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."
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."
This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.
Reviews
Find Best Price at Amazon"Hatcher will (generally speaking) lead you up to the point at which you can finish excavating his logic; at times his definitions are infuriatingly "pretty" and vague, and you will have to check other sources."
"I hate it at first, because it is not quite clearly stated as Munkres."
"The more and more algebraic topology that I learn the more I continue to come back to Hatcher for motivation and examples."
"Hatcher seems to have become the standard text for algebraic topology."
"Although others have commented that Hatcher is insufficiently rigorous or precise, I actually enjoy that aspect of his writing; he seems to know when to write a lot of math and when a pretty picture will suffice."
"The author introduces the concepts in a very clear and intuitive way, which helps a lot the reader."
"Its also free from their website, but having a paper copy I find is much better for studying."
"The book is OK if (and only if) you previously know the matter but the lack of clear definitions, the excessive reliance in reader geometrical intuition, the conversational style of demos the long paragraphs describing obscure geometric objects, etc make it very difficult to follow if it is your first approach to AT."
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 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."
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."