Archive for the ‘algebra’ Category

Stimulating collection of over 300 unusual problems involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms and more. Problems range from easy to difficult. Detailed solutions, as well as brief answers, for all problems are provided.

Challenging Problems in Algebra 2E (Dover) – Posamentier . Salkind

This work blends together classic inequality results with brand new problems, some of which devised only a few weeks ago. What could be special about it when so many inequality problem books have already been written? We strongly believe that even if the topic we plunge into is so general and popular our book is very different. Of course, it is quite easy to say this, so we will give some supporting arguments. This book contains a large variety of problems involving inequalities, most of them difficult, questions that became famous in competitions because of their beauty and difficulty. And, even more importantly, throughout the text we employ our own solutions and propose a large number of new original problems. There are memorable problems in this book and memorable solutions as well. This is why this work will clearly appeal to students who are used to use Cauchy-Schwarz, Schur, AM-GM, etc. as a verb and want to further improve their algebraic skills and techniques. They will find here tough problems, new results, and even problems that could lead to research. The student who is not as keen in this field will also be exposed to a wide variety of moderate and easy problems, ideas, techniques, and
all the ingredients leading to a good preparation for mathematical contests. Some of the problems we chose to present are known, but we have included them here with new solutions which show the diversity of ideas pertaining to inequalities. Anyone will find here a challenge to prove his or her skills. If we have not convinced you, then please take a look at the problems from this book and hopefully you will agree with us.

This book contains 101 highly rated problems used in training and testing the USA IMO Team. It gradually builds students algebraic skills and techniques and aims to broaden students views of mathematics and better prepare them for participation in mathematics competitions. It provides in-depth enrichment in important areas of algebra by reorganizing and enhancing students problem-solving tactics and stimulates interest for future study of mathematics. The problems are carefully graded, ranging from quite accessible towards quite challenging. The problems have been well developed and are highly recommended to any student aspiring to participate at National or International Mathematical Olympiads.

101 problems in Algebra

This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and elds. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown signi cantly.