Peter Smith — новинки

"New Inspiration" builds on the success of the Inspiration series and brings it up to date with new and fresh content.The four-level course takes teenagers from beginner to intermediate level, evolving with the students, reflecting their changing needs and interests.

The new series takes all that is best from the original series and improves it with:
• new and updated cross-curricular and cultural content;
• a more task-based approach encouraging students to focus on their personal reactions to topics and texts;
• an updated design, new photos and artwork and updated photo stories;
• more differentiation for mixed-ability classes, including extension activities in every lesson;
• a greater focus on vocabulary building;
• a greater emphasis on learner independence and self assessment.

In 1931, the young Kurt Godel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Godel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.

Book DescriptionRevised to incorporate and reflect changes and advances since it was first published the new edition of Architecture in a Climate of Change provides the latest basic principals of sustainability and the future of sustainable

Book DescriptionBefore seven-year-old Sam Smith discovered the Beatles, he and his father had little in common. Like so many other kids his age, Sam was drawn first to the Fab Four by their trivia as much as by their music and personalities. Peter

Book DescriptionThis clear and accessible guide provides a comprehensive outline on how to convert your house into a more 'green' home. Buildings are the greates energy wasters and for those of us concerned about the environment, and household