Algebra Un Approccio Algoritmico Book PDF, EPUB Download & Read Online Free

Algebra

Algebra

Author: Giulia Maria Piacentini Cattaneo
Publisher:
ISBN: 8808162702
Pages: 434
Year: 1996

Elementary Number Theory, Cryptography and Codes

Elementary Number Theory, Cryptography and Codes

Author: M. Welleda Baldoni, Ciro Ciliberto, G.M. Piacentini Cattaneo
Publisher: Springer Science & Business Media
ISBN: 3540692002
Pages: 522
Year: 2008-11-28
In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic residues, primality tests, continued fractions, etc.) which in recent years have proven to be extremely useful for applications to cryptography and coding theory. Both cryptography and codes have crucial applications in our daily lives, and they are described here, while the complexity problems that arise in implementing the related numerical algorithms are also taken into due account. Cryptography has been developed in great detail, both in its classical and more recent aspects. In particular public key cryptography is extensively discussed, the use of algebraic geometry, specifically of elliptic curves over finite fields, is illustrated, and a final chapter is devoted to quantum cryptography, which is the new frontier of the field. Coding theory is not discussed in full; however a chapter, sufficient for a good introduction to the subject, has been devoted to linear codes. Each chapter ends with several complements and with an extensive list of exercises, the solutions to most of which are included in the last chapter. Though the book contains advanced material, such as cryptography on elliptic curves, Goppa codes using algebraic curves over finite fields, and the recent AKS polynomial primality test, the authors' objective has been to keep the exposition as self-contained and elementary as possible. Therefore the book will be useful to students and researchers, both in theoretical (e.g. mathematicians) and in applied sciences (e.g. physicists, engineers, computer scientists, etc.) seeking a friendly introduction to the important subjects treated here. The book will also be useful for teachers who intend to give courses on these topics.
Curves and Surfaces

Curves and Surfaces

Author: M. Abate, F. Tovena
Publisher: Springer Science & Business Media
ISBN: 8847019419
Pages: 396
Year: 2012-06-11
The book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible definitions of the concept of curve, proving in particular the classification of 1-dimensional manifolds. We then present the classical local theory of parametrized plane and space curves (curves in n-dimensional space are discussed in the complementary material): curvature, torsion, Frenet’s formulas and the fundamental theorem of the local theory of curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves. The local theory of surfaces begins with a comparison of the concept of parametrized (i.e., immersed) surface with the concept of regular (i.e., embedded) surface. We then develop the basic differential geometry of surfaces in R3: definitions, examples, differentiable maps and functions, tangent vectors (presented both as vectors tangent to curves in the surface and as derivations on germs of differentiable functions; we shall consistently use both approaches in the whole book) and orientation. Next we study the several notions of curvature on a surface, stressing both the geometrical meaning of the objects introduced and the algebraic/analytical methods needed to study them via the Gauss map, up to the proof of Gauss’ Teorema Egregium. Then we introduce vector fields on a surface (flow, first integrals, integral curves) and geodesics (definition, basic properties, geodesic curvature, and, in the complementary material, a full proof of minimizing properties of geodesics and of the Hopf-Rinow theorem for surfaces). Then we shall present a proof of the celebrated Gauss-Bonnet theorem, both in its local and in its global form, using basic properties (fully proved in the complementary material) of triangulations of surfaces. As an application, we shall prove the Poincaré-Hopf theorem on zeroes of vector fields. Finally, the last chapter will be devoted to several important results on the global theory of surfaces, like for instance the characterization of surfaces with constant Gaussian curvature, and the orientability of compact surfaces in R3.
Un invito all'Algebra

Un invito all'Algebra

Author: S. Leonesi, C. Toffalori
Publisher: Springer Science & Business Media
ISBN: 8847005175
Pages: 432
Year: 2007-04-16
L'opera è un libro di testo, rivolto agli studenti universitari che devono affrontare il corso di algebra e matematica discreta. Temi quali gruppi, anelli e campi sono dapprima introdotti attraverso esempi semplici (così come numeri, polinomi e permutazioni) e sono successivamente discussi in modo approfondito nella seconda parte del libro. Vengono anche trattati temi come applicazioni alla crittografia, codici, informatica, fornendo anche cenni storici. Il volume mira ad offrire un'introduzione all'algebra in modo schematico e facilmente comprensibile.
Quaderni del Bobbio n. 4 anno 2012-2013

Quaderni del Bobbio n. 4 anno 2012-2013

Author:
Publisher: IIS "Bobbio" di Carignano
ISBN:
Pages:
Year:

NUMERI PRIMI

NUMERI PRIMI

Author: Massimiliano Fiordelisi
Publisher: Lulu.com
ISBN: 0244117381
Pages:
Year:

Topology

Topology

Author: Marco Manetti
Publisher: Springer
ISBN: 3319169580
Pages: 309
Year: 2015-06-19
This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.
Unknown Quantity:

Unknown Quantity:

Author: John Derbyshire
Publisher: National Academies Press
ISBN: 030909657X
Pages: 390
Year: 2006-05-02
Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages -- and it promises to be just what his die-hard fans have been waiting for. "Here is the story of algebra." With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel's proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics -- it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.
Groups

Groups

Author: Antonio Machì
Publisher: Springer Science & Business Media
ISBN: 8847024218
Pages: 371
Year: 2012-04-05
Groups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hölder’s program for attacking this problem in the case of finite groups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied both in the finite and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups; the latter with special emphasis on the extension problem. The sections are followed by exercises; hints to the solution are given, and for most of them a complete solution is provided.
Fourier Analysis on Groups

Fourier Analysis on Groups

Author: Walter Rudin
Publisher: Courier Dover Publications
ISBN: 0486821013
Pages: 304
Year: 2017-04-19
Written by a master mathematical expositor, this classic text reflects the results of the intense period of research and development in the area of Fourier analysis in the decade preceding its first publication in 1962. The enduringly relevant treatment is geared toward advanced undergraduate and graduate students and has served as a fundamental resource for more than five decades. The self-contained text opens with an overview of the basic theorems of Fourier analysis and the structure of locally compact Abelian groups. Subsequent chapters explore idempotent measures, homomorphisms of group algebras, measures and Fourier transforms on thin sets, functions of Fourier transforms, closed ideals in L1(G), Fourier analysis on ordered groups, and closed subalgebras of L1(G). Helpful Appendixes contain background information on topology and topological groups, Banach spaces and algebras, and measure theory.
Archimede

Archimede

Author:
Publisher:
ISBN:
Pages:
Year: 2001

A Book of Abstract Algebra

A Book of Abstract Algebra

Author: Charles C Pinter
Publisher: Courier Corporation
ISBN: 0486474178
Pages: 384
Year: 2010-01-14
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Catalogo dei libri in commercio

Catalogo dei libri in commercio

Author:
Publisher: Editrice Bibliografica
ISBN:
Pages:
Year: 1981

Bibliografia nazionale italiana

Bibliografia nazionale italiana

Author:
Publisher:
ISBN:
Pages:
Year: 1997

Elementi di Psicometria Computazionale

Elementi di Psicometria Computazionale

Author: Pietro Cipresso
Publisher: Lulu.com
ISBN: 1291743138
Pages: 702
Year: 2014-03-20
Lo psicologo contemporaneo deve fare i conti con sfide sempre maggiori e opportunita di studio e di ricerca usando nuove tecnologie fino a pochi anni fa impensabili. Elementi di Psicometria Computazionale, rappresenta un prezioso strumento per formare gli psicologi di domani, attenti al passato, orientati al futuro e con una corposa conoscenza del presente. In modo pratico e semplice il volume accompagna il lettore all'uso degli strumenti della misura in psicologia, alla luce delle piu recenti tecnologie. Un percorso che parte dall'acquisizione dei dati con questionari elettronici, biosensori, social networks, realta virtuale e altro, per proseguire con la gestione avanzata dei dati e chiudere con una prima introduzione ai modelli computazionali. Caratteristica importante del volume e il totale orientamento al mondo open source e la costante disponibilita di software gratuito per tutti gli strumenti utilizzati.