The best mathematics books for quant finance

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. 

The books I picked & why

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Modern Mathematical Statistics with Applications

By Jay L. DeVore, Kenneth N. Berk,

Book cover of Modern Mathematical Statistics with Applications

Why this book?

One of my favorite professors, Gretchen Martinet, used this to teach a course called “Mathematical Statistics” when I was at the University of Virginia. It is an extremely profound course full of dense but fundamental mathematical proofs in classical statistics. 

You will learn why the formula for the normal distribution is the way it is, why the sum of squares appears everywhere in statistics, and how to fit a linear regression by hand. In the same way calculus elevates our understanding of rates of changes, the book elevates your understanding of samples, averages, and distributions. Quant trading requires an intuitive sense of how data, models, and aggregates work, making this content essential for your success.

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

By Michael A. Bean,

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

Why this book?

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.

Introduction to Modern Nonparametric Statistics

By James J. Higgins,

Book cover of Introduction to Modern Nonparametric Statistics

Why this book?

This is one of my favorite underappreciated statistics books of all time. Non-parametric statistics can be otherwise described as statistics without assumptions. The entire goal of this field of study is to prove X is greater than Y without making any assumptions about the underlying distributions of X or Y. The methods are different, and they require more data than other methods, but the learning journey is invaluable.

I personally believe that modern machine learning is simply the modeling section of the school of non-parametric statistics. Working through this book will give you a much deeper understanding of why tools like decision trees are so valuable. It will also to teach you to design rigorous numerical experiments on data sets that are beyond the help of classical statistics.

The Elements of Statistical Learning: Data Mining, Inference, and Prediction

By Trevor Hastie, Robert Tibshirani, Jerome Friedman

Book cover of The Elements of Statistical Learning: Data Mining, Inference, and Prediction

Why this book?

This book might as well be called Introduction to machine learning, and it is probably one of the only books truly deserving of the title. Did you know neural networks have been used for decades to scan checks at the bank? They are called Boltzman Machine. Have you ever heard of how decision trees were used in old-school data mining? You could only get them from proprietary software packages from the early 2000s.

In quant trading, you will constantly face compute power constraints, so it is invaluable to understand the mathematical foundations of the most old-school machine learning methods out there. Researchers 20 years ago used to do a lot of impressive work with a lot less computing power.

The Mathematical Theory of Communication

By Claude E. Shannon, Warren Weaver,

Book cover of The Mathematical Theory of Communication

Why this book?

While studying computer networks, Claude Shannon did something pretty impressive. He reformulated the majority of classical statistics from scratch using the language and concepts of computer science. 

Statistical noise? There’s a new word for that; it’s called entropy. Also, it turns out it is a good thing, not a bad thing because entropy is equal to the information content or a data set. Tired of minimizing the squared error of everything? That’s fine, minimize the log of its likelihood instead. It does the same thing. This book challenges the assumptions of classical statistics in a way that fits neatly in the mind of a computer scientist. As a quant trader, this book will help you understand and measure the information content of data, which is critical to your success.

5 book lists we think you will like!

Interested in math, machine learning, and statistics?

5,309 authors have recommended their favorite books and what they love about them. Browse their picks for the best books about math, machine learning, and statistics.

Math Explore 98 books about math
Machine Learning Explore 31 books about machine learning
Statistics Explore 16 books about statistics

And, 3 books we think you will enjoy!

We think you will like Mathematics for Machine Learning, Computer Vision, and Statistics and Data Analysis for Financial Engineering if you like this list.