The most recommended books about mathematical models

Who picked these books? Meet our 23 experts.

23 authors created a book list connected to mathematical models, and here are their favorite mathematical model books.
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Book cover of Vision: A Computational Investigation into the Human Representation and Processing of Visual Information

Mark S. Nixon Author Of Feature Extraction and Image Processing for Computer Vision

From my list on computer vision from a veteran professor.

Why am I passionate about this?

It’s been fantastic to work in computer vision, especially when it is used to build biometric systems. I and my 80 odd PhD students have pioneered systems that recognise people by the way they walk, by their ears, and many other new things too. To build the systems, we needed computer vision techniques and architectures, both of which work with complex real-world imagery. That’s what computer vision gives you: a capability to ‘see’ using a computer. I think we can still go a lot further: to give blind people sight, to enable better invasive surgery, to autonomise more of our industrial society, and to give us capabilities we never knew we’d have.

Mark's book list on computer vision from a veteran professor

Mark S. Nixon Why did Mark love this book?

David Marr shaped the field of computer vision in its early days. His seminal book laid the structure for interpreting images and one which is still largely followed. He popularised notions of the primal sketch and his work on edge detection led to one of the most sophisticated approaches. His work and influence continue to endure despite his early death: we missed and miss him a lot.

By David Marr,

Why should I read it?

1 author picked Vision as one of their favorite books, and they share why you should read it.

What is this book about?

Available again, an influential book that offers a framework for understanding visual perception and considers fundamental questions about the brain and its functions.

David Marr's posthumously published Vision (1982) influenced a generation of brain and cognitive scientists, inspiring many to enter the field. In Vision, Marr describes a general framework for understanding visual perception and touches on broader questions about how the brain and its functions can be studied and understood. Researchers from a range of brain and cognitive sciences have long valued Marr's creativity, intellectual power, and ability to integrate insights and data from neuroscience, psychology, and computation. This…


Book cover of Algorithms to Live By: The Computer Science of Human Decisions

Michael L. Littman Author Of Code to Joy: Why Everyone Should Learn a Little Programming

From my list on computing and why it’s important and interesting.

Why am I passionate about this?

Saying just the right words in just the right way can cause a box of electronics to behave however you want it to behave… that’s an idea that has captivated me ever since I first played around with a computer at Radio Shack back in 1979. I’m always on the lookout for compelling ways to convey the topic to people who are open-minded, but maybe turned off by things that are overly technical. I teach computer science and study artificial intelligence as a way of expanding what we can get computers to do on our behalf.

Michael's book list on computing and why it’s important and interesting

Michael L. Littman Why did Michael love this book?

I always find myself applying algorithmic thinking in my everyday life—it affects the way I put away dishes, navigate to the store, and organize my to-do lists. And I think others could benefit from that mindset.

So, when I read this book, my reaction was "Yes! That's what I want people to know. I just wish I could have said it that well!" The authors (who I know, but didn't know they wrote a book together), did a fantastic job of selecting algorithms with deep human connections. Really! And they explain them just right, without getting too mathematical but while still hitting the key ideas with clarity and accuracy. Fantastic!

By Brian Christian, Tom Griffiths,

Why should I read it?

5 authors picked Algorithms to Live By as one of their favorite books, and they share why you should read it.

What is this book about?

A fascinating exploration of how computer algorithms can be applied to our everyday lives.

In this dazzlingly interdisciplinary work, acclaimed author Brian Christian and cognitive scientist Tom Griffiths show us how the simple, precise algorithms used by computers can also untangle very human questions. Modern life is constrained by limited space and time, limits that give rise to a particular set of problems. What should we do, or leave undone, in a day or a lifetime? How much messiness should we accept? The authors explain how to have better hunches and when to leave things to chance, how to deal…


Book cover of Advances in Financial Machine Learning

Ernest P. Chan Author Of Quantitative Trading: How to Build Your Own Algorithmic Trading Business

From my list on quantitative trading for beginners.

Why am I passionate about this?

A noted quantitative hedge fund manager and quant finance author, Ernie is the founder of QTS Capital Management and Predictnow.ai. Previously he has applied his expertise in machine learning at IBM T.J. Watson Research Center’s Human Language Technologies group, at Morgan Stanley’s Data Mining and Artificial Intelligence Group, and at Credit Suisse’s Horizon Trading Group. Ernie was quoted by Bloomberg, the Wall Street Journal, New York Times, Forbes, and the CIO magazine, and interviewed on CNBC’s Closing Bell program. He is an adjunct faculty at Northwestern University’s Master’s in Data Science program and supervises student theses there. Ernie holds a Ph.D. in theoretical physics from Cornell University.

Ernest's book list on quantitative trading for beginners

Ernest P. Chan Why did Ernest love this book?

By now, you may notice that I like to recommend textbooks. I use this bestseller for my course in Financial Machine Learning at Northwestern University, but really, nobody interested in financial machine learning hasn’t read this book. The topics are highly relevant to every investor or trader – I read it at least 5 times to digest every nugget and have put them to very productive use in my trading as well as in my fintech firm predictnow.ai. It covers basic techniques such as random forest to advanced techniques such as Hierarchical Risk Parity, which is a big improvement over traditional portfolio optimization methods.

Marcos used to be Head of Machine Learning at AQR (AUM=$143B), and now is the Global Head of Quant Research at Abu Dhabi Investment Authority. He is also very approachable to his readers and students. There was seldom an email or message from me to which…

By Marcos Lopez de Prado,

Why should I read it?

1 author picked Advances in Financial Machine Learning as one of their favorite books, and they share why you should read it.

What is this book about?

Learn to understand and implement the latest machine learning innovations to improve your investment performance

Machine learning (ML) is changing virtually every aspect of our lives. Today, ML algorithms accomplish tasks that - until recently - only expert humans could perform. And finance is ripe for disruptive innovations that will transform how the following generations understand money and invest.

In the book, readers will learn how to:

Structure big data in a way that is amenable to ML algorithms Conduct research with ML algorithms on big data Use supercomputing methods and back test their discoveries while avoiding false positives

Advances…


Book cover of An Introduction to Systems Biology: Design Principles of Biological Circuits

Charlie Hodgman Author Of BIOS Instant Notes in Bioinformatics

From my list on the intersection of Bioinformatics and Systems Biology.

Why am I passionate about this?

Mathematics and chemistry were my strongest subjects at school, and I started programming computers when I was 16, but life seemed most important. Hence I studied biochemistry in university but moved into molecular biology with programming to assist the data analysis. My track record in successfully predicting new biology through computing led to a pharmaceutical company recruiting me to do bioinformatics for them. However, not content with studying genes and proteins, I pushed for bioinformatics to move up into metabolism, anatomy, and physiology. That’s when I discovered systems biology. My international reputation lies at this interface and includes discoveries in microbial physiology, botany, agriculture, animal biology, and antenatal diseases.

Charlie's book list on the intersection of Bioinformatics and Systems Biology

Charlie Hodgman Why did Charlie love this book?

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.

By Uri Alon,

Why should I read it?

1 author picked An Introduction to Systems Biology as one of their favorite books, and they share why you should read it.

What is this book about?

Praise for the first edition:

... superb, beautifully written and organized work that takes an engineering approach to systems biology. Alon provides nicely written appendices to explain the basic mathematical and biological concepts clearly and succinctly without interfering with the main text. He starts with a mathematical description of transcriptional activation and then describes some basic transcription-network motifs (patterns) that can be combined to form larger networks. - Nature

[This text deserves] serious attention from any quantitative scientist who hopes to learn about modern biology ... It assumes no prior knowledge of or even interest in biology ... One final…


Book cover of Escape from Model Land: How Mathematical Models Can Lead Us Astray and What We Can Do about It

David Healy Author Of Shipwreck of the Singular: Healthcare's Castaways

From David's 3 favorite reads in 2023.

Why am I passionate about this?

Author Doctor Professor Believer in patient expertise Attempting to stem an incoming polypharmacy tide

David's 3 favorite reads in 2023

David Healy Why did David love this book?

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.

By Erica Thompson,

Why should I read it?

1 author picked Escape from Model Land as one of their favorite books, and they share why you should read it.

What is this book about?

Shortlisted for Best Maths Book of 2022 by Chaulkdust Magazine

'A brilliant account of how models are so often abused and of how they should be used' John Kay

How do mathematical models shape our world - and how can we harness their power for good?

Models are at the centre of everything we do. Whether we use them or are simply affected by them, they act as metaphors that help us better understand the increasingly complex problems facing us in the modern world. Without models, we couldn't begin to tackle three of the major challenges facing modern society: regulation…


Book cover of Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street

Barbara Rockefeller Author Of Technical Analysis For Dummies

From my list on for traders using technical analysis.

Why am I passionate about this?

Economics isn't really a good starting point for financial market analysis for the simple reason that its models are wildly inaccurate. As behaviorial economists like Daniel Kahneman have been showing, irrationality and the inability to measure risk properly are a very big component of the investment and trading decisions. But statistical risk management is also sloppy when applied to human behavior because people are not objects that reliably behave the same way under similar circumstances. So when you read an economist about markets or an engineer about risk management, you're missing a lot of the story. In the end, technical analysis is fascinating because how and why humans behave is an enduring mystery.

Barbara's book list on for traders using technical analysis

Barbara Rockefeller Why did Barbara love this book?

The subtitle is The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street. This book is an easy-to-read narrative of the intersection of the grimy underbelly of betting--with high-minded math. It reminds you that trading is not conducted in a clean little bubble. Technical analysis can give you an edge, but trading is still engaging in battle with opposing forces; strategy and tactics can count as much as building an elegant technical system. 

Your opponent on the trading battlefield will try to trick you, like a general in real warfare. He may keep selling and selling after you have bought, triggering a sell signal in your trading system. He is hunting for your sell signal. The mechanical response is to sell—your system says sell, and you should follow your system. To exit a position when the market goes against you is named a stop,…

By William Poundstone,

Why should I read it?

1 author picked Fortune's Formula as one of their favorite books, and they share why you should read it.

What is this book about?

In 1956, two Bell Labs scientists discovered the scientific formula for getting rich. One was mathematician Claude Shannon, neurotic father of our digital age, whose genius is ranked with Einstein's. The other was John L. Kelly Jr., a Texas-born, gun-toting physicist. Together they applied the science of information theory—the basis of computers and the Internet—to the problem of making as much money as possible, as fast as possible.

Shannon and MIT mathematician Edward O. Thorp took the "Kelly formula" to Las Vegas. It worked. They realized that there was even more money to be made in the stock market. Thorp…


Book cover of Technical Analysis of the Financial Markets: A Comprehensive Guide to Trading Methods and Applications

Alan Northcott Author Of Mastering Technical Analysis: Strategies and Tactics for Trading the Financial Markets

From my list on cracking the trading code.

Why am I passionate about this?

I came from a left-brained family, with my father a bank Forex manager and my mother in the tax office before motherhood. I've always been mathematically minded and went into mechanical engineering before my second career in trading and finance. But saying this sustains the fallacy that you have to have a head for numbers to trade. That is nothing like the truth, and I hope my last book pick shows that I have learnt and come a long way from my initial beliefs. Trading is anything but mathematical, mechanistic, or even natural, you have to study and learn new ways of thinking and doing, and you can only succeed if you are open to this.

Alan's book list on cracking the trading code

Alan Northcott Why did Alan love this book?

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.

By John J. Murphy,

Why should I read it?

1 author picked Technical Analysis of the Financial Markets as one of their favorite books, and they share why you should read it.

What is this book about?

John J. Murphy has now updated his landmark bestseller Technical Analysis of the Futures Markets, to include all of the financial markets.

This outstanding reference has already taught thousands of traders the concepts of technical analysis and their application in the futures and stock markets. Covering the latest developments in computer technology, technical tools, and indicators, the second edition features new material on candlestick charting, intermarket relationships, stocks and stock rotation, plus state-of-the-art examples and figures. From how to read charts to understanding indicators and the crucial role technical analysis plays in investing, readers gain a thorough and accessible overview…


Book cover of Social Foraging Theory

Paul E. Smaldino Author Of Modeling Social Behavior: Mathematical and Agent-Based Models of Social Dynamics and Cultural Evolution

From my list on (human) behavior that reward working through the math.

Why am I passionate about this?

I am fascinated with the relationship between our individual behaviors and the social structures and institutions in which we live—and how these influence each over time. I think this sort of understanding is important if we want to consider the kind of world we want to live in, and how we might get there from where we are. I take insights from many disciplines, from physics and biology to the cognitive and social sciences, from philosophy and art to mathematics and engineering. I am currently a professor of cognitive and information sciences at the University of California, Merced, and an external professor at the Santa Fe Institute. 

Paul's book list on (human) behavior that reward working through the math

Paul E. Smaldino Why did Paul love this book?

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. 

By Luc-Alain Giraldeau, Thomas Caraco,

Why should I read it?

1 author picked Social Foraging Theory as one of their favorite books, and they share why you should read it.

What is this book about?

Although there is extensive literature in the field of behavioral ecology that attempts to explain foraging of individuals, social foraging--the ways in which animals search and compete for food in groups--has been relatively neglected. This book redresses that situation by providing both a synthesis of the existing literature and a new theory of social foraging. Giraldeau and Caraco develop models informed by game theory that offer a new framework for analysis. Social Foraging Theory contains the most comprehensive theoretical approach to its subject, coupled with quantitative methods that will underpin future work in the field. The new models and approaches…


Book cover of Option Trading: Pricing and Volatility Strategies and Techniques

Ernest P. Chan Author Of Quantitative Trading: How to Build Your Own Algorithmic Trading Business

From my list on quantitative trading for beginners.

Why am I passionate about this?

A noted quantitative hedge fund manager and quant finance author, Ernie is the founder of QTS Capital Management and Predictnow.ai. Previously he has applied his expertise in machine learning at IBM T.J. Watson Research Center’s Human Language Technologies group, at Morgan Stanley’s Data Mining and Artificial Intelligence Group, and at Credit Suisse’s Horizon Trading Group. Ernie was quoted by Bloomberg, the Wall Street Journal, New York Times, Forbes, and the CIO magazine, and interviewed on CNBC’s Closing Bell program. He is an adjunct faculty at Northwestern University’s Master’s in Data Science program and supervises student theses there. Ernie holds a Ph.D. in theoretical physics from Cornell University.

Ernest's book list on quantitative trading for beginners

Ernest P. Chan Why did Ernest love this book?

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. 

By Euan Sinclair,

Why should I read it?

1 author picked Option Trading as one of their favorite books, and they share why you should read it.

What is this book about?

An A to Z options trading guide for the new millennium and the new economy Written by professional trader and quantitative analyst Euan Sinclair, Option Trading is a comprehensive guide to this discipline covering everything from historical background, contract types, and market structure to volatility measurement, forecasting, and hedging techniques. This comprehensive guide presents the detail and practical information that professional option traders need, whether they're using options to hedge, manage money, arbitrage, or engage in structured finance deals. It contains information essential to anyone in this field, including option pricing and price forecasting, the Greeks, implied volatility, volatility measurement…


Book cover of Investment Science

John M. Mulvey Author Of Worldwide Asset and Liability Modeling

From my list on how to achieve your financial goals.

Why am I passionate about this?

In my first year as an undergraduate in computer science at the University of Illinois, I took two classes that set the course for my 54-year career (6 years at TRW Systems aerospace firm, and 48 years teaching at Harvard and Princeton Universities): 1) introduction to optimization, and 2) computer algorithms. These topics continue to fascinate me, especially as they relate to improving investment performance via modern optimization technology and data sciences. Optimization plays a critical role in many domains, including supply chains, quantitative finance, and machine learning algorithms. Everyone interested in improving performance ought to understand the successful uses of this proven technology.

John's book list on how to achieve your financial goals

John M. Mulvey Why did John love this book?

This book is an outgrowth of a course at Stanford University on applying quantitative methods to improve financial decision making. 

Professor Luenberger has a superior talent at writing clear and logical textbooks on optimization topics. He shows the benefits of employing nonlinear programs for several applications, including pricing complex options, and achieving rebalancing gains over time. In his telling, volatility provides an opportunity to improve performance. The linkage of optimization and investing is a special treat.

By David G. Luenberger,

Why should I read it?

1 author picked Investment Science as one of their favorite books, and they share why you should read it.

What is this book about?

Investment Science, Second Edition, provides thorough and highly accessible mathematical coverage of the fundamental topics of intermediate investments, including fixed-income securities, capital asset pricing theory, derivatives, and innovations in optimal portfolio growth and valuation of multi-period risky investments. Eminent scholar and teacher David G. Luenberger, known for his ability to make complex ideas simple, presents essential ideas of investments and their applications, offering students the most comprehensive treatment of the subject available. New to this edition Three new chapters: Risk Management, Credit Risk, and Data and Statistics Updated content and expanded coverage of many topics, including the capital asset pricing…


Book cover of Vision: A Computational Investigation into the Human Representation and Processing of Visual Information
Book cover of Algorithms to Live By: The Computer Science of Human Decisions
Book cover of Advances in Financial Machine Learning

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