This book is intended for seniors and beginning graduate students. It is self-contained and covers the topics usually taught at this level.

The book is divided into five parts (see diagram). Part I (Chapters 1-3) is a prerequisite for the rest of the book. It contains an informal introduction to sets, number systems, matrices, and determinants. Results proved in Chapter 1 include the Schröder–Bernstein theorem and the cardinality of the set of real numbers. In Chapter 2, starting from the well-ordering principle of natural numbers, some important algebraic properties of integers have been proved. Chapter 3 deals with matrices and determinants. It is expected that students would already be familiar with most ...

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