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Download e-book for iPad: Von den natürlichen Zahlen zu den Quaternionen: Basiswissen by Jürg Kramer,Anna-Maria von Pippich

By Jürg Kramer,Anna-Maria von Pippich

ISBN-10: 3658020547

ISBN-13: 9783658020545

Dieses Buch richtet sich an Bachelor- und Lehramtsstudierende der ersten Semester und vermittelt einen fundierten Aufbau der Zahlbereiche. Ausgehend von den natürlichen Zahlen werden systematisch die ganzen, rationalen, reellen und komplexen Zahlen bis hin zu den Hamiltonschen Quaternionen konstruiert. Dazu werden jeweils die aus der Algebra benötigten Grundlagen bereitgestellt und motiviert. Für den Bachelor-Studiengang Mathematik bietet das Buch einen vielseitigen Aufbau der Zahlbereiche, für den in den Anfängervorlesungen oftmals die Zeit fehlt. Lehramtsstudierenden verhilft dieses Buch zu einem anschaulichen Verständnis der Zahlbereiche von einem mathematisch-fachwissenschaftlichen Standpunkt, welches für die mathematikdidaktische Ausbildung eine wesentliche Grundlage darstellt und für die mathematische Kompetenz im Lehrerberuf unabdingbar ist. Das Buch enthält zum besseren Verständnis zahlreiche Aufgaben und Lösungen.

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Get Algebraic Number Theory (Springer Undergraduate Mathematics PDF

By Frazer Jarvis

ISBN-10: 3319075446

ISBN-13: 9783319075440

The technical problems of algebraic quantity thought frequently make this topic seem tricky to newcomers. This undergraduate textbook offers a welcome method to those difficulties because it offers an approachable and thorough creation to the topic.

Algebraic quantity Theory takes the reader from targeted factorisation within the integers via to the modern day quantity box sieve. the 1st few chapters reflect on the significance of mathematics in fields better than the rational numbers. while a few effects generalise good, the original factorisation of the integers in those extra normal quantity fields frequently fail. Algebraic quantity thought goals to beat this challenge. such a lot examples are taken from quadratic fields, for which calculations are effortless to perform.

The center part considers extra basic conception and effects for quantity fields, and the ebook concludes with a few subject matters that are prone to be compatible for complex scholars, specifically, the analytic classification quantity formulation and the quantity box sieve. this is often the 1st time that the quantity box sieve has been thought of in a textbook at this level.

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Get A Comprehensive Course in Number Theory PDF

By Alan Baker

ISBN-10: 110701901X

ISBN-13: 9781107019010

ISBN-10: 110760379X

ISBN-13: 9781107603790

built from the author's well known textual content, A Concise advent to the idea of Numbers, this publication presents a complete initiation to the entire significant branches of quantity conception. starting with the rudiments of the topic, the writer proceeds to extra complex themes, together with parts of cryptography and primality checking out, an account of quantity fields within the classical vein together with houses in their devices, beliefs and perfect periods, points of analytic quantity thought together with stories of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, an outline of the Hardy-Littlewood and sieve tools from respectively additive and multiplicative quantity conception and an exposition of the mathematics of elliptic curves. The ebook contains many labored examples, workouts and extra examining. Its wider insurance and flexibility make this ebook compatible for classes extending from the trouble-free to starting graduate studies.

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Download PDF by Kristina Reiss,Gerald Schmieder: Basiswissen Zahlentheorie: Eine Einführung in Zahlen und

By Kristina Reiss,Gerald Schmieder

ISBN-10: 3540212485

ISBN-13: 9783540212485

Kenntnisse über den Aufbau des Zahlsystems und über elementare zahlentheoretische Prinzipien gehören zum unverzichtbaren Grundwissen in der Mathematik. Das vorliegende Buch spannt den Bogen vom Rechnen mit natürlichen Zahlen über Teilbarkeitseigenschaften und Kongruenzbetrachtungen bis hin zu zahlentheoretischen Funktionen und Anwendungen wie der Kryptographie und Zahlencodierung. Wert wird dabei auf eine verständliche und umfassende Darstellung des Stoffes gelegt. Beweisideen, die hinter stringent durchgeführten Beweisen stehen, und die Verknüpfung von Fachwissen mit Schulbezügen sind dabei als besondere Merkmale hervorzuheben. Ergänzt wird die Darstellung durch viele Übungsaufgaben, die mit Lösungshinweisen und vollständigen Lösungen versehen sind.

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Download e-book for iPad: Unimath: Hidden Supersymmetry in All Number Sequences by Joyce Bowen

By Joyce Bowen

ISBN-10: 1475061420

ISBN-13: 9781475061420

Unimath is the mathematical software utilized in Uniphysics, the technological know-how of Synthesis. It analyzes the increments among numbers in numerical sequences, and has came across an grand legislations of Digit stability in which all sequences sum to 0 with ensuing balanced binaries, developing mirrors with greater than 60 digits. It additionally finds notable, non-random styles within the digits of pi, e, major numbers, Lucas numbers, Fibonacci numbers, and extra! Unimath opens up a complete new road within the box of quantity theory

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Download e-book for iPad: P-adic Analysis: A Short Course on Recent Work (London by Neal Koblitz

By Neal Koblitz

ISBN-10: 0521280605

ISBN-13: 9780521280600

This advent to contemporary paintings in p-adic research and quantity idea will make obtainable to a comparatively basic viewers the efforts of a couple of mathematicians during the last 5 years. After reviewing the fundamentals (the development of p-adic numbers and the p-adic analog of the complicated quantity box, energy sequence and Newton polygons), the writer develops the homes of p-adic Dirichlet L-series utilizing p-adic measures and integration. p-adic gamma features are brought, and their dating to L-series is explored. Analogies with the corresponding advanced analytic case are under pressure. Then a formulation for Gauss sums when it comes to the p-adic gamma functionality is proved utilizing the cohomology of Fermat and Artin-Schreier curves. Graduate scholars and learn staff in quantity concept, algebraic geometry and components of algebra and research will welcome this account of present research.

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The Book of Numbers by John H. Conway,Richard Guy PDF

By John H. Conway,Richard Guy

ISBN-10: 038797993X

ISBN-13: 9780387979939

ISBN-10: 1461284880

ISBN-13: 9781461284888

"...the nice characteristic of the booklet is that anybody can learn it with no over the top head scratching...You'll locate lots the following to maintain you occupied, amused, and knowledgeable. purchase, dip in, wallow." -IAN STEWART, NEW SCIENTIST
"...a pleasant examine numbers and their roles in every thing from language to vegetation to the imagination." -SCIENCE NEWS
"...a enjoyable and interesting travel of numerical issues and ideas. it is going to have readers considering principles they could by no means have idea have been comprehensible or maybe possible." -WISCONSIN BOOKWATCH
"This popularization of quantity conception appears like one other classic." -LIBRARY JOURNAL

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Read e-book online Die Wechselwirkung zwischen Zahlenrechnen und Zahlentheorie PDF

By Ph. Maennchen

ISBN-10: 3663154912

ISBN-13: 9783663154914

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer booklet information mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

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Download e-book for kindle: Number, Shape, & Symmetry: An Introduction to Number Theory, by Diane L. Herrmann,Paul J. Sally Jr.

By Diane L. Herrmann,Paul J. Sally Jr.

ISBN-10: 1466554649

ISBN-13: 9781466554641

Through a cautious remedy of quantity conception and geometry, Number, Shape, & Symmetry: An advent to quantity thought, Geometry, and team Theory is helping readers comprehend critical mathematical principles and proofs. Classroom-tested, the booklet attracts at the authors’ winning paintings with undergraduate scholars on the collage of Chicago, 7th to 10th grade mathematically gifted scholars within the college of Chicago’s younger students application, and basic public institution lecturers within the Seminars for Endorsement in technology and arithmetic schooling (SESAME).



The first half the ebook makes a speciality of quantity conception, starting with the principles of mathematics (axioms for the integers). The authors then current the entire easy principles and functions of divisibility, primes, and modular mathematics. in addition they introduce the summary thought of a gaggle and contain a variety of examples. the ultimate subject matters on quantity conception encompass rational numbers, genuine numbers, and concepts approximately infinity.



Moving directly to geometry, the textual content covers polygons and polyhedra, together with the development of normal polygons and common polyhedra. It reports tessellation by means of taking a look at styles within the airplane, particularly these made via average polygons or units of standard polygons. The textual content additionally determines the symmetry teams of those figures and styles, demonstrating how teams come up in either geometry and quantity theory.


The booklet is acceptable for pre-service or in-service education for basic tuition lecturers, basic schooling arithmetic or math for liberal arts undergraduate-level classes, and enrichment actions for top college scholars or math clubs.

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