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The Theory of Probability
From classical foundations to advanced modern theory, this self-contained and comprehensive guide to probability weaves together mathematical proofs, historical context and richly detailed illustrative applications. A theorem discovery approach is used throughout, setting each proof within its historical setting and is accompanied by a consistent emphasis on elementary methods of proof. Each topic is presented in a modular framework, combining fundamental concepts with worked examples, problems and digressions which, although mathematically rigorous, require no specialised or advanced mathematical background. Augmenting this core material are over 80 richly embellished practical applications of probability theory, drawn from a broad spectrum of areas both classical and modern, each tailor-made to illustrate the magnificent scope of the formal results. Providing a solid grounding in practical probability, without sacrificing mathematical rigour or historical richness, this insightful book is a fascinating reference and essential resource, for all engineers, computer scientists and mathematicians.
eBook
Classic topics on the history of modern mathematical statistics : from Laplace to more recent times
\"There is nothing like it on the market...no others are as encyclopedic...the writing is exemplary: simple, direct, and competent.\"
—George W. Cobb, Professor Emeritus of Mathematics and Statistics, Mount Holyoke College
Written in a direct and clear manner, Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times presents a comprehensive guide to the history of mathematical statistics and details the major results and crucial developments over a 200-year period. Presented in chronological order, the book features an account of the classical and modern works that are essential to understanding the applications of mathematical statistics.
Divided into three parts, the book begins with extensive coverage of the probabilistic works of Laplace, who laid much of the foundations of later developments in statistical theory. Subsequently, the second part introduces 20th century statistical developments including work from Karl Pearson, Student, Fisher, and Neyman. Lastly, the author addresses post-Fisherian developments. Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times also features:
* A detailed account of Galton's discovery of regression and correlation as well as the subsequent development of Karl Pearson's X 2 and Student's t
* A comprehensive treatment of the permeating influence of Fisher in all aspects of modern statistics beginning with his work in 1912
* Significant coverage of Neyman–Pearson theory, which includes a discussion of the differences to Fisher's works
* Discussions on key historical developments as well as the various disagreements, contrasting information, and alternative theories in the history of modern mathematical statistics in an effort to provide a thorough historical treatment
Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times is an excellent reference for academicians with a mathematical background who are teaching or studying the history or philosophical controversies of mathematics and statistics. The book is also a useful guide for readers with a general interest in statistical inference.
eBook
The science of conjecture : evidence and probability before Pascal
How did we make reliable predictions before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? In The Science of Conjecture, James Franklin examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates.
The Science of Conjecture provides a history of rational methods of dealing with uncertainty and explores the coming to consciousness of the human understanding of risk.
eBook
The theory of probability
From classical foundations to advanced modern theory, this self-contained and comprehensive guide to probability weaves together mathematical proofs, historical context and richly detailed illustrative applications. A theorem discovery approach is used throughout, setting each proof within its historical setting and is accompanied by a consistent emphasis on elementary methods of proof. Each topic is presented in a modular framework, combining fundamental concepts with worked examples, problems and digressions which, although mathematically rigorous, require no specialised or advanced mathematical background. Augmenting this core material are over 80 richly embellished practical applications of probability theory, drawn from a broad spectrum of areas both classical and modern, each tailor-made to illustrate the magnificent scope of the formal results. Providing a solid grounding in practical probability, without sacrificing mathematical rigour or historical richness, this insightful book is a fascinating reference and essential resource, for all engineers, computer scientists and mathematicians.
eBook
Beruhmte Aufgaben der Stochastik: Von den Anfangen bis heute
Over the centuries, mathematicians have proposed many problems in stochastics and combinatorial analysis and discovered ingenious solutions for them. This book offers a selection of the most interesting problems. The arithmetic skill and methodology used to tackle them long ago is surprising. Their traces are still reflected in today's schoolbooks and university texts. The 2nd edition has been revised for even better comprehension.
eBook
Randomness
From the ancients' first readings of the innards of birds to your
neighbor's last bout with the state lottery, humankind has put
itself into the hands of chance. Today life itself may be at stake
when probability comes into play-in the chance of a false negative
in a medical test, in the reliability of DNA findings as legal
evidence, or in the likelihood of passing on a deadly congenital
disease-yet as few people as ever understand the odds. This book is
aimed at the trouble with trying to learn about probability. A
story of the misconceptions and difficulties civilization overcame
in progressing toward probabilistic thinking, Randomness
is also a skillful account of what makes the science of probability
so daunting in our own day. To acquire a (correct) intuition of
chance is not easy to begin with, and moving from an intuitive
sense to a formal notion of probability presents further problems.
Author Deborah Bennett traces the path this
process takes in an individual trying to come to grips with
concepts of uncertainty and fairness, and also charts the parallel
path by which societies have developed ideas about chance. Why,
from ancient to modern times, have people resorted to chance in
making decisions? Is a decision made by random choice \"fair\"? What
role has gambling played in our understanding of chance? Why do
some individuals and societies refuse to accept randomness at all?
If understanding randomness is so important to probabilistic
thinking, why do the experts disagree about what it really is? And
why are our intuitions about chance almost always dead wrong?
Anyone who has puzzled over a probability conundrum is struck by
the paradoxes and counterintuitive results that occur at a
relatively simple level. Why this should be, and how it has been
the case through the ages, for bumblers and brilliant
mathematicians alike, is the entertaining and enlightening lesson
of Randomness .
eBook
The Binomial Distribution: Historical Origin and Evolution of Its Problem Situations
The increase in available probabilistic information and its usefulness for understanding the world has made it necessary to promote probabilistic literate citizens. For this, the binomial distribution is fundamental as one of the most important distributions for understanding random phenomena and effective decision making, and as a facilitator for the understanding of mathematical and probabilistic notions such as the normal distribution. However, to understand it effectively, it is necessary to consider how it has developed throughout history, that is, the components that gave it the form and meaning that we know today. To address this perspective, we identify the problem situations that gave origin to the binomial distribution, the operational and discursive practices developed to find solutions, and the conflicts that caused a leap in mathematical and probability heuristics, culminating in what is now known as the binomial distribution formula. As a result, we present five historical links to the binomial phenomenon where problem situations of increasing complexity were addressed: a case study using informal means (such as direct counting), the formalization of numerical patterns and constructs related to counting cases, specific probability calculus, the study and modeling of probability in variable or complex phenomena, and the use of the distribution formula as a tool to approaching notions such as the normal distribution. The periods and situations identified correspond to a required step in the design of binomial distribution learning from a historical epistemological perspective and when solving conflicts.
Journal Article
The Science of Conjecture
How did we make reliable predictions before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? In The Science of Conjecture, James Franklin examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates.
The Science of Conjecture provides a history of rational methods of dealing with uncertainty and explores the coming to consciousness of the human understanding of risk.
eBook