https://mklab.gr/ Wed, 29 Jul 2026 01:10:48 +0000 MyBB https://mklab.gr/showthread.php?tid=1403 Wed, 29 Jul 2026 03:16:37 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1403 Seeing Theory 
by Daniel Kunin

Summary


Seeing Theory is an interactive web project created at Brown University designed to make probability and statistics more accessible and intuitive through visual learning. Created by Daniel Kunin and his team using D3.js interactive visualizations, the site guides learners through six core chapters: Basic Probability, Compound Probability, Probability Distributions, Frequentist Inference, Bayesian Inference, and Regression Analysis. By allowing users to manipulate parameters and observe statistical concepts dynamically in real time, the platform bridges the gap between abstract mathematical formulas and practical, visual understanding.

WEB PROJECT]]> Seeing Theory 
by Daniel Kunin

Summary


Seeing Theory is an interactive web project created at Brown University designed to make probability and statistics more accessible and intuitive through visual learning. Created by Daniel Kunin and his team using D3.js interactive visualizations, the site guides learners through six core chapters: Basic Probability, Compound Probability, Probability Distributions, Frequentist Inference, Bayesian Inference, and Regression Analysis. By allowing users to manipulate parameters and observe statistical concepts dynamically in real time, the platform bridges the gap between abstract mathematical formulas and practical, visual understanding.

WEB PROJECT]]> https://mklab.gr/showthread.php?tid=1099 Mon, 13 Jul 2026 18:43:34 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1099

Introduction to Probability for Data Science 
by [Stanley Chan]

Summary:

Introduction to Probability for Data Science by Stanley H. Chan is a comprehensive textbook that explains how probability provides the mathematical foundation for understanding data, uncertainty, and modern machine learning. The book connects traditional probability theory with practical data science applications, helping readers see why concepts such as random variables, distributions, estimation, regression, and hypothesis testing matter in real-world problems.

Unlike purely theoretical probability books, it combines mathematical explanations with visual intuition and programming examples using tools such as Python and MATLAB. The goal is to help students build both the theoretical knowledge and practical skills needed to analyze data effectively. The author emphasizes that data science is not only about using algorithms but also about understanding the uncertainty behind the results. 

Through clear explanations, illustrations, and applications, the book creates a bridge between probability theory, statistics, and machine learning, making it a valuable resource for students and anyone interested in learning the mathematical ideas behind data-driven decision making. 


BOOK]]>

Introduction to Probability for Data Science 
by [Stanley Chan]

Summary:

Introduction to Probability for Data Science by Stanley H. Chan is a comprehensive textbook that explains how probability provides the mathematical foundation for understanding data, uncertainty, and modern machine learning. The book connects traditional probability theory with practical data science applications, helping readers see why concepts such as random variables, distributions, estimation, regression, and hypothesis testing matter in real-world problems.

Unlike purely theoretical probability books, it combines mathematical explanations with visual intuition and programming examples using tools such as Python and MATLAB. The goal is to help students build both the theoretical knowledge and practical skills needed to analyze data effectively. The author emphasizes that data science is not only about using algorithms but also about understanding the uncertainty behind the results. 

Through clear explanations, illustrations, and applications, the book creates a bridge between probability theory, statistics, and machine learning, making it a valuable resource for students and anyone interested in learning the mathematical ideas behind data-driven decision making. 


BOOK]]> https://mklab.gr/showthread.php?tid=995 Thu, 09 Jul 2026 02:23:29 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=995 BY Rick Durrett

Summary

In his textbook, Elementary Probability for Applications, Rick Durrett provides a comprehensive and accessible introduction to the fundamental concepts of probability theory and its diverse real-world applications. The text systematically transitions from foundational combinatorial probability—grounded in classical examples like coin flips, card games, and dice rolls—to more complex frameworks including conditional probability, independent events, and random variables.
 By establishing the core axioms of probability, Durrett bridges intuitive frequency interpretations with mathematical rigor, guiding readers through critical limit theorems, the law of large numbers, and the central limit theorem. Additionally, the book covers essential applied statistical tools like confidence intervals and introduces multi-stage systems through Markov chains, exploring concepts such as stationary distributions and absorbing states.
Ultimately, the manuscript demonstrates how a discipline that originated from simple gambling games has evolved into a vital instrument for modern decision-making.
 By analyzing unpredictable loads in telephone networks, evaluating risks in the insurance sector, and parsing volatility within the stock market, Durrett illustrates how probabilistic modeling underpins contemporary science and commerce. Understanding these structural frameworks is crucial for anyone looking to navigate data-driven fields, as mastering probability theory allows researchers and professionals to quantify uncertainty and make informed, strategic choices in an increasingly unpredictable world.

BOOK (PDF)]]> BY Rick Durrett

Summary

In his textbook, Elementary Probability for Applications, Rick Durrett provides a comprehensive and accessible introduction to the fundamental concepts of probability theory and its diverse real-world applications. The text systematically transitions from foundational combinatorial probability—grounded in classical examples like coin flips, card games, and dice rolls—to more complex frameworks including conditional probability, independent events, and random variables.
 By establishing the core axioms of probability, Durrett bridges intuitive frequency interpretations with mathematical rigor, guiding readers through critical limit theorems, the law of large numbers, and the central limit theorem. Additionally, the book covers essential applied statistical tools like confidence intervals and introduces multi-stage systems through Markov chains, exploring concepts such as stationary distributions and absorbing states.
Ultimately, the manuscript demonstrates how a discipline that originated from simple gambling games has evolved into a vital instrument for modern decision-making.
 By analyzing unpredictable loads in telephone networks, evaluating risks in the insurance sector, and parsing volatility within the stock market, Durrett illustrates how probabilistic modeling underpins contemporary science and commerce. Understanding these structural frameworks is crucial for anyone looking to navigate data-driven fields, as mastering probability theory allows researchers and professionals to quantify uncertainty and make informed, strategic choices in an increasingly unpredictable world.

BOOK (PDF)]]> https://mklab.gr/showthread.php?tid=727 Thu, 25 Jun 2026 13:30:32 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=727 Probability Theory Notes 
by Amir Dembo


These Stanford probability theory notes by Amir Dembo provide a rigorous introduction to modern probability, building the subject from its mathematical foundations rather than focusing only on calculations. The notes begin with measure theory, probability spaces, random variables, and integration, then develop key concepts such as independence, conditional expectation, convergence of random variables, and important inequalities. 

From there, they explore the major limit theorems that explain the behavior of randomness in large systems, including the Law of Large Numbers and the Central Limit Theorem. Throughout, the emphasis is on understanding why probabilistic results are true through precise proofs and mathematical reasoning. As a result, the notes serve as an advanced guide for students in mathematics, statistics, data science, and related fields who want a deep theoretical understanding of uncertainty and stochastic processes rather than just practical statistical methods. 

BOOK]]> Probability Theory Notes 
by Amir Dembo


These Stanford probability theory notes by Amir Dembo provide a rigorous introduction to modern probability, building the subject from its mathematical foundations rather than focusing only on calculations. The notes begin with measure theory, probability spaces, random variables, and integration, then develop key concepts such as independence, conditional expectation, convergence of random variables, and important inequalities. 

From there, they explore the major limit theorems that explain the behavior of randomness in large systems, including the Law of Large Numbers and the Central Limit Theorem. Throughout, the emphasis is on understanding why probabilistic results are true through precise proofs and mathematical reasoning. As a result, the notes serve as an advanced guide for students in mathematics, statistics, data science, and related fields who want a deep theoretical understanding of uncertainty and stochastic processes rather than just practical statistical methods. 

BOOK]]> https://mklab.gr/showthread.php?tid=348 Sun, 14 Jun 2026 16:03:34 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=348 Lady Luck : the theory of probability
by Weaver, Warren, 1894-1978

Summary  Lady Luck: The Theory of Probability by Dr. Warren Weaver is an acclaimed, accessible introduction to probability and statistics. The book demystifies how chance operates in daily life, games, and science, explaining core mathematical concepts without requiring advanced training

BOOK PAGE]]> Lady Luck : the theory of probability
by Weaver, Warren, 1894-1978

Summary  Lady Luck: The Theory of Probability by Dr. Warren Weaver is an acclaimed, accessible introduction to probability and statistics. The book demystifies how chance operates in daily life, games, and science, explaining core mathematical concepts without requiring advanced training

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=341 Sun, 14 Jun 2026 15:38:49 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=341 Theory of Probability 
by Gnedenko

Summary  Boris V. Gnedenko's The Theory of Probability is a classic mathematics textbook that provides a rigorous yet accessible introduction to probability and statistics. It bridges classical probability, relative frequency, and modern axiomatic approaches.

BOOK PAGE]]> Theory of Probability 
by Gnedenko

Summary  Boris V. Gnedenko's The Theory of Probability is a classic mathematics textbook that provides a rigorous yet accessible introduction to probability and statistics. It bridges classical probability, relative frequency, and modern axiomatic approaches.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=340 Sun, 14 Jun 2026 15:36:10 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=340 An Elementary Introduction To The Theory Of Probability
by B. V. Gnedenko; A. Ya. Khinchin

Summary 

This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability. It is an introduction, no more: throughout the book the authors discuss the theory of probability for situations having only a finite number of possibilities, and the mathematics employed is held to the elementary level. But within its purposeiy restricted range it is extremely thorough, well organized, and absolutely authoritative. It is the only English translation of the latest revised Russian edition; and it is the only current translation on the market that has been checked and approved by Gnedenko himself.

After explaining in simple terms the meaning of the concept of probability and the means by which an event is declared to be in practice, impossible, the authors take up the processes involved in the calculation of probabilities. They survey the rules for addition and multiplication of probabilities, the concept of conditional probability, the formula for total probability, Bayes's formula, Bernoulli’s scheme and theorem, the concepts of random variables, insuffciency of the mean value for the characterization of a random variable, methods of measuring the variance of a random variable, theorems on the standard deviation, the Chebyshev inequality, normal laws of distribution, distribution curves, properties of normal distribution curves, and related topics.

The book is unique in that, while there are several high school and college textbooks available on this subject, there is no other popular treatment for the layman that contains quite the same material presented with the same degree of clarity and authenticity. The reader who shies away from oversimplified popularizations may be sure that in this book he is getting a perfectly reliable scientific treatment. Anyone who desires a fundamental grasp of this increasingly important subject cannot do better than to start with this book.

BOOK PAGE]]> An Elementary Introduction To The Theory Of Probability
by B. V. Gnedenko; A. Ya. Khinchin

Summary 

This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability. It is an introduction, no more: throughout the book the authors discuss the theory of probability for situations having only a finite number of possibilities, and the mathematics employed is held to the elementary level. But within its purposeiy restricted range it is extremely thorough, well organized, and absolutely authoritative. It is the only English translation of the latest revised Russian edition; and it is the only current translation on the market that has been checked and approved by Gnedenko himself.

After explaining in simple terms the meaning of the concept of probability and the means by which an event is declared to be in practice, impossible, the authors take up the processes involved in the calculation of probabilities. They survey the rules for addition and multiplication of probabilities, the concept of conditional probability, the formula for total probability, Bayes's formula, Bernoulli’s scheme and theorem, the concepts of random variables, insuffciency of the mean value for the characterization of a random variable, methods of measuring the variance of a random variable, theorems on the standard deviation, the Chebyshev inequality, normal laws of distribution, distribution curves, properties of normal distribution curves, and related topics.

The book is unique in that, while there are several high school and college textbooks available on this subject, there is no other popular treatment for the layman that contains quite the same material presented with the same degree of clarity and authenticity. The reader who shies away from oversimplified popularizations may be sure that in this book he is getting a perfectly reliable scientific treatment. Anyone who desires a fundamental grasp of this increasingly important subject cannot do better than to start with this book.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=339 Sun, 14 Jun 2026 15:33:55 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=339 The World Is Built On Probability
by Lev Tarasov

Summary 
This text is divided into two major parts.
The aim of the first part is to convince the reader that the random world begins directly in his or her own living room because, in fact, all modern life is based on probability. The first part is on the concept of probability and considers making decisions in conflict situations, optimizing queues, games, and the control of various processes, and doing random searches.

The second part of this text shows how fundamental chance is in nature using the probabilistic laws of modern physics and biology as examples. Elements of quantum mechanics are also involved, and this allows the author to demonstrate how probabilistic laws are basic to microscopic phenomena. The idea is that the reader, passing from the first part of the book to the second one, would see that probability is not only around us but it is at the basis of everything.

BOOK PAGE]]> The World Is Built On Probability
by Lev Tarasov

Summary 
This text is divided into two major parts.
The aim of the first part is to convince the reader that the random world begins directly in his or her own living room because, in fact, all modern life is based on probability. The first part is on the concept of probability and considers making decisions in conflict situations, optimizing queues, games, and the control of various processes, and doing random searches.

The second part of this text shows how fundamental chance is in nature using the probabilistic laws of modern physics and biology as examples. Elements of quantum mechanics are also involved, and this allows the author to demonstrate how probabilistic laws are basic to microscopic phenomena. The idea is that the reader, passing from the first part of the book to the second one, would see that probability is not only around us but it is at the basis of everything.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=333 Sun, 14 Jun 2026 15:14:59 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=333 Applied Problems In Probability Theory
by E. Wentzel; L. Ovcharov

Summary This book is based on many years of experience of teaching probability theory and its applications at higher educational establishments. It contains many of the problems we ourselves encountered in our
research and consultative work. The problems are related to a variety of fields including electrical engineering, radio engineering, data transmission, computers, information systems, reliability of technical devices, preventive maintenance and repair, accuracy of apparatus, consumer service, transport, and the health service.  The text is divided into eleven chapters; each of winch begins with a short theoretical introduction which is followed by relevant formulas.The problems differ both in the fields of application and in difficulty.
At the beginning of each chapter the reader will find comparatively simple problems whose purpose is to help the reader grasp the fundamental concepts and acquire and consolidate the experience of applying probabilistic methods. Then follow more complicated applied problems, which can be solved only after the requisite theoretical knowledge has been acquired and the necessary techniques mastered.

BOOK PAGE]]> Applied Problems In Probability Theory
by E. Wentzel; L. Ovcharov

Summary This book is based on many years of experience of teaching probability theory and its applications at higher educational establishments. It contains many of the problems we ourselves encountered in our
research and consultative work. The problems are related to a variety of fields including electrical engineering, radio engineering, data transmission, computers, information systems, reliability of technical devices, preventive maintenance and repair, accuracy of apparatus, consumer service, transport, and the health service.  The text is divided into eleven chapters; each of winch begins with a short theoretical introduction which is followed by relevant formulas.The problems differ both in the fields of application and in difficulty.
At the beginning of each chapter the reader will find comparatively simple problems whose purpose is to help the reader grasp the fundamental concepts and acquire and consolidate the experience of applying probabilistic methods. Then follow more complicated applied problems, which can be solved only after the requisite theoretical knowledge has been acquired and the necessary techniques mastered.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=332 Sun, 14 Jun 2026 15:12:19 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=332 Probability Theory (First Steps)
by E. S. Wentzel

Summary  The author of this booklet describes in popular language how probability theory was developed and found wide application in all fields of modern science. This book can be considered as an introduction towards a more thorough study of probability theory and is intended for a wide circle of readers.

BOOK PAGE]]> Probability Theory (First Steps)
by E. S. Wentzel

Summary  The author of this booklet describes in popular language how probability theory was developed and found wide application in all fields of modern science. This book can be considered as an introduction towards a more thorough study of probability theory and is intended for a wide circle of readers.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=291 Thu, 11 Jun 2026 20:06:21 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=291 High Dimensional Probability, 
by Roman Vershynin

Summary  Vershynin, R. Cambridge University Press. High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions.

PDF PAGE
]]> High Dimensional Probability, 
by Roman Vershynin

Summary  Vershynin, R. Cambridge University Press. High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions.

PDF PAGE
]]> https://mklab.gr/showthread.php?tid=284 Wed, 10 Jun 2026 23:58:57 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=284 Introduction to Probability

Charles M. Grinstead

Summary

Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continued to influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a well-established branch of mathematics that finds applications in every area of scholarly activity from music to physics, and in daily experience from weather prediction to predicting the risks of new medical treatments.

BOOK PAGE

]]> Introduction to Probability

Charles M. Grinstead

Summary

Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continued to influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a well-established branch of mathematics that finds applications in every area of scholarly activity from music to physics, and in daily experience from weather prediction to predicting the risks of new medical treatments.

BOOK PAGE

]]> https://mklab.gr/showthread.php?tid=283 Wed, 10 Jun 2026 23:54:35 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=283 Odds & Ends
Introducing Probability & Decision with a Visual Emphasis
Jonathan Weisberg

Summary

This textbook is for introductory philosophy courses on probability and inductive logic. It is based on a typical such course I teach at the University of Toronto, where we offer “Probability & Inductive Logic” in the second year, alongside the usual deductive logic intro.
The book assumes no deductive logic. The early chapters introduce the little that’s used. In fact almost no formal background is presumed, only very simple high school algebra.

BOOK PAGE]]> Odds & Ends
Introducing Probability & Decision with a Visual Emphasis
Jonathan Weisberg

Summary

This textbook is for introductory philosophy courses on probability and inductive logic. It is based on a typical such course I teach at the University of Toronto, where we offer “Probability & Inductive Logic” in the second year, alongside the usual deductive logic intro.
The book assumes no deductive logic. The early chapters introduce the little that’s used. In fact almost no formal background is presumed, only very simple high school algebra.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=248 Wed, 10 Jun 2026 03:36:19 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=248 Theory of Probability: A Historical Essay
by Oscar Sheynin

Summary  This book covers the history of probability up to Kolmogorov with essential additional coverage of statistics up to Fisher. The book covers an extremely wide field, and is targeted at the same readers as any other book on history of science.

BOOK PAGE]]> Theory of Probability: A Historical Essay
by Oscar Sheynin

Summary  This book covers the history of probability up to Kolmogorov with essential additional coverage of statistics up to Fisher. The book covers an extremely wide field, and is targeted at the same readers as any other book on history of science.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=233 Wed, 10 Jun 2026 02:47:06 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=233 A Probability Course for the Actuaries
by Marcel B. Finan

Summary  The present manuscript is designed mainly to help students prepare for the Probability Exam (Exam P/1), the first actuarial examination administered by the Society of Actuaries. This examination tests a student's knowledge of the fundamental probability tools for quantitatively assessing risk. A thorough command of calculus is assumed.

BOOK PAGE]]> A Probability Course for the Actuaries
by Marcel B. Finan

Summary  The present manuscript is designed mainly to help students prepare for the Probability Exam (Exam P/1), the first actuarial examination administered by the Society of Actuaries. This examination tests a student's knowledge of the fundamental probability tools for quantitatively assessing risk. A thorough command of calculus is assumed.

BOOK PAGE]]>