This detailed textbook presents a great deal of material on ordered sets not previously published in the still rather limited textbook literature. It should be suitable as a text for a course on order theory.

Edexcel and A Level Modular Mathematics M2 features: Student-friendly worked examples and solutions, leading up to a wealth of practice questions. Sample exam papers for thorough exam preparation. Regular review sections consolidate learning. Opportunities for stretch and challenge presented throughout the course. 'Escalator section' to step up from GCSE. PLUS Free LiveText CD-ROM, containing Solutionbank and Exam Cafe to support, motivate and inspire students to reach their potential for exam success. Solutionbank contains fully worked solutions with hints and tips for every question in the Student Books. Exam Cafe includes a revision planner and checklist as well as a fully worked examination-style paper with examiner commentary.

This book is about scientific inquiry. Designed for early and mid-career researchers, it is a practical manual for conducting and communicating high-quality research in (mathematics) education. Based on the authors' extensive experience as researchers, as mentors, and as members of the editorial team for the Journal for Research in Mathematics Education (JRME), this book directly speaks to researchers and their communities about each phase of the process for conceptualizing, conducting, and communicating high-quality research in (mathematics) education. In the late 2010s, both JRME and Educational Studies in Mathematics celebrated 50 years of publishing high-quality research in mathematics education. Many advances in the field have occurred since the establishment of these journals, and these anniversaries marked a milestone in research in mathematics education. Indeed, fifty years represents a small step for human history but a giant leap for mathematics education. The educational research community in general (and the mathematics education community in particular) has strongly advocated for original research, placing great emphasis on building knowledge and capacity in the field. Because it is an interdisciplinary field, mathematics education has integrated means and methods for scientific inquiry from multiple disciplines. Now that the field is gaining maturity, it is a good time to take a step back and systematically consider how mathematics education researchers can engage in significant, impactful scientific inquiry.

This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.

This write-in workbook is an invaluable resource to help students improve their Maths and English skills and help prepare for Level 1 and Level 2 Functional Skills exams. The real-life questions are all written with a Retail context to help students find essential Maths and English theory understandable, engaging and achievable. Written by Carole Vella, a lecturer with a wealth of experience in the Retail and Business Administration industry, this workbook is an invaluable resource to support Maths and English learning in the classroom, at work and for personal study at home.

This monograph presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Dirac operators are widely used in physics, differential geometry, and group-theoretic settings (particularly, the geometric construction of discrete series representations). The related concept of Dirac cohomology, which is defined using Dirac operators, is a far-reaching generalization that connects index theory in differential geometry to representation theory. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective. An excellent contribution to the mathematical literature of representation theory, this self-contained exposition offers a systematic examination and panoramic view of the subject. The material will be of interest to researchers and graduate students in representation theory, differential geometry, and physics.

This book provides an introduction to the computer language A Programming Language (APL), providing quick access to the powerful computational capabilities of the language for the newcomer to APL. It focuses on the mathematical nature of the language, and complements standard curricula.

Calculus Reform. Or, as many would prefer, calculus renewal. These are terms that, for better or worse, have become a part of the vocabulary in mathematics departments across the country. The movement to change the nature of the calculus course at the undergraduate and secondary levels has sparked discussion and controversy in ways as diverse as the actual changes. Such interactions range from "coffee pot conversations" to university curriculum committee agendas to special sessions on calculus renewal at regional and national conferences. But what is the significance of these activities? Where have we been and where are we going with calculus and, more importantly, the entire scope of undergraduate mathematics education? In April 1996, I received a fellowship from the American Educational Research Association (AERA) and the National Science Foundation (NSF). This fellowship afforded me the opportunity to work in residence at NSF on a number of evaluation projects, including the national impact of the calculus reform movement since 1988. That project resulted in countless communications with the mathematics community and others about the status of calculus as a course in isolation and as a significant player in the overall undergraduate mathematics and science experience for students (and faculty). While at NSF (and through a second NSF grant received while at the American Association for Higher Education), I also was part of an evaluation project for the Institution-wide Reform (IR) program.

Support achievement in the latest syllabus (9709), for examination from 2020, with a stretching, practice-driven approach that builds the advanced skills required for Cambridge exam success and progression to further study.

• This new edition is fully aligned with the Pure Mathematics 1 part of the latest International AS & A Level syllabus, and contains a comprehensive mapping grid so you can be sure of complete support.
• Get students ready for higher education with a focus on real-world application. From parabolic reflectors to technology in sport, up-to-date, international examples show how mathematics is used in real life.
• Students have plenty of opportunities to hone their skills with extensive graduated practice and thorough worked examples. Plus, give students realistic practice for their exams with exam-style questions covering every topic.
• Answers are included in the back of the book with full step-by-step solutions for all exercises and exam-style questions available on the accompanying support site.

Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

A collection of inter-connected topics in areas of mathematics which particularly interest the author, ranging over the two millennia from the work of Archimedes to the "Werke" of Gauss. The book is intended for those who love mathematics, including undergraduate students of mathematics, more experienced students and the vast unseen host of amateur mathematicians. It is equally a useful source of material for those who teach mathematics.

This book is about the creation and production of textbooks for learning and teaching mathematics. It covers a period from Antiquity to Modern Times. The analysis begins by assessing principal cultures with a practice of mathematics. The tension between the role of the teacher and his oral mode, on the one hand, and the use of a written (printed) text, in their respective relation with the student, is one of the dimensions of the comparative analysis, conceived of as the 'textbook triangle'. The changes in this tension with the introduction of the printing press are discussed. The book presents various national case studies (France, Germany, Italy) as well as analyses of the internationalisation of textbooks via transmission processes. As this topic has not been sufficiently explored in the literature, it will be very well received by scholars of mathematics education, mathematics teacher educators and anyone with an interest in the field.

The book gives an up-to-date account of various approaches availablefor the analysis of infectious disease data. Most of the methods havebeen developed only recently, and for those based on particularlymodern mathematics, details of the computation are carefullyillustrated. Interpretation is discussed at some length and the emphasisthroughout is on making statistical inferences about epidemiologicallyimportant parameters.Niels G. Becker is Reader in Statistics at La Trobe University,Australia.

This book argues that mathematical challenge can be found at any level and at every age and constitutes an essential characteristic of any mathematics classroom aimed at developing the students' mathematical knowledge and skills. Since each mathematics classroom is heterogeneous with respect to students' mathematical potential, quality mathematical instruction results from matching the level of mathematical challenge to different students' potential. Thus, effective integration of mathematical challenge in the instructional process is strongly connected to the equity principle of mathematics education. In the three sections in this volume readers can find diverse views on mathematical challenges in curriculum and instructional design, kinds and variation of mathematically challenging tasks and collections of mathematical problems. Evidence-based analysis is interwoven with theoretical positions expressed by the authors of the chapters. Cognitive, social and affective characteristics of challenging mathematical activities are observed and analyzed. The volume opens new avenues of research in mathematics education, and pose multiple questions about mathematical instruction rich in mathematical challenge for all. The authors invite readers to explore and enjoy mathematical challenges at different levels.

Publication bias is the tendency to decide to publish a study based on the results of the study, rather than on the basis of its theoretical or methodological quality. It can arise from selective publication of favorable results, or of statistically significant results. This threatens the validity of conclusions drawn from reviews of published scientific research.

Meta-analysis is now used in numerous scientific disciplines, summarizing quantitative evidence from multiple studies. If the literature being synthesised has been affected by publication bias, this in turn biases the meta-analytic results, potentially producing overstated conclusions. "Publication Bias in Meta-Analysis" examines the different types of publication bias, and presents the methods for estimating and reducing publication bias, or eliminating it altogether.

Written by leading experts, adopting a practical and multidisciplinary approach.

Provides comprehensive coverage of the topic including:

Different types of publication bias, Mechanisms that may induce them, Empirical evidence for their existence, Statistical methods to address them, Ways in which they can be avoided.Features worked examples and common data sets throughout.Explains and compares all available software used for analysing and reducing publication bias.Accompanied by a website featuring software, data sets and further material.

"Publication Bias in Meta-Analysis" adopts an inter-disciplinary approach and will make an excellent reference volume for any researchers and graduate students who conduct systematic reviews or meta-analyses. University and medical libraries, as well as pharmaceutical companies and government regulatory agencies, will also find this invaluable.

A tribute to the pioneers of oil exploration in Indonesia (1850-1898). Using authentic reports, diaries, relevant texts, personal notes and pictures, Poley brings to life the heroic efforts of Reerink (Cheribon, W. Java), Zijlker and Kessler (Deli, NE Sumatra), Stoop (Surabaya and Rembang, E Java), Menten (Kutei, E Kalimantan), Kessler and IJzerman (Palembang, SE Sumatra), and their crews. They faced almost insurmountable odds in many locations: an impenetrable, cruel jungle, an inclement climate, tropical diseases, technical mishaps, financial restrictions, and, last but not least, government and legal constraints. There was no geological science to guide them, and drilling technology was still in its infancy. Yet it was their vision and perseverance which finally put Indonesia on the world map of oil-producing nations, and which contributed materially to the development of today's life of luxury. Much of the present text and several of the pictures are here presented for the first time to the general public.

Do high-speed, complicated arithmetic in your head using the Trachtenberg Speed System. Ever find yourself struggling to check a bill or a payslip? With The Trachtenberg Speed System you can. Described as the 'shorthand of mathematics', the Trachtenberg system only requires the ability to count from one to eleven. Using a series of simplified keys it allows anyone to master calculations, giving greater speed, ease in handling numbers and increased accuracy. Jakow Trachtenberg believed that everyone is born with phenomenal abilities to calculate. He devised a set of rules that allows every child to make multiplication, division, addition, subtraction and square-root calculations with unerring accuracy and at remarkable speed. It is the perfect way to gain confidence with numbers.

This book discusses examples of discrete mathematics in school curricula, including in the areas of graph theory, recursion and discrete dynamical systems, combinatorics, logic, game theory, and the mathematics of fairness. In addition, it describes current discrete mathematics curriculum initiatives in several countries, and presents ongoing research, especially in the areas of combinatorial reasoning and the affective dimension of learning discrete mathematics. Discrete mathematics is the math of our time.' So declared the immediate past president of the National Council of Teachers of Mathematics, John Dossey, in 1991. Nearly 30 years later that statement is still true, although the news has not yet fully reached school mathematics curricula. Nevertheless, much valuable work has been done, and continues to be done. This volume reports on some of that work. It provides a glimpse of the state of the art in learning and teaching discrete mathematics around the world, and it makes the case once again that discrete mathematics is indeed mathematics for our time, even more so today in our digital age, and it should be included in the core curricula of all countries for all students.

The International Summer School on Statistical Distributions in Scientific Work was held in Trieste during July 1980 for a period of three weeks. The emphasis was on research, review, and exposition concerned with the interface between modem statistical distribution theory and real world problems and issues involving science, technology, and management. Both theory and applications received full attention at the School. The program consisted of a Short Intensive Preparation Course, a NATO Advanced Study Institute, and a Research Conference. While the relative composi- tion of these activities varied somewhat in terms of instruction, exposition, research- review, research, and consultation, the basic spirit of each was essentially the same. Every participant was both a professor and a student. The summer school was sponsored by the NATO Advanced Study Institutes Program; Consiglio Nazionale delle Ricerche, Italy; Regione Autonoma Friuli Ven- ezia Giulia, Italy; National Institutes of Health, USA; Office of Naval Research, USA; The Pennsylvania State University; Universita di Roma; Universita di Trieste; International Statistical Ecology Program; International Transfer of Science and Technology, Belgium; and the participants and their home institutions and organiza- tions. Research papers, research-review expositions and instructional lectures were spe- cially prepared for the program. These materials have been refereed and revised, and are now available in a series of several edited volumes and monographs.