Unnikrishna Pillai of Polytechnic University. The book is intended for a senior/graduate level course in probability and is aimed at students in electrical engineering, math, and physics departments. The authors' approach is to develop the subject of probability theory and stochastic processes as a deductive discipline and to illustrate the theory with basic applications of engineering interest. Approximately 1/3 of the text is new material--this material maintains the style and spirit of previous editions. In order to bridge the gap between concepts and applications, a number of additional examples have been added for further clarity, as well as several new topics.

    This is the currently used textbook for "Probabilistic Systems Analysis," an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains, a number of more advanced topics, from which an instructor can choose to match the goals of a particular course. These topics include transforms, sums of random variables, least squares estimation, the bivariate normal distribution, and a fairly detailed introduction to Bernoulli, Poisson, and Markov processes. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis has been just intuitively explained in the text, but is developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems. The book has been widely adopted for classroom use in introductory probability courses within the USA and abroad.

    Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

    The route takes the walker into France, Switzerland and Italy and is described in both anti-clockwise and clockwise directions, with variants and information about facilities en route.

    Johnson. It was the first book exclusively on the theory of NP-completeness and computational intractability. The book features an appendix providing a thorough compendium of NP-complete problems (which was updated in later printings of the book). The book is now outdated in some respects as it does not cover more recent development such as the PCP theorem. It is nevertheless still in print and is regarded as a classic: in a 2006 study, the CiteSeer search engine listed the book as the most cited reference in computer science literature.

    Essentially, you make an initial guess, and then get more data to improve it. Bayes Theorem, or Bayes Rule, has a ton of real world applications, from estimating your risk of a heart attack to making recommendations on Netflix But It Isn't That Complicated This book is a short introduction to Bayes Theorem. It is only 15 pages long, and is intended to show you how Bayes Theorem works as quickly as possible. The examples are intentionally kept simple to focus solely on Bayes Theorem without requiring that the reader know complicated probability distributions. If you want to learn the basics of Bayes Theorem as quickly as possible, with some easy to duplicate examples, this is a good book for you.

    The exposition is simple and leads to the most complete direct means of solving problems in mechanics. The final sections on adiabatic invariants have been revised and augmented. In addition a short biography of L D Landau has been inserted.

    Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program"

    CONGRATULATIONS TO HERBERT KROEMER, 2000 NOBEL LAUREATE FOR PHYSICS For upper-division courses in thermodynamics or statistical mechanics, Kittel and Kroemer offers a modern approach to thermal physics that is based on the idea that all physical systems can be described in terms of their discrete quantum states, rather than drawing on 19th-century classical mechanics concepts.

    These sections together make an appropriate one-term advanced/graduate level course (mathematical prerequisites: vector analysis and simple partial-differential equations). The book is printed to make it easy for readers to identify these sections.• The remaining Track 2 material provides a wealth of advanced topics instructors can draw from to flesh out a two-term course, with Track 1 sections serving as prerequisites.

    Publilius Syrus, Moral Sayings We've been very fortunate to receive fantastic feedback from our readers during the last four years, since the first edition of How to Solve It: Modern Heuristics was published in 1999. It's heartening to know that so many people appreciated the book and, even more importantly, were using the book to help them solve their problems. One professor, who published a review of the book, said that his students had given the best course reviews he'd seen in 15 years when using our text. There can be hardly any better praise, except to add that one of the book reviews published in a SIAM journal received the best review award as well. We greatly appreciate your kind words and personal comments that you sent, including the few cases where you found some typographical or other errors. Thank you all for this wonderful support.

    Evolutionary Dynamics is concerned with these equations of life. In this book, Martin A. Nowak draws on the languages of biology and mathematics to outline the mathematical principles according to which life evolves. His work introduces readers to the powerful yet simple laws that govern the evolution of living systems, no matter how complicated they might seem. Evolution has become a mathematical theory, Nowak suggests, and any idea of an evolutionary process or mechanism should be studied in the context of the mathematical equations of evolutionary dynamics. His book presents a range of analytical tools that can be used to this end: fitness landscapes, mutation matrices, genomic sequence space, random drift, quasispecies, replicators, the Prisoner's Dilemma, games in finite and infinite populations, evolutionary graph theory, games on grids, evolutionary kaleidoscopes, fractals, and spatial chaos. Nowak then shows how evolutionary dynamics applies to critical real-world problems, including the progression of viral diseases such as AIDS, the virulence of infectious agents, the unpredictable mutations that lead to cancer, the evolution of altruism, and even the evolution of human language. His book makes a clear and compelling case for understanding every living system--and everything that arises as a consequence of living systems--in terms of evolutionary dynamics.

    

    Luckily, Misa's big brother is the captain of the university karate club and is ready to strike a deal: Reiji can join the club if he tutors Misa in linear algebra.Follow along in The Manga Guide to Linear Algebra as Reiji takes Misa from the absolute basics of this tricky subject through mind-bending operations like performing linear transformations, calculating determinants, and finding eigenvectors and eigenvalues. With memorable examples like miniature golf games and karate tournaments, Reiji transforms abstract concepts into something concrete, understandable, and even fun.As you follow Misa through her linear algebra crash course, you'll learn about:Basic vector and matrix operations such as addition, subtraction, and multiplicationLinear dependence, independence, and basesUsing Gaussian elimination to calculate inverse matricesSubspaces, dimension, and linear spanPractical applications of linear algebra in fields like computer graphics, cryptography, and engineeringBut Misa's brother may get more than he bargained for as sparks start to fly between student and tutor. Will Reiji end up with the girl—or just a pummeling from her oversized brother? Real math, real romance, and real action come together like never before in The Manga Guide to Linear Algebra.