The most recommended books about mathematical models

Parents’ and professionals’ judgments of neurodivergent children, which are often based on perceived deficits, can limit those children’s choices and opportunities. Dictating the course of neurodivergent children’s care without involving them as active participants can also have dire, long-lasting consequences.

This book by Martha Leary and Anne Donnellan illustrates the importance of understanding the sensory and movement experiences of autistic people, which is only possible if you take the time to actively listen to those experiences and use them to shape an approach to care. The book helped to inform the care model we use at Cortica and reinforced my commitment to providing a personalized level of support that integrates children’s engagement in the process and honors each child’s unique journey, needs, and strengths.

I confess that I know Trevor Lipscombe, but I would add his book to this list if I did not know him. Like Haché’s book on ice hockey, I was out of my comfort zone while reading a book on rugby. As I write this, I am in the midst of my third sabbatical year. All three of my sabbatical years have been spent researching at universities in Sheffield, England. People are enthusiastic about rugby in England as well as in other parts of the world.

Not only did this book introduce me to a new way to apply physics, but it also taught me so much about rugby that I can cheer with mates in a pub while watching a match! It is the go-to book on rugby science.

In the vast array of quantitative finance relative to financial markets instruments and related risks, the case of credit or counterparty risk remains by far the most complex one, and thus, unsurprisingly, the least mastered by financial markets professionals.

A lot has been done, but a lot remains to be done: covering this is precisely the goal of this book. In a nutshell, the main obstacle to succeed in developing grounded and useful models of default prediction is due to the fact that a default is (fortunately) a rare event, in other words, with a (very) low probability of occurrence, and statistical tools are uncomfortable with very low probability levels. Hence the need of this book, to help the practitioner to go ahead in this matter.

I am an economist by training. I taught economic courses at Rutgers University for two decades but the only economic framework I consider useful for real-world managers is the classical school known as Austrian Economics, of which Murray Rothbard was one of the more eloquent and accessible voices. Mainstream economists busy themselves with complex mathematical models that are in the end utterly useless in explaining the world, or worse, are utterly wrong in predicting the consequences of policies but are provided by “court economists” to support ideologies. Murry Rothbard, in contrast, lays down the principles of economic theory that will guide your investment/competitive strategies based on the most solid and realistic economic reasoning around. The book is not easy to read, but it will change your understanding of the world. It inspired me to get a Ph.D. 

I appreciated how this book took on the challenge of applying advanced mathematical modeling and simulation techniques to gain new insights into the social evolution of norms and institutions in societies, which is a critical topic in many fields, including conflict and peace economics.

I learned much from the book’s coverage of selected conflict and peace topics such as riots, revolutions, the 2010 Arab Spring movement, and the social evolution of cooperation. I especially like how the mathematical models in the book are described intuitively using wonderfully imaginative diagrams.

In this way, both the mathematically and non-mathematically inclined can come away with a richer understanding of human behavior in dynamically changing social systems.

I have always been fascinated by how people join and leave groups.

What are the benefits of joining a particular group? Which group should I join? What happens if someone wants to join a group, but its current members don’t want them to? I once thought such questions were merely qualitative, and when I was a graduate student I thought I’d be the first to tackle them quantitatively.

I was humbled when I stumbled upon this book, written years earlier, in which two behavioral ecologists review game theoretic models that address questions of just this sort, starting simple, and building up models of increasing nuance and complexity. I think anyone interested in the dynamics of group formation in humans or other animals should read this book. 

This is the best scientific novel I have ever read. The story is fiction (not 'science fiction' in the sense of fantasy, but a story that could easily take place in the real world right now), but its portrayal of how science is done, by a bunch of completely believable characters, is really true-to-life. It's a great way for young people considering a research career to taste what they are really like, and a great way for everyone to ask why we do science the way we do, while enjoying a well-paced multi-layer story, that is written with real wit. [Declaration for transparency: I know the author as a scientific collaborator, but this is nothing to do with my recommendation of her fiction]. 

As a math student I found economics a slippery subject and, therefore, was hesitant to read any book on the subject. 

Theory of Value is a short, formal manuscript, that includes the definition of an economy. It was the first book I read in economics and I loved it. It induced me to move to New York and to study the field.

In a world full of buzzwords about the latest AI algorithms, Leslie Valiant is one of the few authors who can shrug off the hype and deliver something truly profound. Valiant is a Turing Award winner whose work has changed the face of computational learning theory. His ideas show how algorithms can arise naturally, as part of evolution. (He calls them ecorithms.) These ideas are stunningly original. I admire Valiant’s no-nonsense prose style immensely—it’s such a pleasure to read something where the ideas and explanations are simultaneously so clear and so deep that they provide their own star power.

Disclaimer: I like Euan’s books not because he is a friend and has endorsed my books. Long before we became friends, I have bought his book, and said to myself “Wow! This is the first book about options trading that is not just a bunch of trite statements about payouts from various straddles and spreads positions!” It talks about some unique arbitrage opportunities that only professionals knew about. On the other hand, the amount of mathematics is very manageable, and can largely be skipped without affecting the practical applications of the concepts.