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Books > Science & Mathematics > Mathematics > Geometry > General

Sutured ECH is a Natural Invariant (Paperback): Cagatay Kutluhan, Steven Sivek, C.H. Taubes Sutured ECH is a Natural Invariant (Paperback)
Cagatay Kutluhan, Steven Sivek, C.H. Taubes
R2,123 Discovery Miles 21 230 Ships in 12 - 17 working days
Tits Polygons (Paperback): Bernhard Muhlherr, Richard M. Weiss Tits Polygons (Paperback)
Bernhard Muhlherr, Richard M. Weiss
R2,121 Discovery Miles 21 210 Ships in 12 - 17 working days
A Concise Introduction to Hypercomplex Fractals (Hardcover): Andrzej Katunin A Concise Introduction to Hypercomplex Fractals (Hardcover)
Andrzej Katunin
R2,372 Discovery Miles 23 720 Ships in 12 - 17 working days

This book presents concisely the full story on complex and hypercomplex fractals, starting from the very first steps in complex dynamics and resulting complex fractal sets, through the generalizations of Julia and Mandelbrot sets on a complex plane and the Holy Grail of the fractal geometry - a 3D Mandelbrot set, and ending with hypercomplex, multicomplex and multihypercomplex fractal sets which are still under consideration of scientists. I tried to write this book in a possibly simple way in order to make it understandable to most people whose math knowledge covers the fundamentals of complex numbers only. Moreover, the book is full of illustrations of generated fractals and stories concerned with great mathematicians, number spaces and related fractals. In the most cases only information required for proper understanding of a nature of a given vector space or a construction of a given fractal set is provided, nevertheless a more advanced reader may treat this book as a fundamental compendium on hypercomplex fractals with references to purely scientific issues like dynamics and stability of hypercomplex systems.

Drawing Circle Images - How to Draw Artistic Symmetrical Images with a Ruler and Compass (Paperback): Musigfi Studio Drawing Circle Images - How to Draw Artistic Symmetrical Images with a Ruler and Compass (Paperback)
Musigfi Studio
R201 Discovery Miles 2 010 Ships in 10 - 15 working days

From simple to complex - use a compass to draw fascinating artistic images. This book includes step-by-step instructions for all symmetries between threefold and twelvefold. Clear and precise black-and-white illustrations will guide you. The book provides ruler and compass constructions that you can draw without using units of measurement for three-, four-, five-, six-, eight-, ten- and twelvefold symmetries. In addition, it gives dimensions in inches (and cm) for all images, which you can use on both A4 and A3 sheets.

Factorization Algebras in Quantum Field Theory (Mixed media product): Kevin Costello, Owen Gwilliam Factorization Algebras in Quantum Field Theory (Mixed media product)
Kevin Costello, Owen Gwilliam
R5,880 Discovery Miles 58 800 Ships in 9 - 15 working days

Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In the first volume of this set, the authors develop the theory of factorization algebras in depth, with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern–Simons theory. In the second volume, they show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies.

Knot Theory - Second Edition (Hardcover, 2nd edition): Vassily Olegovich Manturov Knot Theory - Second Edition (Hardcover, 2nd edition)
Vassily Olegovich Manturov
R3,656 Discovery Miles 36 560 Ships in 12 - 17 working days

Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text. Knot Theory, Second Edition is notable not only for its expert presentation of knot theory's state of the art but also for its accessibility. It is valuable as a profes-sional reference and will serve equally well as a text for a course on knot theory.

Twists, Tilings, and Tessellations - Mathematical Methods for Geometric Origami (Hardcover): Robert J. Lang Twists, Tilings, and Tessellations - Mathematical Methods for Geometric Origami (Hardcover)
Robert J. Lang
R4,626 Discovery Miles 46 260 Ships in 12 - 17 working days

Twists, Tilings, and Tessellation describes the underlying principles and mathematics of the broad and exciting field of abstract and mathematical origami, most notably the field of origami tessellations. It contains folding instructions, underlying principles, mathematical concepts, and many beautiful photos of the latest work in this fast-expanding field.

The Theory of Canonical Moments with Applications in Statistics, Probability and Analysis (Hardcover, New): H Dette The Theory of Canonical Moments with Applications in Statistics, Probability and Analysis (Hardcover, New)
H Dette
R5,120 Discovery Miles 51 200 Ships in 12 - 17 working days

The fascinating world of canonical moments--a unique look at this practical, powerful statistical and probability tool
Unusual in its emphasis, this landmark monograph on canonical moments describes the theory and application of canonical moments of probability measures on intervals of the real line and measures on the circle. Stemming from the discovery that canonical moments appear to be more intrinsically related to the measure than ordinary moments, the book's main focus is the broad application of canonical moments in many areas of statistics, probability, and analysis, including problems in the design of experiments, simple random walks or birth and death chains, and in approximation theory.
The book begins with an explanation of the development of the theory of canonical moments for measures on intervals [a, b] and then describes the various practical applications of canonical moments. The book's topical range includes:
* Definition of canonical moments both geometrically and as ratios of Hankel determinants
* Orthogonal polynomials viewed geometrically as hyperplanes to moment spaces
* Continued fractions and their link between ordinary moments and canonical moments
* The determination of optimal designs for polynomial regression
* The relationships between canonical moments, random walks, and orthogonal polynomials
* Canonical moments for the circle or trigonometric functions
Finally, this volume clearly illustrates the powerful mathematical role of canonical moments in a chapter arrangement that is as logical and interdependent as is the relationship of canonical moments to statistics, probability, and analysis.

Geometric Transformations (Hardcover, 1st ed. 2022): Razvan Gelca, Ionut Onisor, Carlos Yuzo Shine Geometric Transformations (Hardcover, 1st ed. 2022)
Razvan Gelca, Ionut Onisor, Carlos Yuzo Shine
R1,639 Discovery Miles 16 390 Ships in 12 - 17 working days

This textbook teaches the transformations of plane Euclidean geometry through problems, offering a transformation-based perspective on problems that have appeared in recent years at mathematics competitions around the globe, as well as on some classical examples and theorems. It is based on the combined teaching experience of the authors (coaches of several Mathematical Olympiad teams in Brazil, Romania and the USA) and presents comprehensive theoretical discussions of isometries, homotheties and spiral similarities, and inversions, all illustrated by examples and followed by myriad problems left for the reader to solve. These problems were carefully selected and arranged to introduce students to the topics by gradually moving from basic to expert level. Most of them have appeared in competitions such as Mathematical Olympiads or in mathematical journals aimed at an audience interested in mathematics competitions, while some are fundamental facts of mathematics discussed in the framework of geometric transformations. The book offers a global view of the geometric content of today's mathematics competitions, bringing many new methods and ideas to the attention of the public. Talented high school and middle school students seeking to improve their problem-solving skills can benefit from this book, as well as high school and college instructors who want to add nonstandard questions to their courses. People who enjoy solving elementary math problems as a hobby will also enjoy this work.

Geometry by Discovery (Paperback, New): D Gay Geometry by Discovery (Paperback, New)
D Gay
R5,533 Discovery Miles 55 330 Ships in 12 - 17 working days

A New World of Geometry Awaits Your Discovery! The last stone falls out ... a rush of ancient air ... the glint of gold ... the tingle of discovery ... When explorers first opened the tombs of the ancient pharaohs, they knew that they had discovered something wonderful. That feeling, that same passionate sense of discovery, is one of the most powerful educational tools a text can deliver. Geometry by Discovery is an exciting new approach to geometry. This ground-breaking text taps the pedagogical value of discovery to help students stretch their geometric perspective and hone their geometric intuition. It actively engages students in solving mathematical problems, and empowers them to be successful problem-solvers and discoverers of mathematical ideas.

Platonic and Archimedean Solids (Paperback): Daud Sutton Platonic and Archimedean Solids (Paperback)
Daud Sutton 1
R180 R152 Discovery Miles 1 520 Save R28 (16%) Ships in 12 - 17 working days

What sort of things happen when space crystallises? Why were primordial sages fascinated with five simple forms? Does the three-dimensional jigsaw fit simply together? If so how? Find out about one of the languages spoken throughout the universe! An understanding of the Platonic Solids, and their close cousins, the Archimedean Solids has long been required of students seeking entry into ancient wizdom schools. This book, illustrated by the author, is a beautiful introduction to three-dimensional mathemagical space. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

The Messenger (Hardcover): Joy Hancox The Messenger (Hardcover)
Joy Hancox
R796 R658 Discovery Miles 6 580 Save R138 (17%) Ships in 9 - 15 working days

In this book Joy Hancox, the noted investigator of arcane Hermetic secrets, reveals the culmination of an amazing journey she began 35 years ago when she received the Byrom Collection of geometric drawings in two brown paper bags. It is a story of intrigue, suppression and horror. It is also a message of hope. Coincidences occur uncoincidentally. The hand of fate - or is it fortune? - arrives providentially. Clues are linked together. Characters abound. Reality intervenes. Will the right thing be done? Is there a moral to the story?

The Pythagorean Theorem - A 4,000-Year History (Paperback): Eli Maor The Pythagorean Theorem - A 4,000-Year History (Paperback)
Eli Maor
R394 Discovery Miles 3 940 Ships in 12 - 17 working days

An exploration of one of the most celebrated and well-known theorems in mathematics By any measure, the Pythagorean theorem is the most famous statement in all of mathematics. In this book, Eli Maor reveals the full story of this ubiquitous geometric theorem. Although attributed to Pythagoras, the theorem was known to the Babylonians more than a thousand years earlier. Pythagoras may have been the first to prove it, but his proof-if indeed he had one-is lost to us. The theorem itself, however, is central to almost every branch of science, pure or applied. Maor brings to life many of the characters that played a role in its history, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy.

Amenability of Discrete Groups by Examples (Paperback): Kate Juschenko Amenability of Discrete Groups by Examples (Paperback)
Kate Juschenko
R3,077 Discovery Miles 30 770 Ships in 12 - 17 working days

The main topic of the book is amenable groups, i.e., groups on which there exist invariant finitely additive measures. It was discovered that the existence or non-existence of amenability is responsible for many interesting phenomena such as, e.g., the Banach-Tarski Paradox about breaking a sphere into two spheres of the same radius. Since then, amenability has been actively studied and a number of different approaches resulted in many examples of amenable and non-amenable groups. In the book, the author puts together main approaches to study amenability. A novel feature of the book is that the exposition of the material starts with examples which introduce a method rather than illustrating it. This allows the reader to quickly move on to meaningful material without learning and remembering a lot of additional definitions and preparatory results; those are presented after analyzing the main examples. The techniques that are used for proving amenability in this book are mainly a combination of analytic and probabilistic tools with geometric group theory.

Computational Geometry - Algorithms and Applications (Hardcover, 3rd ed. 2008): Mark De Berg, Otfried Cheong, Marc van Kreveld,... Computational Geometry - Algorithms and Applications (Hardcover, 3rd ed. 2008)
Mark De Berg, Otfried Cheong, Marc van Kreveld, Mark Overmars
R1,366 R1,118 Discovery Miles 11 180 Save R248 (18%) Ships in 9 - 15 working days

This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

Differential Geometry of Plane Curves (Paperback): Hilario Alencar, Walcy Santos, Gregorio Silva Neto Differential Geometry of Plane Curves (Paperback)
Hilario Alencar, Walcy Santos, Gregorio Silva Neto
R1,516 Discovery Miles 15 160 Ships in 12 - 17 working days

This book features plane curves-the simplest objects in differential geometry-to illustrate many deep and inspiring results in the field in an elementary and accessible way. After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of the fundamental theorem of algebra), rotation index, Jordan curve theorem, isoperimetric inequality, convex curves, curves of constant width, and the four-vertex theorem. The last chapter connects the classical with the modern by giving an introduction to the curve-shortening flow that is based on original articles but requires a minimum of previous knowledge. Over 200 figures and more than 100 exercises illustrate the beauty of plane curves and test the reader's skills. Prerequisites are courses in standard one variable calculus and analytic geometry on the plane.

Visual Complex Analysis (Paperback, New edition): Tristan Needham Visual Complex Analysis (Paperback, New edition)
Tristan Needham
R1,857 Discovery Miles 18 570 Ships in 9 - 15 working days

Now available in paperback, this successful radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. With several hundred diagrams, and far fewer prerequisites than usual, this is the first visual intuitive introduction to complex analysis. Although designed for use by undergraduates in mathematics and science, the novelty of the approach will also interest professional mathematicians.

Ibn al-Haytham, New Astronomy and Spherical Geometry - A History of Arabic Sciences and Mathematics Volume 4 (Hardcover):... Ibn al-Haytham, New Astronomy and Spherical Geometry - A History of Arabic Sciences and Mathematics Volume 4 (Hardcover)
Roshdi Rashed
R4,397 Discovery Miles 43 970 Ships in 12 - 17 working days

This volume provides a unique primary source on the history and philosophy of mathematics and science from the mediaeval Arab world. The fourth volume of "A History of Arabic Sciences and Mathematics" is complemented by three preceding volumes which focused on infinitesimal determinations and other chapters of classical mathematics.

This book includes five main works of the polymath Ibn al-Haytham (Alhazen) on astronomy, spherical geometry and trigonometry, plane trigonometry and studies of astronomical instruments on hour lines, horizontal sundials and compasses for great circles.

In particular, volume four examines:

  • the increasing tendency to mathematize the inherited astronomy from Greek sources, namely Ptolemy's "Almagest";
  • the development of celestial kinematics;
  • new research in spherical geometry and trigonometry required by the new kinematical theory;
  • the study on astronomical instruments and its impact on mathematical research. These new historical materials and their mathematical and historical commentaries contribute to rewriting the history of mathematical astronomy and mathematics from the 11th century on.

Including extensive commentary from one of the world s foremost authorities on the subject, this fundamental text is essential reading for historians and mathematicians at the most advanced levels of research."

Elements of Mathematics - A Problem-Centered Approach to History and Foundations (Paperback, 1st ed. 2021): Gabor Toth Elements of Mathematics - A Problem-Centered Approach to History and Foundations (Paperback, 1st ed. 2021)
Gabor Toth
R1,369 R1,300 Discovery Miles 13 000 Save R69 (5%) Ships in 9 - 15 working days

This textbook offers a rigorous presentation of mathematics before the advent of calculus. Fundamental concepts in algebra, geometry, and number theory are developed from the foundations of set theory along an elementary, inquiry-driven path. Thought-provoking examples and challenging problems inspired by mathematical contests motivate the theory, while frequent historical asides reveal the story of how the ideas were originally developed. Beginning with a thorough treatment of the natural numbers via Peano's axioms, the opening chapters focus on establishing the natural, integral, rational, and real number systems. Plane geometry is introduced via Birkhoff's axioms of metric geometry, and chapters on polynomials traverse arithmetical operations, roots, and factoring multivariate expressions. An elementary classification of conics is given, followed by an in-depth study of rational expressions. Exponential, logarithmic, and trigonometric functions complete the picture, driven by inequalities that compare them with polynomial and rational functions. Axioms and limits underpin the treatment throughout, offering not only powerful tools, but insights into non-trivial connections between topics. Elements of Mathematics is ideal for students seeking a deep and engaging mathematical challenge based on elementary tools. Whether enhancing the early undergraduate curriculum for high achievers, or constructing a reflective senior capstone, instructors will find ample material for enquiring mathematics majors. No formal prerequisites are assumed beyond high school algebra, making the book ideal for mathematics circles and competition preparation. Readers who are more advanced in their mathematical studies will appreciate the interleaving of ideas and illuminating historical details.

Number, Shape, & Symmetry - An Introduction to Number Theory, Geometry, and Group Theory (Hardcover, New): Diane L Herrmann,... Number, Shape, & Symmetry - An Introduction to Number Theory, Geometry, and Group Theory (Hardcover, New)
Diane L Herrmann, Paul J. Sally Jr
R2,565 Discovery Miles 25 650 Ships in 12 - 17 working days

Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors' successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago's Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.

Asymptotic, Algebraic and Geometric Aspects of Integrable Systems - In Honor of Nalini Joshi On Her 60th Birthday, TSIMF,... Asymptotic, Algebraic and Geometric Aspects of Integrable Systems - In Honor of Nalini Joshi On Her 60th Birthday, TSIMF, Sanya, China, April 9-13, 2018 (Hardcover, 1st ed. 2020)
Frank Nijhoff, Yang Shi, Dajun Zhang
R3,641 Discovery Miles 36 410 Ships in 12 - 17 working days

This proceedings volume gathers together selected works from the 2018 "Asymptotic, Algebraic and Geometric Aspects of Integrable Systems" workshop that was held at TSIMF Yau Mathematical Sciences Center in Sanya, China, honoring Nalini Joshi on her 60th birthday. The papers cover recent advances in asymptotic, algebraic and geometric methods in the study of discrete integrable systems. The workshop brought together experts from fields such as asymptotic analysis, representation theory and geometry, creating a platform to exchange current methods, results and novel ideas. This volume's articles reflect these exchanges and can be of special interest to a diverse group of researchers and graduate students interested in learning about current results, new approaches and trends in mathematical physics, in particular those relevant to discrete integrable systems.

Differential Function Spectra, the Differential Becker-Gottlieb Transfer, and Applications to Differential Algebraic $K$-Theory... Differential Function Spectra, the Differential Becker-Gottlieb Transfer, and Applications to Differential Algebraic $K$-Theory (Paperback)
Ulrich Bunke, David Gepner
R2,129 Discovery Miles 21 290 Ships in 12 - 17 working days
Integrability, Quantization, and Geometry - II. Quantum Theories and Algebraic Geometry (Paperback): Sergey Novikov, Igor... Integrability, Quantization, and Geometry - II. Quantum Theories and Algebraic Geometry (Paperback)
Sergey Novikov, Igor Krichever, Oleg Ogievetsky, Senya Shlosman
R3,395 Discovery Miles 33 950 Ships in 12 - 17 working days

This book is a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: ``Integrable Systems'' and ``Quantum Theories and Algebraic Geometry'', reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.

Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties (Paperback): Hiroshi Iritani, Todor Milanov, Yongbin Ruan,... Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties (Paperback)
Hiroshi Iritani, Todor Milanov, Yongbin Ruan, Yefeng Shen
R2,118 Discovery Miles 21 180 Ships in 12 - 17 working days
Topics in Geometric Group Theory (Paperback, 2nd Ed.): Pierre de la Harpe Topics in Geometric Group Theory (Paperback, 2nd Ed.)
Pierre de la Harpe
R1,231 Discovery Miles 12 310 Ships in 12 - 17 working days

Groups as abstract structures were first recognized by mathematicians in the nineteenth century. Groups are, of course, sets given with appropriate "multiplications," and they are often given together with actions on interesting geometric objects. But groups are also interesting geometric objects by themselves. More precisely, a finitely-generated group can be seen as a metric space, the distance between two points being defined "up to quasi-isometry" by some "word length," and this gives rise to a very fruitful approach to group theory.
In this book, Pierre de la Harpe provides a concise and engaging introduction to this approach, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe uses a hands-on presentation style, illustrating key concepts of geometric group theory with numerous concrete examples.
The first five chapters present basic combinatorial and geometric group theory in a unique way, with an emphasis on finitely-generated versus finitely-presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group," an infinite finitely-generated torsion group of intermediate growth which is becoming more and more important in group theory. Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research questions in the field. An extensive list of references directs readers to more advanced results as well as connectionswith other subjects.

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