Best Differential Geometry
Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field. A noteworthy feature of the presentation is that dynamical systems, which are introduced in the second chapter, are used systematically to illustrate concepts and as a source of applications.
Reviews
Find Best Price at Amazon"Each of the 9 chapters of the book offers intuitive insight while developing the main text and it does so without lacking in rigor. The first 6 chapters (which deal with manifolds, vector fields and dynamical systems, Riemannian metrics, Riemannian connections and geodesics, curvature and tensors and differential forms) make up an introduction to dynamical systems and Morse theory (the subject of chapter 8)."
"This joyful aspect of the book was achieved by the authors by setting the advanced material of differential geometry and topology as if on a “mobile bridge” or a “crossroad” that associates a(n) (primarily) unfamiliar abstract part of the text with elementary math theories. Besides the basic theory, centered around analytical properties of manifolds (mostly endowed with additional, in particular Riemannian, structures and vector or tensor fields defined on them) and their applications, it also provides a good introductory approach to some deeper topics of differential topology such as Fixed Points theory, Morse theory, and hyperbolic systems throughout the rest of the book."
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Reviews
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Over 36,000 copies sold worldwide Accessible, practical yet rigorous approach to a complex topic--also suitable for self-study Extensive update of appendices on Mathematica and Maple software packages Thorough streamlining of second edition's numbering system Fuller information on solutions to odd-numbered problems Additional exercises and hints guide students in using the latest computer modeling tools. Includes fully updated computer commands in line with the latest software Barrett O'Neill is currently a Professor in the Department of Mathematics at the University of California, Los Angeles.
Reviews
Find Best Price at Amazon"I think that after working through this book a student will be well prepared to take on a more advanced book like Riemannian Geometry by do Carmo or Differential Geometry by Kuhnel."
"This book is not like new, but very new."
"An excellent intro to diffy geo."
"The book was difficult in areas, but I think it covers the subject area well."
"Great book, fast shipping!"
"In fact, all the subsequent geometry is based on pullbacks and pushforwards.This itself motivates the more abstract definition of a differentiable manifold with its coordinate charts. Chapter 2 describes the language of frame field and connection forms and derives the Frenet-Serret equations in terms of moving frames and structure equations. After reading this book, one would be equipped to handle do Carmo's book on Riemannian geometry, or O'Neill's book on Semi-Riemanninan geometry, or the more recent book by Lee, again on Riemannian geometry."
"The original second edition (from 1997) contained numerous typos, but luckily, the revised 2006 issue takes care of these and also streamlines the section numbering formats which had made the referencing and following through with the material a bit cumbersome. As some of the other reviewers have mentioned, the emphasis here is on the low (= 2 and 3) dimensional geometry, formulated in the language of differential forms (Cartan's early 20th century approach). The appendices include help on using popular computer algebra systems (with updates in the latest revised edition), and another appendix providing solutions to many of the odd-numbered exercises in the book. Afterwards, one can certainly continue the study of the essentials by reading other advanced material such as William Boothby's "An Introduction to Differentiable Manifolds and Riemannian Geometry"."
Best Topology
Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology.
Reviews
Find Best Price at Amazon"In particular, it was great for self-study as Mendelson doesn't shy away from fully fleshing-out proofs and repeating relatively similar cases with some additional notes (e.g. when going from metric to topological spaces and proving several ideas there)."
"You'll find that the results from problems you solved are used to develop the theory in later chapters. Pure mathematics is difficult and solving problems takes some time even if you are very bright. On average it probably takes me 5 or 6 hours to solve all the problems within a section, which in my opinion is fairly quickly. With 6-8 sections per chapter and 30-50 problems/chapter, even if you are solving the problems at a very fast pace of say 30 min/problem on average. There are like 5 or 6 chapters in the book or something like that and my calculations do not account for the time to work through the proofs and read each chapter. I would argue that the other reviewers commenting on time required to complete this text are either already familiar with the material, not working all of the problems at the end of each section, or not delving into the material with the depth that it really requires."
"You will need of course, a previous knowledge of mathematics to understand the great part of this book, but this is topology, ones of the fields more difficult in mathematic, even the more easy handbook will seem very high abstracted book if you doesn't know anything about theory of sets and functions."
"Intended for the advanced undergraduate student with a respectable level of mathematical maturity, Mendelson begins with the necessary review of set theory."
Best General Geometry
Generations of readers have relished Polya's deft—indeed, brilliant—instructions on stripping away irrelevancies and going straight to the heart of the problem. The traditional mathematics professor who reads a paper before one of the Mathematical Societies might also learn something from the book: 'He writes a, he says b, he means c; but it should be d.' " --E. T. Bell, Mathematical Monthly "[This] elementary textbook on heuristic reasoning, shows anew how keen its author is on questions of method and the formulation of methodological principles. "Every mathematics student should experience and live this book" -- Mathematics Magazine. "In an age that all solutions should be provided with the least possible effort, this book brings a very important message: mathematics and problem solving in general needs a lot of practice and experience obtained by challenging creative thinking, and certainly not by copying predefined recipes provided by others. John H. Conway is professor emeritus of mathematics at Princeton University.
Reviews
Find Best Price at Amazon"I'm a math professor and this has completely changed the way I approach my lectures."
"Good condition, needed for class."
"The chapters related to the methodology should be included in any course of algorithm design."
"The only reason I subtracted a star was because I found the text difficult to parse, which slowed down my reading."
"Good book for learning how to solve mathematical problems, wish I had this 30 years ago in HS."
"It will very useful to mathematicians, physists, and engineering students, as well as professors in making."
"There is a reason that this book has been in print for decades."
Best Analytic Geometry
This all-in-one-package includes more than 1,100 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 30 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! 1,105 fully solved problems Concise explanations of all calculus concepts Expert tips on using the graphing calculator. Frank Ayres Jr., PhD , was a professor and a department head at Dickinson College in Carlisle, Pennsylvania.
Reviews
Find Best Price at Amazon"Awesome practice problems for calculus students."
"Excellent, like all Schaumburg outline books in math."
"paper quality is extremely poor."
Best Algebraic Geometry
What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. In Prime Obsession , John Derbyshire deals brilliantly with both Riemann's life and that problem: proof of the conjecture, "All non-trivial zeros of the zeta function have real part one-half." Though the statement itself passes as nonsense to anyone but a mathematician, Derbyshire walks readers through the decades of reasoning that led to the Riemann Hypothesis in such a way as to clear it up perfectly. Prime Obsession offers alternating chapters of step-by-step math and a history of 19th-century European intellectual life, letting readers take a breather between chunks of well-written information. Derbyshire treats the hypothesis historically, tracking increments of progress with sketches of well-known people, such as David Hilbert and Alan Turing, who have been stymied by it.
Reviews
Find Best Price at Amazon"I bought this book together with "The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics"."
"I bought the book because of the political and current events writing of Derbyshire are always meaty , informative and original."
"The math required is limited to 2d semester calculus, tho' it helps immensely to have had real and complex analysis, some number theory and abstract algebra."
"Naturally, he had to omit some of the more mathematically sophisticated details, including questions of convergence, how to extend the domain of the zeta function from the series definition, and how exactly you calculate the zeros of the zeta function."
"It compares favorably to the other popular books on the same topic because it takes the trouble to SHOW the deep beauty of the Riemann hypothesis by laying out the mathematics in some detail, while always keeping the explanations accessible to the thoughtful layperson."
"The hypothesis was first introduced by Bernhard Riemann's paper "On the Number of Prime Numbers Less Than a Given Quantity" in August 1859. "If either...or...could have proved the truth of the [Riemann] Hypothesis, the PNT would have followed at once...They couldn't of course...The PNT [could] follows from a much weaker result...: All non-trivial zeros of the zeta function have real part less than one." Riemann Hypothesis is similar to the above weaker result: all non-trivial zeros of the zeta function have real part one-half."
Best Non-Euclidean Geometries
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Reviews
Find Best Price at Amazon"I've been researching Ethereum for 2 weeks before reading this book."
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"Excellent, concise and easy read intended for those desiring an introduction to ether technology."
"The book covers a lot of ground with regards to Ethereum and its token Ether."
"A good primer for understanding the difference between bitcoin and ethereal and what reverential is for smart contracts."
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"Great conceptual overview for someone who doesn't know anything about Ethereum."