Giuseppe Modica Livres

The book addresses the crucial role of mathematics in intellectual development, highlighting its decline in educational settings. It critiques the current teaching methods that focus on rote problem-solving rather than fostering genuine understanding and independence. The authors emphasize the need for a more engaging approach that connects mathematics with real-life applications and other disciplines, while avoiding excessive technicality. They advocate for a presentation of mathematics that inspires curiosity and comprehension, rather than mere routine learning.

Focusing on the study of approximation and discrete processes, this volume is structured into two parts. The first part covers numerical systems including reals, integers, and complex numbers, introducing sequences and rethinking limits and continuity. It also explores combinatorial calculus and the fundamental theorem of algebra. The second part delves into discrete processes, discussing infinite summation and power series, culminating in an introduction to discrete dynamical systems, encouraging further exploration in the field.

Examines linear structures, the topology of metric spaces, and continuity in infinite dimensions, with detailed coverage at the graduate level Includes applications to geometry and differential equations, numerous beautiful illustrations, examples, exercises, historical notes, and comprehensive index May be used in graduate seminars and courses or as a reference text by mathematicians, physicists, and engineers