Mathematics and its cognition

Author: Gao Longchang
Publisher:
Publish Date: 2001-10-01
Features: This book integrates mathematics, science, and philosophy, using mathematical thinking to understand mathematics. The overall spirit is to focus on applied mathematics and gain a panoramic view of the entire field of mathematics. The topics are chosen in a cross-sectional and comprehensive manner, following the historical development to tell the story. It emphasizes information content, introducing the major thought systems of mathematics, and paying attention to inspiring mathematical thinking and mathematical awareness. The main content of this book includes: the fundamental characteristics of mathematics; an exploration of the logical categories of mathematics; the understanding of dualism; a re-examination of algebra; a re-examination of real numbers; an understanding of the essence of complex numbers; periodic mathematics and its understanding; the essence of infinitesimals and its understanding; the essence of modern mathematics and its relationship with the essence of social sciences; and so on. The preliminary lectures of this book have been used for 5 years and have been very popular with students. The writing style of this book is relaxed and versatile, enabling students to understand more mathematical concepts and inspiring their thoughts. The content of this book includes: several fundamental characteristics of mathematics; duality, dualism, and complete spaces; an understanding of the logical categories of mathematics; a re-examination of real numbers; periodic mathematics and its understanding; the foundation of the "marriage" between modern mathematics and social sciences, etc.