# discrete probability undergraduate texts in mathematics

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## Discrete Probability

**Author :**Hugh Gordon

**ISBN :**9781461219668

**Genre :**Mathematics

**File Size :**48. 82 MB

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Intended as a first course in probability at post-calculus level, this book is of special interest to students majoring in computer science as well as in mathematics. Since calculus is used only occasionally in the text, students who have forgotten their calculus can nevertheless easily understand the book, and its slow, gentle style and clear exposition will also appeal. Basic concepts such as counting, independence, conditional probability, random variables, approximation of probabilities, generating functions, random walks and Markov chains are all clearly explained and backed by many worked exercises. The 1,196 numerical answers to the 405 exercises, many with multiple parts, are included at the end of the book, and throughout, there are various historical comments on the study of probability. These include biographical information on such famous contributors as Fermat, Pascal, the Bernoullis, DeMoivre, Bayes, Laplace, Poisson, and Markov. Of interest to a wide range of readers and useful in many undergraduate programs.

## Basic Probability Theory With Applications

**Author :**Mario Lefebvre

**ISBN :**9780387749952

**Genre :**Mathematics

**File Size :**21. 4 MB

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The main intended audience for this book is undergraduate students in pure and applied sciences, especially those in engineering. Chapters 2 to 4 cover the probability theory they generally need in their training. Although the treatment of the subject is surely su?cient for non-mathematicians, I intentionally avoided getting too much into detail. For instance, topics such as mixed type random variables and the Dirac delta function are only brie?y mentioned. Courses on probability theory are often considered di?cult. However, after having taught this subject for many years, I have come to the conclusion that one of the biggest problems that the students face when they try to learn probability theory, particularly nowadays, is their de?ciencies in basic di?erential and integral calculus. Integration by parts, for example, is often already forgotten by the students when they take a course on probability. For this reason, I have decided to write a chapter reviewing the basic elements of di?erential calculus. Even though this chapter might not be covered in class, the students can refer to it when needed. In this chapter, an e?ort was made to give the readers a good idea of the use in probability theory of the concepts they should already know. Chapter 2 presents the main results of what is known as elementary probability, including Bayes’ rule and elements of combinatorial analysis.

## Discrete Mathematics

**Author :**László Lovász

**ISBN :**9780387217772

**Genre :**Mathematics

**File Size :**69. 42 MB

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Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

## Introduction To Probability With Statistical Applications

**Author :**Géza Schay

**ISBN :**9783319306209

**Genre :**Mathematics

**File Size :**45. 34 MB

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Now in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand’s paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics. Key features in new edition: * 35 new exercises * Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples * New section on regression * Online instructors' manual containing solutions to all exercises“/p> Advanced undergraduate and graduate students in computer science, engineering, and other natural and social sciences with only a basic background in calculus will benefit from this introductory text balancing theory with applications. Review of the first edition: This textbook is a classical and well-written introduction to probability theory and statistics. ... the book is written ‘for an audience such as computer science students, whose mathematical background is not very strong and who do not need the detail and mathematical depth of similar books written for mathematics or statistics majors.’ ... Each new concept is clearly explained and is followed by many detailed examples. ... numerous examples of calculations are given and proofs are well-detailed." (Sophie Lemaire, Mathematical Reviews, Issue 2008 m)

## Elementary Probability Theory

**Author :**Kai Lai Chung

**ISBN :**9780387215488

**Genre :**Mathematics

**File Size :**83. 77 MB

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This book provides an introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, which is illustrated with a large number of samples. The fourth edition adds material related to mathematical finance as well as expansions on stable laws and martingales. From the reviews: "Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." -- STATISTICAL PAPERS

## Probability For Engineering Mathematics And Sciences

**Author :**Chris P. Tsokos

**ISBN :**9781111430276

**Genre :**Mathematics

**File Size :**44. 40 MB

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This text blends theory and applications, reinforcing concepts with practical real-world examples that illustrate the importance of probability to undergraduate students who will use it in their subsequent courses and careers. The author emphasizes the study of probability distributions that characterize random variables, because this knowledge is essential in performing parametric statistical analysis. Explanations include the why as well as the how of probability distributions for random variables to help engage students and further promote their understanding. In addition, the text includes a self-contained chapter on finite Markov chains, which introduces the basic aspects of Markov chains and illustrates their usefulness with several real examples. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

## Basic Discrete Mathematics

**Author :**Richard Kohar

**ISBN :**9789814730419

**Genre :**Mathematics

**File Size :**88. 17 MB

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This lively introductory text exposes the student in the humanities to the world of discrete mathematics. A problem-solving based approach grounded in the ideas of George Pólya are at the heart of this book. Students learn to handle and solve new problems on their own. A straightforward, clear writing style and well-crafted examples with diagrams invite the students to develop into precise and critical thinkers. Particular attention has been given to the material that some students find challenging, such as proofs. This book illustrates how to spot invalid arguments, to enumerate possibilities, and to construct probabilities. It also presents case studies to students about the possible detrimental effects of ignoring these basic principles. The book is invaluable for a discrete and finite mathematics course at the freshman undergraduate level or for self-study since there are full solutions to the exercises in an appendix. "Written with clarity, humor and relevant real-world examples, Basic Discrete Mathematics is a wonderful introduction to discrete mathematical reasoning."- Arthur Benjamin, Professor of Mathematics at Harvey Mudd College, and author of The Magic of Math

## Undergraduate Algebra

**Author :**Serge Lang

**ISBN :**9780387274751

**Genre :**Mathematics

**File Size :**49. 1 MB

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The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group

## An Introduction To Probabilistic Modeling

**Author :**Pierre Bremaud

**ISBN :**9781461210467

**Genre :**Mathematics

**File Size :**41. 41 MB

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Introduction to the basic concepts of probability theory: independence, expectation, convergence in law and almost-sure convergence. Short expositions of more advanced topics such as Markov Chains, Stochastic Processes, Bayesian Decision Theory and Information Theory.

## Probability Models

**Author :**John Haigh

**ISBN :**9781447153436

**Genre :**Mathematics

**File Size :**46. 66 MB

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The purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability, such as that of a dice or cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. This textbook contains many worked examples and several chapters have been updated and expanded for the second edition. Some mathematical knowledge is assumed. The reader should have the ability to work with unions, intersections and complements of sets; a good facility with calculus, including integration, sequences and series; and appreciation of the logical development of an argument. Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics.