This book introduces all the important topics in the field: complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form and more. Includes many engaging exercises.

Written in an informal style that intersperses history and philosophy with mathematics, this class-tested, self-contained book demonstrates how some simple construction tools can be associated with various fields of real numbers through coordinate geometry.

This text is intended for an honors calculus course or for an introduction to  analysis. Involving rigorous analysis, computational dexterity, and a breadth of  applications, it is ideal for undergraduate majors. This third edition includes  corrections as well as some additional material.  Some features of the text: The text is completely self-contained and starts with the real number  axioms; There is a heavy emphasis on computational problems; There are applications from many parts of analysis, e.g., convexity, the  Cantor set, continued fractions, the AGM, the theta and zeta functions, and many more; Traditionally transcendentally presented material, such as infinite  products, the Bernoulli series, and the zeta functional equation, is developed  over the reals; There are 385 problems with all the solutions at the back of the text.