Go Beyond is an exciting 6-level American English course for teenagers learning English. The course covers CEFR levels A1+ through to B2, with all levels being based on mapping of the requirements of the CEFR and international exams. Go Beyond comprehensively addresses all key language skills through a thorough and detailed subskills syllabus. Go Beyond also has a strong life skills feature specially designed to support students with the life skills they require, both during their education and in their life beyond.
Grammar and Beyond is a four-level North American grammar course informed by a collection of over one billion words of authentic language, ensuring that students learn grammar the way it is used in real spoken and written English. The Class Audio CD includes all of the audio for the exercises in the Student's Book. CEF: B1-B2.
Grammar and Beyond is a four-level North American grammar course informed by a collection of over one billion words of authentic language, ensuring that students learn grammar the way it is used in real spoken and written English. The Class Audio CD includes all of the audio for the exercises in the Student's Book. CEF: B1-B2.
An updated and revised edition of the Objective CAE course, which prepares students for Cambridge English: Advanced, also known as Certificate in Advanced English (CAE). The syllabus for this exam has changed and this book has now been replaced by 9781107691889 Objective Advanced Fourth edition Student's Book Pack (Student's Book with answers with CD-ROM and Class Audio CDs (2)).
Taking you further! Open World pushes students beyond the boundaries between exam preparation and real-world language, preparing learners for B1 Preliminary. Each unit of the Student's Book with answers explores a different topic, allowing students to build up their confidence as they acquire the language and skills needed for everyday English situations as well as exams. Exam Training tasks build confidence allowing them to progress to full task practice in the Exam focus. Optional Push yourself sections throughout the book extend students' capability and confidence to B2 First level, and the dedicated English for Spanish Speakers section helps them avoid typical mistakes.
This book provides a contemporary and critical examination of the theoretical and pedagogical impact of Michael Byram’s pioneering work on intercultural communicative competence and intercultural citizenship within the field of language education and beyond. The chapters address important theoretical and empirical work on the teaching, learning, and assessment of intercultural learning, and highlight how individual language educators and communities of practice enact intercultural learning in locally appropriate ways. The book offers comprehensive, up-to-date and accessible knowledge for researchers, teachers, teacher-trainers and students.
This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad ratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.
A collection of twelve lessons that teach English language grammar, vocabulary, functional language, listening and pronunciation, reading and writing and speaking.