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Books > Science & Mathematics > Mathematics > Geometry

Riemann-Roch Algebra (Hardcover, 1985 ed.): William Fulton, Serge Lang Riemann-Roch Algebra (Hardcover, 1985 ed.)
William Fulton, Serge Lang
R2,993 Discovery Miles 29 930 Ships in 18 - 22 working days
Dynamical And Complex Systems (Hardcover): Shaun Bullett, Tom Fearn, Frank Smith Dynamical And Complex Systems (Hardcover)
Shaun Bullett, Tom Fearn, Frank Smith
R2,402 Discovery Miles 24 020 Ships in 18 - 22 working days

This book leads readers from a basic foundation to an advanced level understanding of dynamical and complex systems. It is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as applied dynamical systems, Lotka-Volterra dynamical systems, applied dynamical systems theory, dynamical systems in cosmology, aperiodic order, and complex systems dynamics.Dynamical and Complex Systems is the fifth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.

Real Algebraic Geometry (Hardcover, 1998 ed.): Jacek Bochnak, Michel Coste, Marie-Francoise Roy Real Algebraic Geometry (Hardcover, 1998 ed.)
Jacek Bochnak, Michel Coste, Marie-Francoise Roy
R4,927 Discovery Miles 49 270 Ships in 18 - 22 working days

This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.

Trigonometry: Notes, Problems And Exercises (Paperback): Roger Delbourgo Trigonometry: Notes, Problems And Exercises (Paperback)
Roger Delbourgo
R756 Discovery Miles 7 560 Ships in 10 - 15 working days

This book provides a thorough, intermediate-level yet concise course in Trigonometry for use in colleges. There are 37 short chapters, each treating one specific theme and containing worked examples and easy exercises. Central to the work are the trigonometric properties of triangle ABC and its associated points. A small appendix contains some Spherical Trigonometry with interesting problems related to the earth; a larger one for enthusiastic students provides further lengthier exercises for extra practice, and full solutions are supplied in the conclusion.Compared with other books on Trigonometry, this book covers the vast spread of topics. Especially, the author reminds readers of the historical importance of theorems enunciated by such contributors as Ptolemy, Euler, Morley, etc. Their names not only invite the readers to appreciate the beauty of these results, but also direct readers to mystery unknown.

Trigonometry: Notes, Problems And Exercises (Hardcover): Roger Delbourgo Trigonometry: Notes, Problems And Exercises (Hardcover)
Roger Delbourgo
R1,450 Discovery Miles 14 500 Ships in 18 - 22 working days

This book provides a thorough, intermediate-level yet concise course in Trigonometry for use in colleges. There are 37 short chapters, each treating one specific theme and containing worked examples and easy exercises. Central to the work are the trigonometric properties of triangle ABC and its associated points. A small appendix contains some Spherical Trigonometry with interesting problems related to the earth; a larger one for enthusiastic students provides further lengthier exercises for extra practice, and full solutions are supplied in the conclusion.Compared with other books on Trigonometry, this book covers the vast spread of topics. Especially, the author reminds readers of the historical importance of theorems enunciated by such contributors as Ptolemy, Euler, Morley, etc. Their names not only invite the readers to appreciate the beauty of these results, but also direct readers to mystery unknown.

Lecture Notes on Elementary Topology and Geometry (Hardcover, Reprint 1976.): I. M. Singer, J.A. Thorpe Lecture Notes on Elementary Topology and Geometry (Hardcover, Reprint 1976.)
I. M. Singer, J.A. Thorpe
R1,873 Discovery Miles 18 730 Ships in 18 - 22 working days

At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis."

Precalculus - An Investigation of Functions (Paperback, 2nd ed.): David Lippman, Melonie Rasmussen Precalculus - An Investigation of Functions (Paperback, 2nd ed.)
David Lippman, Melonie Rasmussen
R803 Discovery Miles 8 030 Ships in 9 - 17 working days
Geometry - Our Cultural Heritage (Hardcover, 2nd ed. 2010): Audun Holme Geometry - Our Cultural Heritage (Hardcover, 2nd ed. 2010)
Audun Holme
R2,198 Discovery Miles 21 980 Ships in 18 - 22 working days

This book contains selected topics from the history of geometry, with "modern" proofs of some of the results, as well as a fully modern treatment of selected basic issues in geometry. It is geared towards the needs of future mathematics teachers. One of my goals for this book is to open up for the dynamic character of geometry as such, and to extend an invitation to geometry as a gateway to mathematics in general. It is unfortunate that today, at a time when mathematics is more important than ever, phrases like math avoidance and math anxiety are very much in the public vocabulary. Making a serious effort to heal these ills is an essential task. Thus the book also aims at an informed public, interested in making a new beginning in math For the 2nd edition, some of the historical material has been expanded and numerous illustrations have been added, as has a chapter on polyhedra and tessellations and their symmetries. A large number of exercises with some suggestions for solutions is also included.

Nearrings, Nearfields And Related Topics (Hardcover): Kuncham, Syam Prasad, Kedukodi Babushri Srinivas, Panackal Harikrishnan,... Nearrings, Nearfields And Related Topics (Hardcover)
Kuncham, Syam Prasad, Kedukodi Babushri Srinivas, Panackal Harikrishnan, Bhavanari Satyanarayana; Edited by (associates) Kent Neuerburg, …
R3,111 Discovery Miles 31 110 Ships in 18 - 22 working days

Recent developments in various algebraic structures and the applications of those in different areas play an important role in Science and Technology. One of the best tools to study the non-linear algebraic systems is the theory of Near-rings.The forward note by G

Periods and Nori Motives (Hardcover, 1st ed. 2017): Annette Huber Periods and Nori Motives (Hardcover, 1st ed. 2017)
Annette Huber; Contributions by Benjamin Friedrich, Jonas Von Wangenheim; Stefan Muller-Stach
R3,495 R2,441 Discovery Miles 24 410 Save R1,054 (30%) Ships in 10 - 15 working days

This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori's abelian category of mixed motives. It develops Nori's approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties. Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori's unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting. Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is self-contained.

Trigonometric Functions And Complex Numbers: In Mathematical Olympiad And Competitions (Hardcover): Desheng Yang Trigonometric Functions And Complex Numbers: In Mathematical Olympiad And Competitions (Hardcover)
Desheng Yang; Translated by Chunhui Shen
R1,761 Discovery Miles 17 610 Ships in 10 - 15 working days

Trigonometric Functions and Complex Numbers covers the followings areas in the International Mathematical Olympiad (IMO) and other mathematical competitions. The contents are essential for the IMO. A good help for students who want to improve in these areas.

Undergraduate Convexity: Problems And Solutions (Paperback): Mikkel Slot Nielsen, Victor Ulrich Rohde Undergraduate Convexity: Problems And Solutions (Paperback)
Mikkel Slot Nielsen, Victor Ulrich Rohde
R999 Discovery Miles 9 990 Ships in 18 - 22 working days

This solutions manual thoroughly goes through the exercises found in Undergraduate Convexity: From Fourier and Motzkin to Kuhn and Tucker. Several solutions are accompanied by detailed illustrations and intuitive explanations. This book will pave the way for students to easily grasp the multitude of solution methods and aspects of convex sets and convex functions. Companion Textbook here

Undergraduate Convexity: Problems And Solutions (Hardcover): Mikkel Slot Nielsen, Victor Ulrich Rohde Undergraduate Convexity: Problems And Solutions (Hardcover)
Mikkel Slot Nielsen, Victor Ulrich Rohde
R1,678 Discovery Miles 16 780 Ships in 18 - 22 working days

This solutions manual thoroughly goes through the exercises found in Undergraduate Convexity: From Fourier and Motzkin to Kuhn and Tucker. Several solutions are accompanied by detailed illustrations and intuitive explanations. This book will pave the way for students to easily grasp the multitude of solution methods and aspects of convex sets and convex functions. Companion Textbook here

Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2013 Villa De Leyva Summer School... Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2013 Villa De Leyva Summer School (Hardcover)
Alexander Cardona, Hernan Ocampo, Andres F. Reyes-Lega, Leonardo Cano
R4,709 Discovery Miles 47 090 Ships in 18 - 22 working days

Based on lectures held at the 8th edition of the series of summer schools in Villa de Leyva since 1999, this book presents an introduction to topics of current interest at the interface of geometry, algebra, analysis, topology and theoretical physics. It is aimed at graduate students and researchers in physics or mathematics, and offers an introduction to the topics discussed in the two weeks of the summer school: operator algebras, conformal field theory, black holes, relativistic fluids, Lie groupoids and Lie algebroids, renormalization methods, spectral geometry and index theory for pseudo-differential operators.

Trigonometric Functions And Complex Numbers: In Mathematical Olympiad And Competitions (Paperback): Desheng Yang Trigonometric Functions And Complex Numbers: In Mathematical Olympiad And Competitions (Paperback)
Desheng Yang; Translated by Chunhui Shen
R1,028 Discovery Miles 10 280 Ships in 10 - 15 working days

Trigonometric Functions and Complex Numbers covers the followings areas in the International Mathematical Olympiad (IMO) and other mathematical competitions. The contents are essential for the IMO. A good help for students who want to improve in these areas.

Dynamical Scale Transform In Tropical Geometry (Hardcover): Tsuyoshi Kato Dynamical Scale Transform In Tropical Geometry (Hardcover)
Tsuyoshi Kato
R1,943 Discovery Miles 19 430 Ships in 18 - 22 working days

This book provides comprehensive analysis of dynamical systems in tropical geometry, which include the author's significant discoveries and pioneering contributions. Tropical geometry is a kind of dynamical scale transform which connects real rational dynamics with piecewise linear one presented by max and plus algebras. A comparison method is given which estimates orbits corresponding to different rational dynamics by reduction to the piecewise linear dynamics.Both rational and piecewise linear dynamics appear in many important branches of mathematics. Tropical geometry can play a role or function to bridge between different subjects in mathematics. This book contains detailed accounts of basic strategy on how to apply tropical geometry to analysis in various mathematical subjects by presenting several applications which include: a rough classification of partial differential equations from the point of view of global behavior of solutions; construction of the infinite quasi-recursive rational dynamics, based on the automaton of the Burnside group by Aleshin-Grigorchuk; study on nearly periodicity of the pentagram map on the moduli space of the twisted polygons; spectral coincidence between lamplighter group in theory of automata groups and Box and ball systems corresponding to KdV equation in soliton theory.This book is self-contained, and detailed accounts of theory of automata groups, BBS and the pentagram map are also included.

B-Model Gromov-Witten Theory (Hardcover, 1st ed. 2018): Emily Clader, Yongbin Ruan B-Model Gromov-Witten Theory (Hardcover, 1st ed. 2018)
Emily Clader, Yongbin Ruan
R4,355 Discovery Miles 43 550 Ships in 10 - 15 working days

This book collects various perspectives, contributed by both mathematicians and physicists, on the B-model and its role in mirror symmetry. Mirror symmetry is an active topic of research in both the mathematics and physics communities, but among mathematicians, the "A-model" half of the story remains much better-understood than the B-model. This book aims to address that imbalance. It begins with an overview of several methods by which mirrors have been constructed, and from there, gives a thorough account of the "BCOV" B-model theory from a physical perspective; this includes the appearance of such phenomena as the holomorphic anomaly equation and connections to number theory via modularity. Following a mathematical exposition of the subject of quantization, the remainder of the book is devoted to the B-model from a mathematician's point-of-view, including such topics as polyvector fields and primitive forms, Givental's ancestor potential, and integrable systems.

Geometry II - Spaces of Constant Curvature (Hardcover, 1993 ed.): E.B. Vinberg Geometry II - Spaces of Constant Curvature (Hardcover, 1993 ed.)
E.B. Vinberg; Translated by V. Minachin; Contributions by D.V. Alekseevskij, O.V. Shvartsman, A.S. Solodovnikov, …
R3,669 Discovery Miles 36 690 Ships in 10 - 15 working days

Spaces of constant curvature, i.e. Euclidean space, the sphere, and Loba chevskij space, occupy a special place in geometry. They are most accessible to our geometric intuition, making it possible to develop elementary geometry in a way very similar to that used to create the geometry we learned at school. However, since its basic notions can be interpreted in different ways, this geometry can be applied to objects other than the conventional physical space, the original source of our geometric intuition. Euclidean geometry has for a long time been deeply rooted in the human mind. The same is true of spherical geometry, since a sphere can naturally be embedded into a Euclidean space. Lobachevskij geometry, which in the first fifty years after its discovery had been regarded only as a logically feasible by-product appearing in the investigation of the foundations of geometry, has even now, despite the fact that it has found its use in numerous applications, preserved a kind of exotic and even romantic element. This may probably be explained by the permanent cultural and historical impact which the proof of the independence of the Fifth Postulate had on human thought."

Commutative Algebra - with a View Toward Algebraic Geometry (Hardcover): David Eisenbud Commutative Algebra - with a View Toward Algebraic Geometry (Hardcover)
David Eisenbud
R2,504 Discovery Miles 25 040 Ships in 10 - 15 working days

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.

Contact and Symplectic Geometry (Hardcover, New): Charles Benedict Thomas Contact and Symplectic Geometry (Hardcover, New)
Charles Benedict Thomas
R3,230 Discovery Miles 32 300 Ships in 10 - 15 working days

This volume presents some of the lectures and research during the special programme held at the Newton Institute in 1994. The book, in two parts, begins with an introductory overview. The two parts each contain a mix of substantial expository articles and research papers that outline important and topical ideas. Many of the results have not been presented before. Symplectic methods are one of the most active areas of research in mathematics currently, and this volume will attract much attention.

Brief Introduction To Symplectic And Contact Manifolds, A (Hardcover): Augustin Banyaga, Djideme F. Houenou Brief Introduction To Symplectic And Contact Manifolds, A (Hardcover)
Augustin Banyaga, Djideme F. Houenou
R1,857 Discovery Miles 18 570 Ships in 18 - 22 working days

The book introduces the basic notions in Symplectic and Contact Geometry at the level of the second year graduate student. It also contains many exercises, some of which are solved only in the last chapter.We begin with the linear theory, then give the definition of symplectic manifolds and some basic examples, review advanced calculus, discuss Hamiltonian systems, tour rapidly group and the basics of contact geometry, and solve problems in chapter 8. The material just described can be used as a one semester course on Symplectic and Contact Geometry.The book contains also more advanced material, suitable to advanced graduate students and researchers.

Projective Geometry and Modern Algebra (Hardcover, 1995 ed.): Lars Kadison, Matthias T. Kromann Projective Geometry and Modern Algebra (Hardcover, 1995 ed.)
Lars Kadison, Matthias T. Kromann
R1,525 Discovery Miles 15 250 Ships in 18 - 22 working days

The techniques and concepts of modern algebra are introduced for their natural role in the study of projectile geometry; groups appear as automorphism groups of configurations, division rings appear in the study of Desargues' theorem and the study of the independence of the seven axioms given for projectile geometry.

"Golden" Non-euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, And The Fine-structure... "Golden" Non-euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, And The Fine-structure Constant (Hardcover)
Alexey Stakhov, Samuil Aranson
R2,857 Discovery Miles 28 570 Ships in 18 - 22 working days

This unique book overturns our ideas about non-Euclidean geometry and the fine-structure constant, and attempts to solve long-standing mathematical problems. It describes a general theory of 'recursive' hyperbolic functions based on the 'Mathematics of Harmony,' and the 'golden,' 'silver,' and other 'metallic' proportions. Then, these theories are used to derive an original solution to Hilbert's Fourth Problem for hyperbolic and spherical geometries. On this journey, the book describes the 'golden' qualitative theory of dynamical systems based on 'metallic' proportions. Finally, it presents a solution to a Millennium Problem by developing the Fibonacci special theory of relativity as an original physical-mathematical solution for the fine-structure constant. It is intended for a wide audience who are interested in the history of mathematics, non-Euclidean geometry, Hilbert's mathematical problems, dynamical systems, and Millennium Problems.See Press Release: Application of the mathematics of harmony - Golden non-Euclidean geometry in modern math

Recent Progress in Mathematics (Hardcover, 1st ed. 2022): Nam-Gyu Kang, Jaigyoung Choe, Kyeongsu Choi, Sang Hyun Kim Recent Progress in Mathematics (Hardcover, 1st ed. 2022)
Nam-Gyu Kang, Jaigyoung Choe, Kyeongsu Choi, Sang Hyun Kim
R1,413 Discovery Miles 14 130 Ships in 18 - 22 working days

This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future direction. Four of the chapters are expository in nature while one is based more directly on research. All deal with important areas of mathematics, however, such as algebraic geometry, topology, partial differential equations, Riemannian geometry, and harmonic analysis. This book is addressed to researchers who are interested in those subject areas. Young-Hoon Kiem discusses classical enumerative geometry before string theory and improvements after string theory as well as some recent advances in quantum singularity theory, Donaldson-Thomas theory for Calabi-Yau 4-folds, and Vafa-Witten invariants. Dongho Chae discusses the finite-time singularity problem for three-dimensional incompressible Euler equations. He presents Kato's classical local well-posedness results, Beale-Kato-Majda's blow-up criterion, and recent studies on the singularity problem for the 2D Boussinesq equations. Simon Brendle discusses recent developments that have led to a complete classification of all the singularity models in a three-dimensional Riemannian manifold. He gives an alternative proof of the classification of noncollapsed steady gradient Ricci solitons in dimension 3. Hyeonbae Kang reviews some of the developments in the Neumann-Poincare operator (NPO). His topics include visibility and invisibility via polarization tensors, the decay rate of eigenvalues and surface localization of plasmon, singular geometry and the essential spectrum, analysis of stress, and the structure of the elastic NPO. Danny Calegari provides an explicit description of the shift locus as a complex of spaces over a contractible building. He describes the pieces in terms of dynamically extended laminations and of certain explicit "discriminant-like" affine algebraic varieties.

Hilbert Modular Surfaces (Hardcover, 1988 ed.): Gerard van der Geer Hilbert Modular Surfaces (Hardcover, 1988 ed.)
Gerard van der Geer
R5,197 Discovery Miles 51 970 Ships in 18 - 22 working days

Over the last 15 years important results have been achieved in the field of "Hilbert Modular" Varieties. Though the main emphasis of this book is on the geometry of Hilbert modular surfaces, both geometric and arithmetic aspects are treated. An abundance of examples - in fact a whole chapter - completes this competent presentation of the subject. This "Ergebnisbericht" will soon become an indispensible tool for graduate students and researchers in this field.

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