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The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course on 'Conjecture and Proof'. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of e, the Banach-Tarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps. Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader. ... Read more

Customer Reviews (3)

A Book from Hungary, an Inventive Country, for New Ways of Thinking about Mathematical Problems
"Conjecture and Proof" is a collection of the lecture notes designed for a one-semester course in Hungary for American and Canadian students. The course was intended for creative problem solving and for conveying the tradition of Hungarian mathematics. Other purpose of the book includes showing the spirit of mathematics.

Hungary is a country well-known for inventions. Her inventions include Rubik cube, fuel injector, helicopter, stereo, television, transformer, generator, ball pen, telephone switch, neutron bomb, and contact lens. Her scientists have been awarded for Nobel prizes at the least 11 times. With knowing the history of Hungary, the expectation of the book is logical. Even though the book is intended for undergraduate students, it exposure the readers on many deep, interesting, and important theorems with completed proofs but easily accessible methods on
1. the irrationality of the number of the square root of 2, of the number e, and of the number pi,
2. the three classical geometric construction problems,
3. constructible regular polygons (Gauss Theorem),
4. e is transcendental,
5. Banach-Tarski Paradox.

The book also comes with a sketch of the proof of Hilbert's third problem, which states that the regular tetrahedron is not equidecomposable to the cube nor to any rectangular box of the same volume. The proof is based on an additive and invariant function. The value of the function at a regular tetrahedron is nonzero, but the value of the function at the cube is zero.

The first time I read the book while I was an undergraduate. Most of the material covers on the book were new to me other than the irrationality of square root of 2, the pigeonhole principle, countable and uncountable sets. The chapters 2, 3, 6, 7, 11, 13, 15, 16 impressed me the most. They were geometry related, especially the proofs on the three classical geometric construction problems (doubling the cube, trisection of angles, and squaring the circle). Banach-Tarski Paradox was another shock. If a solid ball can be broken down into infinite points and "then be put back together in a different way," two identical copies of the original ball can be yield.

Anyway, I own the book now for the provided proofs.

Good problems, beautiful proofs
I have recently acquired a copy of the Hungarian edition (apparently a translation of this English edition) and I can tell you, these guys have selected some of the best and most representative problems in Mathematics. The proofs are very concise and you really do not need much more than high school/early college math to follow them. There are a number of exercises for each chapter (topic) and some of them also come with hints. I would also consider these exercises to tease brighter high school math wizards. For those who have already seen them during their studies, it is surely worth another look. I have not seen the English edition, but reading the Hungarian version, I assume it must also be very well written.

The basics of proof techniques covered in sufficient depth
As the title indicates, the legendary Paul Erdos was involved in the creation of this book. In 1983, Erdos and other Hungarian mathematicians started the Budapest Semester in Mathematics (BSM), a program for American and Canadian undergraduate students. One of the courses in this program involves creative problem solving, which was the motivation for the material in this book. As is the case with books on problem solving, no particular area of mathematics is examined. The emphasis is on proof techniques, which are largely independent of the mathematical topic.
Of course, the quality of any book of this type is largely dependent on the choice of problems that are described, and in this case the chosen topics are excellent. The book is split into two main sections, which are further split into the following subsections:

I) Proofs of Impossibility, Proofs of Nonexistence.
1) Proofs of Irrationality.
2) The Elements of the Theory of Geometric Constructions.
3) Constructible Regular Polygons.
4) Some Basic Facts About Linear Spaces and Fields.
5) Algebraic and Transcendental Numbers.
6) Cauchy's Functional Equation.
7) Geometric Decompositions.

II)Constructions, Proofs of Existence.
8) The Pigeonhole Principle.
9) Liouville Numbers.
10) Countable and Uncountable Sets.
11) Isometries of R^n.
12) The Problem of Invariant Measures.
13) The Banach-Tarski Paradox.
14) Open and Closed Sets in R. The Cantor Set.
15) The Peano Curve.
16) Borel Sets.
17) The Diagonal Method.

While each of these topics is introduced, that does not mean that the coverage is superficial. The book is advertised as having more than elementary coverage, and I concur with that assessment. Detailed proofs of the main ideas are included with exercises at the end of each section. Hints for the solution of many of the problems are included in an appendix.
This is an excellent short introduction to many of the proof techniques that are the staple of working mathematicians. I strongly recommend it as a primary or secondary text for any course where the goal is to teach basic proof techniques to advanced undergraduates. ... Read more

Customer Reviews (1)

Review for "Conjecture & Proof" by D.D. Schwartz
This book is primarily designed as a textbook for a "transition" college course (the kind of course at the sophomore level that helps students make the transition from calculus and calculation intensivecourses to more abstract mathematics), and it does an excellent job. Whilethe structure of the book is quite standard for a text of this kind,students find it accessible and user-friendly. To achieve the goal ofhelping students grow comfortable with abstract mathematical structures,Dr. Diane Driscoll Schwartz presents at first an introduction to logic andits use in the construction of mathematical proofs. The topics included inthe two chapters cover several standard proof techniques, such as the useof the contrapositive and of the principle of mathematical induction. Thispart is followed by the discussion of a number of mathematical topics suchas sets, functions, relations, groups, modular arithmetic, combinatoricsand cardinality. While the sets of exercises include a sufficient number ofproblems, it would be nice to see this number increased. Some of theproblems are designed for group-work and provide a good starting point forclassroom discussion and for "non standard" homework assignments.The book is accompanied by an Instructor's Guide, which includessuggestions for class preparation and hints for some of the problems. Forthose schools that provide a technology-intensive environment, the text canbe use with the computer language ISETL. The software can be downloadedfrom the Web Sites indicated in the book. ... Read more

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Of paramount importance to the natural sciences, the principles of Darwinism, which involve variation, inheritance, and selection, are increasingly of interest to social scientists as well. But no one has provided a truly rigorous account of how the principles apply to the evolution of human society—until now.

In Darwin’s Conjecture, Geoffrey Hodgson and Thorbjørn Knudsen reveal how the British naturalist’s core concepts apply to a wide range of phenomena, including business practices, legal systems, technology, and even science itself. They also critique some prominent objections to applying Darwin to social science, arguing that ultimately Darwinism functions as a general theoretical framework for stimulating further inquiry. Social scientists who adopt a Darwinian approach, they contend, can then use it to frame and help develop new explanatory theories and predictive models.

This truly pathbreaking work at long last makes the powerful conceptual tools of Darwin available to the social sciences and will be welcomed by scholars and students from a range of disciplines.

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The authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's theory. Deligne's work is closely related to the sheaf theoretic theory of perverse sheaves. In this framework Deligne's results on global weights and his notion of purity of complexes obtain a satisfactory and final form. Therefore the authors include the complete theory of middle perverse sheaves. In this part, the l-adic Fourier transform is introduced as a technique providing natural and simple proofs. To round things off, there are three chapters with significant applications of these theories. ... Read more

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These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds are given. Finally, the most recent developments concerning these conjectures are surveyed, including a detailed status report.
The prerequisites consist of a solid knowledge of the basics about manifolds, vector bundles, (co-) homology and characteristic classes.

Customer Reviews (1)

An effective overview
In its simplest form, the Novikov conjecture asserts that if there is a map f from a closed smooth manifold M and a classifying space of a group, and if g is a homotopy equivalence from a closed smooth manifold N to M, then the `higher signatures' of (M, f) and (N, fg) agree. The goal of this book is to introduce the reader to the precise notion of `higher signature' and to discuss various concepts and tools used in attempted resolutions of the conjecture. Also discussed in some details are conjectures that are related to the Novikov conjecture. Readers will needto have a strong background in algebraic and differential topology in order to appreciate the content of the book, but the authors develop some of the needed material in it, such as h- and s-cobordism, simple homotopy, surgery theory, and the classification problem for manifolds via characteristic classes. Without too many exceptions the authors motivate the concepts exceedingly well, especially in chapter 12 where they give one of the best explanations in print for the surgery obstruction groups.

When reading the book it becomes apparent that the Novikov conjecture has many guises, and attempts to resolve it have involved some quite esoteric constructions. The main strategy used in its resolution involves a generalization of the Hirzebruch signature, called a `higher signature' and the notion of an `assembly map.' The assembly map, as the name implies, collects all the higher signatures into a single invariant: essentially the image of the Poincare dual of the L-class under the map induced from f. One then constructs a homomorphism (the assembly map) from the Poincare duals of the Pontrjagin classes to a particular Abelian group L(G), such that the value of the assembly map on the image is a homotopy invariant. The Novikov conjecture is the assertion that the assembly map is an isomorphism. Much of the first part of the book discusses how to make these notions meaningful and how to interpret them geometrically via the surgery obstruction groups.

The authors also discuss them in a purely algebraic context, constructing an algebraic notion of bordism in the context of chain complexes and the notions of symmetric and quadratic forms over chain complexes. Algebraic cobordism allows the definition of a symmetric and quadratic algebraic L-group. The nth symmetric algebraic L-group of a ring R with involution is defined as the collection of cobordism classes of n-dimensional symmetric algebraic Poincare complexes, and the quadratic L-group of R, with a similar definition for the quadratic case. From these constructions the reader is introduced to the subject of L-theory, which has been the subject of intense research in the last two decades.

Central to the research into the Novikov conjecture is the category of `spectra', which is usually encountered in any treatment of algebraic topology but is discussed here with examples given in K- and L-theory and the famous Thom spectrum of a stable vector bundle. The discussion of spectra involves the important notion of a `homotopy pushout', which are defined so as to commute with the suspension with the unit circle, and the `homotopy pullback', which commutes with the loop functor. Both homotopy pushouts and pullbacks are homotopy equivalences.

Given a discrete group G, a family of subgroups of G, and an equivariant homology theory with respect to G, after constructing the classifying space of the family of subgroups, the authors want to show that the assembly map induced from the projection of the family to the one-point space is an isomorphism. To understand for which groups this is true, the authors must first define the notion of a G-homology theory. They use the notion of a G-CW-complex that they defined when discussing classifying spaces of families of subgroups to define this homology theory. For a group G and an associative commutative ring Q with unit it consists of a collection of covariant functors from the category of G-CW-pairs to the category of Q-modules indexed by the integers that satisfies the usual properties such as G-homotopy invariance, the existence of a long exact sequences for pairs, and excision. An equivariant homology theory is then a G-homology theory that has a `induction structure', the latter of which is a collection of isomorphisms between the nth G-homology groups and nth homology groups of a group that has a homomorphism into G. The authors then show how to obtain an equivariant homology from a spectrum. Central to their construction is the `orbit category Or(G)' of a group G. The objects of this category are homogeneous G-spaces and the morphisms are G-maps. For a small category C they define a `C-space' to be a functor from C to the set of compactly generated spaces. A `C-spectrum' is a functor from C to the category of spectra. After defining a notion of smash product for a C-space and a C-spectrum, the authors then quote a lemma that illustrates how one can obtain a G-homology theory from an Or(G)-spectrum. In order to obtain an induction structure, the Or(G)-spectrum must be obtained from a spectrum of groupoids. The authors show how to do this and thus obtain an equivariant homology theory. Therefore the K- and L-theory spectra over groupoids that were constructed earlier thus give rise to equivariant homology theories.

These G-homology theories reduce to the K- and L-theory of the group ring when evaluated on a one-point space, and the topological K-theory of the reduced C*-algebra. The Farell-Jones conjecture claims that the assembly maps from the equivariant homology groups for K and L-theory to the one-point homology are isomorphisms. The Baum-Connes conjecture does the same for topological K-theory. If these conjectures were answered positively then they would allow the computation of the K- and L-groups from the K- and L- finite or virtually cyclic subgroups of G. The authors spend two chapters discussing for what groups these conjectures have been found to be true, and also a chapter on how the Novikov conjecture follows from these conjectures. ... Read more

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Work as center of life has such an important role in our lives; it bears a standard by which we measure our success. It is a major component of self actualization and well-being. Professional life offers the hope of rewarding work, not just financially but work that is fulfilling. However, professions are also riddled with complexities and ethical conflicts that obstruct the goal of meaningful work. Our jobs are fraught with moral ambiguities and dilemmas; these become sources of frustration and alienation. What is needed is a transformation, a renewal of our professional lives and the institutional contexts in which we operate, to humanize the alienating aspects of work and professions. Thomas Merton (1915-1968), though a cloistered monk, wrote extensively on spiritual and social issues. He has been called 'a spiritual master' for contemporary times. He possessed an uncanny sense of self-awareness and moral imagination. His life and writings have inspired countless persons on life's spiritual journey. Yet, while people have looked to Merton for guidance on spiritual issues, the implications of his thought for several other areas of life are open to exploration. This book focuses on the significance of his reflections in "Conjectures of a Guilty Bystander", which offer one the confidence to embark on a journey that seeks to transcend the complexities of professional life, and courage to transform the negative features of workplaces and organizations through reasoned moral action, moral imagination, and leadership. ... Read more

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Motivated by some notorious open problems, such as the Jacobian conjecture and the tame generators problem, the subject of polynomial automorphisms has become a rapidly growing field of interest. This book, the first in the field, collects many of the results scattered throughout the literature. It introduces the reader to a fascinating subject and brings him to the forefront of research in this area. Some of the topics treated are invertibility criteria, face polynomials, the tame generators problem, the cancellation problem, exotic spaces, DNA for polynomial automorphisms, the Abhyankar-Moh theorem, stabilization methods, dynamical systems, the Markus-Yamabe conjecture, group actions, Hilbert's 14th problem, various linearization problems and the Jacobian conjecture. The work is essentially self-contained and aimed at the level of beginning graduate students. Exercises are included at the end of each section. At the end of the book there are appendices to cover used material from algebra, algebraic geometry, D-modules and Gröbner basis theory. A long list of ''strong'' examples and an extensive bibliography conclude the book. ... Read more

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This book contains a concise introduction to the techniques used to prove the Baum-Connes conjecture.

The Baum-Connes conjecture predicts that the K-homology of the reduced C^*-algebra of a group can be computed as the equivariant K-homology of the classifying space for proper actions. The approach is expository, but it contains proofs of many basic results on topological K-homology and the K-theory of C^*-algebras. It features a detailed introduction to Bredon homology for infinite groups, with applications to K-homology. It also contains a detailed discussion of naturality questions concerning the assembly map, a topic not well documented in the literature.

The book is aimed at advanced graduate students and researchers in the area, leading to current research problems. ... Read more

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This is the third in the series of volumes of essays that Robin Fox began with Reproduction and Succession and continued with The Challenge of Anthropology. Fox who has been described as "the conscience of anthropology" continues to have the same aim: to expose readers in the social sciences and beyond to the consequences of "the biosocial orientation," and to assess the "state of the art" in anthropology in particular and the social sciences in general. As always he encompasses a wide range of topics: Why do bureaucracies fail? Are we really an innovative animal? Is nationalism a purely constructed phenomenon? What is the role of sexual competition in epic literature? In all these enquiries he tries to show in non-technical language how the evolutionary approach throws new light on old problems-and even raises new and more interesting problems. He pursues the issue of whether we have a naturally developed moral sense, and if so what it could possibly be (on the way attempting a definitive definition of the good); he looks at the status of the idea of self-interest in economic and biological science; he examines the current state of archaeology as a basis for a renewed scientific anthropology; and he tries to adjudicate the debate between the scientific and humanistic camps in the social sciences. ... Read more

Customer Reviews (1)

Thoughtful, amusing, and challenging - as Fox always is
Robin Fox is one of the few social scientists who is fun to read.He doesn't go along with the crowd -- so be prepared to expand your horizons ... Read more

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Copyright © 2010 by Eric Gill ... Read more

Customer Reviews (2)

Queen 9 Connecture
This book was authored by my nephew. It was a high interest level book, filled with an enormous amount of technical information. He amazes me in how he knows all of this and intertwined it so perfectly into this book.

Queen 9 Stands for Women
Queen 9 Conjecture accurately portrays the reality of today's work place. This is an amazingly honest book, written from a middle-class perspective. It is about power and choice. It's about today's women, our inner peace and extreme strength. It's about our future--the important role women have played and will continue to play in a changing world. Queen 9 Conjecture left no doubt in my mind that there really are strange deals being made at our expense. It's a skillfully written story that made me stop and think about what's going on behind closed doors in today's workplace. The author weaves numerous exciting subplots. I felt a familiar connection with every character, from the clear descriptions of their attire to the deepest feelings of their souls. Each chapter is like a short story that flows into the next without coming across as scripted. My favorite character was Vedalia. She is intuitive and sincere, and very smart. She commands the respect modern women like myself grew up expecting from others. The author understands working-class women. He gets that we are tired of being used by politicians to advance the agendas of other political groups. We will no longer be interrupted in public discussions. We will be heard, supported and yes, even admired. The book is extremely well written, with a clear voice and constant rhythm that held my interest and kept me reading into the night. The words flow consistently and honestly all the way through to the final page. My only gripe is that the author left me wondering, "Who is Queen 9?" Is it one mysterious person, or many? In any case, this is a rare literary/adventure novel. It's definitely at the top of my list of "must read" recommendations. ... Read more

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Uncle Petros is a family joke - an ageing recluse in a suburb of Athens, playing chess and gardening. His young nephew soon discovers his uncle was once a celebrated mathematician who staked all on solving the problem of Goldbach's Conjecture. ... Read more

Customer Reviews (3)

are mathematicians born or made
This book is a compulsively readable exploration of the nature and source of mathematical compulsion.It shows how exhilarating and destructive mathematics can be; it contains some salutary warnings as well for those who would tackle "big" issues in math.The book will teach you some math along the way.

highly recommended Greek tragedy in less then 200 pages about theoretical maths
Uncle Petros and Golbach's Conjecture was originally a best selling Greek novel and has now been published over 20 languages so don't get switched off by the title and subject matter. Forget about it being about maths and in fact think of Moby Dick to place this book. It's about obsession and pride in chasing the impossible dream. You understand the thrill and terror of chasing impossible dreams.

Right now let's get the maths out of the way. Golbach's Conjecture first stated in the 18th century suggests that:

Every even integer greater than 2 can be written as the sum of two primes.

But mathematicians lack proof that in all circumstance it would hold.For example think about Physics where if dealing with the very big or the very small ordinary scientific understanding ceases to work.So could this be the case in Mathematics? Yes over my head as well!But the author is a childhood mathematical genius who submitted original research at 15 before even starting his degree and also an acclaimed film maker and writer.So he both understands the mathematical issues and can write so that we understand and care.

We first meet Uncle Petros in the 1970's through the eyes of the beloved favourite nephew as a teenager. Petros is dismissed as the family failure that supports him through the family business while he does nothing but read books and plays chess.He leaves his home only once a month to do the books of a charity founded by his father. The beloved favourite nephew is met by a wall of adult silence when he tried to find out what the anger of the family is about. A chance phone call and a subsequent letter lead him to discover thatfar from a failureUncle Petros had been a professor of mathematics in the 20's and 30's at a prestigious German University. This makes him as obsessive as his Uncle as he struggles to discover the Truth of the family scandal.

He tries to become a mathematician to help him challenge and understand what had obsessed his Uncle. This causes huge family problems- this is a Greek family remember where honouring your family and Father is a top rule in life. He finally manages to get the story of his Uncles obsessive hunt out in the open but at a high personal cost to his own ambitions. It is clear that Uncle Petros is a genius who will never be known as his hopes are dashed in the 30's by the publication of Kurt Godel's Theorem. Yes more maths but not much so don't leave. This solves the problem of completeness by showing that any theory of numbers will contain unprovable propositions. Alan During (him of how do we know a computer hashuman intelligence- asked before computers were developed- now that's what being clever is about) then demonstrates that theorists have no idea which proposition is merely hard to prove and which are impossible to prove.

Hence, Uncle Petros has no way of knowing if spending all his life in trying solve the Golbach's Conjecture is a possible but hard task or impossible task. He gives up, his dreams and hopes ended. The beloved nephew is finding the truth is released from his obsession and so escapes the fate of his Uncle but then realises that a psychological lie has taken place which he needs to lance but this has tragic consequences.

Uncle Petros and Golbach's Conjecture is highly recommended Greek tragedy in less then 200 pages about theoretical maths and why love and life isabout how you answer the Bette Davis Theorem:

Oh, don't let's ask for the moon. We've already got the stars.

A very good read.
Congratulations to my Greek compatriot for a very good read. The translation is very good, too. An interesting story of an interesting man, uncle Petros; a story that can easily be followed, even if one (as myself), does not posses a degree or a
big interest in mathematics. The story makes you think about what is truly important in life, and how one can easily get engulfed chasing a life's dream.
I am surprised, yet happy, however, that Doxiadis has been translated in English, when so many other contemporary Greek writers have not yet been translated. I sincerely hope that many more worthy authors from such a small in population country, that can boast two Nobel prizes in literature (i.e. Elytis and Seferis), will soon be translated in English.

P.S. Congratulations to Amazon for coming to Canada and giving the locals some competition... ... Read more

Product Description
Stark's conjectures on the behavior of $L$-functions were formulated in the 1970s. Since then, these conjectures and their generalizations have been actively investigated. This has led to significant progress in algebraic number theory.

The current volume, based on the conference held at Johns Hopkins University (Baltimore, MD), represents the state-of-the-art research in this area. The first four survey papers provide an introduction to a majority of the recent work related to Stark's conjectures. The remaining six contributions touch on some major themes currently under exploration in the area, such as non-abelian and $p$-adic aspects of the conjectures, abelian refinements, etc. Among others, some important contributors to the volume include Harold M. Stark, John Tate, and Barry Mazur.

The book is suitable for graduate students and researchers interested in number theory. ... Read more

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I discovered a method of proving the Collatz Conjecture, an unsolved problem in mathematics.The Collatz Conjecture claims that any non-zero positive integer will reach 1 if the following rules are applied:If the integer is odd, multipy by 3 and add 1 (3x+1), if it is even, divide by 2 (x/2).I noticed that thereare only a finite number of possible combinations for3-digit integers when the 3x+1 and x/2 rules arefollowed.I also used the fact I proved that powers of2 added to any of the positive integers cause agreement.My brother (Michael Fleming) wrote a computer program with my instructions that proved that all integers subcoll (a chosen integer subcolls if it reaches an integer less than itself), a known sole requirement for the proof of the validity of the Collatz Conjecture.He was on the team for the special effects of themovie True Lies (nominated for an academy award inBest Special Effects), and the movie Species.He alsodid some of the special effects for the children'sshow Barney. ... Read more

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Focusing on Sobolev inequalities and their applications to analysis on manifolds and Ricci flow, Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincaré Conjecture introduces the field of analysis on Riemann manifolds and uses the tools of Sobolev imbedding and heat kernel estimates to study Ricci flows, especially with surgeries. The author explains key ideas, difficult proofs, and important applications in a succinct, accessible, and unified manner.

The book first discusses Sobolev inequalities in various settings, including the Euclidean case, the Riemannian case, and the Ricci flow case. It then explores several applications and ramifications, such as heat kernel estimates, Perelman’s W entropies and Sobolev inequality with surgeries, and the proof of Hamilton’s little loop conjecture with surgeries. Using these tools, the author presents a unified approach to the Poincaré conjecture that clarifies and simplifies Perelman’s original proof.

Since Perelman solved the Poincaré conjecture, the area of Ricci flow with surgery has attracted a great deal of attention in the mathematical research community. Along with coverage of Riemann manifolds, this book shows how to employ Sobolev imbedding and heat kernel estimates to examine Ricci flow with surgery.

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In this magisterial history of intellectual life, Michael O'Brien analyzes the lives and works of antebellum Southern thinkers and reintegrates the South into the larger tradition of American and European intellectual history.

O'Brien finds that the evolution of Southern intellectual life paralleled and modified developments across the Atlantic by moving from a late Enlightenment sensibility to Romanticism and, lastly, to an early form of realism. Volume 1 describes the social underpinnings of the Southern intellect by examining patterns of travel and migration; the formation of ideas on race, gender, ethnicity, locality, and class; and the structures of discourse, expressed in manuscripts and print culture.In Volume 2, O'Brien looks at the genres that became characteristic of Southern thought. Throughout, he pays careful attention to the many individuals who fashioned the Southern mind, including John C. Calhoun, Louisa McCord, James Henley Thornwell, and George Fitzhugh.

Placing the South in the larger tradition of American and European intellectual history while recovering the contributions of numerous influential thinkers and writers, O'Brien's masterwork demonstrates the sophistication and complexity of Southern intellectual life before 1860. ... Read more

Customer Reviews (1)

Intense Look at the Mind of the Old South
A recent book covering American literature until 1877 had no Southern writers besides Poe and, in a detailed section on the Civil War, did not offer a single pro-Confederate work. This textbook only serves the myth, perpetuated by Henry Adams and even W.J.Cash, that the Old South had no intellectual culture to speak of. Michael O'Brien has railed against this myth in his previous works. In these two volumes, he utterly destroys it.

In the almost 1500 pages, O'Brien offers an outstanding work of intellectual history. Almost everyone ever associated with the Old South is here. Political theorists like Calhoun and Upshur; women like Mary Chestnut and Louisa McCord; Joel Poinsett is mined for how the Old South saw South America; Edmund Ruffin, Hugh Legare (an old O'Brien favorite), James Henley Thornwell, James Henry Hammond, William G. Simms, the list goes on and on. O'Brien's synthesis is truly amazing as he portrays the mind of the Old South.

This is a work that should not be ignored but I fear is doomed to collect dust. The book is way, way too long and casual students of American intellectual history will more likely than not ignore it. O'Brien set out to destroy the myth that the Old South had no mind. Despite a good writing style and a valiant effort, I wonder if O'Brien's thoroughness undermines his attempt-again the work is almost 1500 pages long. Want proof? This is the first customer review despite the work being out for six years already. ... Read more

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This cutting-edge, standard-setting text explores the spectral geometry of Riemannian submersions. Working for the most part with the form valued Laplacian in the class of smooth compact manifolds without boundary, the authors study the relationship-if any-between the spectrum ofp on Y andp on Z, given thatp is the p form valued Laplacian and pi: Z Y is a Riemannian submersion. After providing the necessary background, including basic differential geometry and a discussion of Laplace type operators, the authors address rigidity theorems. They establish conditions that ensure that the pull back of every eigenform on Y is an eigenform on Z so the eigenvalues do not change, then show that if a single eigensection is preserved, the eigenvalues do not change for the scalar or Bochner Laplacians. For the form valued Laplacian, they show that if an eigenform is preserved, then the corresponding eigenvalue can only increase. They generalize these results to the complex setting as well. However, the spinor setting is quite different. For a manifold with non-trivial boundary and imposed Neumann boundary conditions, the result is surprising-the eigenvalues can change.Although this is a relatively rare phenomenon, the authors give examples-a circle bundle or, more generally, a principal bundle with structure group G where the first cohomology group H1(G;R) is non trivial. They show similar results in the complex setting, show that eigenvalues can decrease in the spinor setting, and offer a list of unsolved problems in this area.Moving to some related topics involving questions of positive curvature, for the first time in mathematical literature the authors establish a link between the spectral geometry of Riemannian submersions and the Gromov-Lawson conjecture.Spectral Geometry, Riemannian Submersions, and the Gromov-Lawson Conjecture addresses a hot research area and promises to set a standard for the field. Researchers and applied mathematicians interested in mathematical physics and relativity will find this work both fascinating and important. ... Read more

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Recent Renaissance research has placed great stress on the importance of textual criticism and attitudes toward classical texts as a basis for understanding the ideas of the Renaissance humanists. John D'Amico turns to the German humanist, Beatus Rhenanus, and forms exciting new opinions about his work. Beatus was a close associate of Erasmus and learned much from the celebrated Dutch scholar, yet his critical method marked a break with Erasmus because he articulated a strict manuscript-based procedure for extracting new readings of ancient texts. His attempt to be faithful to the classical manuscripts he edited was not always successful, but he assuredly understood the use of textual criticism for historical studies and was, D'Amico claims, the most accomplished historian of the German Renaissance.
Not only Renaissance historians but also literary critics, students of historiography and of German history and literature, and classicists will find this book illuminating. ... Read more