Category: Number Theory

Pell and Pell–Lucas Numbers with Applications by Thomas Koshy

By Thomas Koshy

Pell and Pell–Lucas numbers, just like the famous Fibonacci and Catalan numbers, proceed to intrigue the mathematical global with their attractiveness and applicability. they give possibilities for experimentation, exploration, conjecture, and problem-solving recommendations, connecting the fields of study, geometry, trigonometry, and numerous parts of discrete arithmetic, quantity conception, graph concept, linear algebra, and combinatorics. Pell and Pell–Lucas numbers belong to a longer Fibonacci family members as a robust software for extracting various attention-grabbing houses of an unlimited array of quantity sequences.

A key characteristic of this paintings is the ancient taste that's interwoven into the broad and in-depth assurance of the topic. an attractive array of purposes to combinatorics, graph idea, geometry, and fascinating mathematical puzzles is one other spotlight attractive the reader. The exposition is straightforward, but rigorous, in order that a vast viewers inclusive of scholars, math lecturers and teachers, desktop scientists and different execs, besides the mathematically curious will all make the most of this book.

Finally, Pell and Pell–Lucas Numbers offers entertainment and pleasure whereas polishing the reader’s mathematical abilities regarding trend reputation, proof-and-problem-solving techniques.​

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Theory of Categories (Pure and Applied Mathematics (Academic by Barry Mitchell

By Barry Mitchell

Conception of different types. writer: Barry Mitchell. educational Press 1965. a few refined humans are likely to disparage class concept as continuously as others disparage yes sorts of classical song. for that reason, the writer provides to the standard prerequisite that the reader have a good quantity of mathematical sophistication. functions of Adjoint Functors, Extensions, Satellites, worldwide size, Sheaves.

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Mathematics and Its History by John Stillwell

By John Stillwell

From a overview of the second one edition:

"This e-book covers many attention-grabbing subject matters now not frequently lined in a gift day undergraduate path, in addition to sure simple subject matters resembling the advance of the calculus and the answer of polynomial equations. the truth that the themes are brought of their old contexts will let scholars to higher savour and comprehend the mathematical principles involved...If one constructs an inventory of issues valuable to a historical past direction, then they might heavily resemble these selected here."

(David Parrott, Australian Mathematical Society)

This publication deals a suite of historic essays detailing a wide number of mathematical disciplines and concerns; it’s obtainable to a wide viewers. This 3rd variation comprises new chapters on easy teams and new sections on alternating teams and the Poincare conjecture. Many extra routines were further in addition to observation that is helping position the workouts in context.

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Fundamentals of Number Theory by William J. LeVeque

By William J. LeVeque

This first-class textbook introduces the fundamentals of quantity idea, incorporating the language of summary algebra. a data of such algebraic thoughts as team, ring, box, and area isn't assumed, even if; all phrases are outlined and examples are given — making the ebook self-contained during this respect.
The writer starts off with an introductory bankruptcy on quantity concept and its early background. next chapters take care of distinct factorization and the GCD, quadratic residues, number-theoretic services and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diophantine approximation, and extra. incorporated are discussions of subject matters now not continuously present in introductory texts: factorization and primality of enormous integers, p-adic numbers, algebraic quantity fields, Brun's theorem on dual primes, and the transcendence of e, to say a few.
Readers will discover a vast variety of well-chosen difficulties, besides many notes and bibliographical references chosen for clarity and relevance. 5 valuable appendixes — containing such examine aids as an element desk, computer-plotted graphs, a desk of indices, the Greek alphabet, and an inventory of symbols — and a bibliography around out this well-written textual content, that's directed towards undergraduate majors and starting graduate scholars in arithmetic. No post-calculus prerequisite is believed. 1977 edition.

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Introduction to Classical Mathematics I: From the Quadratic by Helmut Koch

By Helmut Koch

` suggested for all libraries, this unmarried quantity may perhaps fill many gaps in smaller collections. '
Science & Technology

`The e-book is well-written, the presentation of the fabric is apparent. ... This very necessary, very good e-book is suggested to researchers, scholars and historians of arithmetic attracted to the classical improvement of arithmetic. '
Acta Scientiarum Mathematicarum, 56:3-4

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Number Theory 1: Fermat's Dream by Kazuya Kato, Visit Amazon's Nobushige Kurokawa Page, search

By Kazuya Kato, Visit Amazon's Nobushige Kurokawa Page, search results, Learn about Author Central, Nobushige Kurokawa, , Takeshi Saito

This can be the English translation of the unique jap publication. during this quantity, "Fermat's Dream", middle theories in smooth quantity idea are brought. advancements are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the quantity fields. This paintings offers a chic point of view at the ask yourself of numbers. quantity concept 2 on type box concept, and quantity conception three on Iwasawa thought and the idea of modular types, are approaching within the sequence.

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Introduction to Modern Prime Number Theory by T. Estermann

By T. Estermann

This booklet used to be first released in 1952. it really is principally dedicated to the thing of proving the Vinogradov-Goldbach theorem: that each sufficiently huge bizarre quantity is the sum of 3 primes. during proving this, T. Estermann, previously Professor of arithmetic on the college of London, provides quite a few theories and effects on characters and primes in mathematics progressions. the writer additionally guarantees that the proofs provided to the reader are either transparent and remarkably concise. the quantity to hand addresses the Riemann zeta functionality, primes in arithmetical development, and the ways that abnormal numbers might be represented because the sum of 3 primes. on the finish of the ebook is an index and a seven-page portion of theorems and formulae for reference. This quantity is either attention-grabbing and obtainable, and may entice all with an enthusiasm for arithmetic and challenge fixing.

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