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Discrete Mathematics

The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints andsolutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level. Praise for the German edition ... This book is a well-written introduction to discrete mathematics and is highly recommended to every student ofmathematics and computer science as well as to teachers of these topics. --Konrad Engel for MathSciNet Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of theMAA for expository writing, and his book Proofs from the BOOK with Gunter M. Ziegler has been an international success with translations into 12 languages.

Praise for the German edition ... This book is a well-written introduction to discrete mathematics and is highly recommended to every student ofmathematics and computer science as well as to teachers of these topics.

Discrete Mathematics of Neural Networks

Selected Topics

This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory. It considers select areas of discrete mathematics linking combinatorics and the theory of the simplest types of artificial neural networks. Neural networks have emerged as a key technology in many fields of application, and an understanding of the theories concerning what such systems can and cannot do is essential. Some classical results are presented with accessible proofs, together with some more recent perspectives, such as those obtained by considering decision lists. In addition, probabilistic models of neural network learning are discussed. Graph theory, some partially ordered set theory, computational complexity, and discrete probability are among the mathematical topics involved. Pointers to further reading and an extensive bibliography make this book a good starting point for research in discrete mathematics and neural networks.

This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory.

A Reference Grammar of Modern Italian

This Italian reference grammar provides students, teachers and others interested in the Italian language with a comprehensive, accessible and jargon-free guide to the forms and structure of Italian. Whatever their level of knowledge of the language, learners of Italian will find this book indispensable: it gives clear and detailed explanations of everything from the most elementary facts such as the relation between spelling and pronunciation, or the forms of the article, to more advanced points such as the various nuances of the subjunctive. Formal or archaic discourse is distinguished from informal, everyday usage, and regionalisms are also indicated where appropriate. The authors have taken care to make it an easy and illuminating reference tool: extensive cross-referencing enables readers to quickly find the information they require, and also stimulates them to discover new, related facts.

This book aims to provide a comprehensiveworkofreference for learners of Italian
whose native languageisEnglish,orwhopossess a very good knowledge of
English. It is not intended as a course in Italian grammar, but it is meant to be
accessible to all learners of Italian, whatever their level of knowledge of the
language. So a beginner who needs to check the distinction between the forms
ofthearticleil and lo should find this book as useful asanadvanced learnerwhois
interested, say, ...

Improving Learning in College

Rethinking Literacies Across the Curriculum

What's the problem with literacy at college? How might everyday literacy be harnessed for educational ends? Based on the first major study of literacy practices in colleges in the UK, this book explores the reading and writing associated with learning subjects across the college curriculum. It investigates literacy practices in which students engage outside of college, and teaching and learning strategies through which these can help support the curriculum. With insightful analyses of innovative practices, it considers ways of changing teaching practices to enable students to draw upon their full potential. Recent research work has challenged the myth of individual student deficit, arguing cogently that people have ‘funds of knowledge’ from diverse and vibrant cultural roots, and that these have been misguidedly disqualified by the education system. It has claimed that different ‘ways with words’ can provide valuable resources for learning. However, the empirical exploration of this claim has lagged far behind the theoretical debate. Improving Learning in College resolves this by showing the integrity and richness of the literacy practices of a significant population, not previously the focus of such research: those who take vocational and academic college courses in colleges. It addresses an issue which has not until now been developed within this research tradition: that of how these practices can not only be valued and validated, but mobilised and harnessed to enhance learning in educational settings. This book will interest all teachers, teacher-educators and researchers concerned with post-compulsory education and vocational education in compulsory schooling.

Barton, D. (2000) 'Researching literacy practices:learningfrom activities with
teachersand students',in D. Barton, M. Hamilton and R. Ivanič (eds) Situated
Literacies: Reading and Writing in Context, London: Routledge. Barton, D. (2001)
'Directions forliteracy research: analysing languageand social practices in a
textuallymediated world', Language and Education, 15 (2):92–104. Barton,D.(
2007) Literacy:an Introduction to theEcologyof Written Language, 2nd edn,
Oxford: Blackwell.

Metode Penelitian Dalam Ilmu Sosial

Metode Penelitian adalah panduan langkah demi langkah untuk pemula penelitian, dan peserta didik penelitian lanjutan di Ilmu Pengetahuan Sosial dan Ilmu Pengetahuan Murni. Telah ditulis secara khusus untuk mereka yang tidak memiliki pengalaman sebelumnya dalam penelitian atau metodologi penelitian. Buku ini memandu Anda melalui proyek Anda dari awal sampai akhir dengan menawarkan saran praktis:* merumuskan pertanyaan penelitian* pertimbangan etis* melakukan tinjauan pustaka* memilih desain penelitian* memilih sampel* mengumpulkan dan menganalisa data kualitatif dan kuantitatif* menulis sebuah laporan penelitian tesis mendetailBuku ini merupakan bacaan penting bagi mahasiswa sarjana dan pascasarjana dalam ilmu sosial yang memulai penelitian kuantitatif atau kualitatif. Buku ini sama-sama bermanfaat bagi siswa metode penelitian lanjutan yang mempertahankan gelar PhD mereka dalam berbagai mata pelajaran Ilmu Pengetahuan, Bisnis, Pendidikan, Publik Kesehatan, disiplin terkait dan bahkan mata pelajaran Ilmu Pengetahuan.Teks ini menunjukkan kepada para peneliti pemula bagaimana merancang, mengumpulkan, dan menganalisis data kualitatif dan kemudian mempresentasikan hasilnya kepada komunitas ilmiah. Buku ini menekankan pentingnya etika dalam penelitian dan meluangkan waktu untuk merancang dan memikirkan dengan benar melalui usaha penelitian apa pun. Setelah menyelesaikan buku ini, pembaca harus dapat:* Merancang secara efektif, mengumpulkan, mengatur, dan menganalisa data dan kemudian mempresentasikan hasilnya ke komunitas ilmiah* Gunakan Internet sebagai sumber dan sarana untuk mengakses data kualitatif* Menjelajahi isu terkini di dunia periset, yang mencakup kekhawatiran serius tentang perilaku etis dan protokol dalam penelitian dan peran yang lebih refleksif dan sensitif bagi peneliti.* Kenali pentingnya masalah etika sebelum mereka benar-benar memulai pengumpulan, pengorganisasian, dan proses penelitian* Memahami elemen dasar yang berhubungan dengan refleksivitas peneliti dan penelitian suaraIni adalah sumber yang komprehensif dan kompak untuk konsep dasar dan lanjutan dalam penelitian, dan dapat berfungsi sebagai teks yang berdiri sendiri atau sebagai pelengkap pembacaan penelitian di kelas sarjana atau doktoral atau kelas metode penelitian. Buku ini saat ini digunakan sebagai teks penelitian di universitas-universitas di enam benua.

Metode Penelitian adalah panduan langkah demi langkah untuk pemula penelitian, dan peserta didik penelitian lanjutan di Ilmu Pengetahuan Sosial dan Ilmu Pengetahuan Murni.

World English 1

Teachers Edition

Featuring content from national Geographic and TED, the new edition of the four-level World English series brings the most amazing stories about our planet and compelling ideas from around the world to the integrated-skills classroom.

Featuring content from national Geographic and TED, the new edition of the four-level World English series brings the most amazing stories about our planet and compelling ideas from around the world to the integrated-skills classroom.

National Geographic World English ME 2 SB

World English is an exciting new four-skills general English series which uses National Geographic content, images and video to teach the language that learners need to succeed in their daily lives. The series is built upon clear and practical learning goals which are presented and practiced through appropriate themes and topics. A competency-based series, World English uses real people, real places and real language to connect learners of English to the world.

The series is built upon clear and practical learning goals which are presented and practiced through appropriate themes and topics.

World English 2e 2 Student Book + Owb Pac: Real People Real

Featuring content from National Geographic and TED, the new edition of the four-level, integrated skills World English series brings amazing stories about our planet and compelling ideas from around the world to the classroom. Riveting images, fascinating topics, and inspiring video will motivate learners to engage with ideas and each other. The second edition of World English introduces students to some of the world’s most fascinating people and places and builds upon an effective competency-based approach to provide 21st century learners with the English skills needed for success.

The second edition of World English introduces students to some of the world's most fascinating people and places and builds upon an effective competency-based approach to provide 21st century learners with the English skills needed for ...