Mathematics and Models -- Mathematics and Sociology -- Equilibria of Culture Contact Derived from In-Group and Out-Group Attitudes -- Society from the Statistical Mechanics Perspective -- Objects, Words and Actions: Some Reasons Why Embodied Models are Badly Needed in Cognitive Psychology -- Shared Culture Needs Large Social Networks -- Mathematical Models of Financial Markets -- Tackling Climate Change Through Energy Efficiency: Mathematical Models to Offer Evidence-Based Recommendations for Public Policy -- An Application of the Multilevel Regression Technique to Validate a Social Stratification Scale -- The Academic Mind Revisited: Contextual Analysis via Multilevel Modeling -- Mathematics and Neural Networks -- The General Philosophy of the Artificial Adaptive Systems -- Auto-contractive Maps, the H Function, and the Maximally Regular Graph (MRG): A New Methodology for Data Mining -- An Artificial Intelligent Systems Approach to Unscrambling Power Networks in Italy’s Business Environment -- Multi–Meta-SOM -- How to Perform Data Mining: The “Persons Arrested” Dataset -- Medicine and Mathematics of Complex Systems: An Emerging Revolution -- J-Net System: A New Paradigm for Artificial Neural Networks Applied to Diagnostic Imaging -- Digital Image Processing in Medical Applications, April 22, 2008 -- Mathematics and Art -- Mathematics, Art, and Interpretation: A Hermeneutic Perspective -- Point, Line and Surface, Following Hilbert and Kandinsky -- Figurative Arts and Mathematics: Pipes, Horses, Triangles and Meanings -- The Idea of Space in Art, Technology, and Mathematics -- Mathematical Structures and Sense of Beauty -- Visual Impact and Mathematical Learning -- Art by Numbers -- My Way of Playing with the Computer: Suggestions for a Personal Experience in Vector Graphics -- Four-Dimensional Ideas -- From Art to Mathematics in the Paintings of Theo van Doesburg -- Erratum to: Art by Numbers.

This book is set up in a non-traditional way, yet it takes a systematic approach. There are four parts. The first part is historical and deals with the changes that have taken place in recent years in the relationship between mathematics and sociology: an analysis is made of Paul F. Lazarsfeld’s mathematical models, models of simulation and artificial societies, and models of artificial neural networks. The second part compares and contrasts mathematical models that come from physics and linguistics and those that come from sociology and economics. The third part analyzes models of artificial neural networks in detail. The final part examines the relationship between mathematics and the arts. The book will be of interest to everyone involved in the application of mathematics to the social sciences and the use of technological innovations to improve the quality of life, and their distribution among the various creative arts.