The Art of Mathematical Research

This book is based on lecture notes from the author's general elective course Mathematical Methodology at Sun Yat-sen University. It is organized into ten chapters that cover key mathematical methods including reduction analogy induction association intuition abstraction reasoning modeling experimentation and aesthetics. Additionally the book explores notable mathematical conjectures and classic research methods in mathematics. This book serves as a valuable resource for both undergraduate and graduate students across various disciplines providing insights into fundamental research methods in mathematics. It is also a useful reference for individuals engaged in mathematical research offering an in-depth exploration of essential methodologies that support rigorous study and innovation in the field.