Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Encyclopaedia of Mathematical Sciences)

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Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Encyclopaedia of Mathematical Sciences)

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Wonderful Arithmetic Geometry Book.......2006-08-20

This Book is a cornerstone in Arithmetic Geometry.

It is the first time in a single Book so different
arguments find a common place.

Let me say that the idea of dividing the work into
three parts,depending on the approach, is entirely
new. In fact,

Part 1 starts with elementary theory & applications(primes,diophantine equations& approx)

Part 2 gives an account of recent ideas and theory
(ch.3:Logic & Recursion, with a sketch of proof of
Matiyasevic's Theorem;ch.4:Algebraic NumberTheory;
ch.5:Arithmetic of Algebraic Varieties;ch.6: deals
with Zeta functions and modular forms;ch.7:gives a
picture, complete indeed, of Wiles'proof of Fermat
Last Theorem)

Part 3 gives "Analogies and Visions",i.e. the link
between numbers fields and function fields(usually
this analogy is only admitted, but never explained
in other books) and other analogies involving many
recent arguments in Arithmetic Geometry (such as :
Schottky uniformization, Arakelov Geometry, Zetas,
Dynamics and Cohomology).

Elementary Geometry of Algebraic Curves: An Undergraduate Introduction

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Does what it claims

Elementary Geometry of Algebraic Curves: An Undergraduate Introduction
C. G. Gibson
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521641403

Book Description

Here is an introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book is well illustrated and contains several hundred worked examples and exercises. From the familiar lines and conics of elementary geometry the reader proceeds to general curves in the real affine plane, with excursions to more general fields to illustrate applications, such as number theory. By adding points at infinity the affine plane is extended to the projective plane, yielding a natural setting for curves and providing a flood of illumination into the underlying geometry. A minimal amount of algebra leads to the famous theorem of Bezout, while the ideas of linear systems are used to discuss the classical group structure on the cubic.

Customer Reviews:

Does what it claims.......2001-05-04

We used this for a class introducing algebraic geometry. It's necessary to know linear algebra and multivariable calculus, and very helpful to know groups, rings, and fields. The book keeps it's feet on the ground (equal distribution of computation and abstraction in problems). Some examples throughout. Very good as an introduction.

Elementary Geometry of Differentiable Curves: An Undergraduate Introduction

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Elementary Geometry of Differentiable Curves: An Undergraduate Introduction
C. G. Gibson
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521011078

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Here is a genuine introduction to the differential geometry of plane curves for undergraduates in mathematics, or postgraduates and researchers in the engineering and physical sciences. This well-illustrated text contains several hundred worked examples and exercises, making it suitable for adoption as a course text. Key concepts are illustrated by named curves, of historical and scientific significance, leading to the central idea of curvature. The author introduces the core material of classical kinematics, developing the geometry of trajectories via the ideas of roulettes and centrodes, and culminating in the inflexion circle and cubic of stationary curvature.

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Unabridged audiobook in MP3 format.

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Two literary gems from the pen of pyschological realism master Fyodor Dostoevsky.......2007-07-11

Penguin classic has included two of Fyodor Dostoevsky's greatest short pieces of fiction in one volume.
"Notes from Underground" was published in 1864 shortly before the novelist produced his classic novel "Crime and Punishment". This shorter work informs the characterization of Raskolnikov in "Crime and Punishment." The anonymous narrator presents himself in print as a person who is deeply disillusioned with his life. He is a failure in life, love and quest for meaning in a St. Petersburg fog of bureacracy and poverty. He meets a prostitute named Lisa but she disappears in a swirling St. Petersburg fog. He views himself as an "insect". The work is a precursor of such works as Franz Kafka's "Metamorphosis" in which the main charcter is turned into a beetle. Dostoevsky is not for those seeking a cheerful, sunlit read on a lovely beach! The narrator of the tale is very skeptical of human goodness. He is distrustful of everyone believing that life is a succession of troubles until the final chapter ends in the obscurity of the grave.
The early story "The Double" is the most interesting of the two included in this Penguin Classics Edition. The tale focuses on a nonentity named Golyadkin who is tortured by the appearance of a man who is his exact image! (He is called Goldyadkin Jr!). Golyadkin is a wretch of an individual. He reminds this reader of a character out of Gogol who specialized in portraying the lives of St. Petersburg's poor caught in the web of Tsarist governmental ministries. The tale ends in a macabre way as Golyadkin is taken away to what is, probably, a mental institution.
Does Golyadkin Jr. exist or is he a figment of the imagination of Golyadkin Sr? We not know. This tale is written as the fog of St. Petersburg wraps the main character in obscurity and despair.
These two tales are good introductions to Dostoevsky's shorter fiction. The themes evident in these tales are:
a. A feeling of despairing anomie
b. A person who believes he is trapped like an insect in the webs of modern society.
c. A belief that life is difficult, complex and often confusing to ordinary people.

Existentialist Literature.......2007-05-31

Dostoyevsky's 'Notes from Underground,' is often called the first truly existential work of literature in the history of the west. Yet I think it is read today for the very seem reasons we always read Dostoevsky: for his command over intensity, his genuine and masterly sense of atmosphere, and his ability to psychologize those who are suffering. 'Notes from Underground,' is a true masterpiece in that it recreates the truth of genuine alienation and hatred. It laid the basis for all great works of existential art to follow, from the Stranger to Taxi Driver. Truly a dark gem of European literature.

I found the Double, by contrast, to be rather tired and uninteresting. Perhaps it is because Kakfa and Freud has handled the theme of the doppelganger far more interestingly. I found it difficult to get into this one. It seems to me that the translation rang a little flat in comparison to Notes. Nevertheless, its an entertaining read, though one could never put it in the same class as great Dostoyevsky.

A few comments and an interesting fact.......2004-03-01

Dostoyevsky is of interest for another reason that has only recently come to the attention of medical science. Based on the notes in his diaries, Dostoyevsky may have had the very unusual neurological condition known as temporal-lobe epilepsy. This form of epilepsy produces no motor convulsions or seizures as in the classical Jacksonian epilepsy that is so well known. Rather, the effects are on the person's mental and emotional state.

In his notebooks Dostoyevsky reported experiencing visions and emotional states of such an intense nature, saying that that were so ecstatic that one would be willing give up one's life to experience it one more time, that it seems likely he did indeed have this rare neurological syndrome. It can produce intensely vivid imagery and visions, and ecstatic and euphoric emotional states. However, in some cases, it also produces uncontrollable rage and violence, but it appears that Dostoyevsky had the more pleasant and benign form of this disease.

Having studied the excerpts from his diaries describing these experiences and compared them to contemporary patients who have been diagnosed with the disease, the evidence seems compelling to me too that he did indeed have this condition. How it ultimately affected his writing I don't know, but perhaps this will be something that will enable us to gain further insight into his writings in the future.

Contrasting Tales.......2003-11-26

The book comprises two novellas.

"Notes from the Underground" is a strange, puzzling tale, a confession of an unnamed character. He rails against traits in modern thought which attempt to rationale human existence - this, in his view, is essentially futile in that it cannot alter humankind's true nature. Yet the paradox is that if humans adhere to their true nature, then their atavistic brutality and destructiveness come to the fore. As if to illustrate this, in the second part of the novella, the character acts in a deliberately cruel manner to other characters in the novel. "Notes" is more of a philosophical piece than a novel of entertainment. Nonetheless, it's interesting in that it might at least partly open the way to interpretation of Dostoyevsky's later works.

"The Double" on the other hand, is pure entertainment. The official Golyadkin's life is destroyed gradually following the appearance of his double. The story is either a nightmare, or an puzzle (is there really a double, or does the double represent the other side of Golyadkin's nature?). "The Double" is written in a lively style (or it might be better to say is translated in a lively style) which makes it a pleasure to read. Yet, due to the fact that many other writers (such as RL Stevenson and Kafka) have explored similar themes, it might seem a little familiar.

G Rodgers

Mixture of literary and philosophical value.......2002-02-26

"The Double" is a delightful tale written very much in the manner of Gogol. In his "Lectures on Russian Literature," Nabokov says, "The very best thing he [Dostoyevsky] ever wrote seems to me to be 'The Double.' It is the story -- told very elaborately, in great, almost Joycean detail ..., and in a style intensely saturated with phonetic and rhythmical expressiveness -- of a government clerk who goes mad, obsessed by the idea that a fellow clerk has usurped his identity. It is a perfect work of art, that story ...." But Nabokov does not think so well of Dostoyevsky's other works. He finds his work wanting both in art and in genius. Dostoyevsky was too much influenced by mystery and sentimental novels.

Perhaps Nabokov's dismissal of "Notes from Underground" is appropriate from a purely literary point of view, but the novel is of interest from a philosophical point of view. In the first part of the novel, the narrator is speaking to an imaginary audience. The narrator is obsessed with free will and is at pains to argue against the Enlightenment view that freedom and happiness are complementary. He is spiteful, not from some personality disorder, but rather from his philosophy. The second part involves detailed, and at times humorous, remembered humiliations. And then the noble prostitute. As Nabokov says at this point, "The conversations are very garrulous and very poor, but please go on to the bitter end. Some of you may like it more than I do."

Average customer rating:

Good Quality Edition

A few comments & an interesting medical fact

Deeply inciteful into the human conscious and a great sampling of this author

A goldmine for the Dostoyevsky reader

Notes from the Underground, The Double and Other Stories (B&N Classics)
Fyodor Dostoevsky
Manufacturer: Barnes & Noble Classics
ProductGroup: Book
Binding: Mass Market Paperback

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ASIN: 1593080379

Book Description

Often considered a prologue to Dostoevsky’s brilliant novels, the story “Notes from Underground” introduces one of the great anti-heroes in literature: the underground man, who lives on the fringes of society. In an impassioned, manic monologue this character—plagued by shame, guilt, and alienation—argues that reason is merely a flimsy construction built upon humanity’s essentially irrational core. Internal conflict is also explored in “The Double,” a surreal tale of a government clerk who meets a more unpleasant version of himself and is changed as a result.

In addition to these two existential classics, this collection also includes the psychologically probing stories “The Meek One,” “The Dream of a Ridiculous Man,” and “White Nights.”

Customer Reviews:

Good Quality Edition.......2007-01-09

As everyone's said, these are good short stories by Dostoevsky to have read. They're all available for free online, of course, but I prefer to have a book such as this on hand instead, even if it means paying the five dollars.

For one, there is the motivational factor involved. I bought this book largely for the Notes From Underground, but the fact that there are other stories on there, and the fact that I payed for them, led me to read them as well. In this way, I discovered how great a story White Nights is, and I doubt I would have read it without buying this book.

Then there is also the introduction and footnotes that expand on the numerous aspects of the stories that by now are not readily apparent to the reader, especially if he's not Russian. Who, after all, knows what a "white night" is in the first place? I didn't think the introduction too great a piece of writing, and disagreed with in on some issues, but it is still a nice piece of critical writing on the stories to have. Certainly, it is better than what you'd find on Wikipedia.

Lastly, this book's paper has a pulpy feel, but the ink doesn't rub off on your fingers, and so it's quite nice to just sit down with it and read it. I, for one, always found reading books more enjoyable in a living room chair than in front of a computer screen.

A few comments & an interesting medical fact.......2005-12-26

Dostoyevski's underground man character, although conceived in 1864, presages by more than 50 years the alienation and disaffection that became so widespread in the 20th century, especially in the so-called "lost generation" that grew up between the two world wars. As such, it became the pattern for generations of other literary anti-heroes whose existential angst was to reverberate through literature for the next hundred years and beyond. Overall, still a great classic and one whose philosophical and literary influences still resonate today.

An interesting comparison is with Daniel Defoe's Robinson Crusoe, regarded by some critics as the first true novel, preceeding the usually proposed Samual Richardson's Pamela, or Virtue Rewarded, from several decades later, if I remember right. The Crusoe character is marooned for 17 or 18 years on the island and when some fellow Englishmen finally arrive to save him he's singularly inhospitable and suspicious of them. And overall the Crusoe character isn't especially likeable or social and seems to have a fairly prounounced anti-social streak, if not a deep antipathy, toward his fellow humans. In that way he's not so different from the Underground Man.

Dostoyevsky is of interest for another reason that has only recently come to the attention of medical science. Based on the notes in his diaries, Dostoyevsky may have had the very unusual neurological condition known as temporal-lobe epilepsy. This form of epilepsy produces no motor convulsions or seizures as in the classical Jacksonian epilepsy that is so well known. Rather, the effects are on the person's mental and emotional state.

In his notebooks Dostoyevsky reported experiencing visions and emotional states of such an intense nature, saying that that were so ecstatic that one would be willing give up one's life to experience it one more time, that it seems likely he did indeed have this rare neurological syndrome. It can produce intensely vivid imagery and visions, and ecstatic and euphoric emotional states. However, in some cases, it also produces uncontrollable rage and violence, but it appears that Dostoyevsky had the more pleasant and benign form of this disease.

Having studied the excerpts from his diaries describing these experiences and compared them to contemporary patients who have been diagnosed with the disease, the evidence seems compelling to me too that he did indeed have this condition. How it ultimately affected his writing I don't know, but perhaps this will be something that will enable us to gain further insight into his writings in the future.

Deeply inciteful into the human conscious and a great sampling of this author.......2005-07-14

What makes this a promising edition is the notes and introduction, in addition to the great stories by Russian writer Dosteovsky. Dubbed a writer whose works include the element of socialism and psychology, this handy book is a great sampling of some of his shorter stories and novellas.

Psychological and symbolic in nature, one of the stories, "The Double" is the story of a man who literally believes that he has a double, a man who looks like him and bears the same name of Golyadkin. Therefore, our protagonist becomes Golyadkin senior, and the antagonist, the "malevolent" side of the twin, is Golyadkin junior. Golyadkin becomes aware that this twin of his is methodically ruining his life by scarring his reputation with peers and making his own name become synonymous with shame. The story itself is a study in duality and shame of individuals-Golyadkin senior becomes obsessed with correcting all the wrongs that his lower twin creates and tries to become the highly thought of individual that he once was. His downfall, and lowering place in society, is as much physical to him as it is metaphorical to us the readers. While the story takes a little patience to begin to appreciate and understand, the overall impact is impressive.

Also included within this edition are other stories from Dostoevsky, such as "Notes from Underground", "White Nights", "The Meek One", and "The Dream of a Ridiculous Man." Also included is both a brief introduction to all the stories, as well as a timeline and information about the author.This is recommended, specifically for the reason that you get a great sampling of this author for a relatively cheap price. My only small qualm with the book is the very small print; hence 4 stars instead of 5.

A goldmine for the Dostoyevsky reader.......2003-09-24

This great paperback omnibus collects Fyodor Dostoyevsky's two most famous short novels, Notes From the Underground and The Double, as well as three short stories: White Nights, The Meek One, and The Dream of a Ridiculous Man. All five are essential reads for fans of the great Russian author. This book also serves as a good starting point for the neophyte who is just looking to jump into Dostoyevsky: it contains an array of short works that serve to introduce the unfamiliar reader to the author's writing style. This is very valuable, because, after all, one would not be wise to jump into the author's immense novels unprepared. All of these stories introduce themes that Dostoyevsky would develop more fully in his great novels -- suicide, madness, nihilism, the existence of God. The author always was one to deal with life's Big Things, and he does not hesitate to do so even in his shorter works. All of the stories exhibit the vivid psychological realism that was Dostoyevsky's trademark. Never one for beautiful prose, Dostoyevsky much preferred to get down and dirty with the inner working of the human mind, never afraid to back away from all of the dark and terrible things that he found there.

Notes From the Underground, one of the greatest short novels of all-time, portrays one man in the depths of despair. A vivid depiction of the dark side of human nature, Notes is a great classic that perfectly evokes the feelings of isolation, despair, narcissism, and paranoia that continue to afflict the mass of men. The Double is another interesting story. Though an early work and not as well-crafted, it manages to put a new spin on the doppelganger phenomenon. In it, Dostoyevsky very skillfully portrays one man's lonely descent into madness -- and manages to be screamingly funny while doing so. White Nights is a brilliant short work, beautifully written, a testament to the eternal, if occasionally capricious, nature of love. The Meek One is a very dark story that examines the roots of suicide. The Dream of a Ridiculous Man offers a unique take on the nature of evil.

I should take time out here to note how wonderful these Barnes & Noble Classics Editions are. They offer a wide range of supplementary materials to the readings, of interest to both the general reader and the Dostoyevsky reader, not to mention the literary scholar. These include: a short profile of the author, a timeline of his life, a substantial critical introduction, effective but not overlong notes, an offering of critical opinion and commentary on the text, and even a list of discussion questions. Not least of all, they are extremely affordable. I highly recommend this volume to anyone looking to get into the author, and also to dedicated fans looking to have all of these stories in one place.

Average customer rating:

just read the notes!

Notes from the Underground & the Double
Fyodor Dostoyevsky
Manufacturer: North Books
ProductGroup: Book
Binding: Hardcover

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ASIN: 0939495155

Customer Reviews:

just read the notes!.......1999-12-23

Notes from the underground is one of the best books I have ever read, and so are Crime and punishment and The brothers Karamazov. I was therefore really disappointed with The Double. I just didn't understand what it was all about. The double seems to me to be a bad version of NFU, with its obsessive-compulsive main character. The double is somewhat like how I imagined Dostojevskijs work to be, before I yet had had the pleasure to prove myself wrong. The novel is uncomprehensible and very, very boring. But then again I really didn't understand any of it. My suggestion therefore is: read Notes from underground which is an absolutely work of art, and skip the rest.

THREE SHORT NOVELS OF DOSTOEVSKY: The Double, Notes From the Underground, The Eternal Husband

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THREE SHORT NOVELS OF DOSTOEVSKY: The Double, Notes From the Underground, The Eternal Husband

Manufacturer: International Collectors Library
ProductGroup: Book
Binding: Hardcover
ASIN: B000FF8PY8

Product Description

Victoria binding,decorated gilt cover and lettering, imitation leather, matching ribbon marker. Pub. info sheet laid in.

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Three Short Novels of Dostoevsky: The Double, Notes From the Underground, The Eternal Husband

Manufacturer: Anchor Books
ProductGroup: Book
Binding: Mass Market Paperback
ASIN: B000CSFBSQ

THREE SHORT NOVELS THE DOUBLE NOTES FROM THE UNDERGROUND THE ETERNAL HUSBAND

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THREE SHORT NOVELS THE DOUBLE NOTES FROM THE UNDERGROUND THE ETERNAL HUSBAND
Fyodor Dostoyevsky
Manufacturer: Anchor Books
ProductGroup: Book
Binding: Paperback

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Notes from Underground the Double

Manufacturer: Penguin USA (Paper)
ProductGroup: Book
Binding: Paperback
ASIN: 999206143X

Notes from Underground the Double: The Double

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Notes from Underground the Double: The Double

Manufacturer: Penguin USA
ProductGroup: Book
Binding: Mass Market Paperback
ASIN: B000HILNBA

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Notes from Underground the Double: The Double
Fyodor; Dostoevsky, Fedor Mikhailovich; Dostoyevsky, Fyodor Dvoinik Dostoyevsky
Manufacturer: Penguin USA
ProductGroup: Book
Binding: Mass Market Paperback
ASIN: B000UBXR4U

Notes from Underground; The Double (Penguin Classics)

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Notes from Underground; The Double (Penguin Classics)
Jesse Coulson Fyodor Dostoyevsky
Manufacturer: Penguin Classics
ProductGroup: Book
Binding: Paperback
ASIN: B000OJ9882

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