Books in Algebra and number theory

Linear Algebra

4th Edition
February 27, 2023
Richard Bronson + 3 more
English
Paperback
9 7 8 - 0 - 1 2 - 8 2 3 4 7 0 - 9
eBook
9 7 8 - 0 - 3 2 3 - 9 8 4 2 7 - 0

Linear Algebra: Algorithms, Applications, and Techniques, Fourth Edition offers a modern and algorithmic approach to computation while providing clear and straightforward theoretical background information. The book guides readers through the major applications, with chapters on properties of real numbers, proof techniques, matrices, vector spaces, linear transformations, eigen values, and Euclidean inner products. Appendices on Jordan canonical forms and Markov chains are included for further study. This useful textbook presents broad and balanced views of theory, with key material highlighted and summarized in each chapter. To further support student practice, the book also includes ample exercises with answers and hints.

Factorization of Boundary Value Problems Using the Invariant Embedding Method

1st Edition
October 12, 2016
Jacques Henry + 1 more
English
Hardback
9 7 8 - 1 - 7 8 5 4 8 - 1 4 3 - 7
eBook
9 7 8 - 0 - 0 8 - 1 0 1 0 9 0 - 7

Factorization Method for Boundary Value Problems by Invariant Embedding presents a new theory for linear elliptic boundary value problems. The authors provide a transformation of the problem in two initial value problems that are uncoupled, enabling you to solve these successively. This method appears similar to the Gauss block factorization of the matrix, obtained in finite dimension after discretization of the problem. This proposed method is comparable to the computation of optimal feedbacks for linear quadratic control problems.

A Collection of Contributions in Honour of Jack van Lint

1st Edition
June 6, 2016
P.J. Cameron + 1 more
English
eBook
9 7 8 - 1 - 4 8 3 2 - 9 4 1 9 - 3

This collection of contributions is offered to Jack van Lint on the occasion of his sixtieth birthday and appears simultaneously in the series Topics in Discrete Mathematics and as a special double volume of Discrete Mathematics (Volumes 106/107). It is hoped that the papers selected, all written by experts in their own fields, represent the many interesting areas that together constitute the discipline of Discrete Mathematics. It is in this sphere that van Lint has become the acknowledged master and this expansive volume serves to demonstrate the enormous significance he has had on the development of Discrete Mathematics during the last 30 years.

Nonarchimedean Fields and Asymptotic Expansions

1st Edition
February 17, 2016
A. H. Lightstone + 1 more
English
eBook
9 7 8 - 1 - 4 8 3 2 - 5 7 4 4 - 0

North-Holland Mathematical Library, Volume 13: Nonarchimedean Fields and Asymptotic Expansions focuses on the connection between nonarchimedean systems and the orders of infinity and smallness that are related with the asymptotic behavior of a function. The publication first explains nonarchimedean fields and nonstandard analysis. Discussions focus on the method of mathematical logic, ultrapower construction, principles of permanence, internal functions, many-sorted structures, nonarchimedean fields and groups, and fields with evaluation. The text then discusses the Euler-Maclaurin expansions and the formal concept of asymptotic expansions. Topics include a generalized criterion for asymptotic expansions, asymptotic power series, Watson's Lemma, asymptotic sequences, and the Euler-Maclaurin formula. The manuscript examines Popken space, including asymptotically finite functions, convergence, norm, algebraic properties of the norm, and Popken's description of the norm. The text is a dependable reference for mathematicians and researchers interested in nonarchimedean fields and asymptotic expansions.

Algebraic and Discrete Mathematical Methods for Modern Biology

1st Edition
March 25, 2015
Raina Robeva
English
Hardback
9 7 8 - 0 - 1 2 - 8 0 1 2 1 3 - 0
eBook
9 7 8 - 0 - 1 2 - 8 0 1 2 7 1 - 0

Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution.

Mathematical Problems and Puzzles

1st Edition
June 28, 2014
S. Straszewicz
I. N. Sneddon + 1 more
English
eBook
9 7 8 - 1 - 4 8 3 2 - 8 0 3 1 - 8

Popular Lectures in Mathematics, Volume 12: Mathematical Problems and Puzzles: From the Polish Mathematical Olympiads contains sample problems from various fields of mathematics, including arithmetic, algebra, geometry, and trigonometry. The contest for secondary school pupils known as the Mathematical Olympiad has been held in Poland every year since 1949/50. This book is composed of two main parts. Part I considers the problems and solutions about integers, polynomials, algebraic fractions and irrational experience. Part II focuses on the problems of geometry and trigonometric transformation, along with their solutions. The provided solutions aim to extend the student’s knowledge of mathematics and train them in mathematical thinking. This book will prove useful to secondary school mathematics teachers and students.

Contributions to Universal Algebra

1st Edition
May 15, 2014
B. Csákány + 1 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 0 3 0 2 - 0

Contributions to Universal Algebra focuses on the study of algebra. The compilation first discusses the congruence lattice of pseudo-simple algebras; elementary properties of limit reduced powers with applications to Boolean powers; and congruent lattices of 2-valued algebras. The book further looks at duality for algebras; weak homomorphisms of stone algebras; varieties of modular lattices not generated by their finite dimensional members; and remarks on algebraic operations of stone algebras. The text describes polynomial normal forms and the embedding of polynomial algebras; coverings in the lattice of varieties; embedding semigroups in semigroups generated by idempotents; and endomorphism semigroups and subgroupoid lattices. The book also discusses a report on sublattices of a free lattice, and then presents the cycles in finite semi-distributive lattices; cycles in S-lattices; and summary of results. The text also describes primitive subsets of algebras, ideals, normal sets, and congruences, as well as Jacobson’s density theorem. The book is a good source for readers wanting to study algebra.

A Concrete Approach To Abstract Algebra,Student Solutions Manual (e-only)

1st Edition
April 15, 2010
Jeffrey Bergen
English
eBook
9 7 8 - 0 - 1 2 - 3 8 4 6 8 1 - 5

A Concrete Approach to Abstract Algebra begins with a concrete and thorough examination of familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials, in this unique approach, the author builds upon these familar objects and then uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. The text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics wich arise in courses in algebra, geometry, trigonometry, precalculus and calculus. The final four chapters present the more theoretical material needed for graduate study.