MathematiconA Lexicon of Basic Mathematical Notions and Interesting Facts and IdeasMarcel DanesiUniversity of Toronto & Fields Institute for Research in Mathematical SciencesThis mathematicon is a lexicon of mathematics, designed to explain basic ideas, notions, theories, applications, in mathematics, as well as to describe classic problems and puzzles and their importance to the history of mathematics. It is intended for a general public, and especially for students of mathematics (in high school or college), as well as math teachers. This book falls under the rubric of emphasizing the importance of mathematics to a broad public, which is a major goal of the CogSci Network of the Fields Institute for Research in Mathematical Sciences.Each entry is written in a clear style, making no assumptions as to background knowledge on the part of the reader. Illustrations, applications, and comments of a historical-cultural nature are incorporated into most of the entries. This book is not a typical dictionary, but a glossary of mathematical facts and ideas that could be read as a general overview of what mathematics is and what it allows us to accomplish. For students, the mathematicon might help them gain the confidence needed to do well in the discipline; for the general reader, my hope is that it will provide insights on the relevance of mathematics today in a world where “partnerships between mathematicians and computer scientists are bulling into whole new domains of business and imposing efficiencies in math,” as the New York Times journalist, Thomas Friedman, has so aptly put it.ISBN 9783969390634. 398pp. mathematics 01. 2022.EnigmatologyThe Science of PuzzlesMarcel DanesiUniversity of TorontoPuzzles and games have been around since the dawn of history. What are they? And what do they imply for the study of mind? These questions have rarely been studied to any depth, even though puzzles are found across cultures and across time. This book aims to address these questions in a systematic way, dealing with all kinds verbal and nonverbal puzzles and games in order to understand what they mean in psychological terms and what they have implied for human history.Puzzles may indeed provide a valuable key to understanding the human brain, for what are puzzles if not creative artifacts that are constructed with imaginative and strategies possessed by all humans? The field that aims to study puzzles scientifically is called enigmatology - a term coined by Will Shortz in 1974 as a student at Indiana University in Bloomington, who became a famous puzzle editor at The New York Times. Enigmatology is the “science of puzzles.” As far as can be determined, there is no comprehensive introduction or overview of enigmatology as a distinct discipline or field of inquiry. The purpose of this book is to fill in this gap.ISBN 9783862889792. LINCOM Studies and Texts in Enigmatology 01. 375pp. 2019.A primer of Hilbert spaceClaudi MeneghinMIUR (Ministero dell'Istruzione Università e Ricerca)This book deals with the very basic theory of Hilbert space. Chapter 1 deals with the fundamental theory of vector spaces. The notion of a vector space is recalled, together with related techniques. Key definitions and theorems concerning vector spaces in general and linear independence are then reviewed.In chapter 2 the notions of a inner product, normed space and metric space are examined, together with their mutual relationships.Finally, in chapter 3 the very basic tools in the theory of Hilbert space are studied, introducing the natural generalisation of the customary vector space notions to the inﬁnite dimensional framework. In particular, the matter of expanding a vector in terms of a (not necessarily ﬁnite) orthogonal basis is introduced. Several examples, problems and exercises are proposed.ISBN 9783862884278. LINCOM Textbooks in Mathematics 01.110pp. 2013.