This lively, problem-oriented text is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered — either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Holder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.

Scott Ambler, award-winning author of Building Object Applications that Work, Process Patterns, and More Process Patterns, has revised his acclaimed first book, The Object Primer. Long prized in its original edition by both students and professionals as the best introduction to object-oriented technology, this book is now completely up-to-date, with all modeling notation rewritten in the just-released UML 2.0. All chapters have been revised to take advantage of Agile Modeling (AM), which is presented in the new chapter 2 along with other important new modeling techniques. Review questions at the end of each chapter allow readers to test their newly acquired knowledge. In addition, the author takes time to reflect on the lessons learned over the past few years by discussing the proven benefits and drawbacks of the technology. This is the perfect book for any software development professional or student seeking an introduction to the concepts and terminology of object technology.

Contains four complete tests for the First Certificate exam from Cambridge ESOL. These past examination papers provide the most authentic exam preparation available, allowing candidates to familiarise themselves with the content of the exam and to practise exam techniques. Colour visual material for Paper 5 is included with each test. The Student's Book is also available as a 'with answers' edition, suitable for self study.

The second edition contains new units, more exercises, and a free Audio CD with recordings of example sentences so students can hear the grammar structures they are learning. The Basic Grammar in Use Workbook provides students with further opportunities to practice difficult grammar points. It also helps to consolidate their understanding of related grammar topics, such as the different ways of expressing the future. This Workbook offers a wide range of activity types that include opportunities to work with grammatical structures in meaningful contexts. It also includes review sections for each group of units in the Student's Book. These groups, such as the Present and Past, Modals, and Articles, are listed in the table of contents of each Student's Book. This workbook comes with an answer key (an edition without an answer key is also available).

Business Explorer is an exciting three level course in American English for learners of Business English. With an emphasis on listening and speaking but with many opportunities for reading and writing, Business Explorer addresses learners' everyday language needs in business situations. The accompanying Teacher's Book contains clear, easy-to-follow lesson plans, extra photocopiable activities and five photocopiable progress tests.

From 'living large' to 'who's your daddy?' this book unlocks the meaning of more than 5000 idiomatic phrases used in American English today. The paperback edition explains more than 5,000 idioms commonly used in spoken and written American English. Clear definitions are written using the 2,000-word Cambridge American Defining Vocabulary. This dictionary features full-sentence examples showing how idioms are really used, usage and origin notes that expand on the definitions, and ample cross-references. There is also a topic index that assists learners in finding idioms related to health, money, feelings, truth, and many other subjects. It is ideal for classroom use or for personal reference. Based on the Cambridge International Corpus, a database that includes more than 200 million words of current written and spoken American, the Cambridge Dictionary of American Idioms is the last word on American idioms.

Rarely has a book so packed with accurate and well researched factual information been so widely read and popularly acclaimed. This Second Edition of The Cambridge Encyclopedia of the English Language has been fully revised for a new generation of language-lovers. The book is longer and includes extensive new material on world English and Internet English, in addition to completely updated statistics, further reading suggestions and other references. David Crystal is a leading authority on language, and author of many books, including most recently Shakespeare's Words (Penguin, 2002), Language and the Internet (Cambridge, 2001) and Language Death (Cambridge, 2000). An internationally renowned writer, journal editor, lecturer and broadcaster, he received an Order of the British Empire in 1995 for his services to the English language. • The most successful general book on the English language (its past, present and future) • Packed with colour illustrations, maps, tables and graphics • Difficult concepts explained in a simple and accessible way

Cambridge KET 1 contains four complete papers for the Cambridge Key English Test from University of Cambridge ESOL Examinations. These past examination papers provide the most authentic exam preparation available. They allow candidates to familiarise themselves with the content and format of the examination and to practise useful examination techniques. These papers follow the March 2004 revised exam specifications. The Student's Book with Answers also contains a comprehensive section of keys and recording scripts, making it suitable for self-study. The Self-study Pack also contains the Student's Book with Answers and the Audio CD.

Cambridge KET 1 contains four complete papers for the Cambridge Key English Test from University of Cambridge ESOL Examinations. These past examination papers provide the most authentic exam preparation available. They allow candidates to familiarise themselves with the content and format of the examination and to practise useful examination techniques. These papers follow the March 2004 revised exam specifications. The Student's Book with Answers also contains a comprehensive section of keys and recording scripts, making it suitable for self-study. The Self-study Pack also contains the Student's Book with Answers and the Audio CD.

Cambridge KET 1 contains four complete papers for the Cambridge Key English Test from University of Cambridge ESOL Examinations. These past examination papers provide the most authentic exam preparation available. They allow candidates to familiarise themselves with the content and format of the examination and to practise useful examination techniques. These papers follow the March 2004 revised exam specifications. The Student's Book with Answers also contains a comprehensive section of keys and recording scripts, making it suitable for self-study. The Self-study Pack also contains the Student's Book with Answers and the Audio CD.

Cambridge KET 2 contains four complete papers for the Cambridge Key English Test from University of Cambridge ESOL Examinations. These past examination papers provide the most authentic exam preparation available. They allow candidates to familiarise themselves with the content and format of the examination and to practise useful examination techniques. These papers follow the March 2004 revised exam specifications. The Student's Book with Answers also contains a comprehensive section of keys and recording scripts, making it suitable for self-study. The Self-study Pack also contains the Student's Book with Answers and the Audio CD.

Cambridge KET 2 contains four complete papers for the Cambridge Key English Test from University of Cambridge ESOL Examinations. These past examination papers provide the most authentic exam preparation available. They allow candidates to familiarise themselves with the content and format of the examination and to practise useful examination techniques. These papers follow the March 2004 revised exam specifications. The Student's Book with Answers also contains a comprehensive section of keys and recording scripts, making it suitable for self-study. The Self-study Pack also contains the Student's Book with Answers and the Audio CD.

Cambridge KET 3 contains four complete papers for the Cambridge Key English Test from University of Cambridge ESOL Examinations. These past examination papers provide the most authentic exam preparation available. They allow candidates to familiarise themselves with the content and format of the examination and to practise useful examination techniques. These papers follow the March 2004 revised exam specifications. The Student's Book with Answers also contains a comprehensive section of keys and recording scripts, making it suitable for self-study. The Self-study Pack also contains the Student's Book with Answers and the Audio CD.

Cambridge KET 3 contains four complete papers for the Cambridge Key English Test from University of Cambridge ESOL Examinations. These past examination papers provide the most authentic exam preparation available. They allow candidates to familiarise themselves with the content and format of the examination and to practise useful examination techniques. These papers follow the March 2004 revised exam specifications. The Student's Book with Answers also contains a comprehensive section of keys and recording scripts, making it suitable for self-study. The Self-study Pack also contains the Student's Book with Answers and the Audio CD.

Cambridge KET 3 contains four complete papers for the Cambridge Key English Test from University of Cambridge ESOL Examinations. These past examination papers provide the most authentic exam preparation available. They allow candidates to familiarise themselves with the content and format of the examination and to practise useful examination techniques. These papers follow the March 2004 revised exam specifications. The Student's Book with Answers also contains a comprehensive section of keys and recording scripts, making it suitable for self-study. The Self-study Pack also contains the Student's Book with Answers and the Audio CD.

These tests provide candidates with an excellent opportunity to familiarise themselves with the updated 2004 PET exam and to practise examination techniques. The Student's Book contains practice material for Paper 1 (Reading and Writing) and Paper 2 (Listening), along with attractive colour visual material for Paper 3 (Speaking), enabling students to prepare thoroughly for the paired Speaking test. The Student's Book is available with or without answers. The 'with answers' edition contains a comprehensive section of keys and tapescripts, making it ideal for self-study. The Audio CD Set contains the listening material for Paper 2 in the same timed format as the exam itself.

These tests provide candidates with an excellent opportunity to familiarise themselves with the updated 2004 PET exam and to practise examination techniques. The Student's Book contains practice material for Paper 1 (Reading and Writing) and Paper 2 (Listening), along with attractive colour visual material for Paper 3 (Speaking), enabling students to prepare thoroughly for the paired Speaking test. The Student's Book is available with or without answers. The 'with answers' edition contains a comprehensive section of keys and tapescripts, making it ideal for self-study. The Audio CD Set contains the listening material for Paper 2 in the same timed format as the exam itself.

These tests provide candidates with an excellent opportunity to familiarise themselves with the updated 2004 PET exam and to practise examination techniques. The Student's Book contains practice material for Paper 1 (Reading and Writing) and Paper 2 (Listening), along with attractive colour visual material for Paper 3 (Speaking), enabling students to prepare thoroughly for the paired Speaking test. The Student's Book is available with or without answers. The 'with answers' edition contains a comprehensive section of keys and tapescripts, making it ideal for self-study. The Audio CD Set contains the listening material for Paper 2 in the same timed format as the exam itself.

These tests provide candidates with an excellent opportunity to familiarise themselves with the updated 2004 PET exam and to practise examination techniques. The Student's Book contains practice material for Paper 1 (Reading and Writing) and Paper 2 (Listening), along with attractive colour visual material for Paper 3 (Speaking), enabling students to prepare thoroughly for the paired Speaking test. The Student's Book is available with or without answers. The 'with answers' edition contains a comprehensive section of keys and tapescripts, making it ideal for self-study. The Audio CD Set contains the listening material for Paper 2 in the same timed format as the exam itself.