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Schaum's Outline of Differential Equations
by Richard Bronson
Average Customer Review: 4.0 out of 5 stars
Paperback (01 January, 1994)
list price: $16.95 -- our price: $11.53
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Reviews (9)

5-0 out of 5 stars Wonderfully written, straight-to-the-point book
Whenever I want to brush up my ODE and PDE skills, I will reach out to this one. It is like instant "stock-up", refresh my memories very fast. Good buy.

5-0 out of 5 stars Good, to-the-point, well-balanced.
I like this book a lot more than my Diff. Eq. textbook, mostly because it focuses on application rather than abstraction. Bronson does a good job of explaining the mechanisms and applications of DE, while cutting through most of the kludgy rhetoric and laborious explanations of my course textbook. The examples are straight-forward without too much of a stretch to see how they work, while the explanations are quick and to-the-point.

I would thoroughly recommend buying the Schaum's Easy Outline for DE in addition to this book, since I find the Easy Outline to be easier to pick up quickly on a first read. The Easy Outline is essentially the Outline, boiled down to the bare essentials and re-written to be easier to absorb quickly. The regular outline (this book) does a good job of filling in the gaps and providing more examples on top of the Easy Outilne.

My copy (2nd edition, current) shows an original copyright date of 1973, with another in 1994 to reflect the Library of Congress title update (the title change was minute, and not worth repeating). I was surprised by the extreme similarity between some examples in the Ouline versus those in my course textbook (carrying a 2003 copyright in its 7th edition). It makes you wonder if this is the reference for the textbook writers!

My only criticism of this book is that it is not a textbook. If it were, I wouldn't have to spend four times as much on another book which I use for not much more than the exercises. Oh, and the Outline HAS plenty of problems, both solved and not.

5-0 out of 5 stars Differential Equations-Schaum's Outline Series
I have reviewed several versions of this work in connection
with taking the course and passing the Engineering In Training
Licensure Examination. Topics; such as, valuation of parameters,
constants of integration, homogeneous and non-homogeneous
solutions, nth order equations, applications of differential
equations, equations in electric circuits and gram mixtures
in organic chemistry are all covered in considerable detail.
This work together with Boyce and DiPrima plus the professor's notes helped me to get an "A" in the course. Differential
Equations is a course requiring considerable practice to master
the various techniques. I spent between 15 minutes and 2 hours
per day depending upon the juncture point in the course.
Obviously, studying for the mid-term and final exam required
more concentrated study. Overall, this book is a gem.
You will need it to handle the various twists and turns
in the subject. It is geared toward the math major or engineering perspective so that the problems vary from simple to complex.
In this course, you cannot let the so-called grass grow
under your feet; otherwise, the pace of the presentation
will bury you in confusing details before long. ... Read more

Isbn: 0070080194
Sales Rank: 21729
Subjects:  1. Differential Equations    2. Reference    3. Study & Teaching    4. Study Guides    5. Mathematics / Calculus   


Schaum's Outline of Tensor Calculus (Schaum's)
by David C. Kay
Average Customer Review: 4.0 out of 5 stars
Paperback (01 April, 1988)
list price: $16.95 -- our price: $11.53
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Reviews (8)

4-0 out of 5 stars As an Outline...
This is not a book to learn tensor calculus from.It is an outline only, no greath depth or insight is presented.This book works perfectly as a supplement to a course in tensor calculus, or as a quick reference for the various techniques and concepts involved, provided one is already somewhat familiar with the material.It would be possible to learn the basics of tensor calculus from this book with some effort, and reflection on the implications of the concepts dealt with, however as a complete course in the subject it is insufficient, and I believe intentionally so.
The more modern aspects of tensor analysis on manifolds are largely ignored in this treatment, but also intentionally so, an approach which I found useful practically.
The book does not aim to be an all-inclusive course in the applications of tensor concepts to all areas of mathmatics, but rather a quick-reference guide supplementing more complete treatments, and as such, is largely successful.

1-0 out of 5 stars Disappointed.
This book is substandard for the Schaum's Outline Series. The descriptions for the techniques are much too brief, and as a result, it's hard to follow what's going on. The summaries are so thin that it's even difficult to learn how to do the mechanics of tensor operations, a real deficit for an outline book! I have a pretty good background in advanced math, but I don't think I could learn tensor analysis from this book. I was especially disappointed because I have had good luck with other books in the Schaum's series. I'm planning on looking for a more traditional book with more discussion and background of the different techniques.

1-0 out of 5 stars disappointing
I am surprised by the high marks given by other reviewers. The book has no insight, depth, or explanation about what tensor calculus is. It is merely a cookbook for doing some manipulations with summations over more than one index. You cannot learn tensor calculus from this shallow excuse for a book. If you want to learn tensor calculus and other advanced mathematics for physicists, pick up "Mathematics of Classical and Quantum Mechanics," by Byron and Fuller; it is the best math methods book I have ever used. ... Read more

Isbn: 0070334846
Sales Rank: 54158
Subjects:  1. Calculus    2. Calculus of tensors    3. Problems, exercises, etc    4. Study Guides    5. Tensorial Calculus    6. Vector Analysis    7. Mathematics / Calculus   


Elementary Real and Complex Analysis (Dover Books on Mathematics)
by Georgi E. Shilov, Richard A. Silverman
Average Customer Review: 4.5 out of 5 stars
Paperback (01 February, 1996)
list price: $19.95 -- our price: $13.57
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Reviews (6)

5-0 out of 5 stars Getting started in math analysis
This book by Shilov covers the fundamentals in beginning analysis(both real and complex). It has in common with Walter Rudin's book (entitled 'Real and Complex Analysis') that it covers both real functions (integration theory and more), as well as Cauchy's theorems for analytic functions. Shilov's book is at an undergraduate level, and it can easily be used for self-study. The Dover edition is affordable. Rudin's book is for the beginning graduate level, and it is widely used in math departments around the world. Both books have stood the test of time.
Comparison of Shilov with Rudin: Rudin's 'Real and Complex' has become an institution, and I have to admit I have loved it since I was a student myself, but conventional wisdom will have it that Shilov is a lot gentler on students, and much easier to get started with: It stresses motivation a bit more, the exercises are easier (some of Rudin's exercises are notorious, but I find the challenge charming--not all of my students do though!), and finally Shilov gets to touch upon a few applications; fashionable these days. But that part easily gets dated. I will expect that beginning students will enjoy Shilov's book.
Personally, I find that with perseverance, students who keep at it with Rudin's book, will end up with a lot stronger foundation. They are more likely to have proofs in their blood. I guess Shilov can always serve as a leisurely supplementary reading to Rudin.
There will never be another book like Rudin's 'Real and Complex', just like there will never be another van Gogh. But the fact that we love van Gogh doesn't prevent us from enjoying other paintings.

3-0 out of 5 stars Possibly too simple
As Shilov write in the introduction "I have tried to accomodate the interests of larger population of those concerned with mathematics" and at that he seems to do. However, the book does require some mathematical background as he appears to omit defining a few things. I believe the book would be ideal for those who want a handy reference, or an easier book when struggling with an analysis course.

However, for the more mathematically inclined readers, the problems are often too easy, and many things are proved that could be better left as exercises. For a more difficult Analysis book, I would reccomend Rudin.

5-0 out of 5 stars A wonderful text -- Highly recommended!
I purchased this book as a reference book for my first analysis course.It is very well written, and easy to follow.Dr. Shilov has a very nice way of organizing this text:He puts all the definitions at the beginning of the chapter and the subsequent sections are results of those definitions.It makes for a very quick reference.His presentation of the included proofs is also very nice.There were several occasions I found myself thumbing through it for a second perspecitve.

As far as the actual material presented, Dr. Shilov starts off with funtions of one real variable, then rather quickly generalizes to complex variables and N dimensional functions, so you'll quickly see metric theory and some topology.He does keep in mind this is intended for undergrads and first year grads though.

Oh, another nice feature is the price!I'd recommend this book to any math enthusiast as a reference, or to someone going through an early analysis course. ... Read more

Isbn: 0486689220
Sales Rank: 120397
Subjects:  1. Calculus    2. Mathematical analysis    3. Mathematics    4. Science/Mathematics   


Differential Geometry
by Erwin Kreyszig
Average Customer Review: 4.0 out of 5 stars
Paperback (01 June, 1991)
list price: $14.95 -- our price: $10.17
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Reviews (10)

3-0 out of 5 stars Very bad book
If you want to study differential geometry for the first time, I would recommend the book "Differential geometry of curves and surfaces", by M. do Carmo, instead of this one. I bought Kreyzig's book for self-study but gave up after a few weeks. I then bought do Carmo's book and felt relieved that it was totally different from Kreyzig's.

Kreyzig's book has several issues, especially when compared to do Carmo's book: it is too small for the number of topics it deals with, it has few exercises and the notation is cumbersome. Part of these issues is probably due to the fact that this book was first published in 1959, and though I have seen older math books which haven't fallen behind, this one seems to have suffered from this. It took me a lot of time to understand some of the sections because of the bad notation, and the lack of some good exercises contributed to this problem. The book does cover the standard material that is expected of it and has a reasonable number of exercises, but, still, the exposition is very bad, and you get the feeling that the book could have been much better.

Despite the (important) fact that it costs about 10 times less than do Carmo's book, I strongly recommend that you save your time and enhance your learning by buying do Carmo's book instead.

5-0 out of 5 stars Agree -- one of the best; elegant; beautiful
I had been seeking a book on differential geometry for self-study, as a preface to learning general relativity. A seasoned mathematics friend recommended Kreyszig.

So, I waded in, and patiently made my way through every page of the first six chapters, working the problems along the way, at a pace of a few pages per day.Now that the journey is behind me, I can say that I appreciated this book. It compares favorably to some other texts I had tried reading, with less success.

I realize that the author's approach is an old-style classical one, with a reliance on specific coordinate systems and transformations between coordinate systems.To work the problems requires a fair amount of paper and pencil work.Nonetheless, this approach worked well for me. On those occasions when my reading bogged down, inevitably there was a good reason. If I went back carefully, re-read and pondered, doodled on paper, and tried to visualize what Kreyszig was describing, it always worked!The light would soon go on, usually with a pleasurable sense of discovery.

I went back to re-read certain sections of the book to refresh my memory, and realized how elegant the writing is.Crystal clear, right to the heart, and always trustworthy. Everything follows in a gentle persuasive way; there are no jarring leaps or gaps.

Additionally, I had a nice sense of the different flavor brought to the field by the French geometers who made many of the key advances around the turn of the 19th-20th century.

Finally, the summary of key results and equations at the end is very smart and helpful.

Since finishing Kreysig, I did find it helpful to push on and try to grasp these same ideas from the standpoint of one-forms and the coordinate-free approach to tensors. But I'm not sorry I came at the subject this way first.

I do recommend this book, and think that a beginner needs only a moderate amount of stamina and patience here.

A postscript -- the book is also beautiful. I like that in a math book.

5-0 out of 5 stars One of the best
Good, thorough, self-contained.Spend a little more time on the first three chapters, and the understanding will follow.What can I say?Just rush out and get it! ... Read more

Isbn: 0486667219
Sales Rank: 85091
Subjects:  1. Geometry - Differential    2. Geometry, Differential    3. Mathematics    4. Science/Mathematics    5. Mathematics / General   


Fundamentals of Complex Analysis for Mathematics, Science And Engineering (2nd Edition)
by E.B. Saff, A.D. Snider
Average Customer Review: 4.0 out of 5 stars
Hardcover (10 February, 1993)
list price: $98.00
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Reviews (2)

4-0 out of 5 stars Good Introductory Book
This was the book that I learned Complex Analysis from. Definitely made the subject accessible to pretty much any reader. Plenty of exercises: some more theoretical, some more applied. It skillfully straddles the gap between being a theoretical math book and a math book for people with more applied aims (such as engineers). Most topics are covered thoroughly, though certain more complicated subjects such as winding number are left out for simplicity.

This book definitely prepared me for tackling the dense, theoretical, and exceptional "Complex Analysis" by Ahlfors. I'd recommend it as an introductory book for anyone trying to get into the subject who is intimidated by Ahlfors, as well as for anyone who is only interested in the essential commonly-applied tools.

4-0 out of 5 stars down to earth book for people like you and me
I have just finished a class using this book, and on the whole its done a good job.I didn't find it in any way super special or anything, but I could read it and understand it.As far as math books go that is pretty good. Lots of exercises with answers in the back, which is what you need.Usually there are worked out examples of the most standard problems, but not always, e.g. there is no example of residue calculus with a Log function. ... Read more

Isbn: 0133274616
Sales Rank: 459562
Subjects:  1. Applied    2. Engineering - General    3. Functions Of Complex Variables    4. Mathematical Analysis    5. Mathematics    6. Science/Mathematics   

Schaum's Outline of Linear Algebra
by SeymourLipschutz, MarcLipson
Average Customer Review: 3.5 out of 5 stars
Paperback (06 December, 2000)
list price: $16.95 -- our price: $16.95
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Reviews (12)

1-0 out of 5 stars too many wrong solutions
too many wrong solutions and typo~~~~
I don't recommend ppl buy this study guide!!!
This book confused ppl even more!!

5-0 out of 5 stars Good for all science/Linear Algebra courses and exams
This study aid provides information about all possible content on linear algebra courses. I passed all algebra tests with the help of this and other nessecary books. Everyone should have material such as this piece. Not only do I reccomend this book, but it also works for everything possible. The guidelines in this book help you know the subject, and this book is easy and hard. For excellent knowledge of mathematics, natural sciences, computer science, etc. you can count on this.

4-0 out of 5 stars Very nice book for theory review
I would say that the structure of this book pleased me. I used it as a theory review for my qualifying exam in Linear Algebra. For that purpose it served quite well. It has a nice, constructive structure. It will make your knowledge organized and will not overload you with too much abstractions. Especially I enjoyed the fact that definitions and key theorems are situated separately from their proofs, that allow you to familiarize yourself with theory in general and after you know everything there, you may concentrate on the proofs to make your knowledge more sophisticated. At least this is the way how I did work with this book. As for exercises, they are not very difficult, I would say undergraduate level only, so that it is good for those who has a weak knowledge in this subject. For those who want to go beyond Linear Algebra I would suggest Kostrykin, 3 volumes, but it is in Russian ;-) ... Read more

Isbn: 0071362002
Sales Rank: 39395
Subjects:  1. Algebra - General    2. Algebra - Linear    3. Algebras, Linear    4. Linear Algebra    5. Mathematics    6. Outlines, syllabi, etc    7. Study Guides    8. Mathematics / Algebra / General   


Schaum's Outline of Discrete Mathematics (Schaum's)
by SeymorLipschutz, MarcLipson, Seymor Lipschutz, Marc Lipson
Average Customer Review: 4.0 out of 5 stars
Paperback (01 June, 1997)
list price: $16.95 -- our price: $11.53
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Reviews (4)

3-0 out of 5 stars Not a 5 star!
I waited several weeks for this book to arrive, and was disappointed to see that its 'just another maths book', nothing special. I didn't find this book any easier to understand than any other maths book, I ended up refering to my other book more.

2-0 out of 5 stars Too Simple
I bought this book to help me survive my Discrete Math class, and ended up thoroughly disappointed. It's just too simple to be of any use. The examples it goes over are the obvious ones I've never had any trouble with, but more involved problems or complex proofs are nowhere to be found in the text. In the end I ended up relying on my course text much more than this, and I already had that book to begin with.

5-0 out of 5 stars Overall, a good study aid
This study guide goes over all the topics you would expect it to and explains them more clearly than most texts can. I recommend this to all who plan to take a course in Discrete Mathematics. ... Read more

Isbn: 0070380457
Sales Rank: 17334
Subjects:  1. Algebra    2. Algebra - General    3. Algebra, Abstract    4. Combinatorial Analysis    5. Discrete Mathematics    6. Logic, Symbolic and mathematic    7. Logic, Symbolic and mathematical    8. Mathematics    9. Outlines, syllabi, etc    10. Study & Teaching    11. Study Guides    12. Mathematics / General   


Number Theory with Computer Applications
by Ramanujachary Kumanduri, Christina Romero
Average Customer Review: 4.0 out of 5 stars
Hardcover (04 August, 1997)
list price: $102.00 -- our price: $102.00
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Reviews (2)

3-0 out of 5 stars Riddled with errors
A good intro to Number Theory for non-mathematicians. (Specfically, excellent for anyone who wants to pick up cryptography.)
However, the numerous errors found throughout the book take away from it's impact. Not to mention some outdated algorithms in Chapter 5.
A lower price would make this a better buy.

5-0 out of 5 stars Excellent
This is a wonderfull book for people looking to combine their math skills with technology.The book also is easy to follow and understand for those with no computer skills. ... Read more

Isbn: 013801812X
Sales Rank: 429937
Subjects:  1. Computer-assisted instruction    2. Mathematics    3. Number Theory    4. Science/Mathematics    5. Theory Of Numbers    6. Mathematics / Advanced   


Elementary Number Theory and Its Applications (4th Edition)
by Kenneth H. Rosen
Average Customer Review: 4.5 out of 5 stars
Hardcover (06 January, 2000)
list price: $119.60 -- our price: $119.60
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Reviews (6)

5-0 out of 5 stars Good foundational text for Cryptography
I bought this book as a supplemental study guide - my course was a mix of Number Theory, Abstact Algebra, Finite Fields and Probablility (pre-requisites for Cryptography study).The professor used lectures with hand-written supplements as primary study media.

I found this text to be well-written, each concept was dealt with separately and concisely, then later assimilated with others to form broader ideas.Even though the text is directed at Number Theory,many of the other related concepts I studied were mentioned or covered in this text.

This book will stay on my bookshelf for quite a while.

4-0 out of 5 stars Very helpful resource
I'm currently taking a Discrete Mathematics class that is a stew of number theory, abstract algebra and probability.

This books has been very helpful as a reference as my professor teaches the course from his own lecture materials that often do not provide enough examples or coherent explanations.

The chapters on cryptography add a welcome flavor to the material.

4-0 out of 5 stars Very helpful for the Learning Undergraduate
This books gives an excellent background to elementary number theory. I've found this book gives lots of examples, theorems that are helpful with interesting excercises. What I do find frustrating is that here and there the methods given are innefficient compared to what my proffesor teaches in class. As well some of the proofs are written as one giant run on sentance, and written line by line. This is VERY hard on the eyes and totally annoys me. ... Read more

Isbn: 0201870738
Sales Rank: 315557
Subjects:  1. Advanced    2. Applied    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. Mathematics / Advanced   


Introduction to Analysis (2nd Edition)
by William R. Wade
Average Customer Review: 3.5 out of 5 stars
Hardcover (06 July, 1999)
list price: $102.67 -- our price: $102.67
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Reviews (7)

3-0 out of 5 stars An irritating book.
The strongest point of the book is the exercises.They force you to reread and understand the proofs and they build a foundation for material that is to come.

Chapter 1 (2nd edition) need a complete rewrite.How can you obfuscate something as simple as the Archimedean property in all its forms?Chapter 8 on Euclidean spaces needs to be better integrated with what the student should know from the first linear algebra course.

The author's proofs are not clear and I found myself rewriting many of them in my own words or turning to other references.

The core chapters 2-7 and 11-13 are fine - especially if you buy the approach of doing analysis first in R and then doing it a second time in R^n.This may be especially appropriate in an environment where most of the students are future high school teachers and will only take 1 advanced calculus course.

There are an unusual number of typos in the second edition. They are no longer accessible on the author's website.But hey, the 3rd edition is available, just throw out the 2nd and get the latest.

4-0 out of 5 stars Nice intro, but could use some improvements
I used this book for my first analysis course.Over all, I think it does a nice job, but it could use a little tweeking.Let's start with the good...

First off, Wade understands the difficult time most students have with the transition from the early calculus courses to the higher, more abstract classes.Several proofs in this text are a little more drawn out than in others, and this is to aid the in the understaning of the art of proof writing (and it really is an art).

Another think I liked is the variety of exercises.They range from relatively easy to rather difficult (I was unable to solve some...).

Now for the bad...

I really didn't like the layout of some of the material.Especially in chapter 1.He states a definition, and then it's results.Another definiton will be thrown in along with more results.Especially in chapter 1, it would be nice if all the definitions and axioms are put into one place, and the results to follow in a later section (Shilov does this, and I used his book a lot as well during the course).I find that referencing definitions that are organized in such a fashion much nicer.

If you're a budding mathematician, and would like to get a better understanding of analysis, I'd feel confident about adding this one to your collection.

5-0 out of 5 stars Wonderful book on Analysis
One of the best and clearest book on analysis of all times. Modern introduction. I would like to havea solutions manual so it would be perfect for self study. ... Read more

Isbn: 0130144096
Sales Rank: 437277
Subjects:  1. Mathematical Analysis    2. Mathematics    3. Science/Mathematics    4. Mathematics / Calculus   


Elementary Classical Analysis
by Jerrold E. Marsden, Michael J. Hoffman
Average Customer Review: 3.5 out of 5 stars
Hardcover (15 March, 1993)
list price: $108.95 -- our price: $108.95
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Reviews (9)

3-0 out of 5 stars Don't see why its used in so many classrooms
I am currently taking a course in analysis, and our instructor is using this book as his primary teaching material. I have to say that I am not impressed with this book at all. There are parts where the author goes to great lengths explaining things that seem may evident (to me at least) for any student familiar with calculus, and then there are times I feel helplessly lost in his lack of explanation. The only positive thing about this book is its excercises and problems, they are placed strategically in the book, meaning that the easier problems and the hard ones are placed in the book appropriately. The easy problems inject confidence for beginners while the tougher ones will, no doubt, challenge even the most confident students.

2-0 out of 5 stars Not So Hot.
Unevenly written. Full of typos. Some sections, like the one describing types of matrices, are so incompetently worded as to defy complete comprehension, even with repeated readings. Although some of the coverage of topological material is good, overall the informal explanations don't really do much to supplement the rigorous proofs -- they're just sort of... verbose. Not recommended. (Instead, try "Yet Another Introduction to Analysis" by Victor Bryant, as a fine introduction to the subject.)

5-0 out of 5 stars An excellent introduction to Real Analysis
Marsden and Hoffman have done an admirable job combining clarity and rigor in a book appropriate to the level of an advanced undergrad class at a good university. The organization and tone of the work set it apart from the alternatives. The authors proceed from lesser rigor to greater within each chapter, presenting definitions, theorems, and worked examples before the proofs, which are placed at the end of each chapter. The authors address this somewhat unusual organization in their introduction:

"We decided to retain the format of the first edition, which gives full technical proofs at the end of each chapter but presents some idea of the main point in the text. This seems to have been well-received by the majority of readers... and we still believe that it is a sound pedagogical device for a course like this. It is not meant as a way to shun the proofs; on the contrary it is intended to give to views of the proof: on in the way working mathematicians think about it, (the trade secrets, so to speak), and the other in the way mathematicians write out formal proofs."

Marsden Hoffman is written in a slightly more conversational tone than other rigorous introductions to analysis. However, as a math major at Stanford, I felt like this only made the text more readable.

A side note: Though Marsden and Hoffman do make light of Cantor's quaint, 19th century definition of a set in their intro to set theory, they ultimately do so only to motivate the exposition of a formal, axiomatic view. ... Read more

Isbn: 0716721058
Sales Rank: 371655
Subjects:  1. Mathematical Analysis    2. Mathematics    3. Reference    4. Mathematics / General   


Introduction to Logic
by Patrick Suppes
Average Customer Review: 5.0 out of 5 stars
Paperback (01 May, 1999)
list price: $14.95 -- our price: $10.17
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Reviews (1)

5-0 out of 5 stars Not too introductory, but excellent
I recommend this book to philosophy students who study philosophical logic and wish to get into mathematical logic. The system of natural deduction he uses is not explained in much detail, but as long as you have learned at least one system of natural deduction and perhaps even the tree method of proof, you should be fine. His definitions and explanations of terms and of how one develops logical rules are excellent and explained very well. There is also a treatment of informal proof methods that mathematicians use, a section on basic set theory, and a section on axiomatizing scientific theories--the latter hinting at some of Suppes' own philosophical ideas. ... Read more

Isbn: 0486406873
Sales Rank: 426498
Subjects:  1. General    2. Logic    3. Mathematics    4. Science    5. Science/Mathematics   


Logic, Semantics, Metamathematics
by Alfred Tarski
Average Customer Review: 5.0 out of 5 stars
Paperback (01 January, 1981)
list price: $29.95 -- our price: $29.95
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Reviews (1)

5-0 out of 5 stars Truth and ConseqenceBoth Defined in One Book
This book collects seventeen classic papers on logic, semantics and metamathematics authored or co-authored by the late Alfred Tarski (1901-1983), who is considered to be one of the five greatest logicians of all time (the others being Aristotle, Boole, Frege, and Gödel).Tarski is as famous for his contributions to philosophy as for his contributions to mathematics.His most important contributions to philosophy are two definitions in which he proposes characterizations of concepts that are central to our understanding of the axiomatic method and, more generally, of rationality.In 1933 he published an essay in Polish giving a mathematically precise definition of TRUTH and building the axiomatic foundations on which this definition rests.This truth-definition paper, which has been translated into many languages, may well be the most important paper in philosophical semantics, if not in analytic philosophy broadly considered. This article alone is worth the price of the book. Its 120-page length qualifies it to be regarded as a monograph, not just as an article.It has spawned a huge literature and it continues to be studied not only as an historic breakthrough paper but also as a source of fresh ideas.A revised and corrected version of a 1956 English translation of the truth-definition paper appears in this book in its entirety.In 1936 he wrote two 10-page papers sketching a mathematically precise definition of logical CONSEQUENCE (needed to define validity of arguments), one in German for international readers and one in his native Polish.This book contains an English translation of the German version.This is the only publication of the English translation of the entire Tarski truth-definition paper and it is also the only publication of the original English translation of the German-language consequence-definition paper.Tarski's definitions of truth and of consequence employ the tools of modern mathematical logic in order to characterize classically accepted concepts.They were not intended to displace classical concepts with modern constructions.Accordingly both are based on comprehensive knowledge of the relevant parts of Western philosophy going back to Aristotle and on a deep appreciation of modern mathematics, a field to which Tarski had already made important contributions on his own and in collaboration with acknowledged masters such as Banach and Kuratowski.As Tarski emphasizes in his 1969 "Scientific American" article "Truth and Proof", just as truth, which is ontic and objective, is a precondition for proof (or demonstrative knowledge), which is epistemic and to an extent subjective, consequence is an ontic and objective precondition for inference, which like proof is epistemic and inescapably subjective.Without an understanding of truth and consequence it is impossible to understand proof.Included is an editor's introduction indicating "how Tarski's development of the conceptual framework of the methodology of deductive science can be traced through the articles in this volume". The volume ends with a nearly forty-page analytical index which greatly facilitates use of this work as a reference book on logical terminology. ... Read more

Isbn: 091514476X
Sales Rank: 100191
Subjects:  1. Logic    2. Logic, Symbolic and mathematic    3. Logic, Symbolic and mathematical    4. Philosophy    5. Semantics (Philosophy)   


Sets, Logic and Categories (Springer Undergraduate Mathematics Series)
by Peter J. Cameron
Paperback (05 March, 1999)
list price: $44.95 -- our price: $44.95
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Isbn: 1852330562
Sales Rank: 516154
Subjects:  1. Categories (Mathematics)    2. Category Theory    3. Logic    4. Logic, Symbolic and mathematic    5. Logic, Symbolic and mathematical    6. Mathematics    7. Science/Mathematics    8. Set Theory    9. Mathematics / Logic   


Mathematical Methods in Linguistics (Studies in Linguistics and Philosophy)
by B.H. Partee, A.G. ter Meulen, R. Wall
Average Customer Review: 5.0 out of 5 stars
Paperback (30 April, 1990)
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Reviews (1)

5-0 out of 5 stars Not Just for Linguists
Mathematical Methods in Linquistics is far more about mathematical methods than about linguistics, although in many places linquistics is used as a source of examples.

Instead it covers such mathematical topics as sets (including infinite sets), relations, a good deal of mathematical logic,
automata (up to turing machines), the lambda calculus, lattices and more.

This would be an excellent book for an advanced undergraduate or graduate student in either mathematics or computer science to use
either as a review text, or as a study guide for further investigation. ... Read more

Isbn: 9027722455
Sales Rank: 312233
Subjects:  1. General    2. Language    3. Language Arts & Disciplines    4. Language Arts / Linguistics / Literacy    5. Linguistics    6. Logic    7. Mathematical linguistics    8. Language Arts & Disciplines / Linguistics   


Introductory Real Analysis
by A. N. Kolmogorov, S. V. Fomin
Average Customer Review: 4.5 out of 5 stars
Paperback (01 June, 1975)
list price: $15.95 -- our price: $10.85
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Reviews (22)

3-0 out of 5 stars Are all Silverman's "translations" like this one?
First, let us be precise in reviewing this book. It is NOT a book by Kolmogorov/Fomin, but rather an edited version by Silverman. So, if you read the first lines in the Editor's Preface, it states, "The present course is a freely revised and restyled version of ... the Russian original". Further down it continues, "...As in the other volumes of this series, I have not hesitated to make a number of pedagogical and mathematical improvements that occurred to me...". Read it as a big red warning flag. Alas, I would have to agree with the reader from Rio de Janeiro. I've been working through this book to rehash my knowledge of measure theory and Lebesgue integration as a prerequisite for stochastic calculus. And I've encountered many results of "mathematical improvements" that occurred to the esteemed "translator". Things are fine when topics/theorems are not too sophisticated (I guess not much room for "improvements"). Not so when you work through some more subtle proofs. Most mistakes I discovered are relatively easy to rectify (and I'm ignoring typos). But the latest is rather egregious. The proof of theorem 1 from ch. 9 (p.344-345) (about the Hahn decomposition induced on X by a signed measure F) contains such a blatant error, I am very hard pressed to believe it comes from the original. That book survived generations of math students at Moscow State, and believe me, they would go through each letter of the proofs. Astounded by such an obvious nonsense, I grabed the only other reference book on the subject I had at hand, "Measure Theory" by Halmos. The equivalent there is theorem A, sec. 29 (p.121 of Springer-Verlag edition), which has a correct proof.
For those interested in details, Silverman's proof states that positive integers are strictly ordered: k1Unfortunately, I don't have the Russian original. Instead, I'm trying to get the other, hopefully real translation, "Elements of the Theory of Functions and Functional Analysis". BTW, this is the actual title of the original, not "Introductory Real Analysis". Which apparently is causing significant confussion amoung past and present readers. To give you a background info, the Russian original is (or has been, at least) used as a textbook for a third-year subject for (hard-core) math students. Meaning, in the preceding two years they would complete a pre-requisite four-semester calculus course. For example, criteria of convergence of series and their properties is an assumed knowledge in presentation of Lebesgue integral. So, I think most of the critique from earlier reivews is a bit misdirected. The original book is a great starting book into functional analyis/Lebesgue integration and differentiation, but proofs require solid understanding of fundamentals of calculus.
The best part about Kolmogorov's text is the clarity of conceptual structure of the presented subject a reader would gain, if he/she puts some effort. You would gain a thorough understanding, not just a knowledge of the subject. There is quite a difference between the two, and not that many authors succeed in delivering that.
But to gain that from Kolmogorov, I would suggest the other, "unimproved" but real, translation.

3-0 out of 5 stars Not so "introductory"
This textbook has several major virtues: it is dirt cheap, it is concise, and it touches on many advanced topics. Unfortunately, it has equally major flaws.

Many of the "proofs," especially in the first few chapters, are simply vague outlines of proofs. New notation is introduced without formal definition, terminology is used sloppily (sometimes even inaccurately), and explanations are invariably terse.

Before reading each chapter, I found it was necessary to first consult a more down-to-earth text. Sometimes I got the impression that the authors were more interested in showing off their brilliance than teaching me about analysis.

If you want to learn analysis, I would recommend first working through Rudin's Principles of Mathematical Analysis, then using this book as a source of challenging problems and interesting remarks.

2-0 out of 5 stars Siverman spoiled Kolmogorv
This is one of many Dover's book where the editor Silverma tryed to ''improve'' the original version of a book.

Not having the stature of the authors, the editor failed to understand that no one should try to mess with other's people book. ... Read more

Isbn: 0486612260
Sales Rank: 39839
Subjects:  1. Algebra - General    2. Calculus    3. Functional analysis    4. Functions    5. Mathematics    6. Mathematics / General   


Elements of the Theory of Functions and Functional Analysis
by A. N. Kolmogorov, S. V. Fomin
Average Customer Review: 5.0 out of 5 stars
Paperback (17 February, 1999)
list price: $14.95 -- our price: $10.17
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Reviews (10)

5-0 out of 5 stars It's a classic
I own the book in Spanish language. Some content in the book is not easy stuff, if you study by others books, but Kolmogorov has the gift to make easy things that aren't quite so easy. Perhaps some theory is "old", because all the new books use some diferent approach to the subject, like the chapter dedicated to the Lebesgue integral, the book give the definition of a simple function in a different manner that we use today. The book is a must to have in your library, when you need to work with Functional Analysis.

5-0 out of 5 stars Four stars for the content, five stars for the price.
This book is not quite up-to-date, but still very good as a starting point in (functional) analysis. The virtue of Kolmogorov and Fomin is their user-friendly writing style. I am delighted to find their book being available for less than ten dollars.

5-0 out of 5 stars My math master
I am electrical eng who study math all of my life. I had the Arabic version of it which cover more than the Englishone.I start reading it after Krewsiq book of advance functional analysis. I really like Krewsiq because it is so easy so I cover itwithin 1 year but I need 2.5 year to finish off this one which isfantastic, I really can't compare it with other books, it is a school of functional analysis and master book that you can'treally understand functional analysis without it. ... Read more

Isbn: 0486406830
Sales Rank: 28295
Subjects:  1. Calculus    2. Functional Analysis    3. General    4. Mathematics    5. Science    6. Science/Mathematics    7. Mathematics / General   


Principia Mathematica
by Alfred North Whitehead
Average Customer Review: 4.0 out of 5 stars
Hardcover (01 June, 1962)
list price: $675.00 -- our price: $675.00
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Editorial Review

Could it be true that Whitehead and Russell's Principia Mathematica is the most influential book written in the 20th century?Ask any mathematician or philosopher--or anyone who understands the impact these fields have had on modern thinking--and you'll get a short answer: yes. Their goal, to set mathematics on a firm logical foundation, was revolutionary, and their tools and rigor continue to influence modern professionals. Using Peano's symbolic logic, they formalized axioms and produced theorems (including the famous "1 + 1 = 2") in orderings, continuous functions, and other areas of mathematics.

Although the Principia is far from comprehensive, Whitehead and Russell's method and program captivate their readers. The audacity to hope to formalize all of mathematics logically was inspirational and helped to give great boosts to math and logical philosophy. Though Gödel proved in 1931 that any such program is doomed to incompleteness, the tools found in and developed from the three volumes helped build the atomic bomb and the Internet. It may not be summer-vacation reading (for most), but Principia Mathematica will reward the dedicated student with a deeper understanding of how we got here. --Rob Lightner ... Read more

Reviews (15)

1-0 out of 5 stars ludicrously quixotic work
I have not read this book.I tried, having been fascinated by logic and mathematics since high school, but it has absolutely nothing to offer most people.in fact I find it hard to believe anyone has ever read this book.The 4 and 5 star reviews on this page should be taken as evidence there are some people out there with very different taste from mine, and I bet yours. In fact I have difficulty believing they are serious.

I think only a fanatic could enjoy reading this book, certainly not a budding mathematician.If you are attracted by a book that proves 1+1 = 2 somewhere after 100 pages, this is the book for you!

I admit I have been surprized before at what some people find interesting, but the idea that anyone would pay 5 or 6 hundred dollars for the set!the publishers seem to me to be sniffing glue.(I have a PhD in mathematics, a mathematical library costing thousands of dollars, and tried to read this work at Harvard as a young math student.)

To call this book influential, is to me really ridiculous, since I suspect few people have even looked at it in the last half of the 20th century, nor would want to do so at any length, in my opinion.

But don't take my word for it, go to your scientific library and check it out for yourself.You might like it, but I seriously doubt it.I did not intend to review this book, but some of the reviews here really defy belief.I could not let them pass without comment.

One must assume those reviewers here are serious who praise it, but I suggest almost no mathematics student need give it more than a passing look.The review that stated something like "if you do not already know you want this book, then you do not"is pretty accurate.

OK, a quick re reading of reviews here shows many of them say truthfully that this book is only appropriate fora very small group of readers.However I would suggest that group does not even include most mathematicians.The ones who like it are apparently philosophers, and some are the sort who resort to calling people stupid who disagree with them.

5-0 out of 5 stars A Hallmark in the History of Mathematics and Philosophy.

Much nonsense has been said on the subject of the importance of Principia Mathematica by people ignorant of the history of mathematics and logic. Principia Mathematica together with Frege's Grundgesetze der Arithmetik is the book which gives birth to modern logic. It is absurd to assume that Russell and Whitehead intended their axiomatization of mathematics as a guide to learn the subject, as one reviewer thinks, in fact what they tried to show was that the whole of mathematics could be deduced from a small stock of premises and inference rules and using only notions of first order logic and set theory. In doing this they were following a trend in mathematical thought in the late XIX century, that of introducing more rigour to the subject, they intended to do this by demonstrating that the derivation of mathematics needed only logic (think of Weierstrass, Dedekind, Cantor, Frege). From a philosophical standpoint they also did it to rebut the intuitionist views of Kant and Poincare as well as certain opinions regarding truth coming from British Idealism (think of Bradley). Of course there are much more rigurous treatises on logic, but they would have been impossible without PM because PM was the first thorough treatment of this subject-matter and, indeed, the first book to use the modern day notation. As another reviewer pointed out, Godel's proof would've been impossible without Principia; someone first needed to show that you could reduce mathematics to logic to a great extent (Russell and Whitehead were aware that their treatment used certain axioms unprovable within the system, like the axiom of infinity, but were hopeful a solution would be found, Godel found it, it was a negative solution, there could be no complete system PM like). This book together with Frege's gave birth to modern logic, it gave a tremendous boost to research in set theory, it influenced the presentation of modern mathematics to the extent that every student has to learn about sets at the beginning of a mathematics course, it showed also the scope of the deductive powers of logic and axiomatic systems which made possible the revolution in computers and AI. It developed an influential and responsive philosophy of mathematics, perhaps the most influential of the XX century. In it Russell's superb theory of descriptions, a cornerstone in logic and philosophy, is applied with success. This theory is tremendously important in logic through its use of quantification to break up much more complex expressions revealing their true logical form. In philosophy it provided a theory which would prove immensely useful and important in epistemology, metaphysics and the philosophy of language. Russell's paradox ( regarding those sets of sets which are not members of themselves) is disposed through ramified type-theory, now obsolete in logic (though not in computer science), because, thanks to it, other ways to avoid the paradox were developed, think of Zermelo-Fraenkl or Ramsey's simple type theory. Carnap, Hilbert, Weiner, Ramsey, Quine, Wittgenstein, Turing, Tarski, Godel etc were, as thinkers, tremendously influenced by it. In short, this work is one of the greatest achievements in the history of thought, its importance for mathematics, logic, philosophy (linguistics also) and computer science is first rate, suffice to say that none of these studies would be as advanced as they are now, or as complex, or in the same direction were it not for Russell and Whitehead's groundbreaking scientific work. Of course, like Newton's Philosophia Naturalis Principia Mathematica it is now, because the subjects it initiated are today tremendously advanced, mostly of historical interest, however, for the philosophers at least, Russell's introduction still holds great philosophical interest and rigourous arguments helpful in the contemporary debate. For more details check out Ivor Grattan Guiness's great works on the history of mathematics, logic and set theory.

5-0 out of 5 stars A spoiler!
The denouement in which we discover that the Vicarwas murdered by the Butler, in the Conservatory, with a Candlestick was weak. But the sex scenes, on pages 183 - 879 were the most sensitive yet erotic that I have ever read (except for page 1334 of the "Catalogue of Insects, Arachnids and Marsupialsvol XXIV").

Top work, Whitehead and Russell! I eagerly await volume 4. ... Read more

Isbn: 052106791X
Subjects:  1. General    2. Logic    3. Mathematics    4. Science/Mathematics    5. Mathematical foundations    6. Philosophy of mathematics   


Applied Fourier Analysis (Harcourt Brace Jovanovich College Outline Series)
by Hwei Hsu
Paperback (01 October, 1984)
list price: $19.95 -- our price: $19.95
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Isbn: 0156016095
Sales Rank: 719595
Subjects:  1. Fourier Analysis    2. Mathematical Analysis    3. Study Guides   


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