Geometry Books
Cambridge University Press Projective Differential Geometry Old and New
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£105.45
Cambridge University Press The Geometry of Efficient Fair Division
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£128.25
Cambridge University Press Combinatorial and Computational Geometry 52 Mathematical Sciences Research Institute Publications Series Number 52
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£87.40
Cambridge University Press Theory and Modeling of Rotating Fluids
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£139.65
Cambridge University Press The CubeA Window to Convex and Discrete Geometry
Book SynopsisThis tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them.Trade Review"Because this book is a love letter to the unity of mathematics, readers can hardly but come to share Zong's undisguised enthusiasm...Highly recommended." -- ChoiceTable of ContentsPreface; Basic notation; 0. Introduction; 1. Cross sections; 2. Projections; 3. Inscribed simplices; 4. Triangulations; 5. 0/1 polytopes; 6. Minkowski's conjecture; 7. Furtwangler's conjecture; 8. Keller's conjecture; Bibliography; Index.
£105.45
Cambridge University Press Geometric Folding Algorithms
Book SynopsisEmphasizing algorithmic and computational aspects, this fascinating treatment of the geometry of folding and unfolding presents hundreds of results and over 60 open problems. Aimed at advanced undergraduates and graduates in mathematics or computer science, this lavishly illustrated book will entertain a broad audience, from school students to researchers.Trade Review'Demaine and O'Rourke are among the best-qualified authors for a book on this subject; and the book that they have written is a delight … it is exceptionally clear and readable. It could be read for pleasure by any mathematics undergraduate, and much of it (though not all) by amateurs with a high school mathematics background … although there are sections that some amateurs will skip, the level is always kept as elementary as locally possible. This book should be in all university libraries, and many professional and amateur mathematicians will want to add it to their personal collections.' Robert Dawson (Halifax), Zentralblatt Math'This book is one of those rare mathematics books that I had a hard time putting down. I wanted to keep reading to find the next insight. … This is a serious mathematics book whose explorations have significant applications and real mathematical profundity, wonderfully mixed with some fun recreational mathematics. … The book has a useful index and an extensive bibliography, so when you finish reading, it will remain a valuable resource far into the future. There is a lot of material in this book and it is really a lot of fun. I highly, highly recommend this book to anyone with even a passing interest in folding mathematics.' MAA Reviews'The authors explain step-by-step interesting solutions of some folding problems. This splendidly illustrated book can be interesting for advanced undergraduate students in mathematics and computer science as well as for geometers and computer specialists who can find many new ideas and impulses …' EMS NewsletterTable of ContentsIntroduction; Part I. Linkages: 1. Problem classification and examples; 2. Upper and lower bounds; 3. Planar linkage mechanisms; 4. Rigid frameworks; 5. Reconfiguration of chains; 6. Locked chains; 7. Interlocked chains; 8. Joint-constrained motion; 9. Protein folding; Part II. Paper: 10. Introduction; 11. Foundations; 12. Simple crease patterns; 13. General crease patterns; 14. Map folding; 15. Silhouettes and gift wrapping; 16. The tree method; 17. One complete straight cut; 18. Flattening polyhedra; 19. Geometric constructibility; 20. Rigid origami and curved creases; Part III. Polyhedra: 21. Introduction and overview; 22. Edge unfolding of polyhedra; 23. Reconstruction of polyhedra; 24. Shortest paths and geodesics; 25. Folding polygons to polyhedra; 26. Higher dimensions.
£145.35
Cambridge University Press Hyperbolic Geometry from a Local Viewpoint 68 London Mathematical Society Student Texts Series Number 68
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£100.70
Cambridge University Press Rigidity in Higher Rank Abelian Group Actions Volume 1 Introduction and Cocycle Problem Cambridge Tracts in Mathematics Series Number 185
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£105.45
Cambridge University Press Monopoles and ThreeManifolds 10 New Mathematical Monographs Series Number 10
Book SynopsisThis 2007 book provides a comprehensive treatment of Floer homology, based on the Seiberg–Witten equations. Suitable for beginning graduate students and researchers in the field, this book provides a full discussion of a central part of the study of the topology of manifolds.Trade Review'… there are mathematics books that are classics; these are books that tell a particular story in the right way. As such, they will never go out of date and never be bettered. Kronheimer and Mrowka's book is almost surely such a book. If you want to learn about Floer homology in the Seiberg–Witten context, you will do no better than to read Kronheimer and Mrowka's masterpiece Monopoles and Three-Manifolds.' Clifford Henry Taubes, Bulletin of the American Mathematical Society'This long-awaited book is a complete and detailed exposition of the Floer theory for Seiberg-Witten invariants. It is very nicely written and contains all proofs of results. This makes the book an essential tool for both researchers and students working in this area of mathematics.' Mathematical Reviews'This book is the definitive bible for anyone wanting to learn the full story of the various Seiberg-Witten Floer homology theories … There are mathematics books that are classics. As such, they will never go out of date and never be improved. The present masterpiece is almost surely such a book.' Alexander Felshtyn, Zentralblatt MATHTable of ContentsPreface; 1. Outlines; 2. The Seiberg–Witten equations and compactness; 3. Hilbert manifolds and perturbations; 4. Moduli spaces and transversality; 5. Compactness and gluing; 6. Floer homology; 7. Cobordisms and invariance; 8. Non-exact perturbations; 9. Calculations; 10. Further developments; References; Glossary of notation; Index.
£175.75
Cambridge University Press Algebra and Geometry
Book SynopsisDescribing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and aspects of geometry including groups of isometries, rotations, and spherical geometry. The book emphasises the interactions between topics, and each topic is constantly illustrated by using it to describe and discuss the others. Many ideas are developed gradually, with each aspect presented at a time when its importance becomes clearer. To aid in this, the text is divided into short chapters, each with exercises at the end. The related website features an HTML version of the book, extra text at higher and lower levels, and more exercises and examples. It also links to an electronic maths thesaurus, giving definitions, examples and links both to the book and to external sources.Trade Review'The presentation is traditional, informal, and relaxed.' Zentralblatt MATHTable of ContentsPreface; 1. Groups and permutations; 2. The real numbers; 3. The complex plane; 4. Vectors in three-dimensional space; 5. Spherical geometry; 6. Quaternions and isometries; 7. Vector spaces; 8. Linear equations; 9. Matrices; 10. Eigenvectors; 11. Linear maps of Euclidean space; 12. Groups; 13. Möbius transformations; 14. Group actions; 15. Hyperbolic geometry; Index.
£43.69
Cambridge University Press Corporate Lawyers and Corporate Governance International Corporate Law and Financial Market Regulation
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£118.75
Cambridge University Press Groups Graphs and Trees An Introduction to the Geometry of Infinite Groups London Mathematical Society Student Texts Series Number 73
Book SynopsisThis book presents a modern, geometric approach to group theory. An accessible and engaging approach to the subject, with many exercises and figures to develop geometric intuition. Ideal for advanced undergraduates, it will also interest graduate students and researchers as a gentle introduction to geometric group theory.Trade Review'Meier has the rare ability to make complex concepts accessible to novices while simultaneously challenging the experienced. … With well-chosen illustrations and examples, Meier succeeds brilliantly in this unique approach.' SciTech Book News'… totally accessible to undergraduate students and would be a good textbook for an advanced undergraduate course in group theory, or a graduate course in geometric group theory.' Mathematical Review'… an excellent introduction to geometric group theory. … Carefully chosen examples are an essential part of the exposition and they really help to understand general constructions.' EMS NewsletterTable of ContentsPreface; 1. Cayley's theorems; 2. Groups generated by reflections; 3. Groups acting on trees; 4. Baumslag-Solitar groups; 5. Words and Dehn's word problem; 6. A finitely-generated, infinite, Torsion group; 7. Regular languages and normal forms; 8. The Lamplighter group; 9. The geometry of infinite groups; 10. Thompson's group; 11. The large-scale geometry of groups; Bibliography; Index.
£89.30
Cambridge University Press Stacks Project Expository Collection
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£90.25
Cambridge University Press Computational Topology for Data Analysis
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£47.49
Cambridge University Press LargeScale Convex Optimization
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£56.99
Cambridge University Press The Calabi Problem for Fano Threefolds
Book SynopsisThis book determines whether the general member of each family of smooth Fano threefolds admits a KählerEinstein metric, using K-stability. Complemented by appendices outlining results needed to understand this active area, it will be essential reading for researchers and graduate students working on algebraic and complex geometry.Trade Review'The notion of K-stability for Fano manifold has origins in differential geometry and geometric analysis but is now also of fundamental importance in algebraic geometry, with recent developments in moduli theory. This monograph gives an account of a large body of research results from the last decade, studying in depth the case of Fano threefolds. The wealth of material combines in a most attractive way sophisticated modern theory and the detailed study of examples, with a classical flavour. The authors obtain complete results on the K-stability of generic elements of each of the 105 deformation classes. The concluding chapter contains some fascinating conjectures about the 34 families which may contain both stable and unstable manifolds, which will surely be the scene for much further work. The book will be an essential reference for many years to come.' Sir Simon Donaldson, F.R.S., Imperial College London'It is a difficult problem to check whether a given Fano variety is K-polystable. This book settles this problem for the general members of all the 105 deformation families of smooth Fano 3-folds. The book is recommended to anyone interested in K-stability and existence of Kähler-Einstein metrics on Fano varieties.' Caucher Birkar FRS, Tsinghua University and University of CambridgeTable of ContentsIntroduction; 1. K-stability; 2. Warm-up: smooth del Pezzo surfaces; 3. Proof of main theorem: known cases; 4. Proof of main theorem: special cases; 5. Proof of main theorem: remaining cases; 6. The big table; 7. Conclusion; Appendix. Technical results used in proof of main theorem; References; Index.
£71.25
Cambridge University Press The Geometry of Cubic Hypersurfaces
Book SynopsisThis detailed introduction to cubic hypersurfaces and all the techniques needed to study them leads the reader from classical topics to recent developments studying four-dimensional cubic hypersurfaces. With exercises and careful references to the wider literature, this is an ideal text for graduate students and researchers in algebraic geometry.Trade Review'What a beautiful book. Several turning points in algebraic geometry have in their background a cubic hypersurface. This superb exposition, by one of the masters in the field, takes the reader, in a friendly manner, through the fascinating, and occasionally mysterious, properties of these geometrical objects, and through them offers a glimpse of the underlying Hodge theory, of the theory of periods, the theory of motives, and the theory of derived categories. Graduate students, researchers, and colleagues will all find this unified treatment of cubic hypersurfaces profoundly inspiring.' Enrico Arbarello, Accademia Nazionale dei Lincei'This is just a fantastic book for students and experts alike. The geometry of cubics is a wonderful mix of the classical and the modern; Huybrechts consolidates the diverse results into a coherent account for the first time. His famously lucid writing clearly conveys the beauty of the geometry of these varieties. The book describes a plethora of techniques culminating in new (and really surprising) viewpoints on the subject.' Richard Thomas, Imperial College London'This exceedingly well written monograph covers material ranging from the very beginning of algebraic geometry, the 27 lines on a cubic surface, to highly relevant topical issues. The book will be a most valuable companion to algebraic geometers from graduate students to active researchers.' Klaus Hulek, Leibniz University HannoverTable of Contents1. Basic facts; 2. Fano varieties of lines; 3. Moduli spaces; 4. Cubic surfaces; 5. Cubic threefolds; 6. Cubic fourfolds; 7. Derived categories of cubic hypersurfaces; References; Subject index.
£66.49
Cambridge University Press The Mathematics of Origami
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£94.50
Cambridge University Press Introduction to Vassiliev Knot Invariants
Book SynopsisWith hundreds of worked examples, exercises and illustrations, this detailed exposition of the theory of Vassiliev knot invariants opens the field to students with little or no knowledge in this area. It also serves as a guide to more advanced material. The book begins with a basic and informal introduction to knot theory, giving many examples of knot invariants before the class of Vassiliev invariants is introduced. This is followed by a detailed study of the algebras of Jacobi diagrams and 3-graphs, and the construction of functions on these algebras via Lie algebras. The authors then describe two constructions of a universal invariant with values in the algebra of Jacobi diagrams: via iterated integrals and via the Drinfeld associator, and extend the theory to framed knots. Various other topics are then discussed, such as Gauss diagram formulae, before the book ends with Vassiliev's original construction.Trade Review'It is clear that this book is a labour of love, and that no effort has been spared in making it a useful textbook and reference for those seeking to understand its subject. The target readership consists both of first-time learners, for whom pedagogically sound explanations and numerous well-chosen exercises are provided to enhance comprehension, and of experienced mathematicians, for whom many tables of data and readable concise guides to research literature are provided. Numerous figures are included to supplement written explanations. The content is well-modularized, in the sense that different sections of the book may be read independently of one another, and that when there is an essential dependence between sections then this fact is clearly pointed out and the relationship between the sections is explained. This, and a thorough index, combine to make this book not only a valuable textbook, but also a valuable reference.' Zentralblatt MATH'The book's excellent preface goes on to give an in embryo characterization of the objects in the title … As being a textbook - and an excellent one - the authors take us from a dense but accessible introduction to knots as such to quantum invariants, all in the first two chapters, and then go on to Vassiliev's finite type invariants. Then we get to chord diagrams, Lie algebra connections, Kontsevich's integral, work by Drinfeld, more stuff on the Kontsevich integral, material on braids, and more. The book closes with a chapter on '[t]he space of all knots'. It's very, very attractive material.' Michael Berg, MAA ReviewsTable of Contents1. Knots and their relatives; 2. Knot invariants; 3. Finite type invariants; 4. Chord diagrams; 5. Jacobi diagrams; 6. Lie algebra weight systems; 7. Algebra of 3-graphs; 8. The Kontsevich integral; 9. Framed knots and cabling operations; 10. The Drinfeld associator; 11. The Kontsevich integral: advanced features; 12. Braids and string links; 13. Gauss diagrams; 14. Miscellany; 15. The space of all knots; Appendix; References; Notations; Index.
£66.49
Cambridge University Press Categorical Homotopy Theory 24 New Mathematical Monographs Series Number 24
Book SynopsisThis categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.Table of ContentsPart I. Derived Functors and Homotopy (Co)limits: 1. All concepts are Kan extensions; 2. Derived functors via deformations; 3. Basic concepts of enriched category theory; 4. The unreasonably effective (co)bar construction; 5. Homotopy limits and colimits: the theory; 6. Homotopy limits and colimits: the practice; Part II. Enriched Homotopy Theory: 7. Weighted limits and colimits; 8. Categorical tools for homotopy (co)limit computations; 9. Weighted homotopy limits and colimits; 10. Derived enrichment; Part III. Model Categories and Weak Factorization Systems: 11. Weak factorization systems in model categories; 12. Algebraic perspectives on the small object argument; 13. Enriched factorizations and enriched lifting properties; 14. A brief tour of Reedy category theory; Part IV. Quasi-Categories: 15. Preliminaries on quasi-categories; 16. Simplicial categories and homotopy coherence; 17. Isomorphisms in quasi-categories; 18. A sampling of 2-categorical aspects of quasi-category theory.
£78.84
Cambridge University Press Finite Geometry and Combinatorial Applications 82 London Mathematical Society Student Texts Series Number 82
Book SynopsisThe projective and polar geometries that arise from a vector space over a finite field are particularly useful in the construction of combinatorial objects, such as latin squares, designs, codes and graphs. This book provides an introduction to these geometries and their many applications to other areas of combinatorics. Coverage includes a detailed treatment of the forbidden subgraph problem from a geometrical point of view, and a chapter on maximum distance separable codes, which includes a proof that such codes over prime fields are short. The author also provides more than 100 exercises (complete with detailed solutions), which show the diversity of applications of finite fields and their geometries. Finite Geometry and Combinatorial Applications is ideal for anyone, from a third-year undergraduate to a researcher, who wishes to familiarise themselves with and gain an appreciation of finite geometry.Table of Contents1. Fields; 2. Vector spaces; 3. Forms; 4. Geometries; 5. Combinatorial applications; 6. The forbidden subgraph problem; 7. MDS codes; Appendix A. Solutions to the exercises; Appendix B. Additional proofs; Appendix C. Notes and references; References; Index.
£133.95
Cambridge University Press Factorization Algebras in Quantum Field Theory Volume 2
Book SynopsisIdeal for researchers and graduate students at the interface between mathematics and physics, this text develops quantum field theory from the ground up using a rich mix of modern mathematics. It provides a unified approach to deformation quantization, Hochschild homology, vertex algebras, conformal field theory, quantum groups, and gauge theory.Trade Review'The central achievement of the book is in its development of a formalism that leads to classical and quantum versions of Noether's theorem, itself a familiar topic in physics, using the language of factorization algebras … Institutions employing mathematicians and theoretical physicists actively working in this area should acquire the book … Recommended.' M. C. Ogilvie, Choice ConnectTable of Contents1. Introduction and overview; Part I. Classical Field Theory: 2. Introduction to classical field theory; 3. Elliptic moduli problems; 4. The classical Batalin–Vilkovisky formalism; 5. The observables of a classical field theory; Part II. Quantum Field Theory: 6. Introduction to quantum field theory; 7. Effective field theories and Batalin–Vilkovisky quantization; 8. The observables of a quantum field theory; 9. Further aspects of quantum observables; 10. Operator product expansions, with examples; Part III. A Factorization Enhancement of Noether's Theorem: 11. Introduction to Noether's theorems; 12. Noether's theorem in classical field theory; 13. Noether's theorem in quantum field theory; 14. Examples of the Noether theorems; Appendix A. Background; Appendix B. Functions on spaces of sections; Appendix C. A formal Darboux lemma; References; Index.
£118.75
Cambridge University Press Geometry of Quantum States
Book SynopsisQuantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and KochenSpecker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings'' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers interTrade Review'True story: A few years ago my daughter took a break from her usual question, 'Dad, what is your favourite colour?' and asked instead, 'What is your favourite shape?' I was floored! 'What a wonderful question; my favourite shape is Hilbert space!' 'What does it look like?' she asked. My answer: 'I don't know! But every day when I go to work, that's what I think about.' What I was speaking of, of course, is the geometry of quantum-state space. It is as much a mystery today as it was those years ago, and maybe more so as we learn to focus on its most key and mysterious features. This book, the worn first-edition of which I've had on my shelf for 11 years, is the indispensable companion for anyone's journey into that exotic terrain. Beyond all else, I am thrilled about the inclusion of two new chapters in the new edition, one of which I believe goes to the very heart of the meaning of quantum theory.' Christopher A. Fuchs, University of Massachusetts, Boston'The quantum world is full of surprises as is the mathematical theory that describes it. Bengtsson and Życzkowski prove to be expert guides to the deep mathematical structure that underpins quantum information science. Key concepts such as multipartite entanglement and quantum contextuality are discussed with extraordinary clarity. A particular feature of this new edition is the treatment of SIC generalised measurements and the curious bridge they make between quantum physics and number theory.' Gerard J. Milburn, University of QueenslandPraise for the first edition: 'Geometry of Quantum States can be considered an indispensable item on a bookshelf of everyone interest in quantum information theory and its mathematical background.' Miłosz Michalski, editor of Open Systems and Information DynamicsPraise for the first edition: 'Bengtsson's and Zyczkowski's book is an artful presentation of the geometry that lies behind quantum theory … the authors collect, and artfully explain, many important results scattered throughout the literature on mathematical physics. The careful explication of statistical distinguishability metrics (Fubini-Study and Bures) is the best I have read.' Gerard Milburn, University of QueenslandTable of ContentsPreface; 1. Convexity, colours, and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Discrete structures in Hilbert space; 13. Density matrices and entropies; 14. Distinguishability measures; 15. Monotone metrics and measures; 16. Quantum entanglement; 17. Multipartite entanglement; Appendix 1. Basic notions of differential geometry; Appendix 2. Basic notions of group theory; Appendix 3. Geometry – do it yourself; Appendix 4. Hints and answers to the exercises; Bibliography; Index.
£49.39
Cambridge University Press Principles of Geometry
Book SynopsisHenry Frederick Baker (18661956) was a renowned British mathematician specialising in algebraic geometry. First published between 1922 and 1925, this six-volume work provides a detailed insight into the geometry which was developing at the time of publication. Volume 1 describes the foundations of projective geometry.Table of ContentsPreface; Introductory; 1. Abstract geometry; 2. Real geometry; 3. Abstract geometry, resumed; Bibliographical; Index.
£24.99
Cambridge University Press Oeuvres de Desargues Volume 1
The French mathematician Gérard Desargues (15911661) was one of the founders of projective geometry. His writings, published in two volumes in 1864 by Noël-Germinal Poudra (17941894), reveal Desargues' important role in the scientific debates of the seventeenth century. Volume 1 contains the majority of Desargues' treatises.
£41.79
Cambridge University Press Oeuvres de Desargues
Book SynopsisThe French mathematician Gérard Desargues (15911661) was one of the founders of projective geometry. His writings, published in two volumes in 1864 by Noël-Germinal Poudra (17941894), reveal Desargues' important role in the scientific debates of the seventeenth century. Volume 2 contains reviews and criticism by Desargues' contemporaries.Table of ContentsPreliminaire; Analyse des ouvrages de Bosse; Notices sur Desargues; Diverses notices sur Desargues; Recueil et extraits de divers libelles contre Desargues; Advis charitable; Curabelle; Faiblesse pitoyable.
£37.99
Pearson Education HIGH SCHOOL MATH COMMONCORE GEOMETRY STUDENT
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£127.62
Walker & Co Sacred Geometry
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£15.00
Walker & Co Symmetry The Ordering Principle Wooden Books
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£13.50
Chicago Review Press Junk Drawer Geometry
Book SynopsisTrade Review"This book is full of experiments and gee-whiz coolness." - Times Record"Definitely worth adding to your study of Geometry" - A Net In Time" Junk Drawer Geometry is a great way to make learning math fun!" -- Midwest Book Review"The titular phrase 'Junk drawer geometry' is right on---all materials are inexpensive and easy to gather. A great addition to STEM collections and makerspaces." -- School Library Journal"This entertaining and instructional book is ideal for students studying geometry, exploring STEM concepts, or those who just love solving math puzzles." -- Booklist
£13.25
Random House USA Inc High School Geometry Unlocked High School Subject
Book SynopsisUNLOCK THE SECRETS OF GEOMETRY with THE PRINCETON REVIEW.Geometry can be a daunting subject. That’s why our new High School Unlocked series focuses on giving you a wide range of key techniques to help you tackle subjects like Geometry. If one method doesn't click for you, you can use an alternative approach to understand the concept or problem, instead of painfully trying the same thing over and over without success. Trust us—unlocking geometric secrets doesn't have to hurt!With this book, you’ll discover the link between abstract concepts and their real-world applications and build confidence as your skills improve. Along the way, you’ll get plenty of practice, from fully guided examples to independent end-of-chapter drills and test-like samples. Everything You Need to Know About Geometry.• Complex concepts explained in clear, straightforward ways• Walk-throughs of sample problems for all topics
£13.29
Johns Hopkins University Press Understanding Topology
Book SynopsisA fresh approach to topology makes this complex topic easier for students to master. Topologythe branch of mathematics that studies the properties of spaces that remain unaffected by stretching and other distortionscan present significant challenges for undergraduate students of mathematics and the sciences. Understanding Topology aims to change that. The perfect introductory topology textbook, Understanding Topology requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles. Professor Shaun V. Ault's unique emphasis on fascinating applications, from mapping DNA to determining the shape of the universe, will engage students in a way traditional topology textbooks do not. This groundbreaking new text: presents Euclidean, abstract, and basic algebraic topology explains metric topTrade ReviewA perfect introductory topology textbook, Understanding Topology requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the textbook's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles, and might reasonably be expected to become a standard reference for teaching backgrounds of topology in the years to come.—Marek Golasinski (Olsztyn), Zentralblatt MathA useful book for undergraduates, with the initial introduction to concepts being at the level of intuition and analogy, followed by mathematical rigour.—John Bartlett CMath MIMA, Mathematics TodayTable of ContentsPrefaceI Euclidean Topology1. Introduction to Topology1.1 Deformations1.2 Topological Spaces2. Metric Topology in Euclidean Space2.1 Distance2.2 Continuity and Homeomorphism2.3 Compactness and Limits2.4 Connectedness2.5 Metric Spaces in General3. Vector Fields in the Plane3.1 Trajectories and Phase Portraits3.2 Index of a Critical Point3.3 *Nullclines and Trapping RegionsII Abstract Topology with Applications4. Abstract Point-Set Topology4.1 The Definition of a Topology4.2 Continuity and Limits4.3 Subspace Topology and Quotient Topology4.4 Compactness and Connectedness4.5 Product and Function Spaces4.6 *The Infinitude of the Primes5. Surfaces5.1 Surfaces and Surfaces-with-Boundary5.2 Plane Models and Words5.3 Orientability5.4 Euler Characteristic6. Applications in Graphs and Knots6.1 Graphs and Embeddings6.2 Graphs, Maps, and Coloring Problems6.3 Knots and Links6.4 Knot ClassificationIII Basic Algebraic Topology7. The Fundamental Group7.1 Algebra of Loops7.2 Fundamental Group as Topological Invariant7.3 Covering Spaces and the Circle7.4 Compact Surfaces and Knot Complements7.5 *Higher Homotopy Groups8. Introduction to Homology8.1 Rational Homology8.2 Integral HomologyAppendixesA. Review of Set Theory and FunctionsA.1 Sets and Operations on SetsA.2 Relations and FunctionsB. Group Theory and Linear AlgebraB.1 GroupsB.2 Linear AlgebraC. Selected SolutionsD. NotationsBibliographyIndex
£76.05
Barcharts, Inc Geometry Quickstudy Academic
Book SynopsisThe new QuickStudy Booklets cover the key information on some of the toughest courses today, helping students boost their grades. The books are presented in the clear, concise format readers have come to expect from QuickStudy. Covers the fundamentals of Geometry - formulas, terms, theorems and more.
£999.99
Capstone Press Both Sides Are the Same Wonder Readers Early
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£999.99
Capstone Press Shapes Wonder Readers Early Level
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£999.99
Capstone Press Circles Everywhere Wonder Readers Emergent Level
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£999.99
Capstone Press Tiling Shapes Wonder Readers Fluent Level
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£999.99
Kaplan Publishing Painless Geometry
Book SynopsisWhether you’re a student or an adult looking to refresh your knowledge, Barron’s Painless Geometry provides review and practice in an easy, step-by-step format.An essential resource for: Virtual Learning Homeschool Learning pods Supplementing classes/in-person learning Inside you’ll find: Comprehensive coverage of geometry, including characteristics of distinct shapes, relationships between parallel and perpendicular lines, geometric principles that can solve real-world problems, and much more Diagrams, charts, instructive math illustrations, proofs, and experiments Painless tips, common pitfalls, and math talk boxes that translate complex “math speak” into easy-to-understand language Brain Tickler quizzes and answers throughout each chapter to test your progress
£16.24
Barcharts, Inc Geometry Part 2
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£999.99
Barcharts, Inc Geometric Formulas
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£999.99
Centre for the Study of Language & Information The Philosophical Status of Diagrams
Book SynopsisThe use of diagrams in logic and geometry has encountered resistence throughout the years. For a proof to be valid in geometry it must not rely on the graphical properties of a diagram. In logic the teaching of proofs depends on the sentenial representations, ideas formed as natural language sentences such as "if A is true and B is true...". No serious formal proof system is based on diagrams. This text explores the reasons why structured graphics have been ignored in modern formal theories of axiomatic systems. The effects of historical forces on the evolution of diagrammatically-based systems of inference in logic and geometry are explored, from antiquity to the early 20th-century work of David Hilbert. From this exploration emerges an understanding that the present negative attitudes towards the use of diagrams in logic and geometry owe more to implicit appeals to their history and philosophical background than to any technical incompatibility with modern theories of logical systems.
£999.99
St Augustine's Press Insights and Manipulations – What Classical
Book SynopsisThe past becomes a source of wisdom when the scientific quest for uncovering the roots of things is combined with the humanistic endeavor to make the dead letter come alive in a thoughtful mind. Vague attempts at being “interdisciplinary,” by contrast, merely provide excuses to avoid examining the words set down by the scientific thinkers themselves. If we love wisdom in its wholeness, we must explore the sources of the things that we now take for granted: we must think through the records of the thinking that has demarcated the various fields of study and envisioned what’s to be investigated within them and how it’s to be done. But where shall we start looking for points of view to help us consider what learning is, and what learning has to do with how we live within our world? We couldn’t do better than to climb the two peaks that constitute the subject of this book. these are the classical geometry in which Apollonius presented the conic sections, and that modern transformation over which Descartes presided at its inception. In this effort, a useful link between our two primary texts is provided by examining some work done by Diophantus, by Pappus, and by Viète. While the study of these writings is a formidable enterprise indeed, the two volumes of Insights and Manipulations, offering clear guidance and abundant help, greatly alleviate the requisite labor.
£999.99
Dorling Kindersley Ltd The Humongous Book of Geometry Problems
Book SynopsisAre you a befuddled math student who's struggling with geometry? The Humongous Book of Geometry Problems is like no other geometry workbook on the market and is the answer for anyone who doesn’t speak math. Bestselling author W. Michael Kelley helps make otherwise baffling solutions perfectly clear by taking a typical geometry workbook, filling it with solved problems, and making notes in the margins to add missing steps and simplify concepts. By learning how to interpret and solve problems as they are presented in courses, students will become fully prepared to solve even the most obscure geometry problem. No more solving by trial and error! Here’s what you’ll find in this this fun and simple guide: • 1000 geometry problems and solutions, each solved to completion • Annotations and helpful notes for each problem to help clarify the solutions and fill in the missing steps needed to reach the solutions • Coverage of all the critical geometry concepts, with each explained in detail and in simple, straightforward language that any student can grasp and apply
£20.69
Mark Twain Media Common Core Math Workouts, Grade 8
Book Synopsis
£9.49
Shelter Harbor Press Geometry & Art: How Mathematics transformed Art
Book Synopsis
£23.70
Shelter Harbor Press Geometry (Inside Mathematics): Understanding
Book SynopsisAge range 14+One of the hardest questions that mathematics teachers have to answer is 'Why?' Schoolroom sums are crucial in learning the awesome power of mathematics, but they are often a world away from how the knowledge is applied and where it came from. Inside Mathematics: Geometry is there to fill that gap. The word 'geometry' means to 'measure the Earth.' Ancient mathematicians wanting to do more than count money and merchandise used geometry to model the natural world and then the world of numbers that lies behind it. What began by scratching circles and squares in the dirt has led to to infinitely large shapes you could hold in your hand, a Universe in which straight lines can be curved, and Internet search engines that handle information as structures with hundreds of dimensions. Inside Mathematics: Geometry introduces the amazing people who figured out how shapes work and how they can be used to unlock secrets of nature. Written to engage, and enthuse young people, it show readers how ideas of long-dead geniuses ended up in their homework assignment: Trigonometry is not just about triangles — it can tell you how big the Universe is. Not every polyhedron has three dimensions: The tesseract of sci-fi movies really exists as a four-dimensional cube that can turn itself inside out.
£18.81
Tarquin Publications Birds, Bees and Burgers: Puzzling Geometry from
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£11.41
Wooden Books SYMMETRY
Book Synopsis
£8.87
