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."
* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation. "The book is a real treasure trove of nontrivial elementary key concepts and applications of complex numbers developed in a systematic manner with a focus on problem-solving techniques. The problems are embedded in the text throughout the book, partly as illustrations to the discussed concepts, partly as the testing grounds for the techniques just studied, but mostly I believe to emphasize the centrality of problem solving in the authors' world view.... The book is really about solving problems and developing tools that exploit properties of complex numbers.... "This book is devoted to key concepts and elementary results concerning complex numbers. the targeted audience is not standard and it ‘includes high school students and their teachers, undergraduates, mathematics contestants such as those training for Olympiads or the William Lowell Putnam Mathematical Competition, their coaches, and any person interested in essential mathematics." The reader learns how complex numbers can be used to solve algebraic equations and to understand the geometric interpretation of complex numbers and the operations involving them. A special feature of the book is the last chapter, a selection of outstanding Olympiad and other important mathematical contest problems solved by employing the methods already presented. The target audience includes undergraduates, high school students and their teachers, mathematical contestants (such as those training for Olympiads or the W. L. Putnam Mathematical Competition) and their coaches, as well as anyone interested in essential mathematics.
Reviews
Find Best Price at Amazon"When I first started reading the book it looked like a typical math book with the kind of math proofs that I hated in high school and college."
"Anyway, I would recommend this book to anyone who wants to take complex analysis because a lot of us don't have enough knowledge about complex numbers but the complex analysis class is based on the assumption that we are already masters of it."
"The theory of complex numbers is built up in black and white, no frills (i.e. don't expect to find any silly historical notes or color pictures typical of modern textbooks) and I have a feeling that the reader who even thinks about buying this book would prefer it this way."
"The aim of this book is to stimulate young people to become interested in mathematics, to enthuse, inspire, and challenge them, their parents and their teachers with the wonder, excitement, power, and relevance of mathematics. As stated. by the authors, the targeted audience is not standard and it "includes high school students and their teachers, undergraduates, mathematics contestants such as those training for Olympiads or the William Lowell Putnam Mathematical Competition, their coaches, and any person interested in essential mathematics." An important feature of this marvelous book is that. it presents a wide range of problems of all degrees of difficulties, but also. that it includes easy proofs and natural generalizations of many theorems in elementary geometry. Chapter 3 is devoted to the applications of complex numbers in solving problems in Plane and Analytic Geometry. This chapter also includes a marvelous theorem known in the mathematical. folklore under the name of "Morley's Miracle" and which simply states that "the three points of intersection. of the adjacent trisectors of any triangle form an equilateral triangle"."
"Goes over the basics of complex numbers from A to Z and is absolutely loaded with examples and practice problems."
"Comprehensive and yet concise enough to cover lots of material."
"This is a complete work about complex numbers."
Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included.Differential geometry, as its name implies, is the study of geometry using differential calculus. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. Differential geometry, as its name implies, is the study of geometry using differential calculus. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. An algebraic geometer by training, he has done research at the interface of algebraic geometry, topology, and differential geometry, including Hodge theory, degeneracy loci, moduli spaces of vector bundles, and equivariant cohomology.
Reviews
Find Best Price at Amazon"There were a few texts that tried to "bridge the gap" so-to-speak, namely the five-volume opus of Spivak and the excellent text of Taubes, but there was a distinct need for a text that could take someone from knowing zero differential geometry, to someone that knows the equivalent of a few good courses in the subject."
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 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 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."
Best Non-Euclidean Geometries
Do you want to know more about the technology that could convert centralized systems across thousands of services into open source, decentralized networks? Unlike Bitcoin, Ethereum is still largely unknown to those who don’t keep up with the cryptocurrency world, so the amount of information available is limited or highly technical. More and more Fortune 500 companies are investing in Ethereum technology as it becomes increasingly lucrative and poises to change business processes as we know them. The book is designed for those who are new to cryptocurrency, but want to invest in it or learn more about it, as well as for more experienced traders looking to expand their portfolios. This book will help you make your own investment decisions and decide if Ethereum is the right coin for you after weighing up the pros and cons that are presented here. Ethereum’s technology is only at the beginning of its potential growth stages, possibly reaching to dozens of industries and thousands of services. Ikuya is now a Cryptocurrency expert & enthusiast with an impressive Cryptocurrency portfolio and investments in several Bitcoin & Ethereum startups.
Reviews
Find Best Price at Amazon"I've been researching Ethereum for 2 weeks before reading this book."
"I liked reading this book."
"This is an awesome book on Ethereum."
"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."
"I really appreciated how easy it was to read this book and all the information it had."
"Great conceptual overview for someone who doesn't know anything about Ethereum."
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."