The most recommended books about mathematical models

We increasingly live in a virtual world of models – pandemic models, climate change models, economic models. These have taken on what seems like a greater reality than the world of people and places we know and what used to be called common sense. 

At one level everyone feels this. Modeling is Thompson’s job. This leaves her ideally placed to grapple with the question of just how real these models are and what weight we should put on these alternate realities and what weight on a reality we grew up in, which feels like its disappearing.

Thompson tackles these complex topics in a down-to-earth way. The title Escape from Model Land tells you she’s on our side rather than the side of the experts.

This looks like it’s the sternest and most boring book ever, but I love Steedman’s cool-and-collected ability to address the implications of the obvious: You can only do one thing at a time. You only have two hands. And when you’re with one set of belongings, you’re neglecting all the other stuff you own.

Peter Turchin has gotten famous recently for predicting the US political upheaval of 2020 way back in 2012.

This book represents the first landmark of Turchin’s attempt to understand the ebbs and flows of history using dynamical models. The book’s centerpiece is a formalization of a theory about how empires rise and fall, first conceived by the 14th century (!) Arab scholar Ibn Khaldun.

The book inspired me to replicate the computational model it presents, and it was remarkably illuminating to watch empires grow, fight, and collapse on my computer screen. 

Finally, for those who are not afraid of math, they should read this book because there is a lot of heavy-duty math. The good news for the rest of us is you can ignore all the math and still get a lot out of it, especially knowledge about market microstructure and how to find the theoretically optimal trading strategies given some assumptions about the price dynamics. Even if you don’t want to or can’t solve those darn stochastic differential equations, you can still implement a numerical approximation. At the minimum, you will learn common trading lingo such as “walking the book” or “the ITCH feed”.

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. 

This book has been the bible for technical analysts since its first iteration in 1985 and is a comprehensive guide to the established knowledge of the markets. It covers chart structure, trends, moving averages, oscillators, technical indicators, and all types of charts in the 542 pages of the 1999 edition, which added candlestick patterns to the older version, and is a great reference guide for all the traditional charting.

However, that is the latest edition, so it contains nothing on Ichimoku (cloud) charting, an incredibly interesting if esoteric development, which is one of the reasons I felt that I should write my book including these latest advances.

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.

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.

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.

Of the various books available on this subject, I very much prefer this one because it makes it far easier to do systems biology.

First, it shows you how to view biological regulatory processes as a set of interacting components and their effect on each other. This alone can give clues to the behaviour of the system under different circumstances. However, it then goes on to show how these processes can be defined mathematically, which then enables us to get a quantitative view of what is going on.

When the predicted and observed numbers don’t match, we know that there is a gap in our knowledge and, hence, the place to discover new biology. Using this approach, I have.