#### An Introduction to Neural Networks

by Kevin Gurney

#### Artificial Neural Networks

by Kevin L. Priddy, Paul E. Keller

#### Applications of Mathematics in Models, Artificial Neural Networks and Arts

by Vittorio Capecchi, Massimo Buscema, Pierluigi Contucci, Bruno D’Amore

The book shows a very original organization addressing in a non traditional way, but with a systematic approach, to who has an interest in using mathematics in the social sciences.

The book is divided in four parts: (a) a historical part, written by Vittorio Capecchi which helps us understand the changes in the relationship between mathematics and sociology by analyzing the mathematical models of Paul F. Lazarsfeld, the model of simulation and artificial societies, models of artificial neural network and considering all the changes in scientific paradigms considered; (b) a part coordinated by Pier Luigi Contucci on mathematical models that consider the relationship between the mathematical models that come from physics and linguistics to arrive at the study of society and those which are born within sociology and economics; (c) a part coordinated by Massimo Buscema analyzing models of artificial neural networks; (d) a part coordinated by Bruno D’Amore which considers the relationship between mathematics and art.

The title of the book “Mathematics and Society” was chosen because the mathematical applications exposed in the book allow you to address two major issues: (a) the general theme of technological innovation and quality of life (among the essays are on display mathematical applications to the problems of combating pollution and crime, applications to mathematical problems of immigration, mathematical applications to the problems of medical diagnosis, etc.) (b) the general theme of technical innovation and creativity, for example the art and mathematics section which connects to the theme of creative cities.

The book is very original because it is not addressed only to those who are passionate about mathematical applications in social science but also to those who, in different societies, are: (a) involved in technological innovation to improve the quality of life; (b) involved in the wider distribution of technological innovation in different areas of creativity (as in the project “Creative Cities Network” of UNESCO).

#### An Introduction to Neural Networks

by James A. Anderson

*An Introduction to Neural Networks* falls into a new ecological niche for texts. Based on notes that have been class-tested for more than a decade, it is aimed at cognitive science and neuroscience students who need to understand brain function in terms of computational modeling, and at engineers who want to go beyond formal algorithms to applications and computing strategies. It is the only current text to approach networks from a broad neuroscience and cognitive science perspective, with an emphasis on the biology and psychology behind the assumptions of the models, as well as on what the models might be used for. It describes the mathematical and computational tools needed and provides an account of the author’s own ideas.

Students learn how to teach arithmetic to a neural network and get a short course on linear associative memory and adaptive maps. They are introduced to the author’s brain-state-in-a-box (BSB) model and are provided with some of the neurobiological background necessary for a firm grasp of the general subject.

The field now known as neural networks has split in recent years into two major groups, mirrored in the texts that are currently available: the engineers who are primarily interested in practical applications of the new adaptive, parallel computing technology, and the cognitive scientists and neuroscientists who are interested in scientific applications. As the gap between these two groups widens, Anderson notes that the academics have tended to drift off into irrelevant, often excessively abstract research while the engineers have lost contact with the source of ideas in the field. Neuroscience, he points out, provides a rich and valuable source of ideas about data representation and setting up the data representation is the major part of neural network programming. Both cognitive science and neuroscience give insights into how this can be done effectively: cognitive science suggests what to compute and neuroscience suggests how to compute it.