Probability and Random Processes 3rd Edition by Grimmett, Stirzaker PDF Download

This book gives an introduction to probability and its many practical application by providing a thorough, entertaining account of basic probability and important random processes, covering a range of important topics. Emphasis is on modelling rather than abstraction and there are new sections on sampling and Markov chain Monte Carlo, renewal-reward, queueing networks, stochastic calculus, and option pricing in the Black-Scholes model for financial markets. In addition, there are almost 400 exercises and problems relevant to the material. Solutions can be found in One Thousand Exercises in Probability.

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Introduction to Probability Theory 1st Edition by Hoel, Port, Stone

An excellent book to learn probability theory for both undergraduates and graduate students.

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Understanding Probability 3rd Edition by Henk Tijms PDF Download

Understanding Probability is a unique and stimulating approach to a first course in probability. The first part of the book demystifies probability and uses many wonderful probability applications from everyday life to help the reader develop a feel for probabilities. The second part, covering a wide range of topics, teaches clearly and simply the basics of probability. This fully revised third edition has been packed with even more exercises and examples and it includes new sections on Bayesian inference, Markov chain Monte-Carlo simulation, hitting probabilities in random walks and Brownian motion, and a new chapter on continuous-time Markov chains with applications. Here you will find all the material taught in an introductory probability course. The first part of the book, with its easy-going style, can be read by anybody with a reasonable background in high school mathematics. The second part of the book requires a basic course in calculus.

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A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory PDF Download

This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.

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An Invitation to Discrete Mathematics by Jiri Matousek, Jaroslav Nesetril PDF Download

This book is a clear and self-contained introduction to discrete mathematics. Aimed mainly at undergraduate and early graduate students of mathematics and computer science. It is written with the goal of stimulating interest in mathematics and an active, problem-solving approach to the presented material. The reader is led to an understanding of the basic principles and methods of actually doing mathematics (and having fun at that) Being more narrowly focused than many discrete mathematics textbooks and treating selected topics in an unusual depth and from several points of view, the book reflects the conviction of the authors, active and internationally renowned mathematicians, that the most important gain from studying mathematics is the cultivation of clear and logical thinking and habits useful for attacking new problems.

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Flatland: A Romance of Many Dimensions by Edwin A. Abbott PDF Download

This masterpiece of science (and mathematical) fiction is a delightfully unique and highly entertaining satire that has charmed readers for more than 100 years. The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square, a mathematician and resident of the two-dimensional Flatland, where women-thin, straight lines-are the lowliest of shapes, and where men may have any number of sides, depending on their social status.
Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions) and ultimately entertains thoughts of visiting a land of four dimensions—a revolutionary idea for which he is returned to his two-dimensional world. Charmingly illustrated by the author, Flatland is not only fascinating reading, it is still a first-rate fictional introduction to the concept of the multiple dimensions of space. "Instructive, entertaining, and stimulating to the imagination.

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Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter PDF Download

Gödel, Escher, Bach: An Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter. The tagline "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll" was used by the publisher to describe the book.[1] By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach, GEB expounds concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself.

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