Among Shakespeare's plays, "Hamlet" is considered by many his masterpiece. Among actors, the role of Hamlet, Prince of Denmark, is considered the jewel in the crown of a triumphant theatrical career. Now Kenneth Branagh plays the leading role and co-directs a brillant ensemble performance. Three generations of legendary leading actors, many of whom first assembled for the Oscar-winning film "Henry V", gather here to perform the rarely heard complete version of the play. This clear, subtly nuanced, stunning dramatization, presented by The Renaissance Theatre Company in association with "Bbc" Broadcasting, features such luminaries as Sir John Gielgud, Derek Jacobi, Emma Thompson and Christopher Ravenscroft. It combines a full cast with stirring music and sound effects to bring this magnificent Shakespearen classic vividly to life. Revealing new riches with each listening, this production of "Hamlet" is an invaluable aid for students, teachers and all true lovers of Shakespeare - a recording to be treasured for decades to come.

HOW TO THINK ABOUT ALGORITHMS
There are many algorithm texts that provide lots of well-polished code and
proofs of correctness. Instead, this one presents insights, notations, and
analogies to help the novice describe and think about algorithms like an
expert. It is a bit like a carpenter studying hammers instead of houses. Jeff
Edmonds provides both the big picture and easy step-by-step methods for
developing algorithms, while avoiding the comon pitfalls. Paradigms such
as loop invariants and recursion help to unify a huge range of algorithms
into a few meta-algorithms. Part of the goal is to teach students to think
abstractly. Without getting bogged down in formal proofs, the book fosters
deeper understanding so that how and why each algorithm works is trans-
parent. These insights are presented in a slow and clear manner accessible
to second- or third-year students of computer science, preparing them to
find on their own innovative ways to solve problems.
Abstraction is when you translate the equations, the rules, and the under-
lying essences of the problem not only into a language that can be commu-
nicated to your friend standing with you on a streetcar, but also into a form
that can percolate down and dwell in your subconscious. Because, remem-
ber, it is your subconscious that makes the miraculous leaps of inspiration,
not your plodding perspiration and not your cocky logic. And remember,
unlike you, your subconscious does not understand Java code.
Bookmarks
Cover
Half-title
Title
Copyright
CONTENTS
PREFACE
Introduction
PART ONE: Iterative Algorithms and Loop Invariants
1 Iterative Algorithms: Measures of Progress and Loop Invariants
1.1 A Paradigm Shift: A Sequence of Actions vs. a Sequence of Assertions
1.2 The Steps to Develop an Iterative Algorithm
1.3 More about the Steps
1.4 Different Types of Iterative Algorithms
1.5 Typical Errors
1.6 Exercises
2 Examples Using More-of-the-Input Loop Invariants
2.1 Coloring the Plane
2.2 Deterministic Finite Automaton
2.3 More of the Input vs. More of the Output
3 Abstract Data Types
3.1 Specifications and Hints at Implementations
3.2 Link List Implementation
3.3 Merging with a Queue
3.4 Parsing with a Stack
4 Narrowing the Search Space: Binary Search
4.1 Binary Search Trees
4.2 Magic Sevens
4.3 VLSI Chip Testing
4.4 Exercises
5 Iterative Sorting Algorithms
5.1 Bucket Sort by Hand
5.2 Counting Sort (a Stable Sort)
5.3 Radix Sort
5.4 Radix Counting Sort
6 Euclid’s GCD Algorithm
7 The Loop Invariant for Lower Bounds
PART TWO: Recursion
8 Abstractions, Techniques, and Theory
8.1 Thinking about Recursion
8.2 Looking Forward vs. Backward
8.3 With a Little Help from Your Friends
8.4 The Towers of Hanoi
8.5 Checklist for Recursive Algorithms
8.6 The Stack Frame
8.7 Proving Correctness with Strong Induction
9 Some Simple Examples of Recursive Algorithms
9.1 Sorting and Selecting Algorithms
9.2 Operations on Integers
9.3 Ackermann's Function
9.4 Exercises
10 Recursion on Trees
10.1 Tree Traversals
10.2 Simple Examples
10.3 Generalizing the Problem Solved
10.4 Heap Sort and Priority Queues
10.5 Representing Expressions with Trees
11 Recursive Images
11.1 Drawing a Recursive Image from a Fixed Recursive and a Base Case Image
11.2 Randomly Generating a Maze
12 Parsing with Context-Free Grammars
PART THREE: Optimization Problems
13 Definition of Optimization Problems
14 Graph Search Algorithms
14.1 A Generic Search Algorithm
14.2 Breadth-First Search for Shortest Paths
14.3 Dijkstra's Shortest-Weighted-Path Algorithm
14.4 Depth-First Search
14.5 Recursive Depth-First Search
14.6 Linear Ordering of a Partial Order
14.7 Exercise
15 Network Flows and Linear Programming
15.1 A Hill-Climbing Algorithm with a Small Local Maximum
15.2 The Primal…Dual Hill-Climbing Method
15.3 The Steepest-Ascent Hill-Climbing Algorithm
15.4 Linear Programming
15.5 Exercises
16 Greedy Algorithms
16.1 Abstractions, Techniques, and Theory
16.2 Examples of Greedy Algorithms 16.2.1 Example: The Job/Event Scheduling Problem
16.2.2 Example: The Interval Cover Problem
16.2.3 Example: The Minimum-Spanning-Tree Problem
16.3 Exercises
17 Recursive Backtracking
17.1 Recursive Backtracking Algorithms
17.2 The Steps in Developing a Recursive Backtracking
17.3 Pruning Branches
17.4 Satisfiability
17.5 Exercises
18 Dynamic Programming Algorithms
18.1 Start by Developing a Recursive Backtracking
18.2 The Steps in Developing a Dynamic Programming Algorithm
18.3 Subtle Points
18.3.1 The Question for the Little Bird
18.3.2 Subinstances and Subsolutions
18.3.3 The Set of Subinstances
18.3.4 Decreasing Time and Space
18.3.5 Counting the Number of Solutions
18.3.6 The New Code
19 Examples of Dynamic Programs
19.1 The Longest-Common-Subsequence Problem
19.2 Dynamic Programs as More-of-the-Input Iterative Loop Invariant Algorithms
19.3 A Greedy Dynamic Program: The Weighted Job/Event Scheduling Problem
19.4 The Solution Viewed as a Tree: Chains of Matrix Multiplications
19.5 Generalizing the Problem Solved: Best AVL Tree
19.6 All Pairs Using Matrix Multiplication
19.7 Parsing with Context-Free Grammars
19.8 Designing Dynamic Programming Algorithms via Reductions
20 Reductions and NP-Completeness
20.1 Satisfiability Is at Least as Hard as Any Optimization Problem
20.2 Steps to Prove NP-Completeness
20.3 Example: 3-Coloring Is NP-Complete
20.4 An Algorithm for Bipartite Matching Using the Network Flow Algorithm
21 Randomized Algorithms
21.1 Using Randomness to Hide the Worst Cases
21.2 Solutions of Optimization Problems with a Random Structure
PART FOUR: Appendix
22 Existential and Universal Quantifiers
23 Time Complexity
23.1 The Time (and Space) Complexity of an Algorithm
23.2 The Time Complexity of a Computational Problem
24 Logarithms and Exponentials
25 Asymptotic Growth
25.1 Steps to Classify a Function
25.2 More about Asymptotic Notation
26 Adding-Made-Easy Approximations
26.1 The Technique
26.2 Some Proofs for the Adding-Made-Easy Technique
27 Recurrence Relations
27.1 The Technique
27.2 Some Proofs
28 A Formal Proof of Correctness
PART FIVE: Exercise Solutions
Chapter 1. Iterative Algorithms: Measures of Progress and Loop Invariants
Chapter 2. Examples UsingMore-of-the-Input Loop Invariant
Chapter 3. Abstract Data Types
Chapter 4. Narrowing the Search Space: Binary Search
Chapter 6. Euclid’s GCD Algorithm
Chapter 7. The Loop Invariant for Lower Bounds
Chapter 8. Abstractions, Techniques, and Theory
Chapter 9. Some Simple Examples of Recursive Algorithms
Chapter 10. Recursion on Trees
Chapter 11. Recursive Images
Chapter 12. Parsingwith Context-Free Grammars
Chapter 14. Graph Search Algorithms
Chapter 15. Network Flows and Linear Programming
Chapter 16: Greedy Algorithms
Chapter 17. Recursive Backtracking
Chapter 18. Dynamic Programming Algorithms
Chapter 19. Examples of Dynamic Programs
Chapter 20. Reductions and NP-Completeness
Chapter 22. Existential and Universal Quantifiers
Chapter 23. Time Complexity
Chapter 24. Logarithms and Exponentials
Chapter 25. Asymptotic Growth
Chapter 26. Adding-Made-Easy Approximations
Chapter 27. Recurrence Relations
CONCLUSION
INDEX

Rigorous probabilistic arguments, built on the foundation of measure theory introduced eighty years ago by Kolmogorov, have invaded many fields. Students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This 2002 book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.

This second edition of Daniel W. Stroock's text is suitable for first-year graduate students with a good grasp of introductory, undergraduate probability theory and a sound grounding in analysis. It is intended to provide readers with an introduction to probability theory and the analytic ideas and tools on which the modern theory relies. It includes more than 750 exercises. Much of the content has undergone significant revision. In particular, the treatment of Levy processes has been rewritten, and a detailed account of Gaussian measures on a Banach space is given.

Few branches of mathematics have been more influential in the social sciences than game theory. In recent years, it has become an essential tool for all social scientists studying the strategic behaviour of competing individuals, firms and countries. However, the mathematical complexity of game theory is often very intimidating for students who have only a basic understanding of mathematics. Insights into Game Theory addresses this problem by providing students with an understanding of the key concepts and ideas of game theory without using formal mathematical notation. The authors use four very different topics (college admission, social justice and majority voting, coalitions and co-operative games, and a bankruptcy problem from the Talmud) to investigate four areas of game theory. The result is a fascinating introduction to the world of game theory and its increasingly important role in the social sciences.

In a world that is constantly awake, illuminated and exposed, there is much to gain from looking into the darkness of times past. This fascinating and vivid picture of nocturnal life in Middle Eastern cities shows that the night in the eighteenth-century Ottoman Empire created unique conditions for economic, criminal, political, devotional and leisurely pursuits that were hardly possible during the day. Offering the possibility of livelihood and brotherhood, pleasure and refuge; the darkness allowed confiding, hiding and conspiring - activities which had far-reaching consequences on Ottoman state and society in the early modern period. Instead of dismissing the night as merely a dark corridor between days, As Night Falls demonstrates how fundamental these nocturnal hours have been in shaping the major social, cultural and political processes in the early modern Middle East.

Twelve fragments of bronze were found near Urbino in the late fifteenth century, engraved with Roman laws - on one side a law concerning extortion, on the other an agrarian law. Dating as they do from the time of the Gracchi and of Marius in the later years of the Roman Republic, the laws are of considerable interest to Roman historians and are important evidence for the understanding of the revolutionary period that led to the overthrow of the Republic. In this volume, Dr Lintott offers a complete re-edition of these complicated and fragmentary texts, including a revision of the relationship between the fragments and full discussion of the manuscript sources of those now lost. The texts are accompanied by facing English translations and the commentary, which follows discusses in detail the issues involved in establishing and restoring the texts. A series of introductory chapters, written as far as possible in non-technical language, give a summary of the context of the laws from both a legal and an historical view point.

Through words and images employed both by individuals and by a range of communities across the Graeco-Roman worlds, this book explores the complexity of multilingual representations of identity. Starting with the advent of literacy in the Mediterranean, it encompasses not just the Greek and Roman empires but also the transformation of the Graeco-Roman world under Islam and within the medieval mind. By treating a range of materials, contexts, languages, and temporal and political boundaries, the contributors consider points of cross-cultural similarity and difference and the changing linguistic landscape of East and West from antiquity into the medieval period. Insights from contemporary multilingualism theory and interdisciplinary perspectives are employed throughout to exploit the material fully.

In this 2010 book, Andrew Riggsby offers a survey of the main areas of Roman law, both substantive and procedural, and how the legal world interacted with the rest of Roman life. Emphasising basic concepts, he recounts its historical development and focuses in particular on the later Republic and early centuries of the Roman Empire. The volume is designed as an introductory work, with brief chapters that will be accessible to college students with little knowledge of legal matters or Roman antiquity. The text is also free of technical language and Latin terminology. It can be used in courses on Roman law, Roman history, or comparative law, but it will also serve as a useful reference for more advanced students and scholars.

For fifty years debate has raged about early European commerce during the period between antiquity and the middle ages. Was there trade? If so, in what - and with whom? New evidence and new ways of looking at old evidence are now breaking the stalemate. Analysis of communications - the movements of people, ideas and things - is transforming our vision of Europe and the Mediterranean in the age of Charlemagne and Harun al Rashid. This is the first comprehensive analysis of the economic transition during this period for over sixty years. Using new materials and new methodology, it will attract all social and economic historians of antiquity and the middle ages, and anyone concerned with the origins of Europe, the history of the slave trade, medicine and disease, cross-cultural contacts, and the Muslim and Byzantine worlds.

Ancient Greece and China Compared is a pioneering, methodologically sophisticated set of studies, bringing together scholars who all share the conviction that the sustained critical comparison and contrast between ancient societies can bring to light significant aspects of each that would be missed by focusing on just one of them. The topics tackled include key issues in philosophy and religion, in art and literature, in mathematics and the life sciences (including gender studies), in agriculture, city planning and institutions. The volume also analyses how to go about the task of comparing, including finding viable comparanda and avoiding the trap of interpreting one culture in terms appropriate only to another. The book is set to provide a model for future collaborative and interdisciplinary work exploring what is common between ancient civilisations, what is distinctive of particular ones, and what may help to account for the latter.

The words you need to communicate with confidence. Vocabulary explanations and practice for upper-intermediate level (B2) learners of English. Perfect for both self-study and classroom activities. Quickly expand your vocabulary with over 100 units of easy to understand explanations and practice exercises. Also inside the book is a code for an ebook. This is the same as the printed book, but with audio so that you can listen to new words as well as reading them. The ebook is online for Windows and Mac users, and can also be downloaded to iPads and Android tablets.

In 1962, a Hiroshima peace delegation and an Auschwitz survivor's organization exchanged relics and testimonies, including the bones and ashes of Auschwitz victims. This symbolic encounter, in which the dead were literally conscripted in the service of the politics of the living, serves as a cornerstone of this volume, capturing how memory was utilized to rebuild and redefine a shattered world. This is a powerful study of the contentious history of remembrance and the commemoration of the atomic bomb in Hiroshima in the context of the global development of Holocaust and World War II memory. Emphasizing the importance of nuclear issues in the fifties and sixties, Zwigenberg traces the rise of global commemoration culture through the reconstruction of Hiroshima as a 'City of Bright Peace', memorials and museums, global tourism, developments in psychiatry, and the emergence of the figure of the survivor-witness and its consequences for global memory practices.

First published in 1978, Reading Greek has become a best-selling one-year introductory course in ancient Greek for students and adults. It combines the best of modern and traditional language-learning techniques and is used widely in schools, summer schools and universities across the world. It has also been translated into several foreign languages. This volume provides full grammatical support together with numerous exercises at different levels. For the second edition the presentations of grammar have been substantially revised to meet the needs of today's students and the volume has been completely redesigned, with the use of colour. Greek-English and English-Greek vocabularies are provided, as well as a substantial reference grammar and language surveys. The accompanying Text and Vocabulary volume contains a narrative adapted entirely from ancient authors in order to encourage students rapidly to develop their reading skills, simultaneously receiving a good introduction to Greek culture.