This introductory text is designed for undergraduate courses in number theory, covering both elementary number theory and analytic number theory. The book emphasises computational aspects, including algorithms and their implementation in Python.The book is divided into two parts. The first part, on elementary number theory, deals with concepts such as induction, divisibility, congruences, primitive roots, cryptography, and continued fractions. The second part is devoted to analytic...

The culmination of more than a decade of research, this compelling volume offers a fresh approach for applying functional linguistics to assess student performance, to inform the teaching and learning of Chinese and to design curriculum and teaching materials. Documenting authentic systemic functional linguistics (SFL) studies in researching and teaching Chinese as a first or second language, this research is set in the multilingual settings of Hong Kong and Australia. The experiences of S...

An accessible and fascinating exploration of how Alan Turing’s mathematical theory gave rise to modern computer science and applications—from the desktops to cell phonesIn 1936, when he was just 24 years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms the basis of computer science. In Turing’s Vision, Chris Be...

Whether we grow up with one, two, or several languages during our early years of life, many of us will learn a second, foreign, or heritage language in later years. The field of Second language acquisition (SLA, for short) investigates the human capacity to learn additional languages in late childhood, adolescence, or adulthood, after the first language --in the case of monolinguals-- or languages --in the case of bilinguals-- have already been acquired. Understanding Second Language A...

500 Ways to Achieve Your Best GradesWe want you to succeed on your college linear algebra midterm and final exams. That's why we've selected these 500 questions to help you study more effectively, use your preparation time wisely, and get your best grades. These questions and answers are similar to the ones you'll find on a typical college exam, so you will know what to expect on test day. Each question includes explanations for right and wrong answers for your full understanding...

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the a...

This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alik...

This book leads readers from a basic foundation to an advanced level understanding of algebra, logic and combinatorics. Perfect for graduate or PhD mathematical-science students looking for help in understanding the fundamentals of the topic, it also explores more specific areas such as invariant theory of finite groups, model theory, and enumerative combinatorics.Algebra, Logic and Combinatorics is the third volume of the LTCC Advanced Mathematics Series. This series is the first to provi...

This book is a guide for parents who wish to raise children with more than one language and literacy. Drawing on interdisciplinary research, as well as the experiences of parents of multilingual children, this book walks parents through the multilingual reading and writing process from infancy to adolescence. It identifies essential literacy skills at each developmental stage and proposes effective strategies that facilitate multiliteracy, in particular, heritage-language literacy developm...

The theory of numbers is generally considered to be the 'purest' branch of pure mathematics and demands exactness of thought and exposition from its devotees. It is also one of the most highly active and engaging areas of mathematics. Now into its eighth edition The Higher Arithmetic introduces the concepts and theorems of number theory in a way that does not require the reader to have an in-depth knowledge of the theory of numbers but also touches upon matters of deep mathematical signifi...

This book applies social theory to curriculum design and sets out a program for language curriculum renewal for the 21st century. It includes many examples of text-based curricula and describes a plan for curriculum renewal based on texts as the unit of analysis for planning, for teaching and for assessment. Underpinned by Halliday’s semiotic theory of language, the book combines the theory of language as a resource for meaning-making with learning language as learning to mean. The curricu...

'… A beautifully written, articulate and compelling argument for a sociocultural perspective on second language teacher education . . . Essential reading for all who wish to understand this perspective.' – David Nunan, University of Hong Kong'…Significant and timely. Johnson is masterful at writing in an engaging, transparent prose about complex concepts. It’s a rare scholar who can write prose like this. Throughout my reading I wanted to engage in...