Reviews (14)

hard analysis
trip., the traditional british oxbridge exam. questions, compareable to the euro. olympia math. questions, it is the hard analysis includeing the elementary functions, the sequel step is whittaker's special functions, it is very important when it is a century ago. preparation to this are pure math. of green, gow, tranter, in important british colony, some school teacher write the solutions. therefore for learning hard analysis pure math., it is very important to collect trip. oxbridge exam. questions.

An Enduring Classic
G. H. Hardy was one of the greatest mathematicians of the 20th century.When the first edition of this book appeared in 1908, it was the only comprehensive introduction to analysis in the English language.Nearly a century later, it remains unsurpassed in that genre in any language.
Hard Core Math
This book is very hard core. I bought it to help with the math in Penrose's Road to Reality. Which is really hard core. So now I need a math book to help with the math in this book. As far as my ability allows I fully agree with the other 5 star reviews of this book.
Read more

Subjects:  1. Calculus    2. Functions    3. Mathematical Analysis    4. Mathematics    5. Mathematics (General)    6. Probability & Statistics - General    7. Science/Mathematics    8. Mathematics / General   

Reviews (66)

this is THE calculus book
in a word, this book is awesome. if i were omnipotent, i would make it required reading for all beginning math majors. it is used in the honors calc course at my university, which i did not have the fortune of taking--but i have worked through the book in combination with ross's elementary analysis, all by way of preparation for tackling the wonderful baby rudin. and in that task i feel it has prepared me exceedingly well. i love just sitting down and reading this book on a rainy day, like spivak is right there talking to me. i love his quotes at the beginning of sections, and his suggested reading could easily provide years if not a lifetime of enjoyment and discovery. absolutely the best textbook i have ever read.
are you a maths major?
If you are a frosh or sophomore who is facile in maths, and wants to major in maths or the physical sciences or engineering, you might want to choose a maths course that has this book as its text.
Mathematics with emotion
There are hundreds, even thousands, of books on Calculus. The good thing is that you can always find one that is best suited for your way of learning, and teachers always know which are best for their courses. The bad thing is that there are so many to choose that one ocasionally doesn't know how to start. I will not say that Spivak's book is the greatest or the worst (as many reviews do), because this is mostly a matter of taste. I will, instead, say what is different in Spivak's book from the other many calculus books that I know. Spivak's book reads as a romance. Indeed, you can be completely taken by his prose, and see the battle for arriving at the concepts in a rigorous, yet flexible, manner. Spivak sees calculus as the evolution of one idea - as he says in the preface to the first edition. And everyone who reads this book with attention understand what is this idea - I will not tell, not say who is the murderer of this romance. Will you finish this book and be a master of calculus? Will the exercises help? This depends mostly on you, as mathematics is, for the most, only understood when you create it in your mind, when you retrace every important step of this human endeavour inside of you. There are easier books, that's true. For those who want just to be able to use calculus, perhaps there are better ways. But Spivak succeeds to do one very difficult thing, that is, to explain mathematics, all its beauty and all its harmony, to a reader that possibly never really understood it. For one thing is to make calculations, learn how to solve equations and the like, but another thing very different is to understand what is mathematics about. To my knowledge, only Courant wrote in such passionately manner - and Spivak is clearly a follower of Courant's way of thinking. The difference between Courant and Spivak is that Courant is more worried about the applications of calculus, and Spivak is more worried about the essence of it (it doesn't make too big a difference, as both are, in a sense, the same thing told in two different ways). There is something that is really fantastic in this book: Spivak usually discuss with a lot of care the evolution of one idea since scratch up to its refined description in mathematical language - see how he arrives at the rigorous definition of a function. He also criticises the notations, and this is pretty useful to understand the concept behind the notation. If you are able to love mathematics (many people aren't), you will with the greatest probability appreciate this book. ... Read more

Subjects:  1. Calculus    2. Mathematics   

Reviews (1)

A pretty good book
While the table of contents is very good, too much time is wasted in developing preliminaries. The text should quickly move into the core of the subject, but instead spends 220 pages developing the elementary material. A good reference for teachers of discrete mathematics with emphasis in combinatorics and not in computer science. ... Read more

Subjects:  1. Advanced    2. Combinatorial Analysis    3. Combinatorics    4. Computer Science    5. Computers    6. Discrete Mathematics (Computer Science)    7. Mathematics    8. Science/Mathematics    9. Applied mathematics    10. Mathematical theory of computation    11. Mathematics / Advanced   

Reviews (21)

Great Book!
This book is great.I used it for a second course in linear algebra.I can really say that I understand the subject now, which I definitely couldn't before.The material is presented in a readable and yet rigorous and abstract fasion.My only problem with this book is that it leaves so many proofs to exercises and doesn't give the answers to most exercises.

blows you away
This book blew me away! it's just great, it really explains everything (also an axiomatic approach of determinants which is very important to gain a thorough understanding of what determinants actually mean and which will help you when you are going to study multilinear algebra, exterior algebras in abstract algebra etc), the book gives you a good insight in the stucture of linear operators on a finite-dimensional vector space and provides lots of examples and useful applications (e.g. in economics and physics). There was a comment of one customer which criticized the fact that the theory doesn't offer an explanation of quotient spaces, this is true but in fact this is not important in the area of linear algebra, quotient structures should be studied in abstract algebra, when more algebraic structure has been developed so that one can really understand what quotients of algebraic structures are about. So the book is great, but I would recommend some knowledge about polynomials, fields, algebraic closure, vector space before starting to read this one.

Excellent!
I am an undergraduate taking a linear algebra course. The course does not use this book, but my friends introduced this book to me and I simply love it.
Read more

Subjects:  1. Algebra - Linear    2. Algebras, Linear    3. Linear Algebra    4. Mathematics    5. Science/Mathematics    6. Mathematics / Algebra / General   

Reviews (19)

Horrible
Reading this book is like riding on the back of a Bull. This book is horribly terrible. It is not an Introduction to Real Analysis as the author assumes the reader has familiarity with most of the topics. There are very few Examples and the worst thing about reading this book for me is coming accross the statement like "We leave it to the reader to show that ..." or another one like "We leave it to the reader to write out the detail of the proof". How can the author(s) say that and yet call the book an "Introduction" when in the real sense they take you half way and leave you there? I regret buying this book. Just looking at the cover makes my bllod pressure rise. There are few explanations, few examples and many excercises. This book is Horrible for a bigginer in Analysis. I wish I never bought this book and I will never ever buy any other book written by the same author(s).

Kohei Sato's review is absolutely correct
Reading the signs while driving on an interstate through a large city only helps if you know where you are going, what highway & exit numbers to look for. Reading this book is like being lost in a big city. It was written for people who already understand real analysis. So, if you're one of the many who begin this book with no previous experience in analysis, and you get a professor that teaches straight from the text, be prepared - you will need at least one tutor. Hopefully, the authors will consider writing a book for undergrad students, with more examples and longer homework solutions. Some of the exercises are so far removed from the text, it makes you wonder if the authors truly believed that students would be able to complete these problems. I made straight A grades through college algebra & trig, as well all three levels of calculus, yet I cannot understand anything in this book after the first chapter. If you want to learn real analysis for the first time, do not waste money on this book.

Good intro to real analysis.
This is a good book from which the neophyte can learn the ropes of mathematical analysis.It is clear, lean, to-the-point, and gives the reader a taste of what doing mathematics is like, viz, theorems and proofs.Most importantly, it does a good job of introducing the epsilon-delta method of proof to the reader, who most likely has up to this point learned mathematics as merely a collection of calculational techniques.
Read more

Subjects:  1. Calculus    2. Functions Of Real Variables    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. Mathematics / General    7. Mathematics for scientists & engineers    8. Real analysis   

Reviews (6)

Going Back to College...
I'm 35 and studying for a COMPASS test (college entrance exam for those who never took the ACT/SAT).I failed Algebra in High School, skipped classes alot, and remembered absolutely nothing, but I have a good head for numbers and logic, so I've found myself able to understand most of the concepts in this book so far.If you have no head for numbers, or feel that you aren't good with logic problems/eyeballing math questions, then you may want to also purchase the "Algebra For Dummies", as this book only *briefly* goes into each concept.
Algebra for Dummies Workbook
I have gone back to college after 20 years and need to take a College Algebra course.This workbook has been very helpful in reviewing things I went over a very long time ago and making sense out of them.I highly recommend it.

An order lost
I never recieved this book.I am still trying to get a credit from the seller ... Read more

Subjects:  1. Algebra    2. Algebra - General    3. General    4. Mathematics    5. Reference    6. Science/Mathematics    7. Workbooks    8. Mathematics / Algebra / General   

Reviews (1)

Clear & simple steps given
I used this book to challenge my Intermediate Algebra course, andI passed the exams. This book explain clearly the steps to the questions. ... Read more

Subjects:  1. Algebra    2. Algebra - Elementary    3. Algebra - General    4. Mathematics    5. Science/Mathematics    6. Mathematics / Algebra / General   

Reviews (13)

Creates astrong foundation in math
Both of our kids used Saxon from 54 to Advanced Math and physics and they have done quite well with it.Although I am not a mathematician, my husband has a degree in mechanical engineering and highly approves of Saxon's format.
I would hate to have had to learn math from this book.
I am nearing the completion of my PhD in physics at a major research university, so I have studied a fair amount of math in my day. All the math I have studied is geared toward problem solving and understanding how we can describe the world around us using mathematics. This, it seems to me, should be what we are trying to communicate to high school students. I have spent the last two months regularly tutoring a poor girl who is trying her best to learn Algebra II from this book that was inflicted upon her, and I think the book is a disgrace.
Excellence in Mathematics
I have been using Saxon mathematics for 15 years, first as a 5th-12th grade student and more recently as a tutor. This program is excellent and like one of the other reviewers I can agree that even my "average" Saxon students have significantly better mathematics skills that those students using other programs.
Read more

Subjects:  1. Algebra - General    2. Mathematics    3. Science/Mathematics   

Reviews (12)

good as a supplement to the class
This is a book that is best for final preparation for the exam.Last year, in BC Calculus, I was absent for the series and sequences lessons due to an illness and I came back for a test studying through the Barron's books and I had trouble understanding it.The tests are definitely a lot harder than the real thing.I studied my [...] off and got a 5 on the actual exam as well as a 5 on the AB subscore.

A Fair Book
This book is very comprehensive, too many details at times.The practice test is a little bit more difficult than the actual test.It is not very well organized or appealing to look.There aren't enough diagrams and pictures for visual learners.

Very helpful
I had several sources to help me do well in AP Calculus AB. One of them was this book.
Read more

Subjects:  1. Advanced Placement    2. Advanced placement programs (Education)    3. Calculus    4. College entrance achievement tests    5. Examinations    6. Study Aids    7. Study Guides    8. Test Prep    9. Calculus & mathematical analysis    10. Study Aids / Advanced Placement    11. Study guides, home study & revision notes   

Reviews (6)

Book needs more explanations and less fluff
Book needs more explanations on problems and less "Study habit reminders" and other fluffy stuff that I just skip over. What student has time to read the "extra optional stuff"?
Sometimes complex
This book covers many problems but lacks descriptive solutions. I could not get a good concept of how to solve the problems because most of the solutions were broken into several sections. This book does give some of the answers but again it does lack descriptive solutions.

I can't wait to get this book!
In my pre-algebra I and II classes, we used Martin-Gay's books.They were wonderful!They're easy to understand and follow with plenty of exercises.I was looking forward to using her books for Intermediate Algebra.I was extremely disappointed to find that the college switched to a different book...one that isn't helpful at all.I'm planning on using Martin-Gay's book along side our college textbook we now have.Hopefully, the lightbulb will be going on much quicker! ... Read more

Subjects:  1. Algebra    2. Algebra - General    3. Algebra - Intermediate    4. Graph Theory    5. Graphic Methods    6. Mathematics    7. Science/Mathematics    8. Mathematics / Algebra / General   

Editorial Review

This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity. The authors present the theory in a concise and straightforward manner, with an eye out for the practical applications. Exercises at the end of each chapter, including some that have been solved, help readers confirm and enhance their understanding of the material. This book is appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments. ... Read more

Reviews (31)

Need some challenge? Come here!
I started to learn this course at the beginning of this semester and I just brought this book from Amazon in August.
first edition is a classic, the second one unremarkable
The first edition is one of the best book in its field. A classic. A reference for many advanced courses in computer theory. Excellent introductory text, but has several weaknesses
This was my textbook for an introductory course on Finite Automata and Languages - I enjoyed it a lot and I think that the chapters until the Turing Machines are covered very well, along with good examples. As one previous reviewer has already mentioned, the exercises can get very hard as compared to what's actually presented - this I found not too good.Read more

Subjects:  1. Computational complexity    2. Computer Science    3. Formal languages    4. Logic    5. Machine theory    6. Mathematics    7. Number Theory    8. Science/Mathematics    9. Artificial intelligence    10. Computers / Computer Science    11. General Theory of Computing    12. Programming languages   

Reviews (16)

Great beginners book
My son is really getting a lot out of "How to Solve Word Problems in Algebra".He is understanding the material and applying it to his homework and tests.

Good book
I'm very happy with this book.It does just what it promises:teaches kids how to solve word problems in beginning-level algebra.I wish I'd had a book like this when I was in school.It gives detailed explanations which are easy to understand.

Good, until the last problems
If you are looking for help in understanding algebra problems then I definitely recommend this book.Inside you will find helpful hints and practice that will help you tackle a wide range of problems from distance, coins, finance, quadratics, work, numbers, etc.The Supplementary problems after each chapter are helpful, and are well explained.So if you make any mistakes in doing them you will be able to go through step by step and see where the mistake was.
Read more

Subjects:  1. Algebra    2. Algebra - General    3. Mathematics    4. Problems, exercises, etc    5. Reference    6. Science/Mathematics    7. Word problems (Mathematics)    8. Mathematics / Algebra / General   

Editorial Review

"God created the integers," wrote mathematician Leopold Kronecker, "All the rest is the work of Man." In this collection of landmark mathematical works, editor Stephen Hawking has assembled the greatest feats humans have ever accomplished using just numbers and their brains. Each of the 17 sections opens with a historical introduction of the featured author, and proceeds to a faithful translation of their most famous work. While most mathematicians will already have complete editions of Isaac Newton's Read more

Reviews (15)

Stephen's talk of stars and the Universe
During his career as a cosmologist Professor Stephen Hawking has proposed many ground-breaking theories. His theories on the origins and nature of the universe are quite complex, but Stephen believes it is important to communicate his ideas to the general public. He has written two books - A Brief History of Time, and The Universe in a Nutshell, to try to explain his ideas to everyone. Hawking is the leading scientist on Quantum Mechanics -- which he describes the behaviour of the smallest particles in the Universe. Unlike everyday objects which tend to obey predictable laws, tiny objects like atoms can behave in very unpredictable ways. Hawking's theories include -- Steady State vs the Big Bang. When Hawking was a student, most cosmologists believed in the steady state theory. The steady state theory says the universe had no beginning and will exist in the same state forever. In contrast, the Big Bang theory says that everything in our Universe (and therefore space, matter and time) began in an explosion about 15 billion years ago. This is the theory that most cosmologists agree on today. The theory of relativity was one of the most important ideas of the twentieth century. Albert Einstein realised that space and time were not independent concepts - how you measure time depends on how you are moving through space, and vice versa. He suggested that gravitational fields could bend what he called space-time. Relativity predicts that time slows down near very massive objects like Black Holes. Black Holes are large stars that have undergone total gravitational collapse and whose gravity is so great that nothing, not even light, can escape from them. The heart of a Black Hole is infinitely dense, and is an example of what mathematicians call a singularity. Singularities are points where space and time are warped so much that the laws of physics break down. Singularities occur at the heart of black holes. The Big Bang is also a singularity; before the Big Bang, time does not mathematically exist.
"The writing fingers having writ ...", In the Shoes of the "God"? - -From the Pen of Dr. Hawking .. ?!
It is no wonder that this great work has attracted so many diverse type of reviews from some of the very competent reviewers.The omissions of many good things bring to the mind the work of (Sir) Roger Penrose; really this great project pales in comparison.
Need an editor, couldn't agree more
I really want to give this book at least 4 stars as I love the idea of encapsulating those great mathematical breakthroughs in one book and giving each a proper account instead of over simplistic summaries like many other math readings do.
Read more

Subjects:  1. History & Philosophy    2. Logic    3. Mathematics    4. Science/Mathematics    5. History of mathematics    6. Popular science   

Subjects:  1. Calculus    2. Mathematics    3. Science/Mathematics    4. Calculus & mathematical analysis    5. Mathematics / Calculus   

Reviews (1)

A great reference source for advanced matrix analysis
Horn and Johnson's MATRIX ANALYSIS AND TOPICS IN MATRIX ANALYSIS are trueclassics (like Knuth's Art of Computer Programming). You will find classictheorems and lemmas in matrix theory and linear algebra here along withtheir proofs (some of these are not found elsewhere).Read more

Subjects:  1. Algebra    2. Mathematical Analysis    3. Mathematics    4. Matrices    5. Probability & Statistics - General    6. Science/Mathematics    7. Linear algebra    8. Mathematics / Algebra / General   

Reviews (3)

A confusing hodgepodge of tangential ideas
I agree completely with J. Elliott.The author states so many propositions without proof, and even the proofs given are too sketchy, forcing the reader to fill in every detail, and in many instances, the author's proofs are simply wrong.Many of his definitions are vague and confusing, in many cases bewildering the reader's mind with all kinds of tangential questions unrelated to the main topic.Paul Taylor misleads the reader with chapter titles like "Posets and Lattices" and "Cartesian Closed Categories" in which he does not stick to the topics he promises to cover but jumps all over the place into unrelated fields.It's like he wants to "introduce" the reader to so much that he has no time to explain anything.
Useful summary, poor exposition
The author's staccato writing style is reminiscent of Gilbert Strang's. Some may like it, but I find it jarring. The content is a concise summary of interesting topics at the confluence of mathematics, logic and computer science (see the table of contents), but it reads like a pr�cis for those who already know the subject. This is no doubt fine if you fall into that category. If you're looking for an expository text, this, alas, isn't it.

needs attention but worth it
this is a a good work, the section about Structural Recursion was very insightful too
Read more

Subjects:  1. Aquatic mammals    2. Behavior    3. Combinatorics    4. Congresses    5. Ecology    6. Foundations Of Mathematics    7. General    8. Mathematics    9. Philosophy Of Mathematics    10. Riparian animals    11. Science/Mathematics    12. Aquatic mammals--Behavior--Congresses    13. Mathematical foundations    14. Mathematics / Combinatorics   

Reviews (15)

A Pleasure to Read
First of let me state that I own the 2nd edition of this book, and that I am a doctoral student in computational physics.
Revolutionize the way calculus is taught
This is the textbook used for the math 223/224 Theoretical Calculus and Linear Algebra sequence in Cornell University. The book is designed for prospective math students. Although the book mainly follows a rigorous development of the theories of multi-dimensional calculus, the mathematical machinery used in developing the theories is immensely broad, especially in linear algebra. The book covers most of the standard topics in a first semester linear algebra course and touches on many other areas of mathematics such as, real and complex analysis, set theory, differential geometry, integration theory, measure theory, numerical analysis, probability theory, topology, etc. The highlight of the book is its introduction of differential forms to generalize the fundamental theorems of vector calculus. The author is not the first one who follows this path. There are many other books written before this one that have similar approach, such as Calculus On Manifolds by Spivak, which was written 40 years ago and was too old to suit modern students.
Confusing book
Math and Physics major
Read more

Subjects:  1. Algebra - Linear    2. Algebras, Linear    3. Calculus    4. Linear Algebra    5. Mathematics    6. Science/Mathematics    7. Differential equations    8. Mathematics / Calculus    9. Vector & tensor analysis   

Reviews (2)

The best introduction to probability and measure
The book very nicely develops the basics of measure theory from a probability perspective (e.g. includes Caratheodory extension theorem, Lebesgue-Stieltjes measures, weak convergence and Kolmogorov extension theorem). It then gives a brief introduction to functional analysis and proceeds to probability theory, martingales and concludes with brownian motion and stochastic integration.
Exceptionally Clear
I first used this text in the earlier version, which comprises the first half of the book, in a one-year course in Hilbert Spaces and Lebesgue Measure theory when in the first year of grad school.The material is presented in a clearly written manner and the exposition is some of the clearest mathematical writing I've seen in a subject which is replete with textbooks.Read more

Subjects:  1. Mathematical Analysis    2. Mathematics    3. Measure Theory    4. Probabilities    5. Probability & Statistics - General    6. Science/Mathematics    7. Set Theory    8. Mathematics / General    9. Probability & statistics   

Reviews (11)

Very in-depth explanations
I bought this book not because I have any interest in computational biology but because at that time I had an interest in (and professional need for) extremely fast and efficient ways to search through massive data stores.In this I was not disappointed, having found thorough treatments of how to do exact pattern matching as well as various types of "closest" match searching though very large data sets in minimal time.
nice intersection of computing and biology
The text sits at the intersection of computer science and computational biology. It centres around the observation made by the author and others that often in CS, one has to manipulate strings of text, which are just sequences of text. While in computational biology, a recurrent theme is how to deal with sequences of molecules. These might be in a DNA sample or in a protein.
What it says, it says best.
If you haven't read this book, you don't know biological string matching. The book's focus is clearly on string algorithms, but the author gives good biological significance to the problems that each technique solves. I came away from this book understanding the algorithms, but also knowing why the algorithms were valuable.Read more

Subjects:  1. Algorithms (Computer Programming)    2. Computational biology    3. Computer Books: General    4. Computer algorithms    5. Computers    6. Computers - General Information    7. Data processing    8. Discrete Mathematics    9. General    10. Molecular Biology    11. Programming - General    12. Algorithms & procedures    13. Computers / General    14. Pattern recognition   

Reviews (2)

Very Helpful Book
This book is very helpful because when someone helps me in Algebra 2, they can read me the problem out of book then I can work it out and they can tell me whether my answer is right or not or else it would take a much longer period of time because they would have to work out the problem and then tell me the answer and it may be wrong. This is the perfect book for kids who want to learn Algebra 2.

Wow!
This book is the one book people who want to learn Algebra 2 need. It completely enhanced my knowledge on the subject, and took me to a higher level. It will truly make your mind capacious! ... Read more

Subjects:  1. Algebra    2. Algebra - General    3. Algebra - Intermediate    4. Children's All Ages - Mathematics    5. Children's Books/All Ages    6. Mathematics    7. Science/Mathematics    8. Juvenile Nonfiction / Mathematics / General