Alain Robert Boeken

Discovered at the turn of the 20th century, p-adic numbers are frequently used by mathematicians and physicists. This text is a self-contained presentation of basic p-adic analysis with a focus on analytic topics. It offers many features rarely treated in introductory p-adic texts such as topological models of p-adic spaces inside Euclidian space, a special case of Hazewinkel’s functional equation lemma, and a treatment of analytic elements.

Focusing on resilience and determination, the narrative follows the Human Spider, who has triumphed over vertigo and numerous injuries to become an accomplished skyscraper climber. Having scaled nearly 100 buildings globally, his journey is a testament to overcoming fear and pushing beyond personal limits, showcasing the power of the human spirit in the face of adversity.

Infinitesimals have been hotly debated since the invention of calculus 300 years ago. This accessible treatment of nonstandard analysis (NSA) presents an elementary, yet rigorous account of the theory of infinitesimals and derives some known mathematical results in a nonclassical way. Provides recent solutions to mathematical questions which remained unsolved until the advent of NSA. Treatment is self-contained and includes exercises with detailed solutions. This wonderful little book...is simple and brilliant, deep and witty, short and far-ranging...''"(--J.-M. Ley-Leblond, European Journal of Physics)"