Abstract Books

Peter J. Cameron's "Introduction to Algebra" is exactly that, an introduction to algebra and a good one at that. I must confess that before reading this book had a very limited knowledge of abstract algebra however with a little bit of time and effort I am now quite comfertable with the subject thanks to this book.

"Algebra" is divided into a 8 sections:
1) Set Theory and Relation Theory
2) Ring Theory
3) Group Theory
4) Vector Spaces
5) Modules
6) Numbers
7) More Rings and Groups
8) Galois theory and coding theory

This book succeeds by having an interesting writing style, not being dry, and at the same time being very rigorous. The rigor is always present and all proofs are carefully developed however the "feel" of the subject is never lost as Cameron strives to help the reader grasp the "shape" of the algebraic structures that he introduces.

This book has a slightly wider scope than many introductory algebra books however it succeeds in covering all of its topics well although the sections on category theory and algebraic geometry are only a page or two long and thus are only present to whet the reader's interest. In addition, Cameron motivates the discussions by drawing the topics together in the end in the applications chapter. This chapter covers the basics of the commonly known Galois theory and the less covered Coding theory which is one of the backbones of the internet.

Final: Buy this book for a good introduction. I have borrowed a number of other introductory books from the university up the hill but this one was the clearest for me.

A nice thing about the new edition is the greatly expanded preliminary chapter which covers most of what a good advanced high school algebra course contains, plus a bit more. Depending on the reader's background, this may be very valuable. Also, this book is surprisingly lightweight (literally), which is good for those of us who carry around a lot of books in our backpacks.

This book presents an excellent introduction to the subject, but also goes beyond that, presenting with a fair amount of the detail the theory of Priestley representation. The excercises start at the basic level of checking the understanding of definitions, allowing the reader to build confidence out of the practice. The fact that Priestley herself co-authored it is definitely a plus.

A set with, at minimum, one binary operation is a groupoid. If a situation involves an equivalence relation or some sort of symmetry, some sort of groupoid applies. If the set has, at minimum, two binary operations, and one operation distributes over the other, you have a ringoid. Ringoids, which include the real field we all use every day, tell us much about number systems.

Let there be a groupoid. Denote its single binary operation by concatenation. Let that operation commute and associate. So far, we have a commutative semigroup. Now add idempotency, so that AA=A. With that seemingly trivial axiom we turn a corner, farewell the groupoids, and find ourselves among the semilattices.

Now let there be two binary operations, + and *, that commute and associate. Moreover, assume that A*(A+B) = A = A+(A*B). A*A=A=A+A is now an easy theorem. What you now have is a lattice, of which the best known example is Boolean algebra (which requires added axioms). More generally, most logics can be seen as interpretations of bounded lattices. Given any relation of partial or total order, the corresponding algebra is lattice theory. Nevertheless, far fewer mathematicians specialize in lattices than in groupoids and ringoids.

Davey and Priestley has become the classic introduction to lattice theory in our time. Sad to say, it has little competition. It is a bit harder than I would prefer, and the authors do not say enough about the value of lattice theory for nonclassical logic. Their book is a classic nonetheless, and here's hoping that Gian Carlo Rota was right when he said that the 21st century shall be the century of lattices triumphant.
Lattice theory is largely due to the work of the American Garrett Birkhoff, writing in the 1930s. He gets my vote for the
greatest American mathematician of all time.

This book is one of the best Joan Mitchell books I have. However, I found it for much much cheaper than 100 dollars. If you can locate a cheaper copy, I would recommend buying this book. The color plates are very good.

The other book that compares is the Whitney Museum book:

The Paintings of Joan Mitchell (Whitney Museum of American Art) by Jane Livingston

The narrative is interesting, but the main purpose for this book, at least for me, is a collection of pictures of her work. This book has the most complete collection of her work that I've found. The plates are large, beautfiul, and very well done, allowing you to see lots of detail! If you are interested in Joan Mitchell you should absolutely get this book.

This book is wonderful for beginners in K-theory of operator algebras because it also covers some fundamentals from other subjects that are needed. The proofs are always very clear. The best of it are the excercises! Very many details of K-theory and its applications become clear when you do the excercises.

This book is a rarity in mathematics - a technical book on a difficult subject that remains entirely readable, even to non-specialists. Rather than the usual 300 pages of dense text and inscrutable proofs, the author gives examples, straightforward proofs, and a writing style that borders on the (gasp!) conversational. Highly recommended, especially for non-mathematicians needing to learn K-theory. :)

I own about a thousand books,and I have been asked which one I value most,or would snatch up in a fire, on my way to safety. I would give up every book I own, if necessary, but would not relinquish this book under any imaginable circumstances.I traveled from Indiana to the Whitney for the Retrospective, and stayed all day. I purchased my copy before leaving.
In our current climate,the Kienholz' work ("Portable War Memorial" comes immediately to mind)speaks with ferocity and immediacy and is a stark critic of hypocrisy and cultural gluttony.
This book is an eternal flame.

Published at the time of the Kienholz Retrospective Show at the Whitney Museum in 1996, this book not only documents that show with over 400 illustrations (many in color), it is also a tribute to Ed Kienholz, who died in 1994. Contributions by art historians, artists, friends and most importantly, Nancy Reddin Kienholz, make up a history that spans 4 decades. It begins with Ed's solo work in the Beat Era of the 1950s and continues with the collaborative work done by Ed and wife Nancy from 1972 to 1994. Even those who are not artists cannot help but be moved by this book. The stories are interesting, often funny and always personal. From collages to life-size environments, the work is not afraid to confront issues of cruelty or to embrace the forgotten in society. Unique vision, artistry and the materials of everyday life (collected at flea markets and junk shops) combine to make art that can be quiet with despair, cry out in anguish, or even make us laugh. Considered by some as ugly, this work is never dull or without compassion. As art historian and curator Walter Hopps says on the book jacket, "The work of Edward and Nancy Reddin Kienholz has had an enormous impact on the development of contemporary sculpture." I recommend this book to anyone interested in contemporary art or social science -- or who just appreciates a beautiful book and fascinating story.

This is a great book about Lee Krasner's life and work. Many survey books leave her out so she may be unknown to some people. This book has great color plates and a lot of text which is nice. There are also nice photographs of her. It is a wonderful book for anyone who appreciates art.

Robert Hobbs' book on Lee Krasner is an excellent introduction to the life and work of this important artist. My first experience of Lee Krasner came through the film "Pollock," a biographical drama about Krasner's husband and fellow artist, Jackson Pollock. I was so impressed by Marcia Gay Harden's passionate portrayal of Krasner in the film that I sought out more information about Krasner, and found Hobbs' book.

This book is filled with full-color reproductions of many of Krasner's paintings. She brought something truly special to the abstract expressionist movement. Her work seems to evoke both the technological energy of an urban environment, as well as primal biological power.

The book also has many wonderful photographs of Krasner at many stages in her life. In his text, Hobbs discusses such subjects as the influence of Krasner's Russian Jewish heritage upon her work. This is a visually striking and thought-provoking book. My suggestion? Read the book, and see the movie "Pollock."

Morton is readable and approachable...until you come upon his allegorical poetry. Dr. Jack Dempsey has unlocked the dense stanzas of Morton. I first encountered Morton years ago and dismissed him as did almost every major New England historian. Not Dempsey. Through his scholarship 'mine eyes have been opened'. Morton loved New England in a very modern sense. His relationship to the Indians and the environment are worth studying. Morton was trained in Latin and understood the mythological figures. Morton related those ancient figures to the circumstances of the 1620's and 1630's. Morton stands in stark contrast to his neighbors twenty five miles away: the Pilgrims at New Plimoth. Adventure, Compassion, Courage...it is all there. Bravo Jack Dempsey!

Thomas Morton's life and influence on early America is under appreciated.In a very entertaining section of the book Dempsey reveals how Morton has been received during the course of our history.Dempsey brings to life the ebullient,prickly,roguish character that Morton was.I learned a great deal about the politics of colonial religious life especially as it effected Native Americans. Of course this influence is still with us today and Dempsey's exegesis on this subject is powerful and persuasive.This book is scholarly but also lots of naughty fun.

Seems to be the first book that truly begins to cover the New York Crowd with any thoroughness...would truly like to have seen representative works by all the painters covered (perhaps in a series of addenda???) Otherwise an invaluable book for reference of that most fruitful ten years in American (and perhaps world) art history.

New York School Abstract Expressionists: Artists Choice by Artists is an important contribution to the study of Abstract Expressionism. 265 artists are documented and 86 are featured. If you are like me, a bit tired of the usually featured artists of the New York School(Pollock, Rothko, Tobey, etc.) then you will be pleasantly suprised by the "Other Talented Artists" that comprised the New York School.

The starting point is the historic 9th Street Show of 1951. This is thoroughly discussed as are the subsequent New York School Artist's Annuals of 1953, 1954, 1955, 1956, and 1957. Numerous charts, posters and photographs are included, showing which artists were in which shows. Scholars have pretty much neglected these significant shows which featured the best of the "New Art".

As I stated earlier, 86 artists are featured. Each of these artists have 2 works shown (full page) and an artist's statement. The reproductions are excellent. There is also a Bio, and a listing of solo exhibitions and group exhibitions for each of these artists. An amazing amount of research and love went into this new production. You can discern that there were many "greats" in the NY School. You can see that the NY School was actually a bonafide community of artists. I will list the artists with an "A" and B" last name, just to give you an idea of the breadth of this work: Aach, Abbott, Abrams, Adams, Agostini, Albers, Albert, Albizu, Alcopley, Anderson, Andrews, Arnold, Asawa, Asher, Avery, Barber, Baziotes, Beauchamp, Beck, Ben, Benton, Biala, Blaine, Bolotowsky, Booth, Bouche, Bourgeois, Brach, Brenson, Briggs, Brooks, Brustlein, Bultman, Busa, and Button.

This 393 page book was sumptuosly printed and has a 12" x 9 1/2" format. It has a black cloth binding and a handsome dust jacket with ALL the names of the NY School artists. This silver dust jacket has black and red lettering which pops-out and is a stunning tribute to the artists.

I can only hope that there will be more books on these "Other Artists of the New York School of Painters and Sculptors".

If you have a serious interest in the type of scientific
research that has been conducted on mental health and
nutrition - than this compilation of research studies
is worth the big bucks.
Might be helpful in working with a physician.
If technical material overwhelmes you than this is not
the book you want...

This book contains a myriad of studies, case reports, theoretical discussions on the effects of nutrition on the major mental disorders. The author clearly points out that the book is not intended for self diagnosis and treatment. However, the ideas are so powerful that many can use some of the ideas for just that purpose. For example, ADHD children don't handle tartrazine (F&D yellow) very well. It chelates out zinc which is needed for many brain metabolic processes, including making omega-3 fatty acids available to the brain, which are also in short supply in ADHD children, in bipolar patients, in depressed patients, and alcoholics. So now we have a logical explanation why many ADHD children react poorly to food colorings and why omega-3 fatty acid supplementation doesn't necessarily help all ADHD children. Here is another one. Excess phosphorus in the diet increases aggressve behavior of ADHD children. This comes from processed meats, cheeses, and colas, among other things. The book is filled with so many mind wrenching surprises that any professional or parent who reads it with an open mind will be unable to continue with business as usual. Too bad the book didn't get published in time for Karen Carpenter. She could have increased her survival chances by simply taking a zinc supplement. After reading this book, I am convinced that the day is coming when we will be looking at today's methods of treating mental disorders and comparing it with discredited practices from a century ago. This book has changed my fundamental views of "mental" disorders which are not "mental" at all, but which are physical "central nervous system disorders."

This is an efficient and careful monograph that succeeds on many levels. Grohmann was Klee's biographer and longtime friend. He is respectful without being sycophantic, and thorough but never plodding. He uses a variety of source materials, including Klee's own writings (diaries and letters). Grohmann establishes Klee's lasting importance to art and to painting by asserting, "It is as though he were still among us, to be consulted on every problem of life and art." Grohmann's generous(40 pages, 58 illustrations) and lively essay on Klee is also charming and personal. It combines biography, criticism, a wealth of references, and thought-provoking appreciation. It's generously illustrated with photographs of Klee and his studio, plus ink, tusche, chalk, and pencil drawings, collage, watercolor, tempera, and oil paintings, a woodcut study, and etchings.

The text that accompanies the following forty color plates (a selection of paintings) is the calm, clear art criticism that Grohmann is so good at. The plates' reproduced colors are good but not great. What's best is that Grohmann is such an able teacher. He describes each painting straightforwardly, and then asks intelligent questions, suggests answers that seem well-thought-out, and inspires one to further thought and research. His friendship with Klee gave him some additional understanding of his friend's work and lifelong passions and motives.

A very worthwhile book on a great artist.

This hardback was issued by the museum when the Klee show toured the USA. It was a spectacular show that captured the essence of this 20th century artistic genius and I was fortunate enough to see the show and buy the book. Paul Klee explored just about every art style there was in his quest to develop modern art and his seemingly simplest paintings were usually his best. Klee lived an often traumatic life as well and when you are exposed to all of his works, you can easily see that quality in his paintings. I found the most eloquent ones were the ones he did as he approached his own painful death. The book does a tour de force job of covering the paintings which were in the show, which is the way the show now lives on.