The best probability books

Many authors have picked their favorite books about probability and why they recommend each book.

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By Michael A. Bean,

Book cover of Probability: The Science of Uncertainty: With Applications to Investments, Insurance, and Engineering

Everyone knows what probability is, and we all understand how a coin flip works, but not everyone can explain the optimal betting strategies for a roulette table. We don’t study probability to understand the likelihood of events. We study probability to understand the expected outcomes of business processes that depend on those events.

In other words, this book won’t just teach you about probabilities, it will teach you about business strategies associated with those probabilities. It will help you answer a question like: How do I maximize the profit on this life insurance policy, given this set of survival probabilities? It isn’t just a likelihood question, it is a business question. I highly recommend that anyone studying probability does so through an actuarial lens.

Who am I?

I am a financial data scientist. I think it is important that data scientists are highly specialized if they want to be effective in their careers. I run a business called Conlan Scientific out of Charlotte, NC where me and my team of financial data scientists tackle complicated machine learning problems for our clients. Quant trading is a gladiator’s arena of financial data science. Anyone can try it, but few succeed at it. I am sharing my top five list of math books that are essential to success in this field. I hope you enjoy.

I wrote...

Algorithmic Trading with Python: Quantitative Methods and Strategy Development

By Chris Conlan,

Book cover of Algorithmic Trading with Python: Quantitative Methods and Strategy Development

What is my book about?

Algorithmic Trading with Python discusses modern quant trading methods in Python with a heavy focus on pandas, numpy, and scikit-learn. After establishing an understanding of technical indicators and performance metrics, readers will walk through the process of developing a trading simulator, strategy optimizer, and financial machine learning pipeline. 

This book maintains a high standard of reproducibility. All code and data are self-contained in a GitHub repo. The data includes hyper-realistic simulated price data and alternative data based on real securities. 

An Introduction to Information Theory

By Fazlollah M. Reza,

Book cover of An Introduction to Information Theory

This is a more comprehensive and mathematically rigorous book than Pierce’s book. For the novice, it should be read-only after first reading Pierce’s more informal text. Due to its vintage, the layout is fairly cramped, but the content is impeccable. At almost 500 pages, it covers a huge amount of material. This was my main reference book on information theory for many years, but it now sits alongside more recent texts, like MacKay’s book (see below). It is also published by Dover, so it is reasonably priced.

Who am I?

My primary interest is in brain function. Because the principal job of the brain is to process information, it is necessary to define exactly what information is. For that, there is no substitute for Claude Shannon’s theory of information. This theory is not only quite remarkable in its own right, but it is essential for telecoms, computers, machine learning (and understanding brain function). I have written ten "tutorial introduction" books, on topics which vary from quantum mechanics to AI. In a parallel universe, I am still an Associate Professor at the University of Sheffield, England.

I wrote...

Information Theory: A Tutorial Introduction

By James V. Stone,

Book cover of Information Theory: A Tutorial Introduction

What is my book about?

Originally developed by Claude Shannon in the 1940s, information theory laid the foundations for the digital revolution, and is now an essential tool in telecommunications, genetics, linguistics, brain sciences, and deep space communication. In this richly illustrated book, accessible examples are used to introduce information theory in terms of everyday games like ‘20 questions’ before more advanced topics are explored. Online MatLab and Python computer programs provide hands-on experience of information theory in action, and PowerPoint slides give support for teaching.

Written in an informal style, with a comprehensive glossary and tutorial appendices, this text is an ideal primer for novices who wish to learn the essential principles and applications of information theory.

Radical Uncertainty

By Mervyn King, John Kay,

Book cover of Radical Uncertainty: Decision-Making Beyond the Numbers

It’s time for some economics. I am embarrassed to say that following the Global Financial Crisis my profession has fallen into acute disarray, its models have proved to be utterly inadequate. Radical Uncertainty in the landmark book explains why this was the case. Economists had reduced all unknowns to quantifiable probabilities, which could then be inserted into models and managed by diversification and insurance. Unfortunately, the world is not like that: with disturbing frequency, people, businesses, and societies are hit by ‘unknown unknowns’ like COVID. Managing uncertainty requires an approach quite alien to economics, its priorities being the resilience of strategies such as built-in redundancy, and rapid recovery that comes from decentralised experiments around a common purpose. Kay was once Britain’s boy-wonder of mathematical economics; King was once a top professor of finance who became the Governor of the Bank of England. Heroically, they have recanted the ideas they once…

Who am I?

Our societies have become increasingly polarised, both materially and psychologically. Our youth are riven with anxieties. Most people expect their children’s lives to be worse than their own. This reflects a staggering failure across business, politics, and public institutions. Fortunately, an intellectual revolution has begun that is resetting our course: you can become part of it. My own life has straddled these increasingly bitter tensions. My parents left school at 12, and we lived in a city whose industry moved to Korea so the jobs evaporated. The lives of my relatives collapsed, but by fortune’s wheel, I became a professor at Oxford, Harvard, and Paris. We can reverse such cruel divides: I want to share what I have learned from my work and my life to show how we can do it.

I wrote...

The Future of Capitalism: Facing the New Anxieties

By Paul Collier,

Book cover of The Future of Capitalism: Facing the New Anxieties

What is my book about?

From world-renowned economist Paul Collier, a candid diagnosis of the failures of capitalism and a pragmatic and realistic vision for how we can repair it.

Deep new rifts are tearing apart the fabric of the United States and other Western societies: thriving cities versus rural counties, the highly skilled elite versus the less educated, wealthy versus developing countries. As these divides deepen, we have lost the sense of ethical obligation to others that was crucial to the rise of post-war social democracy. So far these rifts have been answered only by the revivalist ideologies of populism and socialism, leading to the seismic upheavals of Trump, Brexit, and the return of the far-right in Germany. We have heard many critiques of capitalism but no one has laid out a realistic way to fix it, until now.

In a passionate and polemical book, celebrated economist Paul Collier outlines brilliantly original and ethical ways of healing these rifts--economic, social, and cultural--with the cool head of pragmatism, rather than the fervor of ideological revivalism. He reveals how he has personally lived across these three divides, moving from working-class Sheffield to hyper-competitive Oxford, and working between Britain and Africa, and acknowledges some of the failings of his profession.

Big Maze Book

By Kirsten Robson,

Book cover of Big Maze Book

You can always rely on a children’s book published by Usborne, the Big Maze Book by Kirsten Robson is no exception. It offers 50 different mazes to solve, each charmingly illustrated. The mazes themselves are nice and varied, incorporating different settings, different subject matter, and slightly different visual treatments, which all helps to keep solvers interested. As a whole, this book would probably appeal more to younger children who still enjoy picture books. That being said, the mazes do get progressively harder through the book, so there is something there for the slightly older ones too.

Who am I?

I am an author, illustrator, and award-winning creative director. I have loved to draw and make things since a young age, mostly wacky contraptions (inspired by my love of the Hanna-Barbera Wacky Races cartoons). I’m also passionate about mazes, having spent many family holidays drawing mazes on a small whiteboard for my two boys to complete.

I wrote...

Mega-Maze Adventure!: A Journey Through the World's Longest Maze in a Book

By Scott Bedford,

Book cover of Mega-Maze Adventure!: A Journey Through the World's Longest Maze in a Book

What is my book about?

Not just a maze––the book itself is a maze! Every page (including the cover) has a portal hole cut into it, allowing the maze to run from page to page and make this the world's longest maze in a book. Every spread is a journey through an imaginative world: there's Robot World and Butterfly World, Ski World and Underwater World, Dragon World, and Skyscraper World.

Filled with hypnotic details, hidden surprises, fun facts, and bright, swirling, richly-colored details, every page is a compelling adventure. This maze book is the first of its kind, and a totally immersive, compelling, and challenging experience for young people (and their parents!).

Evidence and Evolution

By Elliott Sober,

Book cover of Evidence and Evolution

This ambitious book, written by a distinguished philosopher, is a contribution to what might be called the “epistemology of evolutionary biology.” Sober starts by offering a general analysis of the concept of evidence based on probability theory, then applies this analysis to issues in the theory of evolution. He explains why the evidence favours evolution over the hypothesis of “intelligent design,” then tackles the thorny methodological problem of how to infer evolutionary history from observations on contemporary species. Though difficult, the book is clearly written and repays close study.

Who am I?

I am Professor of Philosophy of Science at the University of Bristol. I am interested in most areas of contemporary philosophy, in particular the interplay between philosophy and the natural and social sciences. Much of my recent work has focused on evolutionary biology, a science that is replete with implications for traditional philosophical debates about human nature, knowledge, and our place in the world.

I wrote...

Philosophy of Biology: A Very Short Introduction

By Samir Okasha,

Book cover of Philosophy of Biology: A Very Short Introduction

What is my book about?

Throughout most of the 20th century, philosophy of science was a rather physics-centric pursuit. This began to change in the 1970s when philosophy of biology emerged as a distinct sub-field in its own right. My book offers a synoptic overview of this flourishing branch of philosophy, written in a way that presumes no specialist knowledge. The book’s aim is to highlight how pervasive philosophical issues are in the life sciences, and to show how philosophical analysis can be of use to the practicing scientist. Topics discussed included teleology and purpose in nature, altruism and human behaviour, the nature of species, and the concept of the gene.

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