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"

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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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