A first course in rigorous mathematical analysis. Covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, sequences of functions, and metric spaces.
""A Companion to Analysis"" explains the problems that must be resolved in order to procure a rigorous development of the calculus and shows the student how to deal with those problems. Starting with the real line, the book moves on to finite-dimensional spaces and then to metric spaces.
By introducing logic and by emphasizing the structure and nature of the arguments used, this book helps readers transition from computationally oriented mathematics to abstract mathematics with its emphasis on proofs. Uses clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers.
The Oxford Users' Guide to Mathematics represents a comprehensive handbook on mathematics. It covers a broad spectrum of mathematics including analysis, algebra, geometry, foundations of mathematics, calculus of variations and optimization, theory of probability and mathematical statistics, numerical mathematics and scientific computing, and history of mathematics. This is supplemented by numerous tables on infinite series, special functions, integrals, integral transformations, mathematical statistics, and fundamental constants in physics.
These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of pre cise theorems with detailed definitions and technical details on how to carry out proofs and con structions.
Our task was to describe mathematical interrelations as briefly and precisely as possible. Important definitions and groups of formulae are on a yellow background, examples on blue, and theorems on red.