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Analytics Analytics. No one should buy this book or require it for a course at such an exorbitant price. Sep 06, WarpDrive rated it really liked it Shelves: Herstein for the mathematics undergrad.
It is simply disgusting. I feel like the book was good for a few concepts, but for the most part I had to rely on the internet. Colin Grove rated it it was ok Aug 01, This book is the reason I became a mathematician.
Lists with This Book. This book is OK as far as presenting abstract algebra in the usual way to undergrads. There were a few places in the book that took some time to get through and were confusing, however; with some additional aid online made it through to rings.
Numerous easy exercises, which is fine, although it might be nice if there were more challenging ones too. Return abstrwct Book Page. My favorite textbook of all time! Books by Joseph A. May 12, Anne aalgebra it it was amazing Shelves: Thanks for telling us about the problem. I want students to be able to do computations and to write proofs.
I want students to enjoy reading the book. And I want convey to the reader my enthusiasm for this beautiful subject. Educational research has shown that an effective way of learning mathematics is to interweave worked-out examples and practice problems. Thus, I have made examples and exercises the heart of the book. The examples elucidate the definitions, theorems, and proof techniques. The exercises facilitate understanding, provide insight, and develop the ability of the students to do proofs.
Another Persian mathematician Omar Khayyam is credited with identifying the foundations of algebraic geometry and found the general geometric solution of the cubic equation. His book Treatise on Demonstrations of Problems of Algebra , which laid down the principles of algebra, is part of the body of Persian mathematics that was eventually transmitted to Europe. In the 13th century, the solution of a cubic equation by Fibonacci is representative of the beginning of a revival in European algebra.
Another key event in the further development of algebra was the general algebraic solution of the cubic and quartic equations, developed in the midth century. Gabriel Cramer also did some work on matrices and determinants in the 18th century. Paolo Ruffini was the first person to develop the theory of permutation groups, and like his predecessors, also in the context of solving algebraic equations. Abstract algebra was developed in the 19th century, deriving from the interest in solving equations, initially focusing on what is now called Galois theory, and on constructibility issues.
Josiah Willard Gibbs developed an algebra of vectors in three-dimensional space, and Arthur Cayley developed an algebra of matrices this is a noncommutative algebra. Some areas of mathematics that fall under the classification abstract algebra have the word algebra in their name; linear algebra is one example. Others do not: group theory, ring theory, and field theory are examples.
In this section, we list some areas of mathematics with the word 'algebra' in the name. Elementary algebra is the most basic form of algebra. It is taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. In algebra, numbers are often represented by symbols called variables such as a , n , x , y or z.
This is useful because:. A polynomial is an expression that is the sum of a finite number of non-zero terms, each term consisting of the product of a constant and a finite number of variables raised to whole number powers. A polynomial expression is an expression that may be rewritten as a polynomial, by using commutativity, associativity and distributivity of addition and multiplication.
A polynomial function is a function that is defined by a polynomial, or, equivalently, by a polynomial expression. The two preceding examples define the same polynomial function. Two important and related problems in algebra are the factorization of polynomials, that is, expressing a given polynomial as a product of other polynomials that can not be factored any further, and the computation of polynomial greatest common divisors.
A related class of problems is finding algebraic expressions for the roots of a polynomial in a single variable. Abstract algebra extends the familiar concepts found in elementary algebra and arithmetic of numbers to more general concepts.
Here are listed fundamental concepts in abstract algebra. Sets : Rather than just considering the different types of numbers, abstract algebra deals with the more general concept of sets : a collection of all objects called elements selected by property specific for the set.
All collections of the familiar types of numbers are sets. Set theory is a branch of logic and not technically a branch of algebra.
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