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.
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.
This book covers the basic probability of distributions with an emphasis on applications from the areas of investments, insurance, and engineering. Written by a Fellow of the Casualty Actuarial Society and the Society of Actuaries with many years of experience as a university professor and industry practitioner, the book is suitable as a text for senior undergraduate and beginning graduate students in mathematics, statistics, actuarial science, finance, or engineering as well as a reference for practitioners in these fields. The book is particularly well suited for students preparing for professional exams, and for several years it has been recommended as…
I started my career in neuroscience. I wanted to understand brains. That is still proving difficult, and somewhere along the way, I realized my real motivation was to build things, and I wound up working in AI. I love the elegance of mathematical models of the world. Even the simplest machine learning model has complex implications, and exploring them is a joy.
My knees tremble and my heart quakes when I think of how much work must have gone into these two companion volumes. Collectively, they are more than four times the length of my book, covering the whole of machine learning.
It is an essential encyclopedic resource that should be on the desk of anyone serious about machine learning.
A detailed and up-to-date introduction to machine learning, presented through the unifying lens of probabilistic modeling and Bayesian decision theory.
This book offers a detailed and up-to-date introduction to machine learning (including deep learning) through the unifying lens of probabilistic modeling and Bayesian decision theory. The book covers mathematical background (including linear algebra and optimization), basic supervised learning (including linear and logistic regression and deep neural networks), as well as more advanced topics (including transfer learning and unsupervised learning). End-of-chapter exercises allow students to apply what they have learned, and an appendix covers notation.
We’ve all heard (and likely said), “Correlation is not causation,” but after reading this book you’ll look at both correlation and causation in a whole new way.
Not only is the statistical reasoning in this book flawless, but the examples given are surprising and fascinating (like how a genetics researcher is responsible for the Plinko game on the game show The Price Is Right; he built the pinball-sorting board to model how inherited traits distribute into a bell-shaped curve).
'Wonderful ... illuminating and fun to read' - Daniel Kahneman, winner of the Nobel Prize and author of Thinking, Fast and Slow
'"Pearl's accomplishments over the last 30 years have provided the theoretical basis for progress in artificial intelligence and have redefined the term "thinking machine"' - Vint Cerf, Chief Internet Evangelist, Google, Inc.
The influential book in how causality revolutionized science and the world, by the pioneer of artificial intelligence
'Correlation does not imply causation.' This mantra was invoked by scientists for decades in order to avoid taking positions as to whether one thing caused another, such as smoking…
I’m a Swiss researcher and university professor who applies mathematics and psychology to build quantitative models for financial decision-making. Most of my scientific contributions belong to a field of research called behavioral finance, that is, the study of how psychology affects financial decisions. I love mathematics, and I am fascinated by its ability to describe complex mechanisms, including those that generate human behavior.
This book is certainly the most technical among my favorites. However, I cannot resist listing it here because I really love it. Honestly, I highly esteem Peter Wakker, and I learned tremendously much from his scientific papers. Therefore, I read this book with high expectations, and these were fully fulfilled.
I learned from this book what prospect theory is and how it developed. I learned Prof. Wakker’s view on decision theory, and this strongly shaped my personal understanding of many decision-theoretical problems.
Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events (risk) and when we lack them (ambiguity). The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide variety of disciplines. The material in the book has been carefully organized to allow readers to select pathways through the book relevant to…
I’ve wanted to be a philosopher since I read Plato’s Phaedo when I was 17, a new immigrant in Canada. Since then, I’ve been fascinated with time, space, and quantum mechanics and involved in the great debates about their mysteries. I saw probability coming into play more and more in curious roles both in the sciences and in practical life. These five books led me on an exciting journey into the history of probability, the meaning of risk, and the use of probability to assess the possibility of harm. I was gripped, entertained, illuminated, and often amazed at what I was discovering.
I am laughing out loud, even now that I am rereading this book for the umpteenth time. Fraudsters are so clever, and so is advertising. And then there is sloppy journalism with its “wow” statistics.
I like his book enormously, not least because of its witty illustrations. It is subversive, comic, and provocative, and it makes me wise to seductive, misleading practices–and it does so with a light touch.
From distorted graphs and biased samples to misleading averages, there are countless statistical dodges that lend cover to anyone with an ax to grind or a product to sell. With abundant examples and illustrations, Darrell Huff's lively and engaging primer clarifies the basic principles of statistics and explains how they're used to present information in honest and not-so-honest ways. Now even more indispensable in our data-driven world than it was when first published, How to Lie with Statistics is the book that generations of readers have relied on to keep from being fooled.
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.
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.
Written for an engineering audience, this book has a threefold purpose: (1) to present elements of modern probability theory — discrete, continuous, and stochastic; (2) to present elements of information theory with emphasis on its basic roots in probability theory; and (3) to present elements of coding theory. The emphasis throughout the book is on such basic concepts as sets, the probability measure associated with sets, sample space, random variables, information measure, and capacity. These concepts proceed from set theory to probability theory and then to information and coding theories. No formal prerequisites are required other than the usual undergraduate…
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.
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.
How should the concept of evidence be understood? And how does the concept of evidence apply to the controversy about creationism as well as to work in evolutionary biology about natural selection and common ancestry? In this rich and wide-ranging book, Elliott Sober investigates general questions about probability and evidence and shows how the answers he develops to those questions apply to the specifics of evolutionary biology. Drawing on a set of fascinating examples, he analyzes whether claims about intelligent design are untestable; whether they are discredited by the fact that many adaptations are imperfect; how evidence bears on whether…
I'm an executive coach, adjunct faculty at several top-tier business schools, and run a boutique firm consulting firm focused on organizational strategy solutions. My diverse and eclectic background in mergers & acquisitions, organization effectiveness, and strategy execution, coupled with two decades of experience in emerging markets in Asia, the Middle East, and North Africa, helps me grasp challenging people issues. I'm passionate about the topic of leaders as coaches having written several papers and columns. My research, and writing led Penguin to commission my book Coaching: The Secret Code to Uncommon Leadership that, released globally in late 2021 to much acclaim, is recommended by several academics as an essential read for aspiring and experienced managers.
A few years ago at my son’s annual townhall in school, the principal outlined the school’s strategic game plan on a powerpoint presentation.
One of the slides that stayed with me projected a visual from the book The End of Average: How We Succeed in a World That Values Sameness.
I went back and read the book, only to realize that it resonated deeply with how we in the corporate world today (not just in schools at the elementary, middle, or senior levels) are quick to pronounce verdicts: below average, average, exceeds expectations.
The book poses some pertinent questions, and rightly so: Who came up with this principle of average? Why are we following it everywhere?
How often have we as managers just given up on people that we perceive are not ‘leadership’ material. Often these same average or poor performers can be great performers in different contexts.
Are you above average? Is your child an A student? Is your employee an introvert or an extrovert? Every day we are measured against the yardstick of averages, judged according to how closely we come to it or how far we deviate from it.
The assumption that metrics comparing us to an average—like GPAs, personality test results, and performance review ratings—reveal something meaningful about our potential is so ingrained in our consciousness that we don’t even question it. That assumption, says Harvard’s Todd Rose, is spectacularly—and scientifically—wrong.
In The End of Average, Rose, a rising star in the new field…
I have taught undergraduate and PhD students physics and biophysics for 36 years, and I never get tired of it. I always look for hot new topics and everyday things that we all see but rarely notice as interesting. I also look for “how could anything like that possibly happen at all?”-type questions and the eureka moment when some idea from physics or math pries off the lid, making a seemingly insoluble problem easy. Finally, I look for the skills and frameworks that will open the most doors to students in their future work.
Throughout science, math, finance, and your personal life… underlying almost everything is the concept of a random walk. I love how Mlodinow builds our intuition for this simple yet subtle idea. Yes, the expectation may be zero, but the variance grows without limit—it took me years of study to truly feel that statement and others in my bones, but Mlodinow shows this and much more through vivid, often hilarious examples. It is no exaggeration to say that after Chapter 6, you will understand conditional probability—where so many of us stumble when we think about real situations—better than you would after a whole course on statistics.
And although this is a science book, I challenge anyone to read the last five pages and end up dry-eyed. Years later, as I reread them, the impact is undiminished.
Leonard Mlodinow's The Drunkard's Walk: How Randomness Rules Our Lives is an exhilarating, eye-opening guide to understanding our random world.
Randomness and uncertainty surround everything we do. So why are we so bad at understanding them?
The same tools that help us understand the random paths of molecules can be applied to the randomness that governs so many aspects of our everyday lives, from winning the lottery to road safety, and reveals the truth about the success of sporting heroes and film stars, and even how to make sense of a blood test.
The Drunkard's Walk reveals the psychological illusions…
I am proud to be a human (social) scientist but think that we could collectively achieve a much more successful human science enterprise. And I believe that a better human science would translate into better public policy. Most human scientists focus on their own research, paying little attention to how the broader enterprise functions. I have written many works of a methodological nature over the years. I am pleased to point here to a handful of works with sound advice for enhancing the human science enterprise.
I really liked Williams’ writing style. He is very clear, provides good examples, and is very careful in his argumentation.
I very much liked – and indeed borrowed – his strategy of summarizing the main arguments of each chapter. This is especially important since his book addresses a wide range of challenges in social science. I especially liked his discussion of how the variables we measure are never perfect proxies for the phenomena that we hope to understand.
I also liked his careful discussion of how social scientists need to be more reflective in their work. And I found his discussion of the nature of causation in social science deeply insightful.
Realism and Complexity in Social Science is an argument for a new approach to investigating the social world, that of complex realism. Complex realism brings together a number of strands of thought, in scientific realism, complexity science, probability theory and social research methodology.
It proposes that the reality of the social world is that it is probabilistic, yet there exists enough invariance to make the discovery and explanation of social objects and causal mechanisms possible. This forms the basis for the development of a complex realist foundation for social research, that utilises a number of new and novel approaches to…
