Cours in French
Random: An Introduction to Probability – Part 1 (POLYTECHNIQUE PARIS)
École Polytechnique, a renowned institution, offers a fascinating course on Coursera entitled “Random: an introduction to probability – Part 1”. This course, lasting approximately 27 hours spread over three weeks, is an exceptional opportunity for anyone interested in the foundations of probability. Designed to be flexible and adapt to the pace of each learner, this course offers an in-depth and accessible approach to probability theory.
The program consists of 8 engaging modules, each addressing key aspects of probability space, uniform probability laws, conditioning, independence, and random variables. Each module is enriched with explanatory videos, additional readings and quizzes to test and consolidate the knowledge acquired. Students also have the opportunity to earn a shareable certificate upon completion of the course, adding significant value to their professional or academic journey.
The instructors, Sylvie Méléard, Jean-René Chazottes and Carl Graham, all affiliated with École Polytechnique, bring their expertise and passion for mathematics, making this course not only educational, but also inspiring. Whether you are a mathematics student, a professional looking to deepen your knowledge, or simply a science enthusiast, this course offers a unique opportunity to delve into the fascinating world of probability, guided by some of the best minds at École Polytechnique.
Random: An Introduction to Probability – Part 2 (POLYTECHNIQUE PARIS)
Continuing the educational excellence of École Polytechnique, the course “Random: an introduction to probability – Part 2” on Coursera is a direct and enriching continuation of the first part. This course, estimated to last 17 hours spread over three weeks, immerses students in more advanced concepts of probability theory, providing a deeper understanding and broader applications of this fascinating discipline.
With 6 well-structured modules, the course covers topics such as random vectors, generalization of law calculations, the law of large numbers theorem, the Monte Carlo method, and the central limit theorem. Each module includes educational videos, readings and quizzes, for an immersive learning experience. This format allows students to actively engage with the material and apply learned concepts in a practical way.
The instructors, Sylvie Méléard, Jean-René Chazottes and Carl Graham continue to guide students through this educational journey with their expertise and passion for mathematics. Their teaching approach facilitates the understanding of complex concepts and encourages a deeper exploration of probability.
This course is ideal for those who already have a solid foundation in probability and want to broaden their understanding and ability to apply these concepts to more complex problems. By completing this course, students can also earn a shareable certificate, demonstrating their commitment and competence in this specialized area.
Introduction to distribution theory (POLYTECHNIQUE PARIS)
The “Introduction to the theory of distributions” course, offered by École Polytechnique on Coursera, represents a unique and in-depth exploration of an advanced mathematical field. This course, lasting approximately 15 hours spread over three weeks, is designed for those seeking to understand distributions, a fundamental concept in applied mathematics and analysis.
The program consists of 9 modules, each offering a mix of educational videos, readings and quizzes. These modules cover various aspects of distribution theory, including complex issues such as defining the derivative of a discontinuous function and applying discontinuous functions as solutions to differential equations. This structured approach allows students to gradually become familiar with concepts that may seem intimidating at first.
Professors François Golse and Yvan Martel, both distinguished members of École Polytechnique, bring considerable expertise to this course. Their teaching combines academic rigor and innovative teaching approaches, making content accessible and engaging for students.
This course is particularly suitable for students in mathematics, engineering, or related fields who are looking to deepen their understanding of complex mathematical applications. By completing this course, participants will not only have gained valuable knowledge, but will also have the opportunity to earn a shareable certificate, adding significant value to their professional or academic profile.
Introduction to Galois theory (SUPERIOR NORMAL SCHOOL PARIS)
Offered by the École Normale Supérieure on Coursera, the “Introduction to Galois Theory” course is a fascinating exploration of one of the most profound and influential branches of modern mathematics.Lasting approximately 12 hours, this course immerses students in the complex and captivating world of Galois theory, a discipline that has revolutionized the understanding of the relationships between polynomial equations and algebraic structures.
The course focuses on the study of the roots of polynomials and their expression from coefficients, a central question in algebra. It explores the notion of Galois group, introduced by Évariste Galois, which associates each polynomial with a group of permutations of its roots. This approach allows us to understand why it is impossible to express the roots of certain polynomial equations by algebraic formulas, in particular for polynomials of degree greater than four.
The Galois correspondence, a key element of the course, links field theory to group theory, providing a unique perspective on the solvability of radical equations. The course uses basic concepts in linear algebra to approach the theory of bodies and introduce the notion of algebraic number, while exploring the groups of permutations necessary for the study of Galois groups.
This course is particularly notable for its ability to present complex algebra concepts in an accessible and simplified manner, allowing students to quickly achieve meaningful results with a minimum of abstract formalism. It is ideal for math, physics, or engineering students, as well as math enthusiasts looking to deepen their understanding of algebraic structures and their application.
By completing this course, participants will not only gain a deep understanding of Galois theory, but will also have the opportunity to earn a shareable certificate, adding significant value to their professional or academic profile.
Analysis I (part 1): Prelude, basic notions, real numbers (SCHOOL POLYTECHNIQUE FEDERALE DE LAUSANNE)
The course “Analysis I (part 1): Prelude, basic notions, real numbers”, offered by the École Polytechnique Fédérale de Lausanne on edX, is an in-depth introduction to the fundamental concepts of real analysis. This 5-week course, requiring approximately 4-5 hours of study per week, is designed to be completed at your own pace.
The course content begins with a prelude which revisits and deepens essential mathematical notions such as trigonometric functions (sin, cos, tan), reciprocal functions (exp, ln), as well as the calculation rules for powers, logarithms and the roots. It also covers basic sets and functions.
The core of the course focuses on number systems. Starting from the intuitive notion of natural numbers, the course rigorously defines rational numbers and explores their properties. Particular attention is paid to real numbers, introduced to fill in the gaps in rational numbers. The course presents an axiomatic definition of real numbers and studies their properties in detail, including concepts such as infimum, supremum, absolute value and other additional properties of real numbers.
This course is ideal for those who have basic knowledge of mathematics and want to deepen their understanding of real-world analysis. It is particularly useful for students of mathematics, physics, or engineering, as well as anyone interested in a rigorous understanding of the foundations of mathematics.
By completing this course, participants will gain a solid understanding of real numbers and their importance in analysis, as well as the opportunity to earn a shareable certificate, adding significant value to their professional or academic profile.
Analysis I (part 2): Introduction to complex numbers (SCHOOL POLYTECHNIQUE FEDERALE DE LAUSANNE)
The course “Analysis I (part 2): Introduction to complex numbers”, offered by the École Polytechnique Fédérale de Lausanne on edX, is a captivating introduction to the world of complex numbers.This 2-week course, requiring approximately 4-5 hours of study per week, is designed to be completed at your own pace.
The course begins by addressing the equation z^2 = -1, which has no solution in the set of real numbers, R. This problem leads to the introduction of complex numbers, C, a field which contains R and allows us to solve such equations. The course explores different ways of representing a complex number and discusses solutions to equations of the form z^n = w, where n belongs to N* and w to C.
A highlight of the course is the study of the fundamental theorem of algebra, which is a key result in mathematics. The course also covers topics such as the Cartesian representation of complex numbers, their elementary properties, the inverse element for multiplication, the Euler and de Moivre formula, and the polar form of a complex number.
This course is ideal for those who already have some knowledge of real numbers and want to extend their understanding to complex numbers. It is especially useful for students of mathematics, physics, or engineering, as well as anyone interested in a deeper understanding of algebra and its applications.
By completing this course, participants will gain a solid understanding of complex numbers and their crucial role in mathematics, as well as the opportunity to earn a shareable certificate, adding significant value to their professional or academic profile.
Analysis I (part 3): Sequences of real numbers I and II (SCHOOL POLYTECHNIQUE FEDERALE DE LAUSANNE)
The course “Analysis I (part 3): Sequences of real numbers I and II”, offered by the École Polytechnique Fédérale de Lausanne on edX, focuses on sequences of real numbers. This 4-week course, requiring approximately 4-5 hours of study per week, is designed to be completed at your own pace.
The central concept of this course is the limit of a sequence of real numbers. It begins by defining a sequence of real numbers as a function from N to R. For example, the sequence a_n = 1/2^n is explored, showing how it approaches zero. The course rigorously addresses the definition of the limit of a sequence and develops methods to establish the existence of a limit.
In addition, the course establishes a link between the concept of limit and that of the infimum and the supremum of a set. An important application of sequences of real numbers is illustrated by the fact that each real number can be considered as the limit of a sequence of rational numbers. The course also explores Cauchy sequences and sequences defined by linear induction, as well as the Bolzano-Weierstrass theorem.
Participants will also learn about numerical series, with an introduction to different examples and convergence criteria, such as the d'Alembert criterion, the Cauchy criterion, and the Leibniz criterion. The course ends with the study of numerical series with a parameter.
This course is ideal for those who have basic knowledge of mathematics and want to deepen their understanding of real number sequences. It is especially useful for students of mathematics, physics or engineering. By completing this course, participants will enrich their understanding of mathematics and may obtain a shareable certificate, an asset for their professional or academic development.
Discovery of Real and Continuous Functions: Analysis I (part 4) (SCHOOL POLYTECHNIQUE FEDERALE DE LAUSANNE)
In “Analysis I (part 4): Limit of a function, continuous functions”, the École Polytechnique Fédérale de Lausanne offers a fascinating journey into the study of real functions of a real variable.This course, lasting 4 weeks with 4 to 5 hours of weekly study, is available on edX and allows progression at your own pace.
This segment of the course begins with the introduction of real functions, emphasizing their properties such as monotonicity, parity, and periodicity. It also explores operations between functions and introduces specific functions such as hyperbolic functions. Particular attention is given to functions defined stepwise, including Signum and Heaviside functions, as well as affine transformations.
The core of the course focuses on the sharp limit of a function at a point, providing concrete examples of limits of functions. It also covers the concepts of left and right limits. Next, the course looks at infinite limits of functions and provides essential tools for calculating limits, such as the cop theorem.
A key aspect of the course is the introduction of the concept of continuity, defined in two different ways, and its use to extend certain functions. The course ends with a study of continuity on open intervals.
This course is an enriching opportunity for those looking to deepen their understanding of real and continuous functions. It is ideal for students of mathematics, physics or engineering. By completing this course, participants will not only broaden their mathematical horizons, but will also have the chance to obtain a rewarding certificate, opening the door to new academic or professional perspectives.
Exploring Differentiable Functions: Analysis I (part 5) (SCHOOL POLYTECHNIQUE FEDERALE DE LAUSANNE)
The École Polytechnique Fédérale de Lausanne, in its educational offering on edX, presents “Analysis I (part 5): Continuous functions and differentiable functions, the derivative function”. This four-week course, requiring approximately 4-5 hours of study per week, is an in-depth exploration of the concepts of differentiability and continuity of functions.
The course begins with an in-depth study of continuous functions, focusing on their properties over closed intervals. This section helps students understand the maximum and minimum of continuous functions. The course then introduces the bisection method and presents important theorems such as the intermediate value theorem and the fixed point theorem.
The central part of the course is devoted to the differentiability and differentiability of functions. Students learn to interpret these concepts and understand their equivalence. The course then looks at the construction of the derivative function and examines its properties in detail, including algebraic operations on derivative functions.
An important aspect of the course is the study of the properties of differentiable functions, such as the derivative of the composition of functions, Rolle's theorem, and the finite increment theorem. The course also explores the continuity of the derivative function and its implications on the monotonicity of a differentiable function.
This course is an excellent opportunity for those who want to deepen their understanding of differentiable and continuous functions. It is ideal for students of mathematics, physics or engineering. By completing this course, participants will not only broaden their understanding of fundamental mathematical concepts, but will also have the opportunity to earn a rewarding certificate, opening the door to new academic or professional opportunities.
Deepening in Mathematical Analysis: Analysis I (part 6) (SCHOOL POLYTECHNIQUE FEDERALE DE LAUSANNE)
The course “Analysis I (part 6): Studies of functions, limited developments”, offered by the École Polytechnique Fédérale de Lausanne on edX, is an in-depth exploration of functions and their limited developments. This four-week course, with a workload of 4 to 5 hours per week, allows learners to progress at their own pace.
This chapter of the course focuses on the in-depth study of functions, using theorems to examine their variations. After tackling the finite increment theorem, the course looks at its generalization. A crucial aspect of studying functions is understanding their behavior at infinity. To do this, the course introduces the Bernoulli-l'Hospital rule, an essential tool for determining the complex limits of certain quotients.
The course also explores the graphical representation of functions, examining questions such as the existence of local or global maxima or minima, as well as the convexity or concavity of functions. Students will learn to identify the different asymptotes of a function.
Another strong point of the course is the introduction of limited expansions of a function, which provide a polynomial approximation in the vicinity of a given point. These developments are essential to simplify the calculation of limits and the study of the properties of functions. The course also covers integer series and their radius of convergence, as well as the Taylor series, a powerful tool for representing indefinitely differentiable functions.
This course is a valuable resource for those looking to deepen their understanding of functions and their applications in mathematics. It offers an enriching and detailed perspective on key concepts in mathematical analysis.
Mastery of Integration: Analysis I (part 7) (SCHOOL POLYTECHNIQUE FEDERALE DE LAUSANNE)
The course “Analysis I (part 7): Indefinite and definite integrals, integration (selected chapters)”, offered by the École Polytechnique Fédérale de Lausanne on edX, is a detailed exploration of the integration of functions. This module, lasting four weeks with an involvement of 4 to 5 hours per week, allows learners to discover the subtleties of integration at their own pace.
The course begins with the definition of the indefinite integral and the definite integral, introducing the definite integral via Riemann sums and upper and lower sums. It then discusses three key properties of definite integrals: the linearity of the integral, the subdivision of the integration domain, and the monotonicity of the integral.
A central point of the course is the mean theorem for continuous functions on a segment, which is demonstrated in detail. The course reaches its climax with the fundamental theorem of integral calculus, introducing the notion of the antiderivative of a function. Students learn various integration techniques, such as integration by parts, changing variables, and integration by induction.
The course concludes with the study of the integration of particular functions, including the integration of the limited expansion of a function, the integration of integer series, and the integration of piecewise continuous functions. These techniques allow the integrals of functions with special forms to be calculated more efficiently. Finally, the course explores generalized integrals, defined by passing to the limit in integrals, and presents concrete examples.
This course is a valuable resource for those seeking to master integration, a fundamental tool in mathematics. It provides a comprehensive and practical perspective on integration, enriching learners' mathematical skills.
Courses in English
Introduction to Linear Models and Matrix Algebra (Harvard)
Harvard University, through its HarvardX platform on edX, offers the course “Introduction to Linear Models and Matrix Algebra”. Although the course is taught in English, it offers a unique opportunity to learn the foundations of matrix algebra and linear models, essential skills in many scientific fields.
This four-week course, requiring 2 to 4 hours of study per week, is designed to be completed at your own pace. It focuses on using the R programming language to apply linear models in data analysis, particularly in the life sciences. Students will learn to manipulate matrix algebra and understand its application in experimental design and high-dimensional data analysis.
The program covers matrix algebra notation, matrix operations, application of matrix algebra to data analysis, linear models, and an introduction to QR decomposition. This course is part of a series of seven courses, which can be taken individually or as part of two professional certificates in Data Analysis for the Life Sciences and Genomic Data Analysis.
This course is ideal for those looking to gain skills in statistical modeling and data analysis, particularly in the life sciences context. It provides a solid foundation for those who wish to further explore matrix algebra and its application in various scientific and research fields.
Master Probability (Harvard)
LThe “Statistics 110: Probability” playlist on YouTube, taught in English by Joe Blitzstein of Harvard University, is an invaluable resource for those looking to deepen their knowledge of probability. The playlist includes lesson videos, review materials, and over 250 practice exercises with detailed solutions.
This English course is a comprehensive introduction to probability, presented as an essential language and set of tools for understanding statistics, science, risk and randomness. The concepts taught are applicable in various fields such as statistics, science, engineering, economics, finance and daily life.
Topics covered include the basics of probability, random variables and their distributions, univariate and multivariate distributions, limit theorems, and Markov chains. The course requires prior knowledge of one-variable calculus and familiarity with matrices.
For those who are comfortable with English and eager to explore the world of probability in depth, this Harvard course series offers an enriching learning opportunity. You can access the playlist and its detailed contents directly on YouTube.
Probability Explained. Course with French Subtitles (Harvard)
The course “Fat Chance: Probability from the Ground Up,” offered by HarvardX on edX, is a fascinating introduction to probability and statistics. Although the course is taught in English, it is accessible to a French-speaking audience thanks to the French subtitles available.
This seven-week course, requiring 3 to 5 hours of study per week, is designed for those who are new to the study of probability or seeking an accessible review of key concepts before enrolling in a statistics course. University level. “Fat Chance” emphasizes developing mathematical thinking rather than memorizing terms and formulas.
Initial modules introduce basic counting skills, which are then applied to simple probability problems. Subsequent modules explore how these ideas and techniques can be adapted to address a wider range of probability problems. The course ends with an introduction to statistics through the notions of expected value, variance and normal distribution.
This course is ideal for those looking to increase their quantitative reasoning skills and understand the foundations of probability and statistics. It provides an enriching perspective on the cumulative nature of mathematics and how it applies to understanding risk and randomness.
Statistical Inference and Modeling for High-Throughput Experiments (Harvard)
The “Statistical Inference and Modeling for High-throughput Experiments” course in English focuses on the techniques used to perform statistical inference on high-throughput data. This four-week course, requiring 2-4 hours of study per week, is a valuable resource for those seeking to understand and apply advanced statistical methods in data-intensive research settings.
The program covers a variety of topics, including the multiple comparison problem, error rates, error rate control procedures, false discovery rates, q-values, and exploratory data analysis. It also introduces statistical modeling and its application to high-throughput data, discussing parametric distributions such as binomial, exponential, and gamma, and describing maximum likelihood estimation.
Students will learn how these concepts are applied in contexts such as next generation sequencing and microarray data. The course also covers hierarchical models and Bayesian empirics, with practical examples of their use.
This course is ideal for those looking to deepen their understanding of statistical inference and modeling in modern scientific research. It provides an in-depth perspective on the statistical analysis of complex data and is an excellent resource for researchers, students and professionals in the fields of life sciences, bioinformatics and statistics.
Introduction to Probability (Harvard)
The “Introduction to Probability” course, offered by HarvardX on edX, is an in-depth exploration of probability, an essential language and toolset for understanding data, chance, and uncertainty. Although the course is taught in English, it is accessible to a French-speaking audience thanks to the French subtitles available.
This ten-week course, requiring 5-10 hours of study per week, aims to bring logic to a world filled with chance and uncertainty. It will provide the tools needed to understand data, science, philosophy, engineering, economics and finance. You will not only learn how to solve complex technical problems, but also how to apply these solutions in daily life.
With examples ranging from medical testing to sports predictions, you'll gain a solid foundation for the study of statistical inference, stochastic processes, random algorithms, and other topics where probability is necessary.
This course is ideal for those looking to increase their understanding of uncertainty and chance, making good predictions, and understanding random variables. It provides an enriching perspective on common probability distributions used in statistics and data science.
Applied Calculus (Harvard)
The “Calculus Applied!” course, offered by Harvard on edX, is an in-depth exploration of the application of single-variable calculus in the social, life, and physical sciences. This course, entirely in English, is an excellent opportunity for those looking to understand how calculus is applied in real-world professional contexts.
Lasting ten weeks and requiring between 3 and 6 hours of study per week, this course goes beyond traditional textbooks. He collaborates with professionals from various fields to show how calculus is used to analyze and solve real-world problems. Students will explore varied applications, ranging from economic analysis to biological modeling.
The program covers the use of derivatives, integrals, differential equations, and emphasizes the importance of mathematical models and parameters. It is designed for those who have a basic understanding of one-variable calculus and are interested in its practical applications in various fields.
This course is perfect for students, teachers, and professionals looking to deepen their understanding of calculus and discover its real-world applications.
Introduction to mathematical reasoning (Stanford)
The “Introduction to Mathematical Thinking” course, offered by Stanford University on Coursera, is a dive into the world of mathematical reasoning. Although the course is taught in English, it is accessible to a French-speaking audience thanks to the French subtitles available.
This seven-week course, requiring approximately 38 hours in total, or approximately 12 hours per week, is designed for those who wish to develop mathematical thinking, different from simply practicing mathematics as it is often presented in the school system. The course focuses on developing an “outside the box” way of thinking, a valuable skill in today's world.
Students will explore how professional mathematicians think to solve real-world problems, whether they arise from the everyday world, from science, or from mathematics itself. The course helps develop this crucial way of thinking, going beyond learning procedures to solve stereotypical problems.
This course is ideal for those looking to strengthen their quantitative reasoning and understand the foundations of mathematical reasoning. It provides an enriching perspective on the cumulative nature of mathematics and its application to understanding complex problems.
Statistical Learning with R (Stanford)
The “Statistical Learning with R” course, offered by Stanford, is an intermediate-level introduction to supervised learning, focusing on regression and classification methods. This course, entirely in English, is a valuable resource for those seeking to understand and apply statistical methods in the field of data science.
Lasting eleven weeks and requiring 3-5 hours of study per week, the course covers both traditional and exciting new methods in statistical modeling, and how to use them in the R programming language. of the course was updated in 2021 for the second edition of the course manual.
Topics include linear and polynomial regression, logistic regression and linear discriminant analysis, cross-validation and bootstrapping, model selection and regularization methods (ridge and lasso), nonlinear models, splines and generalized additive models, tree-based methods, random forests and boosting, support vector machines, neural networks and deep learning, survival models, and multiple testing.
This course is ideal for those with a basic knowledge of statistics, linear algebra, and computer science, and who are looking to deepen their understanding of statistical learning and its application in data science.
How to Learn Math: A Course for Everyone (Stanford)
The “How to Learn Math: For Students” course, offered by Stanford. Is a free online course for learners of all levels of mathematics. Entirely in English, it combines important information about the brain with new evidence about the best ways to approach mathematics.
Lasting six weeks and requiring 1 to 3 hours of study per week. The course is designed to transform learners' relationship with mathematics. Many people have had negative experiences with math, leading to aversion or failure. This course aims to give learners the information they need to enjoy mathematics.
Covered are topics such as the brain and learning math. Myths about math, mindset, mistakes and speed are also covered. Numerical flexibility, mathematical reasoning, connections, numerical models are also part of the program. The representations of mathematics in life, but also in nature and at work are not forgotten. The course is designed with an active engagement pedagogy, making learning interactive and dynamic.
It is a valuable resource for anyone who wants to see mathematics differently. Develop a deeper and positive understanding of this discipline. It is particularly suitable for those who have had negative experiences with maths in the past and are looking to change this perception.
Probability Management (Stanford)
The “Introduction to Probability Management” course, offered by Stanford, is an introduction to the discipline of probability management. This field focuses on communicating and calculating uncertainties in the form of auditable data tables called Stochastic Information Packets (SIPs). This ten-week course requires 1 to 5 hours of study per week. It is undoubtedly a valuable resource for those seeking to understand and apply statistical methods in the field of data science.
The course curriculum covers topics such as recognizing the “Flaw of Averages,” a set of systematic errors that arise when uncertainties are represented by single numbers, usually an average. It explains why many projects are late, over budget and under budget. The course also teaches Uncertainty Arithmetic, which performs calculations with uncertain inputs, resulting in uncertain outputs from which you can calculate true average results and the chances of achieving specified goals.
Students will learn how to create interactive simulations that can be shared with any Excel user without requiring add-ins or macros. This approach is equally suitable for Python or any programming environment that supports arrays.
This course is ideal for those who are comfortable with Microsoft Excel and are looking to deepen their understanding of probability management and its application in data science.
The Science of Uncertainty and Data (MIT)
The course “Probability – The Science of Uncertainty and Data”, offered by the Massachusetts Institute of Technology (MIT). Is a fundamental introduction to data science through probabilistic models. This course lasts sixteen weeks, requiring 10 to 14 hours of study per week. It corresponds to part of the MIT MicroMasters program in statistics and data science.
This course explores the world of uncertainty: from accidents in unpredictable financial markets to communications. Probabilistic modeling and the related field of statistical inference. Are two keys to analyzing this data and making scientifically sound predictions.
Students will discover the structure and basic elements of probabilistic models. Including random variables, their distributions, means and variances. The course also covers inference methods. The laws of large numbers and their applications, as well as random processes.
This course is perfect for those who want fundamental knowledge in data science. It provides a comprehensive perspective on probabilistic models. From basic elements to random processes and statistical inference. All of this is particularly useful for professionals and students. Particularly in the fields of data science, engineering and statistics.
Computational Probability and Inference (MIT)
The Massachusetts Institute of Technology (MIT) presents the “Computational Probability and Inference” course in English. The program includes an intermediate-level introduction to probabilistic analysis and inference. This twelve-week course, requiring 4-6 hours of study per week, is a fascinating exploration of how probability and inference are used in areas as varied as spam filtering, mobile bot navigation, or even in strategy games like Jeopardy and Go.
In this course, you will learn the principles of probability and inference and how to implement them in computer programs that reason with uncertainty and make predictions. You will learn about different data structures for storing probability distributions, such as probabilistic graphical models, and develop efficient algorithms for reasoning with these data structures.
By the end of this course, you will know how to model real-world problems with probability and how to use the resulting models for inference. You don't need to have prior experience in probability or inference, but you should be comfortable with basic Python programming and calculus.
This course is a substantial resource for those seeking to understand and apply statistical methods in the field of data science, providing a comprehensive perspective on probabilistic models and statistical inference.
At the Heart of Uncertainty: MIT Demystifies Probability
In the course “Introduction to Probability Part II: Inference Processes”, the Massachusetts Institute of Technology (MIT) offers an advanced immersion in the world of probability and inference. This course, entirely in English, is a logical continuation of the first part, diving deeper into data analysis and the science of uncertainty.
Over a period of sixteen weeks, with a commitment of 6 hours per week, this course explores the laws of large numbers, Bayesian inference methods, classical statistics, and random processes such as Poisson processes and chains of Markov. This is a rigorous exploration, intended for those who already have a solid foundation in probability.
This course stands out for its intuitive approach, while maintaining mathematical rigor. It does not just present theorems and proofs, but aims to develop a deep understanding of concepts through concrete applications. Students will learn to model complex phenomena and interpret real-world data.
Ideal for data science professionals, researchers, and students, this course offers a unique perspective on how probability and inference shape our understanding of the world. Perfect for those looking to deepen their understanding of data science and statistical analysis.
Analytical Combinatorics: A Princeton Course for Deciphering Complex Structures (Princeton)
The Analytic Combinatorics course, offered by Princeton University, is a fascinating exploration of analytical combinatorics, a discipline that enables precise quantitative predictions of complex combinatorial structures. This course, entirely in English, is a valuable resource for those seeking to understand and apply advanced methods in the field of combinatorics.
Lasting three weeks and requiring approximately 16 hours in total, or approximately 5 hours per week, this course introduces the symbolic method for deriving functional relationships between ordinary, exponential, and multivariate generating functions. It also explores methods of complex analysis for deriving precise asymptotics from the equations of generating functions.
Students will discover how analytical combinatorics can be used to predict precise quantities in large combinatorial structures. They will learn to manipulate combinatorial structures and use complex analysis techniques to analyze these structures.
This course is ideal for those looking to deepen their understanding of combinatorics and its application in solving complex problems. It offers a unique perspective on how analytical combinatorics shapes our understanding of mathematical and combinatorial structures.
