Mathematics is a fundamental and essential subject that is studied at all levels of education. From basic arithmetic to advanced topics such as calculus, algebra, and geometry, mathematics is the foundation of many fields of study, including science, engineering, and finance.
Thomas W. Hungerford’s Graduate Text in Mathematics is a comprehensive study of mathematical concepts that are essential for students and professionals in a wide range of fields. The book is designed for graduate students and advanced undergraduates who are studying mathematics, as well as for those who are preparing for professional exams in the field.
The book covers a wide range of mathematical topics, including algebra, topology, and analysis. Each chapter is written in a clear and concise manner, making it easy for students to understand the concepts and techniques presented. The book includes numerous examples and exercises, as well as explanations of key concepts, to help students understand and practice the techniques presented.
TABLE OF CONTENTS
Chapter I: Groups
- Semigroups, Monoids and Groups
- Homomorphisms and Subgroups
- Cyclic Groups
- Cosets and Counting
- Normality, Quotient Groups, and Homomorphisms
- Symmetric, Alternating, and Dihedral Groups
- Categories: Products, Coproducts, and Free Objects
- Direct Products and Direct Sums
- Free Groups, Free Products, Generators & Relations
Chapter II: The Structure of Groups
- Free Abelian Groups
- 20 Finitely Generated Abelian Groups
- The Krull-Schmidt Theorem
- The Action of a Group on a Set
- The Sylow Theorems
- Classification of Finite Groups
- Nilpotent and Solvable Groups
- Subnormal Series
Chapter Ill: Rings
- Rings and Homomorphisms
- Ideals
- Factorization in Commutative Rings
- Rings of Quotients and Localization
- Rings of Polynomials and Formal Power Series
- Factorization in Polynomial Rings
Chapter IV: Modules
- Modules, Homomorphisms and Exact Sequences
- Free Modules and Vector Spaces
- Projective and Injective Modules
- Hom and Duality
- Tensor Products
- Modules over a Principal Ideal Domain
- Algebras
Chapter V: Fields and Galois Theory
- Field Extensions
- Appendix: Ruler and Compass Constructions
- The Fundamental Theorem
- Appendix: Symmetric Rational Functions
- Splitting Fields, Algebraic Closure and Normality
- Appendix: The Fundamental Theorem of Algebra
- The Galois Group of a Polynomial
- Finite Fields
- Separability
- Cyclic Extensions
- Cyclotomic Extensions
- Radical Ex tensions
Chapter VI: The Structure of Fields
- Transcendence Bases
- Linear Disjointness and Separability
Chapter VII: Linear Algebra
- Matrices and Maps
- Rank and Equivalence
- Determinants
- Decomposition of a Single Linear Transformation and Similarity
- The Characteristic Polynomial, Eigenvectors and ·Eigenvalues
Chapter VIII: Commutative Rings and Modules
- Chain Conditions.
- Prime and Primary Ideals
- Primary Decomposition
- Noetherian Rings and Modules
- Ring Extensions
- Dedekind Domains
- The Hilbert Nullstellensatz
Chapter IX: The Structure of Rings
- Simple and Primitive Rings
- The Jacobson Radical
- Semisimple Rings
- The Prime Radical; Prime and Semiprime Rings
- Algebras
- Division Algebras
Chapter X: Categories
- Functors and Natural Transformations
- Adjoint Functors
- Morphisms
Download Now Book in PDF
One of the strengths of Hungerford’s book is its focus on the foundations of mathematics. The book covers the basics of mathematical concepts and then builds upon these concepts to explore more advanced topics. This makes it a great resource for students who are just starting to study mathematics, as well as for those who want to deepen their understanding of the subject.
Another great feature of this book is its comprehensive coverage of mathematical concepts. Whether you are a student who needs to learn the basics or an advanced learner looking for a comprehensive review, this book has everything you need. It provides a strong foundation for students who want to move on to more advanced mathematical subjects, such as abstract algebra or differential geometry.
We are pleased to announce that Graduate Text in Mathematics by Thomas W. Hungerford is available in PDF format, so students can easily download and access it. Whether you prefer to study on your own or with a teacher, this book is a valuable resource for anyone who wants to gain a deeper understanding of mathematics.
In conclusion, Graduate Text in Mathematics by Thomas W. Hungerford is a comprehensive study of mathematical concepts. Its clear writing style, comprehensive coverage of concepts, and numerous examples and exercises make it an ideal resource for students, teachers, and anyone looking to improve their understanding of mathematics.
