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Books > Science & Mathematics > Mathematics > Geometry

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.

Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications (Hardcover): Bayram Sahin Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications (Hardcover)
Bayram Sahin
R2,071 R1,908 Discovery Miles 19 080 Save R163 (8%) Ships in 12 - 17 working days

Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications is a rich and self-contained exposition of recent developments in Riemannian submersions and maps relevant to complex geometry, focusing particularly on novel submersions, Hermitian manifolds, and K\{a}hlerian manifolds. Riemannian submersions have long been an effective tool to obtain new manifolds and compare certain manifolds within differential geometry. For complex cases, only holomorphic submersions function appropriately, as discussed at length in Falcitelli, Ianus and Pastore's classic 2004 book. In this new book, Bayram Sahin extends the scope of complex cases with wholly new submersion types, including Anti-invariant submersions, Semi-invariant submersions, slant submersions, and Pointwise slant submersions, also extending their use in Riemannian maps. The work obtains new properties of the domain and target manifolds and investigates the harmonicity and geodesicity conditions for such maps. It also relates these maps with discoveries in pseudo-harmonic maps. Results included in this volume should stimulate future research on Riemannian submersions and Riemannian maps.

Understanding Geometric Algebra for Electromagnetic Theory (Hardcover): JW Arthur Understanding Geometric Algebra for Electromagnetic Theory (Hardcover)
JW Arthur
R3,424 Discovery Miles 34 240 Ships in 12 - 17 working days

This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison. Professors can request a solutions manual by email: [email protected]

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?

Arakelov Geometry and Diophantine Applications (Paperback, 1st ed. 2021): Emmanuel Peyre, Gael Remond Arakelov Geometry and Diophantine Applications (Paperback, 1st ed. 2021)
Emmanuel Peyre, Gael Remond
R764 Discovery Miles 7 640 Ships in 9 - 15 working days

Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry.

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.

Algebraic Geometry - Notes on a Course (Paperback): Michael Artin Algebraic Geometry - Notes on a Course (Paperback)
Michael Artin
R2,148 Discovery Miles 21 480 Ships in 12 - 17 working days

This book is an introduction to the geometry of complex algebraic varieties. It is intended for students who have learned algebra, analysis, and topology, as taught in standard undergraduate courses. So it is a suitable text for a beginning graduate course or an advanced undergraduate course. The book begins with a study of plane algebraic curves, then introduces affine and projective varieties, going on to dimension and construcibility. $\mathcal{O}$-modules (quasicoherent sheaves) are defined without reference to sheaf theory, and their cohomology is defined axiomatically. The Riemann-Roch Theorem for curves is proved using projection to the projective line. Some of the points that aren't always treated in beginning courses are Hensel's Lemma, Chevalley's Finiteness Theorem, and the Birkhoff-Grothendieck Theorem. The book contains extensive discussions of finite group actions, lines in $\mathbb{P}^3$, and double planes, and it ends with applications of the Riemann-Roch Theorem.

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.

Gauge Theories & Differential Geometry (Hardcover): Lance Bailey Gauge Theories & Differential Geometry (Hardcover)
Lance Bailey
R5,739 Discovery Miles 57 390 Ships in 12 - 17 working days

This book revisits the mathematical foundations of thermodynamics and gauge theory by using new differential geometric methods coming from the formal theory of systems of partial differential equations and Lie pseudogroups. The gauge theory of gravity is also established, in which spinorial and ventorial matter fields serve as gravitating sources. The potential applications of the present gauge theory of gravity, including quantum-vacuum-energy gravity, cosmological constant problem and gravity-gauge unification is also addressed. The third chapter focuses on a gravitational gauge theory with spin connection and vierbein as fundamental variables of gravity. Next, the place and physical significance of Poincare gauge theory of gravity (PGTG) in the framework of gauge approach to gravitation is discussed. A cutoff regularization method in gauge theory is discussed in Chapter Five. The remaining chapters in the book focus on differential geometry, in particular, the authors show how fractional differential derived from fractional difference provides a basis to expand a theory of fractional differential geometry which would apply to non-differentiable manifolds; a review of the infinitesimal Baker-Campbell-Hausdorff formula is provided and the book concludes with a short communication where the authors focus on local stability, and describe how this leads naturally into the question of finite-time singularities and generalized soliton solutions.

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.

Etale Cohomology (PMS-33), Volume 33 (Paperback): James S. Milne Etale Cohomology (PMS-33), Volume 33 (Paperback)
James S. Milne
R1,095 Discovery Miles 10 950 Ships in 12 - 17 working days

One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced etale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in several different branches of number theory and in the representation theory of finite and p-adic groups. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to etale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. The author begins with a review of the basic properties of flat and etale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of etale sheaves and elementary etale cohomology, and are followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in etale cohomology -- those of base change, purity, Poincare duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general L-series. Originally published in 1980. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Groups and Topological Dynamics (Paperback): Volodymyr Nekrashevych Groups and Topological Dynamics (Paperback)
Volodymyr Nekrashevych
R2,167 Discovery Miles 21 670 Ships in 12 - 17 working days

This book is devoted to group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to study symbolic dynamics, and other connections between group theory and dynamical systems. One of the main applications of this approach to group theory is the study of asymptotic properties of groups such as growth and amenability. The book presents recently developed techniques of studying groups of dynamical origin using the structure of their orbits and associated groupoids of germs, applications of the iterated monodromy groups to hyperbolic dynamical systems, topological full groups and their properties, amenable groups, groups of intermediate growth, and other topics. The book is suitable for graduate students and researchers interested in group theory, transformations defined by automata, topological and holomorphic dynamics, and theory of topological groupoids. Each chapter is supplemented by exercises of various levels of complexity.

Selected Works of Isadore Singer: Volume 1 - Functional Analysis, Differential Geometry and Eigenvalues (Hardcover): Daniel S.... Selected Works of Isadore Singer: Volume 1 - Functional Analysis, Differential Geometry and Eigenvalues (Hardcover)
Daniel S. Freed, John Lott
R1,305 Discovery Miles 13 050 Ships in 12 - 17 working days

This collection presents the major mathematical works of Isadore Singer, selected by Singer himself, and organized thematically into three volumes: 1. Functional analysis, differential geometry and eigenvalues 2. Index theory 3. Gauge theory and physics Each volume begins with a commentary (and in the first volume, a short biography of Singer), and then presents the works on its theme in roughly chronological order.

Topology, Geometry, and Dynamics - V. A. Rokhlin-Memorial (Paperback): Anatoly M. Vershik, Victor M. Buchstaber, Andrey V... Topology, Geometry, and Dynamics - V. A. Rokhlin-Memorial (Paperback)
Anatoly M. Vershik, Victor M. Buchstaber, Andrey V Malyutin
R3,017 Discovery Miles 30 170 Ships in 12 - 17 working days

Vladimir Abramovich Rokhlin (8/23/1919-12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real algebraic geometry, and ergodic theory. The volume contains the proceedings of the Conference on Topology, Geometry, and Dynamics: V. A. Rokhlin-Memorial, held from August 19-23, 2019, at The Euler International Mathematics Institute and the Steklov Institute of Mathematics, St. Petersburg, Russia. The articles deal with topology of manifolds, theory of cobordisms, knot theory, geometry of real algebraic manifolds and dynamical systems and related topics. The book also contains Rokhlin's biography supplemented with copies of actual very interesting documents.

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.

Cremona Groups and the Icosahedron (Hardcover): Ivan Cheltsov, Constantin Shramov Cremona Groups and the Icosahedron (Hardcover)
Ivan Cheltsov, Constantin Shramov
R4,547 Discovery Miles 45 470 Ships in 12 - 17 working days

Cremona Groups and the Icosahedron focuses on the Cremona groups of ranks 2 and 3 and describes the beautiful appearances of the icosahedral group A5 in them. The book surveys known facts about surfaces with an action of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold V5, and gives a proof of its A5-birational rigidity. The authors explicitly describe many interesting A5-invariant subvarieties of V5, including A5-orbits, low-degree curves, invariant anticanonical K3 surfaces, and a mildly singular surface of general type that is a degree five cover of the diagonal Clebsch cubic surface. They also present two birational selfmaps of V5 that commute with A5-action and use them to determine the whole group of A5-birational automorphisms. As a result of this study, they produce three non-conjugate icosahedral subgroups in the Cremona group of rank 3, one of them arising from the threefold V5. This book presents up-to-date tools for studying birational geometry of higher-dimensional varieties. In particular, it provides readers with a deep understanding of the biregular and birational geometry of V5.

A Concise Introduction to Algebraic Varieties (Paperback): Brian Osserman A Concise Introduction to Algebraic Varieties (Paperback)
Brian Osserman
R2,141 Discovery Miles 21 410 Ships in 12 - 17 working days

A Concise Introduction to Algebraic Varieties is designed for a one-term introductory course on algebraic varieties over an algebraically closed field, and it provides a solid basis for a course on schemes and cohomology or on specialized topics, such as toric varieties and moduli spaces of curves. The book balances generality and accessibility by presenting local and global concepts, such as nonsingularity, normality, and completeness using the language of atlases, an approach that is most commonly associated with differential topology. The book concludes with a discussion of the Riemann-Roch theorem, the Brill-Noether theorem, and applications. The prerequisites for the book are a strong undergraduate algebra course and a working familiarity with basic point-set topology. A course in graduate algebra is helpful but not required. The book includes appendices presenting useful background in complex analytic topology and commutative algebra and provides plentiful examples and exercises that help build intuition and familiarity with algebraic varieties.

Lectures on Poisson Geometry (Paperback): Marius Crainic, Rui Loja Fernandes, Ioan Marcut Lectures on Poisson Geometry (Paperback)
Marius Crainic, Rui Loja Fernandes, Ioan Marcut
R2,172 Discovery Miles 21 720 Ships in 12 - 17 working days
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."

How to Fall Slower Than Gravity - And Other Everyday (and Not So Everyday) Uses of Mathematics and Physical Reasoning... How to Fall Slower Than Gravity - And Other Everyday (and Not So Everyday) Uses of Mathematics and Physical Reasoning (Hardcover)
Paul J. Nahin
R779 R597 Discovery Miles 5 970 Save R182 (23%) Ships in 12 - 17 working days

An engaging collection of intriguing problems that shows you how to think like a mathematical physicist Paul Nahin is a master at explaining odd phenomena through straightforward mathematics. In this collection of twenty-six intriguing problems, he explores how mathematical physicists think. Always entertaining, the problems range from ancient catapult conundrums to the puzzling physics of a very peculiar material called NASTYGLASS-and from dodging trucks to why raindrops fall slower than the rate of gravity. The questions raised may seem impossible to answer at first and may require an unexpected twist in reasoning, but sometimes their solutions are surprisingly simple. Nahin's goal, however, is always to guide readers-who will need only to have studied advanced high school math and physics-in expanding their mathematical thinking to make sense of the curiosities of the physical world. The problems are in the first part of the book and the solutions are in the second, so that readers may challenge themselves to solve the questions on their own before looking at the explanations. The problems show how mathematics-including algebra, trigonometry, geometry, and calculus-can be united with physical laws to solve both real and theoretical problems. Historical anecdotes woven throughout the book bring alive the circumstances and people involved in some amazing discoveries and achievements. More than a puzzle book, this work will immerse you in the delights of scientific history while honing your math skills.

Liutex and Third Generation of Vortex Definition and Identification - An Invited Workshop from Chaos 2020 (Hardcover, 1st ed.... Liutex and Third Generation of Vortex Definition and Identification - An Invited Workshop from Chaos 2020 (Hardcover, 1st ed. 2021)
Chaoqun Liu, Yiqian Wang
R5,235 Discovery Miles 52 350 Ships in 10 - 15 working days

This book collects papers presented in the Invited Workshop, "Liutex and Third Generation of Vortex Definition and Identification for Turbulence," from CHAOS2020, June 9-12, 2020, which was held online as a virtual conference. Liutex is a new physical quantity introduced by Prof. Chaoqun Liu of the University of Texas at Arlington. It is a vector and could give a unique and accurate mathematical definition for fluid rotation or vortex. The papers in this volume include some Liutex theories and many applications in hydrodynamics, aerodynamics and thermal dynamics including turbine machinery. As vortex exists everywhere in the universe, a mathematical definition of vortex or Liutex will play a critical role in scientific research. There is almost no place without vortex in fluid dynamics. As a projection, the Liutex theory will play an important role on the investigations of the vortex dynamics in hydrodynamics, aerodynamics, thermodynamics, oceanography, meteorology, metallurgy, civil engineering, astronomy, biology, etc. and to the researches of the generation, sustenance, modelling and controlling of turbulence.

Essentials of Tropical Combinatorics (Paperback): Michael Joswig Essentials of Tropical Combinatorics (Paperback)
Michael Joswig
R2,159 Discovery Miles 21 590 Ships in 12 - 17 working days

The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universitat Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using $\texttt{polymake}$.

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.

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