Author: Peter Jephson Cameron
Publisher: Oxford University Press, USA
This book is an undergraduate textbook on abstract algebra, beginning with the theories of rings and groups. As this is the first really abstract material students need, the pace here is gentle, and the basic concepts of subring, homomorphism, ideal, etc are developed in detail. Later, as students gain confidence with abstractions, they are led to further developments in group and ring theory (simple groups and extensions, Noetherian rings, and outline of universal algebra, lattices andcategories) and to applications such as Galois theory and coding theory. There is also a chapter outlining the construction of the number systems from scratch and proving in three different ways that trascendental numbers exist.
Author: Peter J. Cameron
Publisher: Oxford University Press on Demand
This Second Edition of a classic algebra text includes updated and comprehensive introductory chapters,new material on axiom of Choice, p-groups and local rings, discussion of theory and applications, and over 300 exercises. It is an ideal introductory text for all Year 1 and 2 undergraduate students in mathematics.
Author: R. Kochendorffer
Publisher: Springer Science & Business Media
This book is intended as a textbook for an undergraduate course on algebra. In most universities a detailed study ·of abstract algebraic systems commences in the second year. By this time the student has gained some experience in mathematical reasoning so that a too elementary book would rob him of the joy and the stimulus of using his ability. I tried to make allowance for this when I chose t4e level of presentation. On the other hand, I hope that I also avoided discouraging the reader by demands which are beyond his strength. So, the first chapters will certainly not require more mathematical maturity than can reasonably be expected after the first year at the university. Apart from one exception the formal prerequisites do not exceed the syllabus of an average high school. As to the exception, I assume that the reader is familiar with the rudiments of linear algebra, i. e. addition and multiplication of matrices and the main properties of determinants. In view of the readers for whom the book is designed I felt entitled to this assumption. In the first chapters, matrices will almost exclusively occur in examples and exercises providing non-trivial instances in the theory of groups and rings. In Chapters 9 and 10 only, vector spaces and their properties will form a relevant part of the text. A reader who is not familiar with these concepts will have no difficulties in acquiring these prerequisites by any elementary textbook, e. g. .
An Introduction to Algebra
Author: Bernard L. Johnston,Fred Richman
Publisher: CRC Press
This textbook presents modern algebra from the ground up using numbers and symmetry. The idea of a ring and of a field are introduced in the context of concrete number systems. Groups arise from considering transformations of simple geometric objects. The analysis of symmetry provides the student with a visual introduction to the central algebraic notion of isomorphism. Designed for a typical one-semester undergraduate course in modern algebra, it provides a gentle introduction to the subject by allowing students to see the ideas at work in accessible examples, rather than plunging them immediately into a sea of formalism. The student is involved at once with interesting algebraic structures, such as the Gaussian integers and the various rings of integers modulo n, and is encouraged to take the time to explore and become familiar with those structures. In terms of classical algebraic structures, the text divides roughly into three parts:
Author: Martin M. Zuckerman
Publisher: Rowman & Littlefield
This book covers the basic topics in arithmetic and algebra with which every college student should be thoroughly familiar. It is written with the student in mind, in a style and at a level appropriate for student understanding.
Author: Kenji Ueno
Publisher: American Mathematical Soc.
This introduction to algebraic geometry allows readers to grasp the fundamentals of the subject with only linear algebra and calculus as prerequisites. After a brief history of the subject, the book introduces projective spaces and projective varieties, and explains plane curves and resolution of their singularities. The volume further develops the geometry of algebraic curves and treats congruence zeta functions of algebraic curves over a finite field. It concludes with a complex analytical discussion of algebraic curves. The author emphasizes computation of concrete examples rather than proofs, and these examples are discussed from various viewpoints. This approach allows readers to develop a deeper understanding of the theorems.
Author: John Milnor
Publisher: Princeton University Press
Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.
Author: Linus Christian Rollman
Publisher: Arbor Center for Teaching
First in the Arbor Algebra series. A writing-based, common sense, whimsical & engaging introduction to algebra for middle-grade math students.