Reviews (3)

To long
I found this book to be long and drawn out. The chapters are very wordy and dont really get to the point.

The (Required) Undergraduate Handbook for Beginning Mathematics
"Proofs and Fundamentals" by Ethan Bloch is undoubtly one of the few books I'd say would be required when beginning (and a light refrence as you progress) the undergraduate mathematics curriculum in most US schools.
an excellent introduction to formal mathematics
This book is an excellent and thorough intorduction to the world of formal mathematics. Typically, a new mathematics student finds himself or herself picking up random mathematical concepts and techniques of proof along the way, without ever having the chance to sit down and go through the fundamentals of formal mathematics and proof. This book covers a little of everything, and has a thorough introduction to sets, functions, inverses, equivalence and order relations. There are also sections on introductory number theory, algebra, combinatorics, logic, and much more. It provides an excellent overview for the student who will be using these tools on a daily basis, for the layman who is interested in finding out what mathematics is really about, or for the seasoned mathematician who needs a good general reference book. There are also extensive and thorough sections on the construction and writing of mathematical proofs -- somthing on which many new and not-so-new mathematicians could use some improvement. ... Read more

Subjects:  1. Logic    2. Mathematical And Symbolic Logic    3. Mathematics    4. Proof theory    5. Science/Mathematics    6. Set Theory    7. Algebra    8. Mathematical foundations    9. Mathematics / Logic    10. abstract mathematics    11. proofs   

Reviews (3)

Clear explanations and fresh approach that enables real understanding
This is a lovely book, which gives a fresh and invigorating account of current developments in computability theory. Personally, I don't feel it can helpfully be compared to Cutland's computability text, as though that book supplies enough background for some undergraduate introductory courses in computability theory, it doesn't reach beyond that level. Cooper sensibly avoids using the same approach as Cutland for the area of over-lap -there would be little point duplicating an existing, in-print work- instead, he has in the early chapters given an intuitive approach to those topics which helps the reader understand what is going on under the morass of symbols which so often obscure rather than promote comprehension. Nor can much useful comparison be drawn with Hartley Roger's classic text, as the main bulk of Cooper's book is concerned with material which post-dates Hartley Rogers.
Not recommended as a starting point
The book is divided into roughly three parts: an introduction to computability theory, followed by a more advanced introduction to the theory of degrees of unsolvability and decidable theories, and finally some newer material on computation and structure.
A Unique Introduction to Computability
This book is an introduction to computability theory. It is organized in three parts, starting with basic computability theory and moving up to advanced topics, some of which cannot be found in textbooks today. Read more

Subjects:  1. Computable functions    2. Computer Science    3. General    4. Logic    5. Mathematics    6. Philosophy Of Mathematics    7. Science/Mathematics    8. Set Theory    9. Theory Of Computing    10. Mathematical theory of computation    11. Mathematics / Set Theory   

Reviews (1)

Not for an Idle Read
This book is a tough read.For starters, there is the subject matter.If you have had a traditional undergraduate training in mathematics, then talking about sets and elements with axioms that deal with functions rather than elements is a stretch.Then, there is the authors' presentation which mixes axiomatic category theory and naive set theory.The approach does motivate category theory with set theory and it does explain how set theory might be replaced with category theory but, as written, it also leaves the reader unsure which mode of thinking is required at any particular moment.This uncertainty is not likely to be fully resolved without a teacher or a second reading.You need one or the other to navigate some early chapters with knowledge gained later. ... Read more

Subjects:  1. Mathematics    2. Science/Mathematics    3. Set Theory    4. Mathematics / Combinatorics   

Reviews (1)

Up-to-date reference.
This thin book (175 pages) provides the newcomer or graduate student with an illustrated introduction to geometric measure theory: the basic ideas, terminology, and results. The author has included a few fundamentalarguments and a superficial discussion of the regularity theory, but hisgoal is merely to introduce the subject and make the standard text,"Geometric Measure Theory" by Federer, more accesible. Thissecond edition includes updated material and references, corrections, and anew chapter on soap bubble clusters.Read more

Subjects:  1. Applied    2. Calculus    3. Geometric measure theory    4. Geometry    5. Geometry - General    6. Mathematics    7. Measure Theory    8. Science/Mathematics    9. Set Theory    10. Mathematics / General   

Subjects:  1. Discrete Mathematics    2. Graphic Methods    3. Mathematics    4. Science/Mathematics    5. Set Theory    6. Combinatorics    7. Combinatorics & graph theory    8. Finte and Infinite Graphs    9. Graph Minors    10. Graph Theory    11. Mathematics / Discrete Mathematics   

Subjects:  1. Artificial Intelligence - General    2. Computer Books: General    3. Computer Science    4. Computers    5. Computers - General Information    6. Fuzzy Sets    7. General    8. Granular computing    9. Set Theory    10. Theory Of Computing    11. Computers / Artificial Intelligence    12. General Theory of Computing    13. Knowledge-based systems / expert systems   

Subjects:  1. Combinatorics    2. Discrete Mathematics    3. Fuzzy Sets    4. Fuzzy graphs    5. Fuzzy hypergraphs    6. General    7. Graph Theory    8. Graphic Methods    9. Mathematics    10. Science/Mathematics    11. Set Theory    12. Combinatorics & graph theory    13. Databases & data structures    14. Fuzzy Graph Theory    15. Fuzzy Graphen    16. Fuzzy Graphentheorie    17. Fuzzy Hypergraph Theory    18. Fuzzy Hypergraphen    19. Fuzzy Mathematics    20. Fuzzy Mathematik    21. Knowledge-based systems / expert systems    22. Mathematics / Discrete Mathematics   

Subjects:  1. Art & Art Instruction    2. Engineering - General    3. Experimental design    4. General    5. Mathematical Statistics    6. Mathematics    7. Measure Theory    8. Multivariate analysis    9. Probability & Statistics - Multivariate Analysis    10. Science/Mathematics    11. Set Theory    12. Engineering measurement & calibration    13. Probability & statistics    14. Technology / Quality Control   

Reviews (3)

Very good book
Lokenath Debnath, like many authors from India, I am finding, write solid mathematical texts.These texts tend to be well-organized, clear, and do not leave out or fail to emphasize important concepts.The proofs are easy to understand.It does not take a week just to read a few pages. Good book to teach yourself this interesting subject
I'm a statistician who has been using Part 1 of this book to teach myself the basics of Hilbert space theory. So far, I've been very pleased with it. Great and Clear
Debhath and Mikusinski used great and clear Mathematics and diagrams to explain the theory and applications. I especially like chapter seven "Mathematical Foundations of Quantum Mechanics" and chapter eight"Wavelet". This book is suitable for graduate engineeringstudents. ... Read more

Subjects:  1. Advanced    2. Applied    3. Hilbert space    4. Mathematics    5. Science/Mathematics    6. Set Theory    7. Functional analysis    8. Mathematics / Advanced   

Reviews (2)

More math books should be written like this one.
I full concur with Greenberg's review. Assimilating Potter's book is also much easier if one has had a prior introduction to mathematical logic and axiomatic set theory.
Unique blending of mathematics and philosophy
I believe one has to have some familiarity with logic and set theory in order to fully appreciate this wonderful book. Granting that, reading it was the first time I have ever read a mathematics book that I could hardly put down, it was so fascinating.
Read more

Subjects:  1. History & Philosophy    2. Logic    3. Mathematics    4. Philosophy    5. Science/Mathematics    6. Set Theory    7. Mathematical logic    8. Philosophy / Logic    9. Philosophy of mathematics    10. Philosophy | Logic & Mathematics   

Reviews (4)

All you need and more
Like the other books of the Schaum's Outline series, "Theory and Problems of Set Theory and Related Topics" provides you with hundreds of problems, which have been worked out step by step, to show you how the theory works.This is similar to a professor in college showing you the problems on the board, but these don't get erased and are much more legible. Provides essential knowledge to e-commerce security pros
This is an excellent introductory text on set theory.It provides a fast and thorough coverage of the basics in an economical, if terse, style.If you diligently go through this short 200 page book you will have a solid grasp of set theory that you can immediately use on the job. excellent book for non-mathematicians
This is THE book to learn set theory if you are not amathematician or mathematics major. Set theory is presented in a non-axiomatic manner. All the basics are covered: elementary set theory, cardinal and ordinal numbers, axiom of choice, and a brief intro to logic. The number of examples is huge. If you need examples when learning,then this is the book for you! ... Read more

Subjects:  1. Outlines, syllabi, etc    2. Problems, exercises, etc    3. Set Theory    4. Study Aids    5. Study Guides    6. Mathematics / General   

Subjects:  1. Cardinal numbers    2. Infinite    3. Infinity    4. Mathematics    5. Science/Mathematics    6. Set Theory    7. Mathematical foundations    8. Mathematics / Infinity   

Reviews (1)

Swell Book
This is a swell introduction to analysis. Plenty of good examples, with a well-ordered approach to the material. I particularly appreciated the section on the mindsets and assumptions that affect how we do mathematics. It's really helpful in seeing that mathematics is creative and intuitive, and not as bluntly algorithmic as so many high school classes seem. A quality read. ... Read more

Subjects:  1. Logic    2. Mathematics    3. Philosophy Of Mathematics    4. Science/Mathematics    5. Set Theory    6. Study & Teaching    7. Mathematics / General   

Reviews (1)

Poor refrence/class textbook. Good preview, general overview for selected topics in FOM
Having purchased this text (as part of the Springer Undergraduate Mathematics Series), I expected a decent publication. I had purchased and used their Number Theory text (Jones & Jones) and I was satisfied with the overal quality of the problem sets and the exposition.
Read more

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. Mathematical logic    10. Mathematics / Logic   

Reviews (2)

An easy and practical approach to fuzzy set theory
The book gives a clear and intuitive description of fuzzy math and its application. The discussions are done neatly and nicely. It doesn't get into hardcore math discussions very much; instead, it focuses on applications and practice. Therefore, it doesn't take much time to get the idea, and you are not bothered with very complex math proofs. The level of the theory is also limited to what needed in application. To my belief this is one of the best books for engineers and applied mathematicians.

Review about Zimmermann's Book !
This book is a kind of essential book. The growth in Fuzzy Science has showed more and more possibilities in applications of its concepts. The book shows the vast applicability of Fuzzy in details and how this new approach can be useful in domains with high degree of uncertainty. Read more

Subjects:  1. Applied    2. Artificial Intelligence - General    3. Fuzzy Sets    4. Mathematics    5. Operations Research    6. Operations Research (Engineering)    7. Science/Mathematics    8. Set Theory    9. Computers-Artificial Intelligence - General    10. Fuzzy set theory    11. Mathematics / Logic    12. Mathematics / Set Theory    13. Mathematics-Applied   

Reviews (3)

He hasn't yet given up on the 'paradoxes'
You'll notice that although GG still lists Cantor's "paradox" in his index, in the text he doesn't quite bring himself to say that there is such a thing.Why not?Because he has read Garciadiego's BERTRAND RUSSELL AND THE ORIGINS OF THE SET-THEORETIC 'PARADOXES,' which shows quite clearly that there is no such thing as Cantor's paradox, or the Burali-Forti paradox, or Russell's for that matter.The so-called "set-theoretic paradoxes" were for the most part inventions of Russell, and not a single one from the period, comes out as anything but a meaningless formulation.
Not what you might expect
I hoped that reading this book would give me a better understanding, in an historical context, of the issues involved in the controversies about the foundations of mathematics a century ago.I found this book fairly interesting, and it was a quick read, but it seems to be written for those who already have an essentially complete understanding of those issues, since the ideas themselves were addressed only tangentially.The focus of the book is much more on:who published what paper when, to what journal did he send it, who was the editor of the journal, who refereed the paper, to whom were offprints sent, in what archives can the manuscript be found, who read whose paper when, who met whom at what conference, who used what notation in writing which paper.This is very much a documentary history, and historians of mathematics will probably love it, but I am probably not the only mathematician who will not find this book completely satisfying.

The best book of its kind in existence
I have owned a copy for over a year, and not a week goes by in which I do not consult it. The 50pp bibliography alone is worth the price.
Read more

Subjects:  1. 19th century    2. 20th century    3. Advanced    4. Arithmetic    5. Foundations    6. History    7. History & Philosophy    8. Mathematics    9. Science/Mathematics    10. Set Theory    11. History of Science and Medicine, Philosophy of Science    12. History of mathematics    13. Mathematical logic    14. Mathematics / Advanced    15. Philosophy    16. Philosophy of mathematics    17. c 1800 to c 1900   

Reviews (2)

Fuzzy subjectivity
I find crisp sets problematic. Hoping to resolve some of the problems (for qualitative and comparative research) of crisp sets, I turned to this text. Ragin repeats himself time and time again in this text. Some complex topics (concentration, dilation, complex theoretical statements) receive minimal attention, leaving readers out in the cold. He fails to establish the efficacy of fuzzy sets for sufficiency or necessity. Ragin also fails to support why necessity is either valuable or possible in social sciences. I would seek to argue that necessity is virtually impossible to determine in social sciences. J.S. Mill was no sociologist. Also, when Ragin attempts to illustrate the application of fuzzy-set methods to IMF protests (chapter 10), he seems to neglect to include certain steps in the calculation of membership scores in the set with severe IMF protests. Ragin does not provide enough qualitative data to support why each country was indicated to have membership in his seven levels of IMF protest membership (p. 265). Also, when Ragin discusses assessment of fuzzy set membership (p. 165 - 171), I feel that fuzzy set membership assignment provides too much flexibility to individual researchers that severely hampers retestability (or even critical analysis) of the data. Ragin skirts the issue of researcher subjectivity when he makes statements like (p. 166, and similar statements in other portions of the text): "The steps I sketch here assume that researchers have a solid understanding of the concepts appearing in their theories and that they have an extensive base of relevant substantive knowledge as well." I certainly feel that the 'crisp-set approach' can be highly problematic, but Ragin's fuzzy-set approach does not seem to be a well-formulated answer to social scientific quandrys presented by crisp sets.

useful place to start but by no means the final story
There are two aspects to Ragin's book. The first part of the book is really an update of his general methodological program first set forth in The Comparative Method. It does add some new things to the older material and is thus worth the look. Ragin has some important points to make and deserves to be paid careful attention by social scientists of both qualitative and quantitative traditions. Read more

Subjects:  1. Fuzzy sets    2. Methodology    3. Research    4. Set Theory    5. Social Science    6. Social sciences    7. Sociology    8. Fuzzy set theory    9. Social Science / Methodology    10. Social research & statistics   

Reviews (1)

What an introductory book on combinatorics should be
Little did I expect of a book that has seemingly not garnered that much attention among professors and students (at least the lack of reviews in Amazon.com might serve as a confirming instance of that speculation), but come exam time, the book proved that such prejudice is outright foolish.Read more

Subjects:  1. Combinatorial Analysis    2. Combinatorics    3. Graph Theory    4. Graphic Methods    5. Mathematics    6. Probability & Statistics - General    7. Science/Mathematics    8. Set Theory    9. Combinatorics & graph theory    10. Mathematics / Discrete Mathematics    11. Mathematics / Graphic Methods    12. Mathematics-Combinatorics    13. Mathematics-Probability & Statistics - General   

Subjects:  1. Logic    2. Mathematics    3. Philosophy    4. Science/Mathematics    5. Set Theory   

Reviews (1)

Interesting but very uneven
The stated goal of the book is to have no prerequisites other than freshman math, but you really need at least undergrad logic and set theory. It is a thick book and covers a lot of interesting stuff, but there can be a frustrating lack of order and detail. He is an engaging writer, but sloppy in that he gives only part of the information you need to understand something, forgetting that he didn't give it or you don't know it. Sections are often either too sketchy or wordy and unfocused. Sometimes, though, he comes through with an elegant explanation of something. He is at his best when relating recursion theory to science, philosophy, and other branches of math. These discussions tend to be rather handwavy, but he gives references to the literature. The book as a whole is not very unified and it doesn't clearly indentify and relate the central ideas of recursion theory, so it wouldn't make a good introductory text. But it is a good reference for those with a moderate background. ... Read more

Subjects:  1. Information Theory    2. Logic    3. Mathematics    4. Science/Mathematics    5. Set Theory    6. Computers / Information Theory    7. Computers-Information Theory    8. Mathematics / Logic    9. Recursion theory    10. Recursivitbe, Thbeorie de la