Электронная книга: Leonid Kurdachenko A. «Algebra and Number Theory. An Integrated Approach»

Algebra and Number Theory. An Integrated Approach

Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors'extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers'retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.

Издательство: "John Wiley&Sons Limited"

ISBN: 9780470640531

электронная книга

Купить за 12355.38 руб и скачать на Litres

Другие книги автора:

КнигаОписаниеГодЦенаТип книги
An Introduction to Essential Algebraic StructuresA reader-friendly introduction to modern algebra with important examples from various areas of mathematics Featuring a clear and concise approach, An Introduction to Essential Algebraic Structures… — John Wiley&Sons Limited, электронная книга Подробнее...6794.91электронная книга
Ranks of Groups. The Tools, Characteristics, and RestrictionsA comprehensive guide to ranks and group theory Ranks of Groups features a logical, straightforward presentation, beginning with a succinct discussion of the standard ranks before moving on to… — John Wiley&Sons Limited, электронная книга Подробнее...7717.99электронная книга

Look at other dictionaries:

  • algebra — /al jeuh breuh/, n. 1. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. 2. any of… …   Universalium

  • University of Maryland, Baltimore County Majors and Programs — The University of Maryland, Baltimore County Majors and Programs include 42 majors, 41 minors and 17 certificate programs. These programs range from the arts, engineering and information technology, humanities, sciences, pre professional studies… …   Wikipedia

  • Dynamical systems theory — is an area of applied mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical …   Wikipedia

  • Boolean algebra (logic) — For other uses, see Boolean algebra (disambiguation). Boolean algebra (or Boolean logic) is a logical calculus of truth values, developed by George Boole in the 1840s. It resembles the algebra of real numbers, but with the numeric operations of… …   Wikipedia

  • Set theory — This article is about the branch of mathematics. For musical set theory, see Set theory (music). A Venn diagram illustrating the intersection of two sets. Set theory is the branch of mathematics that studies sets, which are collections of objects …   Wikipedia

  • Control theory — For control theory in psychology and sociology, see control theory (sociology) and Perceptual Control Theory. The concept of the feedback loop to control the dynamic behavior of the system: this is negative feedback, because the sensed value is… …   Wikipedia

  • Constructivism (learning theory) — Jean Piaget: founder of Constructivism Constructivism is a theory of knowledge (epistemology)[1] that argues that humans generate knowledge and meaning from an interaction between their experiences and their ideas. During infancy, it was an… …   Wikipedia

  • Canonical form (Boolean algebra) — In Boolean algebra, any Boolean function can be expressed in a canonical form using the dual concepts of minterms and maxterms. Minterms are called products because they are the logical AND of a set of variables, and maxterms are called sums… …   Wikipedia

  • Fundamental theorem of algebra — In mathematics, the fundamental theorem of algebra states that every non constant single variable polynomial with complex coefficients has at least one complex root. Equivalently, the field of complex numbers is algebraically closed.Sometimes,… …   Wikipedia

  • Representation theory of SU(2) — In the study of the representation theory of Lie groups, the study of representations of SU(2) is fundamental to the study of representations of semisimple Lie groups. It is the first case of a Lie group that is both a compact group and a non… …   Wikipedia

  • mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium