# Research and Markets: Algebra and Number Theory: An Integrated Approach

DUBLIN--()--Research and Markets (http://www.researchandmarkets.com/research/e3b8aa/algebra_and_number) has announced the addition of John Wiley and Sons Ltd's new report "Algebra and Number Theory: An Integrated Approach" to their offering.

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.

Key Topics Covered:

Chapter 1. Sets.
1.1. Operations on Sets.
1.2. Set mappings.
1.3. Products of Mappings.
1.4. Some properties of integers.

Chapter 2. Matrices and Determinants.
2.1. Operations on matrices.
2.2. Permutations of finite sets.
2.3. Determinants of matrices.
2.4. Computing Determinants.
2.5. Properties of the product of matrices.

Chapter 3. Fields.
3.1. Binary Algebraic Operations.
3.2. Basic Properties of Fields.
3.3. The Field of Complex Numbers.

Chapter 4. Vector Spaces.
4.1. Vector Spaces.
4.2. Dimension.
4.3. The Rank of a Matrix.
4.4. Quotient Spaces.

Chapter 5. Linear Mappings.
5.1. Linear Mappings.
5.2. Matrices of Linear Mappings.
5.3. Systems of Linear Equations.
5.4. Eigenvectors and eigenvalues.

Chapter 6. Bilinear Forms.
6.1. Bilinear Forms.
6.2. Classical Forms.
6.3. Symmetric forms over R.
6.4. Euclidean Spaces.

Chapter 7. Rings.
7.1. Rings, Subrings and Examples.
7.2. Equivalence Relations.
7.3. Ideals and Quotient Rings.
7.4. Homomorphisms of rings.
7.5. Rings of polynomials and formal power series.
7.6. Rings of multivariable polynomials.

Chapter 8. Groups.
8.1. Groups and Subgroups.
8.2. Examples of Groups and Subgroups.
8.3. Cosets.
8.4. Normal subgroups and Factor groups.
8.5. Homomorphisms of Groups.

Chapter 9. Arithmetic Properties of Rings.
9.1. Extending Arithmetic to Commutative Rings.
9.2. Euclidean Rings.
9.3. Irreducible Polynomials.
9.4. Arithmetic Functions.
9.5. Congruences.

Chapter 10. The Real Number System.
10.1. The Natural Numbers.
10.2. The Integers.
10.3. The Rationals.
10.4. The Real Numbers.

Answers to selected exercises.

Index.

Companies Mentioned:

MARTYN R. DIXON, PhD, is Professor in the Department of Mathematics at the University of Alabama, Tuscaloosa. He has authored more than sixty published journal articles on infinite group theory, formation theory and Fitting classes, wreath products, and automorphism groups.

LEONID A. KURDACHENKO, PhD, is Distinguished Professor and Chair of the Department of Algebra at the Dnepropetrovsk National University (Ukraine). Dr. Kurdachenko has authored more than 150 journal articles on the topics of infinite-dimensional linear groups, infinite groups, and module theory.

IGOR YA. SUBBOTIN, PhD, is Professor in the Department of Mathematics and Natural Sciences at National University (California). Dr. Subbotin is the author of more than 100 published journal articles on group theory, cybernetics, and mathematics education.

For more information visit http://www.researchandmarkets.com/research/e3b8aa/algebra_and_number

## Contacts

Research and Markets
Laura Wood, Senior Manager
U.S. Fax: 646-607-1907
Fax (outside U.S.): +353-1-481-1716
press@researchandmarkets.com

## Contacts

Research and Markets
Laura Wood, Senior Manager
U.S. Fax: 646-607-1907
Fax (outside U.S.): +353-1-481-1716
press@researchandmarkets.com