I am pleased to place this Up-to-date First Edition of Mathematics - I in the hands of B.Sc. (Information Technology) students of Mumbai University in particular and other Indian Universities in general. The book is written strictly according to the syllabus of Mathematics-I (B.Sc. Information Technology) of Mumbai University in force.

The book is an outcome of over thirty-five years of teaching Mathematics to students of Engineering and Science, of writing over thirty books on Mathematics and Statistics for degree and diploma courses, of careful study of the syllabus of B.Sc. (I.T.) of University of Mumbai. I have made extensive use of university question papers so that after studying according to the present book, the students will have a clear understanding of the subject, of the type of examples they can expect at the final examination and will be hopefully able to solve them successfully.

Mathematics, no doubt, is a tool for you. But to make it effective, it is imperative for you to know clearly the tool works. This, in turn, requires clear understanding of the concepts and methods of higher mathematics. A teacher of Mathematics has to strike a golden mean between rigorous mathematical proofs of the theorems, which often tend to be tedious, and mere applications of these theorems to problems which tend to be difficult to grasp. With this difficulty in mind, an attempt has been made in this book to explain the theory through illustrations, diagrams and examples whenever it was found sufficient for understanding the concepts involved. Some concepts and theorems are discussed through examples and rigorous mathematical proofs are given where it was found unavoidable. In short, every care has been taken to see that unnecessary material is not presented and necessary material is not left out, and to see that the book is student-friendly.

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To make the matter easy for understanding, main topics have been divided into sub-topics, and illustrative examples with complete solutions are given after theoretical discussion of each topic. Whenever possible, alternative methods of solving problems are given. I have given a large number of examples in the exercises for practice. These examples are mostly taken from the university question papers and some are newly constructed according to the need. This will help students to know the nature of problems they are expected to face and the methods of solving such problems. In addition to this, I have given a large number of miscellaneous examples with complete solutions at the end of each chapter, and an equally large number of examples in the exercise for practice with sufficient hints. These examples are properly graded and carefully classified so that a student can have sufficient drill-work requiring a particular technique. In short, the book noris so designed that it becomes complete in all respects and meets the demands of tonthe students of both average and above-average calibre. It also fulfils tof expectations of the university syllabus in letter and spirit.

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