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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 Modelsis designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics.
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Mathematics in Everyday Life supports beginning university students in science and engineering by offering extra practice in calculus, linear algebra, geometry,trigonometry, elementary number theory, and probability. Students whose degree course includes writing an extended mathematical essay will find many suitable topics here, with pointers to extend and develop the material.
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How does mathematics impact everyday events? The purpose of this book is to show a range of examples where mathematics can be seen at work in everyday life.
From money (APR, mortgage repayments, personal finance), simple first and second order ODEs, sport and games (tennis, rugby, athletics, darts, tournament design, soccer, snooker), business (stock control, linear programming, check digits, promotion policies, investment), the social sciences (voting methods, Simpson’s Paradox, drug testing, measurements of inequality) to TV game shows and even gambling (lotteries, roulette, poker, horse racing), the mathematics behind commonplace events is explored. Fully worked examples illustrate the ideas discussed and each chapter ends with a collection of exercises.Everyday Mathematics supports other first year modules by giving students extra practice in working with calculus, linear algebra, geometry, trigonometry and probability. Secondary/high school level mathematics is all that is required for students to understand the material. Those students whose degree course includes writing an extended mathematical essay will find many suitable topics here, with pointers to extend and develop the material.
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