Best Differential Geometry
Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Requiring only minimal undergraduate prerequisites, "An Introduction to Manifolds" is also an excellent foundation for the author's publication with Raoul Bott, "Differential Forms in Algebraic Topology."
Reviews
Find Best Price at Amazon"It's a very nice text."
"i think there is a jump from ugrad analysis/alg/top etc to early grad school concepts."
"Very good and easy to get idea."
"While Munkres's "Analysis on Manifolds" is a great elementary exposition, suitable for students with limited exposure to higher mathematics and an excellent supplement/replacement for Spivak, this text by Loring Tu is a true introduction, making no demands on any previous knowledge of differential geometry, yet does not shy away from modern, fully general definitions, or the tools of analysis, modern algebra, and topology available to the contemporary mathematician. Tu considers de Rham cohomology to be an especially important construction at the crossroads of algebra, geometry, topology, and analysis, and one of his goals was to ensure that students become comfortable with calculating cohomologies of reasonably "easy" spaces after finishing this book."
"I've been able to compare this book with John Lee's Introduction to Smooth Manifolds, which seems to be one of the standard texts for an introductory geometry course."
"When I first began reading the text, I had a difficult time understanding the concepts, but the presentation of the material really laid bare all of the esoteric topics that I hadn't encountered formally before."
Coverage of the fundamental structure of geometry.
Reviews
Find Best Price at Amazon"Good quick study or quick reference tool."
"Nice laminated reference guide."
"College level.........not so good for elementary but helpful for adults."
"Very helpful - I bought this so that I can help my 8th grade daughter with her homework."
"Good reference for my middle schooler."
"My niece had such a difficult time with Geometry."
"Great review to keep on hand for my math students."
Part 2 of our coverage of the fundamental structure of geometry.
Reviews
Find Best Price at Amazon"I tutor high school and college math and wanted a straightforward study guide to recommend for my students."
"Item arrived very fast and undamaged."
"If the teacher just isn't cutting it, it's better to learn from different aids than to just give up and score poorly in the class."
"Nice laminated reference guide."
"High quality and delivered on time."
"Bought a set for Algebra, Geometry, and Calculus."
"Some good info on this sheet."
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
Coverage of the fundamental structure of geometry.
Reviews
Find Best Price at Amazon"My niece had such a difficult time with Geometry."
"Nice laminated reference guide."
"College level.........not so good for elementary but helpful for adults."
"Very helpful - I bought this so that I can help my 8th grade daughter with her homework."
"Good reference for my middle schooler."
"Great review to keep on hand for my math students."
"Bought a set for Algebra, Geometry, and Calculus."
Best Geometry
The classic Heath translation, in a completely new layout with plenty of space and generous margins. If you want your students to really grapple with Euclid, this is the edition to choose.
Reviews
Find Best Price at Amazon"The pages lay flat when the book is open which is really nice."
"I have wanted a copy of The Elements for years."
"Looking forward to learning from one of histories great textbooks."
"classic."
"If you're a math dork, then you will be happy with this."
"I only have to comment that this book deserves to be both into any student's and any mathematician's library, and not only for encyclopaedic reasons."
Best Analytic Geometry
It takes an intuitive approach to calculus and focuses on the application of methods to real-world problems. GEORGE F. SIMMONS has academic degree from the CAlifornia Institute of Technology, the university of chicago, and Yale University.
Reviews
Find Best Price at Amazon"A very good book for single variable calculus."
"good book meets my need but the cover has been a little bit weared."
"It's a very good Calculus text book."
"I ordered this book for my son."
"I-II for learning the rigorous, theoretical calculus, and Simmons book can even be a stepping-stone toward the introductory analysis (Rudin, Apostol, Pugh, etc.)."
"I've been through four different books all very rigorous, technical, and they all have the things you would expect from a calculus book. For awhile, I was so frustrated and appalled at how horrible the other calculus books are that I was entertaining the idea of writing my own calculus book. I can say now that the George Simmons book has everything I would have changed in modern books and more."
"The problems given expect you to know material that isn't presented in the book until the next chapter."
Best Algebraic Geometry
In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled “On the Number of Prime Numbers Less Than a Given Quantity.” Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it. Partly a biography of Riemann, Derbyshire's work presents more technical details about the hypothesis and will probably attract math recreationists.
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 Topology
This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Topological Spaces and Continuous Functions. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.
Reviews
Find Best Price at Amazon"Munkres does a very good job covering point set topology and introductory algebraic topology."
"nice intro for topology. 1 star for the printing of this "economy" version."
"A thorough and lucid introduction to the subject."
"Amazing and clear book!"
"Printed on cheap paper."
"Exceptional text."
"Best introductory text around for Topology."
"Just a well worded and organized book from what I have seen so far."