I N herstein abstract algebra Pdf

Abstract algebra is a branch of mathematics concerned with the study of algebraic structures. The earliest known writing about abstract algebra was by Arabian mathematician Al-Mahani who wrote his now-lost book “Book of the Balancing and Scales” (كتاب التسليم والمقابلة) circa 830 AD. In this work he used the techniques of diagrammatic algebra (which can be traced back to Diophantus) in order to solve quadratic equations and eventually cubic equations, governed by certain geometric problems. Another early contributor to abstract algebra was Al-Karaji who stated the fundamental theorem of algebra and investigated the general binomial theorem. Another mathematician, Omar Khayyám, studied and generalized binomial expansions before investigating infinite series and developing some very sophisticated mathematical proofs, including a proof that π cannot be exactly calculated.

 

Abelian categories are among the most important and widely used structures in mathematics. An enormous amount of effort has gone into the study of them, culminating in their becoming the basis of algebraic K-theory. This book can be considered an introduction to Abelian categories and K-theory for graduate students or researchers already familiar with algebra and homological algebra. As such, it will not presuppose a background in abstract algebra but will assume that the user is able to work in some related area. The subject is approached from a global perspective where toposes play a key role.

 

I don’t know about you, but I absolutely love learning about the different cultures and places around the world. The scenery and historical landmarks of each country is always so fascinating to me. However, after traveling quite a bit both inside and outside of the United States, there are some countries that I haven’t had the opportunity to see yet. This makes me want to travel even more! Looking at different locations on Google Earth makes me wonder what these places are like in person.