Дискретная математика: подсчеты, графы, случайные блуждания from Coursera

Основная цель этого онлайн-курса — дать введение в разделы дискретной математики, важные для анализа данных. Мы начнем с краткого введения в комбинаторику, раздел математики, изучающий подсчеты. Основы комбинаторики критически важны для всех, кто работает в анализе данных или в Computer Science. В качестве примеров использования комбинаторики мы обсудим вопросы о подсчете размера пространства признаков и об оценке времени работы программ на Python. После этого мы используем наши знания в комбинаторике в изучении дискретной вероятности. Вероятностью в области анализа данных пронизано абсолютно все, и мы еще изучим этот раздел математики в одном из следующих курсов гораздо подробнее. В этом курсе в части вероятности наша цель — дать первоначальное знакомство с этой областью, а также дать нам возможность использовать вероятность в следующей части курса. Наконец, в третьей части курса НИУ ВШЭ мы обсудим комбинаторную структуру, наиболее часто встречающуюся в анализе данных — графы. Графы встречаются повсюду, как в анализе данных, так и в обычной жизни, и мы увидим это на разнообразных примерах. Мы дадим необходимые сведения из теории графов, а в конце курса выполним проект, а именно построим несложную рекомендательную систему, основанную на случайных блужданиях в графах.

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This introduction to Discrete Mathematics includes a project requiring students to build a recommender system using random graph-based walks

Discrete mathematics forms a cornerstone of data science and this course offers an understanding of its three main components: combinatorics, probability, and graphs

Suitable for beginners, this course offers a solid foundation in discrete mathematics for data science

The skills taught in this course, such as counting techniques, probability estimation, and graph analysis, are highly relevant to data science

Reviews summary

Challenging discrete math

This course on discrete mathematics for data analysis is praised for its clear explanations and range of topics, although students found the final project unexpectedly difficult.

Covers multiple math areas

"дает введение в разделы дискретной математики"

"позволяет использовать вероятность в следующей части"

"графы встречаются повсюду"

Easy to understand concepts

"Преподаватель доходчиво объясняет основные моменты"

"Преподаватель является экспертом, поэтому объясняет..."

"Качественные видео и хорошая подача материала!"

Unexpectedly challenging final project

"Финальный проект просто выбил меня"

"Финальная задача была неожиданно тяжелым"

"Особую сложность вызвала реализация случайного блуждания"

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 Дискретная математика: подсчеты, графы, случайные блуждания with these activities:

Review probability concepts

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Strengthen your foundation in probability before starting the course.

Browse courses on Probability

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Revisit your notes or textbooks to refresh your understanding of probability concepts.
Solve practice problems to reinforce your knowledge.

Review basic Python programming

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Brush up on your Python skills to enhance your experience with the course.

Browse courses on Python Programming

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Go through online tutorials or documentation to refresh your understanding of Python basics.
Practice writing simple Python programs to reinforce your knowledge.

Engage in peer study sessions

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Collaborate with peers to discuss course topics and enhance understanding.

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Form study groups with classmates.
Meet regularly to discuss course material, solve problems, and share insights.
Take turns leading discussions and presenting different perspectives.
Provide constructive feedback to each other.

Five other activities

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Practice counting problems

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Reinforce your understanding of counting principles by solving a variety of problems.

Browse courses on Counting

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Find practice problems online or in textbooks.
Solve the problems using the counting principles you have learned.
Check your answers and identify any areas where you need additional practice.

Practice probability problems

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Sharpen your probability skills by solving a range of problems.

Browse courses on Probability

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Gather practice problems from online sources or textbooks.
Utilize the probability concepts you have learned to solve the problems.
Evaluate your solutions and pinpoint areas for improvement.

Explore graph theory tutorials

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Delve deeper into graph theory concepts through guided tutorials.

Browse courses on Graph Theory

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Identify reputable online platforms or books that provide graph theory tutorials.
Follow the tutorials, taking notes and actively engaging with the material.
Attempt the practice exercises and problems included in the tutorials.
Seek clarification on any concepts you find challenging.

Build a simple recommender system

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Apply your knowledge of graphs to create a practical recommender system.

Browse courses on Recommender Systems

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Choose a dataset and define the problem statement for your recommender system.
Design the architecture of your system, including the graph structure and recommendation algorithm.
Implement your system using a programming language of your choice.
Evaluate the performance of your system and make necessary adjustments.

Participate in data analysis competitions

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Challenge yourself and test your skills in real-world data analysis scenarios.

Browse courses on Data Analysis

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Identify relevant data analysis competitions online.
Form a team or work independently to tackle the competition challenges.
Utilize the concepts and techniques learned in the course to solve the problems.
Submit your solutions and receive feedback on your performance.

Career center

Learners who complete Дискретная математика: подсчеты, графы, случайные блуждания will develop knowledge and skills that may be useful to these careers:

Data Analyst

As a Data Analyst, you will interpret large amounts of data to uncover trends, patterns, and insights. To effectively do so, you will need a solid understanding of Discrete Mathematics, as it underpins the algorithms and techniques used in data analysis. This course will help you build a strong foundation in combinatorics, probability, and graph theory, all essential topics that will enhance your data analysis capabilities.

See salaries and explore the career path for Data Analyst

Statistician

Statisticians apply statistical methods to collect, analyze, interpret, and present data. Discrete Mathematics is a cornerstone of statistics as it provides the foundation for probability theory, sampling techniques, and statistical inference. This course will give you a thorough grounding in combinatorics, probability, and graph theory, essential concepts for understanding statistical models and methodologies.

See salaries and explore the career path for Statistician

Data Scientist

Data Scientists are responsible for extracting valuable insights from vast amounts of data using scientific methods and algorithms. Discrete Mathematics plays a crucial role in data science as it provides the foundations for data analysis, machine learning, and statistical modeling. This course will help you grasp the fundamentals of combinatorics, probability, and graph theory, essential tools in the data science toolkit.

See salaries and explore the career path for Data Scientist

Computer Scientist

Computer Scientists design, develop, and implement computer systems and applications. Discrete Mathematics is a core foundation for Computer Scientists as it provides the basis for algorithms, data structures, and software design. This course will give you a comprehensive introduction to combinatorics, probability, and graph theory, essential concepts in computer science.

See salaries and explore the career path for Computer Scientist

Operations Research Analyst

Operations Research Analysts apply mathematical and analytical techniques to optimize decision-making in complex systems. Discrete Mathematics is a cornerstone of operations research, providing the foundation for modeling, simulation, and optimization techniques. This course will give you a strong foundation in combinatorics, probability, and graph theory, essential concepts for understanding operations research models and methodologies.

See salaries and explore the career path for Operations Research Analyst

Information Security Analyst

Information Security Analysts protect computer systems and networks from unauthorized access, use, disclosure, disruption, modification, or destruction. Discrete Mathematics is critical in information security as it provides the basis for cryptography, network security, and intrusion detection systems. This course will give you a thorough understanding of combinatorics, probability, and graph theory, essential concepts for understanding information security principles and techniques.

See salaries and explore the career path for Information Security Analyst

Quantitative Trader

Quantitative Traders use mathematical and statistical models to analyze financial markets and make trading decisions. Discrete Mathematics is essential in quantitative trading as it provides the basis for modeling, simulation, and optimization techniques. This course will introduce you to combinatorics, probability, and graph theory, essential topics for understanding quantitative trading models and methodologies.

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Financial Analyst

Financial Analysts use financial data and models to evaluate investment opportunities, make recommendations, and manage portfolios. Discrete Mathematics is instrumental in financial analysis as it provides the basis for modeling financial instruments, assessing risk, and making optimization decisions. This course will introduce you to combinatorics, probability, and graph theory, essential topics for understanding financial models and methodologies.

See salaries and explore the career path for Financial Analyst

Quantitative Analyst

As a Quantitative Analyst, you will use mathematical and statistical models to analyze financial data, assess risk, and make investment decisions. Discrete Mathematics is essential in quantitative finance as it provides the basis for modeling, simulation, and optimization techniques. This course will provide you with a strong grounding in combinatorics, probability, and graph theory, key areas in quantitative finance.

See salaries and explore the career path for Quantitative Analyst

Risk Manager

Risk Managers identify, assess, and mitigate risks in various contexts, such as finance, insurance, and project management. Discrete Mathematics is vital in risk management as it provides the basis for modeling, quantifying, and managing risks. This course will introduce you to combinatorics, probability, and graph theory, essential topics for understanding risk assessment and management techniques.

See salaries and explore the career path for Risk Manager

Actuary

As an Actuary, you will use mathematical and statistical techniques to assess financial risk and uncertainty. Discrete Mathematics is a core component of actuarial science, providing the foundation for modeling, pricing, and managing financial risks. This course will introduce you to combinatorics, probability, and graph theory, essential topics for understanding actuarial models and methodologies.

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Software Engineer

Software Engineers are responsible for applying mathematical and engineering principles to the design, development, implementation, and maintenance of computer software. Discrete Mathematics is a crucial area of proficiency for Software Engineers as it provides the foundation for data structures, algorithms, and program optimization. This course will give you a comprehensive introduction to combinatorics, probability, and graph theory, essential concepts in software engineering.

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Business Analyst

Business Analysts assess and improve business processes to enhance efficiency and effectiveness. Discrete Mathematics is becoming increasingly important in business analysis as it provides the basis for modeling, simulation, and optimization techniques. This course will introduce you to combinatorics, probability, and graph theory, essential concepts for understanding business analysis models and methodologies.

See salaries and explore the career path for Business Analyst

Research Scientist

In the field of Research Science, you will conduct scientific investigations to advance knowledge and understanding in a specific area. Discrete Mathematics is highly relevant in many research domains, such as computer science, operations research, and cryptography. This course will introduce you to key concepts in combinatorics, probability, and graph theory, valuable tools for conducting research and analyzing data in various scientific fields.

See salaries and explore the career path for Research Scientist

Management Consultant

Management Consultants help organizations improve their performance by analyzing business processes, identifying problems, and developing solutions. Discrete Mathematics may be useful to Management Consultants as it provides a framework for modeling, simulation, and optimization techniques. This course will introduce you to combinatorics, probability, and graph theory, concepts that can be applied to various management consulting projects.

See salaries and explore the career path for Management Consultant

Дискретная математика

подсчеты, графы, случайные блуждания

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Reviews summary

Challenging discrete math

Activities

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