Extension Mathematics

Author: Anthony Gardiner
Publisher: Oxford Universidy Press
ISBN: 9780199151509
Category : Gifted children
Languages : en
Pages : 0

Book Description
This book is aimed at gifted and talented students in year 7, although it can also be used in the primary curriculum for highly able year 6 students. It consists of tightly focused sets of problems, with each set devoted to core ideas from the Framework but approached in a way that cultivatesmore profound mathematical thinking. The book is structured into a number of sections, which comes in three varieties: tasters, core, and extensions, thus recognising differentiation within the gifted spectrum. The materials can be used within ordinary lessons for top sets.

Teaching Mathematics at Secondary Level

Author: Tony Gardiner
Publisher: Open Book Publishers
ISBN: 1783741406
Category : Mathematics
Languages : en
Pages : 248

Book Description
Teaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11 ̶ 14 (Key Stage 3) in particular, this handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles and concepts that need to be borne in mind by all teachers and textbook authors—but which are little appreciated in the UK at present.This study is aimed at anyone who would like to think more deeply about the discipline of ‘elementary mathematics’, in England and Wales and anywhere else. By analysing and supplementing the current curriculum, Teaching Mathematics provides food for thought for all those involved in school mathematics, whether as aspiring teachers or as experienced professionals. It challenges us all to reflect upon what it is that makes secondary school mathematics educationally, culturally, and socially important.

The Gamma Function

Author: Emil Artin
Publisher: Courier Dover Publications
ISBN: 0486803007
Category : Mathematics
Languages : en
Pages : 52

Book Description
This brief monograph on the gamma function was designed by the author to fill what he perceived as a gap in the literature of mathematics, which often treated the gamma function in a manner he described as both sketchy and overly complicated. Author Emil Artin, one of the twentieth century's leading mathematicians, wrote in his Preface to this book, "I feel that this monograph will help to show that the gamma function can be thought of as one of the elementary functions, and that all of its basic properties can be established using elementary methods of the calculus." Generations of teachers and students have benefitted from Artin's masterly arguments and precise results. Suitable for advanced undergraduates and graduate students of mathematics, his treatment examines functions, the Euler integrals and the Gauss formula, large values of x and the multiplication formula, the connection with sin x, applications to definite integrals, and other subjects.

Mathematics for Degree Students (For B.Sc. Third Year)

Author: Rana U.S.
Publisher: S. Chand Publishing
ISBN: 8121941016
Category : Science
Languages : en
Pages : 855

Book Description
Mathematics for Degree Students B.Sc.IIIrd Yr

A Book of Abstract Algebra

Author: Charles C Pinter
Publisher: Courier Corporation
ISBN: 0486474178
Category : Mathematics
Languages : en
Pages : 402

Book Description
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

Cambridge 3 Unit Mathematics Year 12 Enhanced Version

Author: William Pender
Publisher: Cambridge University Press
ISBN: 1107616042
Category : Juvenile Nonfiction
Languages : en
Pages : 521

Book Description
Contains features including a large number of fully worked examples which demonstrate mathematical processes and encourage independent learning

Hopf Algebras and Galois Module Theory

Author: Lindsay N. Childs
Publisher: American Mathematical Soc.
ISBN: 1470465167
Category : Education
Languages : en
Pages : 311

Book Description
Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.

Mathematics for Machine Learning

Author: Marc Peter Deisenroth
Publisher: Cambridge University Press
ISBN: 1108569323
Category : Computers
Languages : en
Pages : 392

Book Description
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Complex Cobordism and Stable Homotopy Groups of Spheres

Author: Douglas C. Ravenel
Publisher: American Mathematical Soc.
ISBN: 082182967X
Category : Mathematics
Languages : en
Pages : 418

Book Description
Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids. The book is intended for anyone wishing to study computational stable homotopy theory. It is accessible to graduate students with a knowledge of algebraic topology and recommended to anyone wishing to venture into the frontiers of the subject.

An Introduction to Measure Theory

Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 1470466406
Category : Education
Languages : en
Pages : 206

Book Description
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.