Introduction to Algebra 2nd Edition by Peter J. Cameron (PDF)

Description

Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of vector spaces andmodules with applications to abelian groups and canonical forms before returning to the construction of the number systems, including the existence of transcendental numbers. The final chapters take the reader further into the theory of groups, rings and fields, coding theory, and Galois theory. Withover 300 exercises, and web-based solutions, this is an ideal introductory text for Year 1 and 2 undergraduate students in mathematics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐It is refreshing to find an author who has expressed a different approach to the subject of Algebra. It provides stimulating insight to the subject in Mathematics.

⭐This is a wonderful introductory textbook. I would say it is one of the most lucid books of mathematics I have ever used.

⭐This is not a bad book but not more than an average text. The introduction is grafted on summary of high school algebra that isn’t very cohesive or structured.The presentations are rigorous but most modern math books are as well. The presentation is dry. I like math and math texts. Some add humor, some add history, and some add examples of applications to make things more interesting. This book could serve as the basis for a good course if the lecturer was dynamic but as a read it is only average.

⭐terrible textbook! I literally only used this for the questions it asked, but my classmates and I ended up teaching ourselves with google on this subject because the textbook was so hard to follow.

⭐Plastic bag of the parcel is very weak,but the ratio quality/price is very good!

⭐A+++++++++++ Excellent Item

⭐I bought the wrong book…probably I misread the description about the book’s content or the description was not clear.

⭐Peter J. Cameron’s “Introduction to Algebra” is exactly that, an introduction to algebra and a good one at that. I must confess that before reading this book had a very limited knowledge of abstract algebra however with a little bit of time and effort I am now quite comfertable with the subject thanks to this book.”Algebra” is divided into a 8 sections: 1) Set Theory and Relation Theory 2) Ring Theory 3) Group Theory 4) Vector Spaces 5) Modules 6) Numbers 7) More Rings and Groups 8) Galois theory and coding theoryThis book succeeds by having an interesting writing style, not being dry, and at the same time being very rigorous. The rigor is always present and all proofs are carefully developed however the “feel” of the subject is never lost as Cameron strives to help the reader grasp the “shape” of the algebraic structures that he introduces.This book has a slightly wider scope than many introductory algebra books however it succeeds in covering all of its topics well although the sections on category theory and algebraic geometry are only a page or two long and thus are only present to whet the reader’s interest. In addition, Cameron motivates the discussions by drawing the topics together in the end in the applications chapter. This chapter covers the basics of the commonly known Galois theory and the less covered Coding theory which is one of the backbones of the internet.Final: Buy this book for a good introduction. I have borrowed a number of other introductory books from the university up the hill but this one was the clearest for me.

⭐Introduction (I. m. h. o)The book wants to build upon the fundamental principles, so jumps ‘feet-first’ by introducing fundamental concepts of algebra. So he establishes by axiomatic reasoning to support deeper works. The author is sympathetic that this will be challenging to most.Then using this earlier works, he continues by exploring sets & rings, field’s polynomials, mod (n), and homomorphism, images and kernels and Group theory basics. The nice thing is some of these questions have worked solutions in the back of the book.With these challenging topics established he continues to build into explorations within basis, vector spaces, matrices, linear transformations, determinants, eigenvectors to solve equations. Later it touches on Galois theory but not in-depth.The stuff your learning here is well directed and will be directly useful in later work on this very topic and Number Theory. I have gone over this book again to refresh my grasp and it’s nice and easy to get hold of the topics.SummaryOverall this is a well-rounded introduction. You begin to see why topics are addressed from differing perspectives to make the area more rewarding, and so the fuller picture is received.

⭐Very clear text book

⭐A MUST HAVE for any new undergraduates who will learn Abstract Algebra. I love how the explanations are clear, and that the author gets straight to the main point. This book is far more useful than my own lecturer.However, I found it strange that you learn about rings before knowing what groups are (since rings are groups).

⭐Introduction to Algebra is a beautifully crafted text, that encourages you to keep on reading. It has a light touch without loosing any rigor. It is well paced and as such it lends itself to self study (my mode of learning); but oh! to have been at Queen Mary and Westfield College to experience the material first hand. A wonderful introduction to Abstract Algebra.

⭐Very detailed and well written.

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