Posted in Reference-Mathematics (Monday, September 8, 2008)
Written by Peter Brucker. By Springer.
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No comments about Scheduling Algorithms.
Posted in Reference-Mathematics (Monday, September 8, 2008)
Written by C. K Smoley. By C.K. Smoley.
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No comments about Smoley's tables.
Posted in Reference-Mathematics (Monday, September 8, 2008)
Written by Joseph Newmark and Frances Lake. By Addison Wesley Publishing Company.
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No comments about I/M Math Second Lang.
Posted in Reference-Mathematics (Monday, September 8, 2008)
Written by L. H. Harper. By Cambridge University Press.
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No comments about Global Methods for Combinatorial Isoperimetric Problems (Cambridge Studies in Advanced Mathematics).
Posted in Reference-Mathematics (Monday, September 8, 2008)
Written by Agnes Azzolino. By Mathematical Concepts.
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No comments about Math Spoken Here!.
Posted in Reference-Mathematics (Monday, September 8, 2008)
Written by Earle Milton Bigsbee. By Littlefield, Adams.
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No comments about Five-place mathematics tables;: With explanation of tables (The New Littlefield college outlines).
Posted in Reference-Mathematics (Monday, September 8, 2008)
By Birkhäuser Boston.
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No comments about The Grothendieck Festschrift, Volume I: A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck (Modern Birkhäuser Classics).
Posted in Reference-Mathematics (Monday, September 8, 2008)
Written by Herbert Bristol Dwight. By Dover Publications.
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No comments about Mathematical tables of elementary and some higher mathematical functions (Dover S445).
Posted in Reference-Mathematics (Monday, September 8, 2008)
Written by Ayman Badawi. By Nova Science Publishers.
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2 comments about Abstract Algebra Manual: Problems and Solutions.
- Just as long as a book has all the solutions to its problems, it will always be a good book. Otherwise, it is just plain talk.
- There are better books available. If you blindly pick up a book, I am sure that it will be better than this one.
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Posted in Reference-Mathematics (Monday, September 8, 2008)
Written by P.J. Freyd and A. Scedrov. By North Holland.
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2 comments about Categories, Allegories (North-Holland Mathematical Library) (North-Holland Mathematical Library).
- This brilliant idiosyncratic book conveys a crystalline insight into category theoretic accounts of structure. The most original aspect is the theory of relations. The approach is spartan in its simplicity. In effect we assume that each relation Rxy has an opposite (as "x is less than y" has opposite "x is greater than y") and suitably matched relations have composites (as the composite of "x is brother to y" with "y is a parent of z" is "x is uncle to z"). We make a few more assumptions none of which involve set theory, and we get a very powerful theory with applications in many situations in logic and category theory.
The main technical tool is representation theorems which in effect show how closely our abstract categorical theories capture various set theoretic ideas. It is distinctively Freyd's view of category theory, with fine contributions by Scedrov. The worst thing about it is the thoroughly private terminology. Even such standards as pullbacks get renamed here (as "levels"). So you more or less have to read the book from the start even to understand it on topics you already know. But it conveys one powerfully original and creative view of the subject, with significant applications.
- The book more than achieves its goals outlined in the preface. Not only does the book serve as an introduction to the subject, illustrate the its geometric nature and explain its connection to mathematical logic, it connects category theory to many every day concepts by giving them a rigorous yet general mathematical interpretation! For instance: relation, closure, reflection. Coming up with just the right name for a concept is important and a lot of fun. It shows how category theory is a foundation for computer science. As far as the terminology goes, I take it as being authoritative. The writing style is wonderfully economical and is replete with carefully crafted phrases that render extremely complex ideas transparent. I recommend this book for everybody. It should be required reading. The idea of representations is important. More real that an abstract ideal or a concrete realization of it is the relationship between them. Armed with the tools in this book, many philosophical questions can be disposed of.
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