Starting Advanced Mathematics

The Essential Foundation

Author: Hugh Neill,Sarah Payne

Publisher: Cambridge University Press

ISBN: 9780521893565

Category: Juvenile Nonfiction

Page: 128

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Starting Advanced Mathematics is a self-study guide for students who will be continuing their study of Mathematics after GCSE either to AS/A level or as part of the International Baccalaureate. It will enable students to consolidate the basic algebra and trigonometry skills that they will require during their study of advanced Mathematics. Other GCSE formulae and results that they may require during their post 16 studies are included for reference. The book is also a valuable revision aid for Higher Tier GCSE students who need more practice in Algebra and Trigonometry.

A Course in Advanced Calculus

Author: Robert S. Borden

Publisher: Courier Corporation

ISBN: 0486150380

Category: Mathematics

Page: 416

View: 1357

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An excellent undergraduate text examines sets and structures, limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, more. Problems with tips and solutions for some.

All the Math You'll Ever Need

A Self-Teaching Guide

Author: Steve Slavin

Publisher: John Wiley & Sons

ISBN: 0471674028

Category: Mathematics

Page: 240

View: 7310

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A sharp mind, like a healthy body, is subject to the same rule of nature: Use it or lose it Need a calculator just to work out a 15 percent service charge? Not exactly sure how to get the calculator to give you the figure you need? Turn to this revised and updated edition of All the Math You'll Ever Need, the friendliest, funniest, and easiest workout program around. In no time, you'll have total command of all the powerful mathematical tools needed to make numbers work for you. In a dollars-and-cents, bottom-line world, where numbers influence everything, none of us can afford to let our math skills atrophy. This step-by-step personal math trainer: Refreshes practical math skills for your personal and professional needs, with examples based on everyday situations. Offers straightforward techniques for working with decimals and fractions. Demonstrates simple ways to figure discounts, calculate mortgage interest rates, and work out time, rate, and distance problems. Contains no complex formulas and no unnecessary technical terms.

Advanced Calculus

Author: H.K Nickerson,D.C. Spencer,N.E. Steenrod

Publisher: Courier Corporation

ISBN: 0486173747

Category: Mathematics

Page: 560

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Starting with an abstract treatment of vector spaces and linear transforms, this introduction presents a corresponding theory of integration and concludes with applications to analytic functions of complex variables. 1959 edition.

Modern advanced mathematics for engineers

Author: Vladimir V. Mitin,Vladimir Vasilʹevich Mitin,Dmitri A. Romanov,M. Polis

Publisher: Wiley-Interscience

ISBN: 9780471417705

Category: Mathematics

Page: 308

View: 7072

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A convenient single source for vital mathematical concepts, written by engineers and for engineers. Builds a strong foundation in modern applied mathematics for engineering students, and offers them a concise and comprehensive treatment that summarizes and unifies their mathematical knowledge using a system focused on basic concepts rather than exhaustive theorems and proofs. The authors provide several levels of explanation and exercises involving increasing degrees of mathematical difficulty to recall and develop basic topics such as calculus, determinants, Gaussian elimination, differential equations, and functions of a complex variable. They include an assortment of examples ranging from simple illustrations to highly involved problems as well as a number of applications that demonstrate the concepts and methods discussed throughout the book. This broad treatment also offers:* Key mathematical tools needed by engineers working in communications, semiconductor device simulation, and control theory * Concise coverage of fundamental concepts such as sets, mappings, and linearity * Thorough discussion of topics such as distance, inner product, and orthogonality * Essentials of operator equations, theory of approximations, transform methods, and partial differential equationsIt makes an excellent companion to less general engineering texts and a useful reference for practitioners.

Galois Theories

Author: Francis Borceux,George Janelidze

Publisher: Cambridge University Press

ISBN: 9780521803090

Category: Mathematics

Page: 341

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Develops Galois theory in a more general context, emphasizing category theory.

Lie Algebras of Finite and Affine Type

Author: Roger William Carter

Publisher: Cambridge University Press

ISBN: 9780521851381

Category: Mathematics

Page: 632

View: 1614

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This book provides a thorough but relaxed mathematical treatment of Lie algebras.

An Introduction to Random Matrices

Author: Greg W. Anderson,Alice Guionnet,Ofer Zeitouni

Publisher: Cambridge University Press

ISBN: 0521194520

Category: Mathematics

Page: 492

View: 3161

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A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

A User's Guide to Spectral Sequences

Author: John McCleary

Publisher: Cambridge University Press

ISBN: 9780521567596

Category: Mathematics

Page: 561

View: 488

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Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.

An Introduction to Contact Topology

Author: Hansjörg Geiges

Publisher: Cambridge University Press

ISBN: 1139467956

Category: Mathematics

Page: N.A

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This text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.

Elementary Point-Set Topology

A Transition to Advanced Mathematics

Author: Andre L. Yandl,Adam Bowers

Publisher: Courier Dover Publications

ISBN: 0486811018

Category: Mathematics

Page: 256

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In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses. Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations. "This is a back-to-basics introductory text in point-set topology that can double as a transition to proofs course. The writing is very clear, not too concise or too wordy. Each section of the book ends with a large number of exercises. The optional first chapter covers set theory and proof methods; if the students already know this material you can start with Chapter 2 to present a straight topology course, otherwise the book can be used as an introduction to proofs course also." — Mathematical Association of America

Differential Geometry

Author: Erwin Kreyszig

Publisher: Courier Corporation

ISBN: 0486318621

Category: Mathematics

Page: 384

View: 5769

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An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.

A Bridge to Advanced Mathematics

Author: Dennis Sentilles

Publisher: Courier Corporation

ISBN: 0486277585

Category: Mathematics

Page: 416

View: 9528

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This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.

An Introduction to Rights

Author: William A. Edmundson

Publisher: Cambridge University Press

ISBN: 1107378621

Category: Political Science

Page: N.A

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An Introduction to Rights is a readable and accessible introduction to the history, logic, moral implications and political tendencies of the idea of rights. It is organized chronologically and discusses important historical events such as the French and American Revolutions. It treats a range of historical figures, including Grotius, Paley, Hobbes, Locke, Bentham, Burke, Godwin, Douglass, Mill and Hohfeld and relates the concept of rights to contemporary debates such as consequentialism versus contractualism. This thoroughly updated second edition includes a new preface and expands the discussion of the surprising role that slavery has played in the history of rights. It includes new material on egalitarianism, distributive justice and what the demand for equal rights means.

Advanced Mathematics for Engineering and Science

Author: Wenfang Chen,D. de Kee Fong,P. N. Kaloni

Publisher: World Scientific

ISBN: 9789812382924

Category: Mathematics

Page: 880

View: 644

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The book comprises ten chapters, Each chapter contains serveral soved problems clarifying the introduced concepts. Some of the examples are taken from the recent literature and serve to illustrate the applications in various fields of engineering and science. At the end of each chapter, there are assignment problems with two levels of difficulty. A list of references is provided at the end of the book. This book is the product of a close collaboration between two mathematicians and an engineer. The engineer has been helpful in pinpointing the problems which engineering students encounter in books written by mathematicians. Contents: Review of Calculus and Ordinary Differential Equations; Series Solutions and Special Functions; Complex Variables; Vector and Tensor Analysis; Partial Differential Equations I; Partial Differential Equations II; Numerical Methods; Numerical Solution of Partial Differential Equations; Calculus of Variations; Special Topics. Readership: Upper level undergraduates, graduate students and researchers in mathematical modeling, mathematical physics and numerical &computational mathematics.

Advanced Mathematics for Applied and Pure Sciences

Author: CF Chan Man Fong,D De Kee

Publisher: CRC Press

ISBN: 9789056996147

Category: Mathematics

Page: 904

View: 3129

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Covers applicable mathematics that should provide a text, at the third year level and beyond, appropriate for both students of engineering and the pure sciences. The book is a product of close collaboration between two mathematicians and an engineer and it is of note that the engineer has been helpful in pinpointing the problems engineering students usually encounter in books written by mathematicians. Instead of just listing techniques and a few examples, or providing a list of theorems along with their proofs, it explains why the techniques work. The emphasis is on helping the student develop an understanding of mathematics and its applications.

Lectures on Arakelov Geometry

Author: C. Soulé,D. Abramovich,J. F. Burnol

Publisher: Cambridge University Press

ISBN: 9780521477093

Category: Mathematics

Page: 177

View: 7054

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Arakelov theory is a new geometric approach to diophantine equations. It combines algebraic geometry, in the sense of Grothendieck, with refined analytic tools such as currents on complex manifolds and the spectrum of Laplace operators. It has been used by Faltings and Vojta in their proofs of outstanding conjectures in diophantine geometry. This account presents the work of Gillet and Soulé, extending Arakelov geometry to higher dimensions. It includes a proof of Serre's conjecture on intersection multiplicities and an arithmetic Riemann-Roch theorem. To aid number theorists, background material on differential geometry is described, but techniques from algebra and analysis are covered as well. Several open problems and research themes are also mentioned.

A Mathematician's Apology

Author: G. H. Hardy

Publisher: Cambridge University Press

ISBN: 1107394473

Category: Mathematics

Page: N.A

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G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his idiosyncrasies and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.