1. Preface

This is a book on algebra, which, covers basics of algebra till high school level. It covers the most essential topics to take up a bachelor’s course where knowledge of algebra is required. There is no specific purpose for writing this book. This is a book for self study and is not recommended for courses in schools and universities. I will try to cover as much as I can and will keep adding new material over a long period. I have no interest in writing a book in a fixedly way which serves a university or college course as I have always loved freedom. Life, freedom and honor in that order are important. That was one of the reasons why I never did a masters course. Enough of personal rant. Let us get on with the actual work.

Algebra is probably one of the most fundamental subjects in Mathematics as further study of subjects like trigonometry, coordinate geometry and rest all depend on it. That is the primary reason I have chosen it to be the first subject in mathematics to be dealt with. It is very important to understand algebra for the readers if they want to advance further in mathematics.

1.1. Why I Wrote This Book?

I wrote this book for myself! No, I did not write it for anybody else. My knowledge, which I have acquired by reading books written by many great mathematicians and authors and interactions with many intelligent people, is what has been put in the book. I have just tried to add my flavor to it. Think of it as notes for me. Just that I like to organize my notes so it has taken form of a book and nothing more. If you benefit from this then that is a pure coincidence and not intentional at all.

1.2. How to Read This Book?

No I will not simply tell that you must solve the problems. My advice would be more detailed. Every chapter will have theory. Read that first. Make sure you understand that. Of course, you have to meet the prerequisites for the book. Then, go on and try to solve the problems. In this book, there are no pure problems. Almost all have answers except those which are of similar kind and repetitive in nature for the sake of practice. If you can solve the problem then all good else look at the answer and try to understand that. Then, few days later take on the problem again. If you fail to understand the answer you can always email me with your work and I will try to answer to the best of my ability. However, if you have a local expert seek his/her advice first. Just that email is bad for mathematics. Someday I will develop an email system with support for scientific symbols and equations.

Note that mathematics is not only about solving problems. If you understand the theory well, then you will be able to solve problems easily. However, problems do help enforce with the enforcement of theory in your mind.

1.3. Who Should Read This Book?

Since this book is written for self study anyone with interest in algebra can read it. That does not mean that school or college students cannot read it. You need to be selective as to what you need for your particular requirements. This is mostly high school course with a little bit of lower classes’ course thrown in with a bit of detail here and there.

1.4. Prerequisite

You should have knowledge till grade 10th course. Attempt has been made to keep it simple and give as much as background to the topic which is reasonable and required. However, not everything will be covered below grade 10.

1.5. Goals for Readers

The goal of for reading this book is becoming proficient in solving simple and basic problems of algebra. Another goal would be to be able to study other subjects which require this knowledge like trigonometry or calculus or physics or chemistry or other subjects. If you can solve 95% problems after 2 years of reading this book then you have achieved this goal.

All of us possess a certain level of intelligence. At average any person can read this book. But what is most important is you have to have interest in the subject. Your interest gets multiplied with your intelligence and thus you will be more capable than you think you can be. One more point is focus and effort. It is not something new which I am telling but I am saying it again just to emphasize the point. Trust me if you are reading this book for just scoring a nice grade in your course then I have failed in my purpose of explaining my ideas.

1.6. Acknowledgments

As with any book there are a lot of people involved with this book but not in traditional sense of a typical book. I have written this book using Sphinx for which entire Sphinx team deserves praise.

There are a lot of diagrams in this text and those have been drawn using Tikz. Thanks for its developers Till Tantau and Christian Feuersaenger along with all the contributors for creating such a wonderful piece of vector graphics library for TeX.

I must say thanks to my family particularly to my parents, wife and my son whose precious time I have taken to write this book and gave them numerous trouble in general. They have been the major force which supported while writing it. This book would not have been possible without their support.

There have been many teachers in my life who have helped me with various lessons in life and otherwise. I will try to remember all of them here and seek forgiveness if I miss anyone. My math teachers Yogendra Yadav, Hriday Nayaran Singh and Satyanand Satyarthi have helped me a lot with basics of Mathematics. Anurag Johri, Sirnivasa Kotu, Shreyas Majthia and Mufti Mohammad for their technical discussions and insight into programming. My professors S. Sen, S. Sengupta and T. K. Basu for showing faith in me during troubled times.

I am not native English speaker and it has gone through only one pair of eyes thus you should expect all kind of errors, particularly related to punctuation. I would be glad if you could report all errors, suggestions and feedback to me at email and those will be incorporated. Language_Tool has been used for grammar checks and all as my English is pathetic. However, if there are still mistakes in grammar and spellings then those mistakes are mine and not of the tool.

Although I would like to give a pdf version of the book for download but the content keep changing and there will be just too many versions of the book. Also, because of several customizations done in the book the pdf version does not come out as nice as html one. Also, for problems only 50 problems are given and same applies for solutions chapter. This is because MathJaX takes a lot of time to render mathematics if all the mathematical formulas are on the same page.

Update: Now I am using KaTeX to prerender the content so new chapters will have problems and solutions in the same page. As I find time I will change all topics to the same format.

Shiv Shankar Dayal

Nalanda, India