Modern Algebra with Applications by William J. Gilbert is a comprehensive and well-written textbook that covers the essential concepts of modern algebra. This book is designed for students of mathematics, science, and engineering who are interested in learning the fundamental theories and applications of modern algebra. The book provides a clear and in-depth explanation of the concepts, making it an ideal resource for students at all levels of mathematical proficiency.
The book is divided into several chapters, each of which covers a specific aspect of modern algebra. Topics covered in the book include groups, rings, fields, and modules. The author has also included numerous examples and exercises throughout the text to help students understand and apply the concepts they are learning.
One of the key strengths of this book is its accessibility. The author has made every effort to ensure that the language used in the book is clear and concise, making it easy for students to understand the material. Additionally, the book is well-organized and easy to navigate, making it a great resource for students who are studying on their own.
TABLE OF CONTENTS
Chapter 1 Introduction
- Classical Algebra
- Modern Algebra
- Binary Operations
- Algebraic Structures
- Extending Number Systems
Chapter 2 Boolean Algebras
- Algebra of Sets
- Number of Elements in a Set
- Boolean Algebras
- Propositional Logic
- Switching Circuits
- Divisors
- Posets and Lattices
- Normal Forms and Simplification of Circuits
- Transistor Gates
- Representation Theorem
Chapter 3 Groups
- Groups and Symmetries
- Subgroups
- Cyclic Groups and Dihedral Groups
- Morphisms
- Permutation Groups
- Even and Odd Permutations
- Cayley’s Representation Theorem
.
Chapter 4 Quotient Groups
- Equivalence Relations
- Cosets and Lagrange’s Theorem
- Normal Subgroups and Quotient Groups
- Morphism Theorem
- Direct Products
- Groups of Low Order
- Action of a Group on a Set
Chapter 5 Symmetry Groups in Three Dimensions
- Translations and the Euclidean Group
- Matrix Groups
- Finite Groups in Two Dimensions
- Proper Rotations of Regular Solids
- Finite Rotation Groups in Three Dimensions
- Crystallographic Groups
Chapter 6 Polya-Burnside Method of Enumeration
- Burnside’s Theorem
- Necklace Theorem
- Coloring Polyhedra
- Counting Switching Circuits
Chapter 7 Monoids and Machines
- Monoids and Semigroups
- Finite-State Machines
- Quotient Monoids and the Monoid of a Machine
Chapter 8 Rings and Fields
- Rings
- Integral Domains and Fields
- Subrings and Morphisms of Rings
- New Rings from Old
- Field of Fractions
- Convolution Fractions
Chapter 9 Polynomial and Euclidean Rings
- Euclidean Rings
- Euclidean Algorithm
- Unique Factorization
- Factoring Real and Complex Polynomials
- Factoring Rational and Integral Polynomials
- Factoring Polynomials over Finite Fields
- Linear Congruence and the Chinese Remainder Theorem
Chapter 10 Quotient Rings
- Ideals and Quotient Rings
- Computations in Quotient Rings
- Morphism Theorem
- Quotient Polynomial Rings That are Fields
Chapter 11 Field Extensions
- Field Extensions
- Algebraic Numbers
- Galois Fields
- Primitive Elements
Chapter 12 Latin Squares
- Latin Squares
- Orthogonal Latin Squares
- Finite Geometries
- Magic Squares
Chapter 13 Geometrical Constructions
- Contructible Numbers
- Duplicating a Cube
- Trisecting an Angle
- Squaring the Circle
- Constructing Regular Polygons
- Non-constructible Number of Degree
Chapter 14 Error-Correcting Codes
- The Coding Problem
- Simple Codes
- Polynomial Representation
- Matrix Representation
- Error Correcting and Decoding
- BCH Codes
Download Now Book in PDF
The book is also available in PDF format, allowing students to easily access and study the material from their computer or mobile device. This is especially useful for students who are unable to attend physical classes or who prefer to study at their own pace. With the PDF format, students can easily search for specific information, make notes, and highlight important sections of the text.
In conclusion, Modern Algebra with Applications by William J. Gilbert is an excellent resource for students who are interested in learning about modern algebra. The book provides a clear and comprehensive overview of the subject, making it an ideal resource for students at all levels of mathematical proficiency. And with the availability of the book in PDF format, students can easily access and study the material at their convenience.
