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Statistical Mechanics

Algorithms and Computations

Werner Krauth

In this course you will learn a whole lot of modern physics (classical and quantum) from basic computer programs that you will download, generalize, or write from scratch, discuss, and then hand in. Join in if you are curious (but not necessarily knowledgeable) about algorithms, and about the deep insights into science that you can obtain by the algorithmic approach.

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What's inside

Syllabus

Monte Carlo algorithms (Direct sampling, Markov-chain sampling)
Dear students, welcome to the first week of Statistical Mechanics: Algorithms and Computations!
Here are a few details about the structure of the course: For each week, a lecture and a tutorial videos will be presented, together with a downloadable copy of all the relevant python programs mentioned in the videos. Some in-video questions and practice quizzes will help you to review the material, with no effect on the final grade. A mandatory peer-graded assignment is also present, for weeks from 1 to 9, and it will expand on the lectures' topics, letting you reach a deeper understanding. The nine peer-graded assignments will make up for 50% of the grade, while the other half will come from a final exam, after the last lecture.
In this first week, we will learn about algorithms by playing with a pebble on the Monte Carlo beach and at the Monaco heliport. In the tutorial we will use the 3x3 pebble game to understand the essential concepts of Monte Carlo techniques (detailed balance, irreducibility, and a-periodicity), and meet the celebrated Metropolis algorithm. Finally, the homework session will let you understand some useful aspects of Markov-chain Monte Carlo, related to convergence and error estimations.
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Note that previous knowledge of quantum mechanics is not really necessary to go through the next three weeks. Follow us in our journey through algorithms and physics, and don't forget to ask on the forum if you have any doubt!

(There is no homework session for Week 10, but don't forget that the final exam is still there!)

Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Recommended for students and professionals in physics who want to gain a deep understanding of modern physics through practical algorithms
Emphasizes algorithmic approaches to provide insights into scientific concepts, particularly for those interested in algorithms
Led by Werner Krauth, a renowned physicist recognized for significant contributions to the field
Covers advanced topics such as quantum statistical mechanics, the Ising model, and dynamic Monte Carlo algorithms
Includes peer-graded assignments and a final exam, providing opportunities for assessment and feedback
May not be suitable for complete beginners in physics, as it assumes some foundational knowledge

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Reviews summary

Statistical mechanics through algorithms and computation

According to learners, this course offers a challenging but highly rewarding journey into statistical mechanics using a unique algorithmic and computational approach. Students appreciate the opportunity to implement physical concepts in Python, finding it a highly effective way to learn and gain deep insights. The assignments are frequently mentioned as being particularly challenging yet valuable, pushing understanding beyond theoretical lectures. While some found the course required a strong foundation in physics and programming, many felt it provided a solid grasp of complex topics. Overall, it is seen as a rigorous and exceptional course for those interested in the intersection of statistical physics and computation.
Lecture style is clear and engaging for complex ideas.
"The lectures were clear and well-structured, breaking down complex concepts into understandable parts."
"I enjoyed the teaching style; the instructors did a great job explaining the intuition behind the algorithms."
"Videos were concise and focused, allowing me to replay sections I found difficult."
"The lecture materials and supplemental Python code were very helpful in following along."
"I found the explanations of Monte Carlo and Markov chains particularly effective in the lectures."
Covers complex topics thoroughly and rigorously.
"The course delves into deep and rich material, covering topics like Monte Carlo, Path Integrals, and phase transitions with rigor."
"I was impressed by the depth of the quantum statistical mechanics section, particularly the discussion of path integrals and BEC."
"The syllabus covers a wide range of fascinating topics, moving from classical Monte Carlo to quantum phenomena."
"This course provides a solid and deep foundation in computational statistical mechanics, perfect for advanced students."
"I feel I gained a comprehensive understanding of key algorithms and models used in statistical physics."
Focus on algorithms provides unique insight.
"The algorithmic perspective on statistical mechanics was incredibly insightful and different from standard approaches I've encountered."
"I loved how the course used computational methods to teach complex physics concepts; it made abstract ideas much more concrete."
"Learning to implement these statistical mechanics concepts computationally gave me a much deeper understanding than purely theoretical study would have."
"The focus on algorithms and coding statistical mechanics problems in Python was the course's greatest strength."
"This approach through algorithms is a fantastic way to learn modern physics. It's very hands-on."
Assignments are tough but crucial for learning.
"The assignments were quite challenging, but working through them was absolutely essential for truly grasping the material."
"I really liked the assignments; they are hard, but after solving them, I feel that I understand the concepts much better."
"The homework is key - it forces you to apply the algorithmic methods taught in the lectures and solidify your understanding. Expect to spend significant time on them."
"While the lectures provide the theory, the hands-on work in the assignments is where the concepts click into place."
"Be prepared for challenging assignments that require serious thought and coding effort, but they are very rewarding."
Needs solid background in physics and coding.
"This course definitely requires a solid background in statistical mechanics, quantum mechanics, and Python programming. It's not for beginners."
"Make sure you have a good grasp of undergraduate statistical mechanics and are comfortable coding in Python before starting this course."
"I struggled a bit because my programming skills weren't as strong as needed. The course moves quickly on the coding side."
"A prior understanding of core physics principles, especially thermodynamics and quantum mechanics, is highly recommended."
"I found prior exposure to computational physics or numerical methods to be very helpful."

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 Statistical Mechanics: Algorithms and Computations with these activities:
Organize and consolidate course content
Organizing and consolidating your course materials will help you retain information more effectively.
Show steps
  • Review your notes, assignments, quizzes, and exams.
  • Identify key concepts and ideas.
  • Create a system for organizing your materials.
Solve Monte Carlo exercises
Give yourself extra practice to strengthen your understanding of Monte Carlo algorithms.
Show steps
  • Work through example exercises provided in the course materials.
  • Attempt practice problems at the end of each chapter or section.
  • Seek out additional practice problems or exercises online.
Explore Monte Carlo tutorials
Watching a video tutorial will serve as a secondary reinforcement of the lecture material on Monte Carlo algorithms.
Show steps
  • Look for tutorials from reputable sources such as Coursera, edX, or YouTube channels like Khan Academy or The Great Courses.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Connect with professionals
Seeking guidance from experienced professionals can provide you with valuable insights and support.
Show steps
  • Attend industry events or conferences.
  • Reach out to professionals on LinkedIn or other social media platforms.
  • Ask your professors for recommendations.
Create a comprehensive resource list
Compiling a list of relevant resources will provide you with a valuable reference for future learning.
Show steps
  • Search for articles, books, websites, and other resources on Monte Carlo algorithms.
  • Evaluate the quality and relevance of each resource.
  • Organize the resources into a coherent structure.
  • Document your findings in a clear and concise manner.
Develop a Monte Carlo simulation
Putting your knowledge into practice by developing your own simulation will deepen your understanding of the concepts.
Show steps
  • Choose a problem or question that interests you and can be solved using a Monte Carlo simulation.
  • Design and implement your simulation.
  • Test and refine your simulation.
  • Document your simulation.
Develop a presentation on a specific topic
Creating a presentation will help you synthesize your knowledge and improve your communication skills.
Show steps
  • Choose a specific topic that you are interested in.
  • Research your topic thoroughly.
  • Develop an outline for your presentation.
  • Create visual aids to support your presentation.
  • Practice your presentation.

Career center

Learners who complete Statistical Mechanics: Algorithms and Computations will develop knowledge and skills that may be useful to these careers:
Data Analyst
Data Analysts use statistical techniques to analyze data and extract insights. They work in a variety of industries, including finance, healthcare, and technology. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate complex systems and how to use statistical techniques to analyze data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of complex systems.
See salaries and explore the career path for Data Analyst
Physicist
Physicists study the fundamental laws of nature. They use a variety of mathematical and statistical techniques to analyze data and develop theories. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate complex systems and how to use statistical techniques to analyze data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of matter and energy.
See salaries and explore the career path for Physicist
Statistician
Statisticians collect, analyze, and interpret data. They work in a variety of fields, including healthcare, education, and government. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate complex systems and how to use statistical techniques to analyze data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of complex systems.
See salaries and explore the career path for Statistician
Data Scientist
Data Scientists use statistical techniques to analyze data and extract insights. They work in a variety of industries, including finance, healthcare, and technology. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate complex systems and how to use statistical techniques to analyze data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of complex systems.
See salaries and explore the career path for Data Scientist
Machine Learning Engineer
Machine Learning Engineers design, develop, and maintain machine learning models. They use a variety of statistical techniques to train and evaluate models. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate complex systems and how to use statistical techniques to analyze data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of machine learning models.
See salaries and explore the career path for Machine Learning Engineer
Financial Engineer
Financial Engineers develop and implement financial models. They use a variety of mathematical and statistical techniques to analyze financial data. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate financial markets and how to use statistical techniques to analyze financial data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of financial markets.
See salaries and explore the career path for Financial Engineer
Risk Analyst
Risk Analysts use mathematical and statistical techniques to assess risk and uncertainty. They work in a variety of industries, including finance, insurance, and healthcare. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate complex systems and how to use statistical techniques to analyze data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of risk and uncertainty.
See salaries and explore the career path for Risk Analyst
Biostatistician
Biostatisticians use statistical techniques to analyze data in the field of biology. They work in a variety of settings, including academia, industry, and government. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate complex systems and how to use statistical techniques to analyze data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of complex biological systems.
See salaries and explore the career path for Biostatistician
Econometrician
Econometricians use statistical techniques to analyze economic data. They work in a variety of settings, including academia, industry, and government. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate complex systems and how to use statistical techniques to analyze data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of complex economic systems.
See salaries and explore the career path for Econometrician
Financial Analyst
Financial Analysts work to assess the performance of stocks, bonds, and other financial instruments. They use a variety of statistical techniques to analyze data. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate financial markets and how to use statistical techniques to analyze financial data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of financial markets.
See salaries and explore the career path for Financial Analyst
Epidemiologist
Epidemiologists use statistical techniques to study the spread of disease. They work in a variety of settings, including academia, industry, and government. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate complex systems and how to use statistical techniques to analyze data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of complex epidemiological systems.
See salaries and explore the career path for Epidemiologist
Operations Research Analyst
Operations Research Analysts use mathematical and statistical techniques to solve problems in a variety of industries, including manufacturing, logistics, and healthcare. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate complex systems and how to use statistical techniques to analyze data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of complex systems.
See salaries and explore the career path for Operations Research Analyst
Software Engineer
Software Engineers design, develop, and maintain software applications. They use a variety of programming languages and tools to create software that meets the needs of users. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate complex systems and how to use statistical techniques to analyze data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of complex systems.
See salaries and explore the career path for Software Engineer
Quantitative Analyst
Quantitative Analysts use mathematical and statistical techniques to analyze financial data. They develop models to predict the performance of stocks, bonds, and other financial instruments. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate financial markets and how to use statistical techniques to analyze financial data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of financial markets.
See salaries and explore the career path for Quantitative Analyst
Actuary
Actuaries use mathematical and statistical techniques to assess risk and uncertainty. They work in a variety of industries, including insurance, finance, and healthcare. The course Statistical Mechanics: Algorithms and Computations will help you develop the skills necessary to be successful in this role. You will learn how to use Monte Carlo algorithms to simulate complex systems and how to use statistical techniques to analyze data. This course will also provide you with a strong foundation in the theory of statistical mechanics, which is essential for understanding the behavior of risk and uncertainty.
See salaries and explore the career path for Actuary

Reading list

We've selected eight 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 Statistical Mechanics: Algorithms and Computations.
Cover image
Statistical Mechanics: Algorithms and Computations
Save
Is the course textbook and provides a comprehensive overview of the topics covered in the course. It valuable resource for both students and instructors.
Statistical Mechanics: Algorithms and Computations...
Paperback
$$$
Statistical Mechanics: Algorithms and Computations...
Kindle Edition
$$$
Cover image
A Guide to Monte Carlo Simulations in Statistical...
Save
Provides a comprehensive overview of Monte Carlo methods in statistical physics. It valuable resource for both students and instructors.
A Guide to Monte Carlo Simulations in Statistical...
Hardcover
$$$
A Guide to Monte Carlo Simulations in Statistical...
Kindle Edition
$$$
A Guide to Monte Carlo Simulations in Statistical...
Hardcover
$$$$
A Guide to Monte Carlo Simulations in Statistical...
Hardcover
$$
Cover image
Solid State Physics
Save
Provides a comprehensive overview of quantum statistical mechanics. It valuable resource for both students and instructors.
Solid State Physics: Essential Concepts
Hardcover
$$$
Solid State Physics: Essential Concepts
Kindle Edition
$$$
Cover image
Simulated Annealing: Theory and Applications
Save
Provides a comprehensive overview of simulated annealing. It valuable resource for students and instructors who are interested in this topic.
Simulated Annealing: Theory and Applications...
Hardcover
$$$
Simulated Annealing: Theory and Applications...
Kindle Edition
$$$$
Cover image
Physics and Our World
Save
Provides a comprehensive overview of statistical mechanics. It valuable resource for students and instructors who are interested in this topic.
Physics And Our World: Reissue Of The Proceedings...
Paperback
$$$
Physics And Our World: Reissue Of The Proceedings...
Kindle Edition
$$
Cover image
Interpreting Quantum Mechanics
Save
Provides a comprehensive overview of quantum mechanics. It valuable resource for students and instructors who are interested in this topic.
Interpreting Quantum Mechanics
Paperback
Check
Interpreting Quantum Mechanics
Kindle Edition
Check
Cover image
Classical Mechanics
Save
Provides a comprehensive overview of classical mechanics. It valuable resource for students and instructors who are interested in this topic.
Classical Mechanics: Pearson New International...
Paperback
$$$
Cover image
Introduction to Electrodynamics
Save
Provides a comprehensive overview of electromagnetism. It valuable resource for students and instructors who are interested in this topic.
Introduction to Electrodynamics
Hardcover
$$$
Introduction to Electrodynamics
Paperback
$$$
INTRODUCTION TO ELECTRODYNAMICS, 4TH EDITION
Paperback
$$
Introduction to Electrodynamics
Hardcover
$$$
Introduction to Electrodynamics
Kindle Edition
$$$
Introduction to Electrodynamics
Kindle Edition
$$$

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Via
Coursera
Institution
École normale supérieure
Instructor
Werner Krauth
Language
English
Transcripts
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Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Recommended for students and professionals in physics who want to gain a deep understanding of modern physics through practical algorithms
Emphasizes algorithmic approaches to provide insights into scientific concepts, particularly for those interested in algorithms
Led by Werner Krauth, a renowned physicist recognized for significant contributions to the field
Covers advanced topics such as quantum statistical mechanics, the Ising model, and dynamic Monte Carlo algorithms
Includes peer-graded assignments and a final exam, providing opportunities for assessment and feedback
May not be suitable for complete beginners in physics, as it assumes some foundational knowledge
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