Focusing on essential concepts in both pure and applied mathematics, this textbook covers key topics such as walks on graphs, the Radon transform, the Matrix-Tree Theorem, and the Sperner property. Designed for undergraduates, it aims to equip future mathematicians with a solid foundation in these critical areas, blending theoretical insights with practical applications.
Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives some basic background and then presents more than 250 exercises and solutions on the properties and applications of these numbers, with difficulty levels ranging from recreational to research.
The second edition of Volume 1 features significant updates, including ten new sections that enhance the content. It also offers over 300 new exercises, providing readers with ample opportunities for practice and application of concepts. This revised edition aims to improve the learning experience and deepen understanding of the subject matter.