Book Description

[see attached for complete text]{\it Calcolo Geometrico}, G. Peano's first publication inmathematical logic, is a model of expository writing, with asignificant impact on 20th century mathematics. Kannenberg's lucid andcrisp translation, {\it Geometric Calculus}, will appeal to historiansof mathematics, researchers, graduate students, and general readersinterested in the foundations of mathematics and the development of aformal logical language. In Chapter IX, with the innocent-sounding title"Transformations of a linear system," one finds the crown jewel of thebook: Peano's axiom system for a vector space, the first-everpresentation of a set of such axioms. The very wording of the axioms(which Peano calls "definitions") has a remarkably modern ring, almostlike a modern introduction to linear algebra. Peano also presents thebasic calculus of set operation, introducing the notation for'intersection,''union,' and 'element of,' many years before it wasaccepted. Despite its uniqueness, {\it Calcolo Geometrico} has beenstrangely neglected by historians of mathematics, and even by scholarsof Peano. The book has never been reprinted in its entirety, and onlytwo chapters have ever been translated into English. In part, thisneglect has been due to Peano's organization of the work. That is, thesection on mathematical logic bears almost no relation to the rest ofthe book, and the material there was superseded only a year after itspublication by Peano's second book.Since all but this first sectionwas generally thought to be expository rather than original work, itwas regarded lightly, if noticed at all, and ultimately all butforgotten. Only in very recent years have the book's unique meritsbegun to be recognized. ... Read more

Book Description

The effects of geometry and linear algebra on each other receive close attention in this examination of geometry’s correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.
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Reviews (4)

A useful High School Geometry book for Computer Graphics
This is essentially a high school geometry book; but with a difference - its fully linear algebra based approach. If you are a beginner in computer graphics, and want to review elements of geometry and linear algebra, you will benefit from studying through this book.

The almost four hundred pages book is remarkably readable and is very consistent at that. There are both worked out examples and exercise problems, for each section - which are very useful for self-study or revision.

If you have never had an introduction to linear algebra before, you may have to supplement this with a linear algebra book. But if you have not had a good course in elementary geometry, and your motivation is getting started with elementary Computer Graphics/CAD and the likes, this is a good book for that.

Interspersed with the subject matter discussed at a elementary level, in a useful, stimulating style are small, interesting discussions on such useful and relatively advanced topics as function spaces, fixed point theorem in affine transformation, simplices, symmetries etc. I rarely have seen any of these topics mentioned in a book aimed at this level.

Highly recommended for freshman undergraduates and those without any mathematics experience who want to start in Graphics, CAD, CAGD and the likes. Recommended also for experienced practitioners in Graphics: it is good to review the fundamentals once in a while, and a well written book that is a quick read helps at that!

Perfect for first and second year, or physicists
The basics of the very deep connection between geometry and vector spaces. If you do undergrad math you will see everything in this book during first and second year. But what this book does is fit those bits together. He does this very nicely at an introductory level. If you are not in math, but need to learn some geometryfor a physics course, this will be a useful book.

It is a formal math book, with axioms, but it is strong on motivation and has some quite amusing examples.

Keywords: tangent spaces, determinants, barycentric, linear transformations.

The best math book I have read
I have been reading many books on vector analysis, geometry, and linear algebra this year. Many of them have been good, but this book stands alone for deriving the basics of determinants, vector products, geometry, etc. in a clear and intuitive manner along with great examples. A wonderful, wonderful book.

I never thought vectors could be so interesting!
Having suffered through enough dry, pointless courses in vector algebra and analysis, this book was a genuine pleasure. Requiring no mathematical background whatsoever, Mr. Hausner makes the properties of vectors and matrices (cross-products, determinants, eigenvalues) intuitively obvious. With detailed descriptions and graphics, the science of vectors is made very clear. Further, Mr. Hausner's use of levity and practical examples makes for a very enjoyable read. ... Read more

Book Description

Professor Honsberger has succeeded in 'finding' and 'extricating' unexpected and little known properties of such fundamental figures as triangles, results that deserve to be better known. He has laid the foundations for his proofs with almost entirely synthetic methods easily accessible to students of Euclidean geometry early on. While in most of his other books Honsberger presents each of his gems, morsels, and plums, as self contained tidbits, in this volume he connects chapters with some deductive treads. He includes exercises and gives their solutions at the end of the book. In addition to appealing to lovers of synthetic geometry, this book will stimulate also those who, in this era of revitalizing geometry, will want to try their hands at deriving the results by analytic methods. Many of the incidence properties call to mind the duality principle; other results tempt the reader to prove them by vector methods, or by projective transformations, or complex numbers. ... Read more

Reviews (2)

A honeypot of sweet problems in geometry
Geometry is such a sweet science and this book is a honeypot. Ross Honsberger is one of the best in creating crafty, delightful problems. In reading this book, you will be amazed at how hard the problems appear whenstated and how simple and elegant the proofs are.
Some topics arerelatively obscure. I am sure that Honsberger is quite correct in statingthat few modern mathematicians have heard of the symmedian point of atriangle. I certainly had not. However, the level of the material is suchthat even teachers of high school geometry will be able to find somesuitable exercises. College instructors will find it essential. Problemsare given at the end of each chapter and detailed solutions are included inan appendix.
It is hard to read this book and not understand why theGreeks were so captivated by geometry. Properly presented, as is done here,it is addictive.

Published in Smarandache Notions Journal,reprinted with permission.

A great geometry book for Olympiad training!
Ross Honsberger presents the articles of modern euclidean geometric properties in a way that is easy to follow and understand.The method of proofs and development of ideas illustrate different solving strategieswhich is valuable for self-studying young students.With the help ofsimple diagrams, I found no difficulties in understanding the articles. Problems are well-graded with solutions are well-presented at the back.AMUST-READ book for students participating maths contest! ... Read more

Book Description

Written by acclaimed author and mathematician George Simmons, this revision is designed for the calculus course offered in two and four year colleges and universities.It takes an intuitive approach to calculus and focuses on the application of methods to real-world problems.Throughout the text, calculus is treated as a problem solving science of immense capability. ... Read more

Reviews (19)

solid calc book
This book is perfect if you are looking for a book that has a nice balance between theory and application.Theory is presented on an as-needed basis and there is more in the appendix if the reader is so inclined.This was an excellent book for me my freshman year and it has been a good reference for me throughout my math career.It is a nice stepping stone on the way to spivak.

Not Helpful in the Least
Another MIT student here... unfortunately not all calc. classes at MIT has stopped using this book. As a result the majority of our class is hopelessly lost... and this is at MIT!!!... now that's a testament to how bad the book is... Things aren't explained well, the examples have nothing to do with the actual problems, and without the "space wasting" graphics that so many other books have it's difficult to visualize what Simmons is talking about, and despite popular opinion visualizing what you are doing is very important to calculus. I'm relying on my HS calc book to get me through the course.

Best! ~ Best! ~ Best!
It definitly helps one who want to master Calculus or join the Calculus competiton of any kinds.

It better than "Calculus With Analytic Geometry, Seventh Edition" for it give you some useful appendixs and very simplify than it. It does not includ differential equation for as the author said that it is not useful when there is a full course on differential equation!!!

safe to say it is the best calc book that is still in print
Out of the millions and millions of textbooks out there and the thousands I have seen since recently completing grad school and teaching undergrad math for the past few years: I have found that a good book is really hard to find. Further, I was recently recommended Simmons's ODE book for a course & really liked the presentation; thus, I wrote McGraw Hill & asked for a copy any of his other books.

Further, they sent me a copy of his calc book (ISBN 0070576424) and it was a pleasant surprise. A well presented and logically order calc book. This book is not a million pages long nor does it ramble on aimlessly about things that are not necessary to the subject (for which I think many authors just put in to make there books look nice).

Simions did stick with the Late transcendental standard approach, but what I found extremely interesting is that he also pushed the tirg items back also; thus, the part one of this book (basic differentiation / integration)could feasible be used for an applied one semester course clac course ( business clac etc.,), but then on the same note all of the material is there to cover very in depth the concepts of integrating trig functions + some of the applications considered in a regular calc w/ anal geom class. Did I mention that he also has a beautiful appendix that really covers what a limit is ( delta / epsilon stuff) and also has some interesting material on functions that cannot be integrated and advanced convergence test + He has two chapters on series (which is nice because that is truly the backbone of calculus & the students need to focus more on that early rather than being pushed through & then later confused in an advanced calc course ). Then in the later chapters ( multi dim calc) he has many neat applications (derivations Maxwell's equations, Graviton laws, derivation of 3 classic PDE's etc.,) + A nice chapter on Line / Surface integral + Green's & Stokes thrms..

So to me this book has solved my problem: when teaching a course I would usually have an adopted textbook that covers most, then I would need to pull some material from somewhere else, but this book eliminates that: it covers what is needed to be a formal "adopted book for a course" but at the same time it has all kinds of neat resources & applications that I can utilize to make the course more interesting + show either applications or dive more into theory.

Thus, I would strongly recommend taking a look at this book for the course you are teaching, & if you are a student I would recommend looking at Simmions' books to study from, his ODE book is very readable + covers a lot of material & his topology book is a classic in the subject but can be read with some patients + a good understanding of introductory real analysis..

Best Textbook Ever!
This is probably the best science textbook ever written and definately the best science textbook I have used.Reading this book you actually find yourself feeling as if the author was actually concerend with educating and keeping the students interested and not just pumping out a text book.Forget a professor,this book is better than any science teacher I ever had.

Somebody mentioned that the author does not have many graphics/diagrams.That is simply becasue the book does not need them.After finding this book I realized why so many other authors dump graphics in their books.It's simply because they don't have the gift for prose that G. Finlay has.

If you want to be excited to learn about calculus buy this book.
Math/Philosophy/History...this book has it all! ... Read more

Reviews (1)

More Problems?
This is not a good book. However, I must admit that it really isn't that bad. The examples are clear, and the solutions are given, with decent explanations.

The bad thing about Calculus with this Study Guide isn'tthat it's poorly written, the bad thing is that it's practically useless.The problems are of the same type as those found in Calculus with AnalyticGeometry, and they are explained in the same dry way. In other words, theCalculus with Analytic Geometry Study Guide doesn't really help to clear upany confusion, nor does it serve as a "guide" of some sort--it'ssimply more textbook problems!

If you are having trouble with Calculuswith Analytic Geometry, the Study Guide will do you no good. There is abook, The Calculus with Analytic Geometry Student Solutions Manual thatexplains problems from the textbook. Buy the solutions manual. ... Read more

Book Description

Book Description

The basics of the theory of elliptic curves should be known to everybody, be he (or she) a mathematician or a computer scientist. Especially everybody concerned with cryptography should know the elements of this theory.

The purpose of the present textbook is to give an elementary introduction to elliptic curves. Since this branch of number theory is particularly accessible to computer-assisted calculations, the authors make use of it by approaching the theory under a computational point of view. Specifically, the computer-algebra package SIMATH can be applied on several occasions. However, the book can be read also by those not interested in any computations. Of course, the theory of elliptic curves is very comprehensive and becomes correspondingly sophisticated. That is why the authors made a choice of the topics treated. Topics covered include the determination of torsion groups, computations regarding the Mordell-Weil group, height calculations, S-integral points. The contents is kept as elementary as possible. In this way it becomes obvious in which respect the book differs from the numerous textbooks on elliptic curves nowadays available. ... Read more

Book Description

This Ninth Edition of Algebra and Trigonometry with Analytic Geometry has been improved in three important ways. First, discussions have been rewritten to enable students to more easily understand the mathematical concepts presented.Second, exercises have been added that require students to estimate, approximate, interpret a result, write a summary, create a model, explore, or find a generalization.Third, graphing calculators have been incorporated to a greater extent through the addition of examples and exercises as well as the inclusion of a cross-referenced appendix on the use of the TI-82/83. All of this has been accomplished without compromising the mathematical integrity that is the hallmark of this text. ... Read more

Reviews (4)

For mathematicians, by mathmematicians
Frankly, I found this text way too brief in its coverage of topics prior to being bombarded with questions. There isn't much good to say about this book other than providing lots of problems to work. Save yourself the money and buy a "10000 problem" text instead.

Solid math textbook
I'm a little torn on what to say about this book. On one hand, I have a huge amount of respect for this book. On the other hand, it's not an easy book to learn from.

I have no doubt that if people work through this book, they will be very knowledgable and skilled in the areas covered. It is, however, a slow, tedious, sometimes frustrating process. The authors are clearly proficient at math, but their style is pretty dry. It's a "just the facts, ma'am" approach to instruction. It would be nice to have perspective, interpretation, and helpful guidance in addition to straight math. It's kind of like reading a technical manual. I prefer a more engaging presentation.

A math book that leaves you stranded
This book is required by my college and dealing with it was the most unpleasant period of my life. Prior to using this book I used the Saxon Math Program in which each lesson contains enough information to learn the material without the help of an instructor. There is no way that you can teach yourself from this book if you don't all ready know the material, and many math professors are lazy and tell you to get the knowledge out of the book. The lesson material is too brief and the explanations are almost cryptic. The solutions manual that comes with it is supposed to have the answers to all the odd problems, but the author decided to leave out a couple of these problems in which the answer would take up a little more paper than the others, these are often the ones you need the solutions to, the book just leaves you stranded. If you have to use this book, I pity you, you better hope that you have a darn good math professor. If you don't have to use it, steer clear of it.

The Most Coherent Math BooK I Have Ever Used in School
It was well-organized without being too formatted and nit-picky. The explanations made sense and it was great for note-taking. The problems were challenging, but not so hard that it was no fun. I strongly recommend this book for use in the classroom and out of it for private use and/or review. ... Read more

Book Description

Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory. The new wave began with seminal papers by Svarc and Milnor on growth of groups and the spectacular proof of the rigidity of lattices by Mostow. This was followed by the creation of the asymptotic metric theory of infinite groups by Gromov. The structural metric approach to the Riemannian category, tracing back to Cheeger's thesis, pivots around the notion of the Gromov-Hausdorff distance between Riemannian manifolds. This distance organizes Riemannian manifolds of all possible topological types into a single connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya, Gromov and Perelman. Also, Gromov found metric structure within homotopy theory and thus introduced new invariants controlling combinatorial complexity of maps and spaces, such as the simplicial volume, which is responsible for degrees of maps between manifolds. During the same period, Banach spaces and probability theory underwent a geometric metamorphosis, stimulated by the Levy-Milman concentration phenomenon, encompassing the law of large numbers for metric spaces with measures and dimensions going to infinity. The first stages of the new developments were presented in a course delivered by Gromov in Paris, and turned into the famous "Green Book" by Lafontaine and Pansu (1979). The present English translation of that work has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices-by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures-as well as an extensive bibliography and index round out this unique and beautiful book. ... Read more

Reviews (1)

The nature of high dimensions: a geometric insight
Formally speaking, this is the second edition of a set of Paris lecture notes published by Gromov two decades ago in the French language. However, such a wealth of entirely new material has been added that in essence weare talking of a new book.

Among the additions, the bulky new chapter 31/2+ stands out, dealing with the phenomenon of concentration of measure onhigh-dimensional structures. This is a relatively recent discovery ofmodern analysis and geometry, tracing its origin to the work of Paul Levyand especially Vitali Milman. The essence of the phenomenon is that on manymultidimensional structures, every `nice' function is constant with highprobability. The manifestations of the phenomenon are many - from geometricfunctional analysis (Dvoretzky theorem) through information theory(blowing-up lemma) and probability (law of large numbers) to graph theory(superconcentrators) and topological dynamics. As Gromov stresses in hisbook, even deeper aspects of the concentration phenomenon have been longsince discovered and are constantly explored in statistical physics in thecontext of phase transitions of various kind, and some of the first knownexamples where phase transitions appear in the context of geometry havebeen discovered by Gromov himself, e.g. for hyperbolic groups. Finding andexploring more instances of phase transitions in mathematics might wellbecome a unifying heuristic principle across a large number ofdisciplines.

The mathematical setting for dealing with concentration andrelated issues is the concept of a metric space equipped with finitemeasure, what Gromov calls an mm-space. Apart from concrete objects (suchas for instance spheres and cubes), there are `higher-level' examples ofmm-spaces, for instance those whose elements are isomorphism classes ofmathematical objects themselves (e.g. Riemanning manifolds or finitelygenerated groups). This leads to a probabilistic treatment of such objects.Of course Gromov's strength is that his treatment is always concrete and henever theorizes without having particular objects and applications inmind.

It is quite safe to claim that the full range and power ofapplications of the interaction between metric and measure are yet to bediscovered, which is what makes this book so important. It is rich in openquestions and suggested new research directions, but more than that, ithelps the reader to develop a good intuitive feeling of where things aregoing these days, what things ought to be done, and what constitutes propermathematics.

Even though I unexpectedly found myself among the privilegedones who received a copy of the book as a gift from the author, I wouldhave certainly purchased it otherwise, as I firmly believe that everymathematical library in the world, be it that of a top-class University orjust a modest, lovingly selected office collection of a humblemathematician, will be wanting without a copy of the monograph underreview, which might well become one of the most important books inmathematical sciences for the early XXIst century. ... Read more

Reviews (6)

A good read for calculus
When using this book, particularly in the multivariable section,
I found that it was pretty good. A good portion of the problems are generally challenging, and one with interest in the physical sciences might find them fun to work at despite the time they take. However I have to point out that a certain degree of intelligence is expected when using this book . . . well I assume this applies to mathematics in general. However I still had to consult the Stewart calculus text for more insight on particular theorems and proofs.
Overall the book is pretty standard.

A bit of a trial by fire
I started using this book during my sophomore year of college and found it to be a bit rough. While the text does do a good job with proofs of theorems and propositions, it fails to show why calculus is important to a math/science student.

In many instances of the text, the material is explained, and the reader is assumed to have comprehended every word without second sight. Then, some of the problems are given and certain stipulations to some arrise and the reader is to assume to have known about it.

Bottom line, the book is great for those who already know, but for someone learning calculus the first time, I would suggest Larson.

Awesome book!
This book is the best book on mathematics I have ever read! very well written! May not be good for people who dont have any time to read though! ;)

It may not be YOUR book
I discovered that most people find this book great. Yet, it may not be what you are looking for if you are a person who (i) have some previous exposure to calculus, or (ii) have planned to do a major (or honours) in applied or pure mathematics. First, I have to stress that I am not saying this is a terrible book although I've giving it one star; it's terrible for some kinds of people, though.

This book would be very wordy to you if you have studied calculus in a very elementary fashion. The writers spend too much time explaining some very simple topics and easy examples. You will find this book covers everything that you need if you take calculus because you are required to do so or you just want to know how to compute derivatives and integrals. However, the theory is either treated poorly or even omitted. For example, the topic on convergence and divergence of improper integral is useless, or you can consider that "it's not there". The most serious omission of topic is the absent of binormal in differential geometry; quoting my instructor, "...the book pretends that binormal doesn't exist, but it's in fact very important."

The books will give you the impression that calculus is easy, as it is said by many instructors; but in fact it doesn't have to be easy. I suppose the book will be very helpful for students seeking the basic calculus for applications in social sciences and economics, but it will not be good if you are in physical science or engineering, and certainly don't even read a word from it if you're in mathematics.

this book changed my life
i was given this book when i was in the 7th grade. it took me 3 or 4 readings to finally grasp all the concepts, but i learned all of elementary calculus from this one text. it is very complete, it covers ever topic thoroughly, except Diff Eqs. due to this book, i began taking college math courses while in high school, and am going off to graduate school next year for math and physics. ... Read more

Book Description

This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometrical images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry.

Well-illustrated with more than 350 figures--reproduceable using the Maple programs in the book--the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, many of the programs can be downloaded from the author's website.

Aimed at a broad audience of students, instructors of mathematics, computer scientists and engineers who have a knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource or self-study reference. With over 100 stimulating exercises, problems and solutions, "Geometry of Curves and Surfaces with Maple" will integrate traditional differential and non-Euclidean geometries with more current computer algebra systems in a practical and user-friendly format. ... Read more

Book Description

The second edition featured a new chapter with a systematic development of variational problems from quantum field theory, in particular the Seiberg-Witten and Ginzburg-Landau functionals. This third edition gives a new presentation of Morse theory and Floer homology that emphasises the geometric aspects and integrates it into the context of Riemannian geometry and geometric analysis. It also gives a new presentation of the geometric aspects of harmonic maps: This uses geometric methods from the theory of geometric spaces of nonpositive curvature and, at the same time, sheds light on these, as an excellent example of the integration of deep geometric insights and powerful analytical tools. These new materials are based on a course at the University of Leipzig, entitled Geometry and Physics, attended by graduate students, postdocs and researchers from other areas of mathematics. Much of this material appears for the first time in a textbook. ... Read more

Reviews (1)

Intro to Riemannian Geom. and Geom. Analysis
Covers standard material on Reimannian Geometry. In addition: variational problems from QFT. Spin geometry and Dirac operators are explained in detail. ... Read more

Book Description

In this book the author has fulfilled the need for a descriptive geometrytextbook in which the fundamentals are presented in the same pedagogicallysound units of work, as they are usually introduced in daily presentation. ... Read more

Reviews (1)

Worst book on descriptive geometry available!
I implore all who take a course in college, high school, or other institution in Descriptive Geometry not to read this book. It reads in a doctorial level of understanding and is only a good book to understand theory rather than application. Moreover, its problems and self-test problems make learning even harder because the author fails to give specific details invaluable to understanding the problem. I give this book one star for weak illustrations and poor explanations. ... Read more

Book Description

A self-contained text for an introductory course, this volume places strong emphasis on physical applications. Key elements of differential equations and linear algebra are introduced early and are consistently referenced, all theorems are proved using elementary methods, and numerous worked-out examples appear throughout. The highly readable text approaches calculus from the student's viewpoint and points out potential stumbling blocks before they develop. A collection of more than 1,600 problems ranges from exercise material to exploration of new points of theory (many of the answers are found at the end of the book; some of them worked out fully so that the entire process can be followed). This well-organized, unified text is copiously illustrated, amply cross-referenced, and fully indexed. Slightly corrected republication of the edition published by The Macmillan Company, New York, 1969. Answers and Solutions. Tables. 394 Figures. Index.
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Book Description

The last ten years have seen rapid advances in the understanding of differentiable four-manifolds, not least of which has been the discovery of new 'exotic' manifolds. These results have had far-reaching consequences in geometry, topology, and mathematical physics,and have proven to be a mainspring of current mathematical research. This book provides a lucid and accessible account of the modern study of the geometry of four-manifolds.Consequently, it will be required reading for all those mathematicians and theoretical physicists whose research touches on this topic. The authors present both a thorough treatment of the main lines of these developments in four-manifold topology--notably the definition of new invariants of four-manifolds--and also a wide-ranging treatment of relevant topics from geometry and global analysis.All of the main theorems about Yang-Mills instantons on four-manifolds are proven in detail.On the geometric side, the book contains a new proof of the classification of instantons on the four-sphere, together with an extensive discussion of the differential geometry of holomorphic vector bundles.At the end of the book the different strands of the theory are brought together in the proofs of results which settle long-standing problems in four-manifolds topology and which are close to the frontiers of current research. Co-author Donaldson is the 1994 co-recipient of the prestigious Crafoord Prize. ... Read more

Reviews (1)

An excellent summary of Donaldson theory
This book brings together the brilliant work Donaldson did at Oxford during the early 1980s. The unique properties of 4-manifolds are clearly and concisely written out with concentration on explaining field theorieslike Yang-Mills and gauge theory with a truly firm mathematical foundation,presented in a book for the first time. A great companion for anyresearcher in the field of geometry and topology, or even loop quantumgravity! ... Read more

Book Description

This book collects invited contributions by specialists in the domain of elliptic partial differential equations and geometric flows. The articles provide a balance between introductory surveys and the most recent research, with a unique perspective on singular phenomena. Notions such as scans and the study of the evolution by curvature of networks of curves are completely new and lead the reader to the frontiers of the domain. The intended readership are postgraduate students and researchers in the fields of elliptic and parabolic partial differential equations that arise from variational problems, as well as researchers in related fields such as particle physics and optimization. ... Read more

Book Description

This book provides an introduction to Riemannian geometry, the geometry of curved spaces.Its main theme is the effect of the curvature of these spaces on the usual notions of geometry, angles, lengths, areas, and volumes, and those new notions and ideas motivated by curvature itself. Isoperimetric inequalities--the interplay of curvature with volume of sets and the areas of their boundaries--is reviewed along with other specialized classical topics. A number of completely new themes are created by curvature: they include local versus global geometric properties, that is, the interaction of microscopic behavior of the geometry with the macroscopic structure of the space. Also featured is an ambitious "Notes and Exercises" section for each chapter that will develop and enrich the reader's appetite and appreciation for the subject. ... Read more