystal structures, and diffraction patterns to understand the structure, properties, and behavior of materials, leading to the development of new and innovative materials with enhanced performance.

See salaries and explore the career path for Materials Scientist