Введение в гладкие многообразия from Coursera

Целью нашего online-курса является дистанционное обучение слушателей основным понятиям и методам анализа на многообразиях их применению. После прохождения курса НИУ ВШЭ слушатель сможет освоить, что такое гладкое многообразие, касательное пространство, векторное поле, дифференциальная форма на многообразии и когомологии де Рама. Уметь вычислять интегралы от дифференциальных форм по многообразию. Дифференцировать и применять другие операции над дифференциальными формами. Понимать, что такое поток векторного поля и находить его траектории. А также освоить понятия когомологий де Рама. Предварительными требованиями к слушателю являются освоение курсов: математического анализа (в том числе нескольких переменных), линейной алгебры и основных фактов курса обыкновенных дифференциальных уравнений.

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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 Введение в гладкие многообразия with these activities:

Organize your notes

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Keeping organized notes will make it easier for you to review the course material later.

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Gather your notes from lectures, readings, and other sources.
Organize your notes by topic or concept.
Create a system for easily finding the information you need.

Join a study group

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Joining a study group can provide you with opportunities to discuss the course material with other students and get help with difficult concepts.

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Find a study group to join, either online or in person.
Attend study group meetings regularly.
Participate in discussions and ask questions.

Watch video tutorials

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Watching video tutorials can help supplement your understanding of the course material by providing a different perspective.

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Search for video tutorials on manifolds and differential geometry.
Watch the tutorials and take notes.
Try to apply the concepts you learned in the tutorials to the course material.

Three other activities

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Create a concept map

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Creating a concept map can help you visualize the relationships between different concepts in the course.

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Identify the key concepts in the course.
Create a diagram that shows the relationships between the concepts.
Add details and examples to the diagram.

Solve practice problems

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Solving practice problems can help you develop your problem-solving skills and reinforce your understanding of the course material.

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Find practice problems from the course textbook or online.
Attempt to solve the problems on your own.
Check your answers and review the solutions.

Contribute to an open-source project

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Contributing to an open-source project can help you gain practical experience with the concepts you are learning in the course.

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Find an open-source project that is related to the course material.
Read the project documentation and familiarize yourself with the codebase.
Make a contribution to the project, such as fixing a bug or adding a new feature.

Career center

Learners who complete Введение в гладкие многообразия will develop knowledge and skills that may be useful to these careers:

Physicist

Physicists study the fundamental laws of nature. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in physics, such as calculus, linear algebra, and differential equations.

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Mathematician

Mathematicians conduct research in pure and applied mathematics. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the concepts of differential geometry, which is a branch of mathematics that studies the geometry of smooth manifolds.

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Statistician

Statisticians collect, analyze, and interpret data to provide insights and make predictions. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in statistics, such as probability theory and Bayesian inference.

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Data Analyst

Data Analysts collect, clean, and analyze data to provide insights and make recommendations. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in data analysis, such as statistics, probability theory, and machine learning.

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Financial Analyst

Financial Analysts analyze financial data and make investment recommendations. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in financial analysis, such as calculus, linear algebra, and probability theory.

See salaries and explore the career path for Financial Analyst

Quantitative Analyst

Quantitative Analysts develop and use mathematical and statistical models to analyze financial data and make investment decisions. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in quantitative finance, such as calculus, linear algebra, and differential equations.

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Actuary

Actuaries use mathematical and statistical methods to assess risk and uncertainty. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in actuarial science, such as probability theory, statistics, and financial mathematics.

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Geostatistician

Geostatisticians apply statistical methods to solve problems in geology and environmental science. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in geostatistics, such as probability theory, statistics, and linear algebra.

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Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to solve problems in business and industry. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in operations research, such as optimization, simulation, and queuing theory.

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Engineer

Engineers design, develop, and build machines, structures, and systems. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in engineering, such as calculus, linear algebra, and differential equations.

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Data Scientist

Data Scientists gather data, analyze it using advanced mathematical methods, and help make data-driven decisions. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in data science, such as linear algebra, differential equations, and probability theory.

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Economist

Economists study the production, distribution, and consumption of goods and services. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in economics, such as calculus, linear algebra, and differential equations.

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Biostatistician

Biostatisticians apply statistical methods to solve problems in biology and medicine. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in biostatistics, such as probability theory, statistics, and linear algebra.

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Computer Scientist

Computer Scientists conduct research in computer science and develop new computing technologies. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in computer science, such as algorithms, complexity theory, and artificial intelligence.

See salaries and explore the career path for Computer Scientist

Software Engineer

Software Engineers design, develop, and maintain software systems. The course Введение в гладкие многообразия may be useful in this role by providing a foundation for understanding the mathematical concepts used in software engineering, such as calculus, linear algebra, and graph theory.

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