Proofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text's third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number theory, this new edition introduces students to the world of advanced mathemat...

Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch explains vectors and tensors in plain language to give undergraduate and beginning graduate students a better understanding of how to use vectors and tensors to solve problems in physics and engineering.

Recent years have seen the development of powerful tools for verifying hardware and software systems, as companies worldwide realise the need for improved means of validating their products. There is increasing demand for training in basic methods in formal reasoning so that students can gain proficiency in logic-based verification methods. The second edition of this successful textbook addresses both those requirements, by continuing to provide a clear introduction to formal reasoning which ...

A textbook for students with some background in probability that develops quickly a rigorous theory of Markov chains and shows how actually to apply it, e.g. to simulation, economics, optimal control, genetics, queues and many other topics, and exercises and examples drawn both from theory and practice.

Are you curious to know what all languages have in common and how they differ? Do you want to find out how language can be used to trace different peoples and their past? Now in its fourth edition, this fascinating book guides beginners through the rich diversity of the world's languages. It presupposes no background in linguistics, and introduces key concepts with the help of problem sets, end-of-chapter exercises and an extensive bibliography. It is illustrated with detailed maps and charts...

In a radical reappraisal of Iran's modern history, Ervand Abrahamian traces the country's traumatic journey from the mid-nineteenth century to the present day, through the discovery of oil, imperial interventions, the rule of the Pahlavis, and the birth of the Islamic Republic. The first edition was named the Choice Outstanding Academic Title in 2009. This second edition brings the narrative up to date, with the Green uprisings of 2009, the second Ahmadinejad administration, the election of R...

An improved, larger-format edition of the Cambridge School Shakespeare plays, extensively rewritten, expanded and produced in an attractive new design. An active approach to classroom Shakespeare enables students to inhabit Shakespeare's imaginative world in accessible and creative ways. Students are encouraged to share Shakespeare's love of language, interest in character and sense of theatre.

Substantially revised and extended in full colour, classroom activities are thematically organised ...

This concise, accessible, market-leading textbook brings together the wide-ranging fundamentals students need to understand rocks and minerals, and shows them how they relate to the broader Earth, materials and environmental sciences. Designed specifically for one-semester courses, it is beautifully illustrated to explain the key concepts in mineralogy and petrology. This edition has been fully updated based on classroom experience, and new features include a completely new chapter providing ...

Measure and integration are key topics in many areas of mathematics, including analysis, probability, mathematical physics and finance. This book offers a concise yet elementary introduction in which the theory is quickly and simply developed. Few prerequisites are required, making the text suitable for undergraduate lecture courses or self-study.

Improve your understanding of idioms in English. Explanations and practice of English idioms, written for advanced-level (C1 to C2) learners of English. Perfect for both self-study and classroom activities.

Learn idioms in context, with lots of different topics, including 'Learning', 'Formal writing' and 'Telling stories'. Be confident about what you are learning, thanks to Cambridge research into how English is really spoken and written, and get better at studying by yourself, with study tip...