The most recommended calculus books

Who picked these books? Meet our 8 experts.

8 authors created a book list connected to calculus, and here are their favorite calculus books.
Shepherd is reader supported. When you buy books, we may earn an affiliate commission.

What type of calculus book?

Loading...

Book cover of Infinite Powers: How Calculus Reveals the Secrets of the Universe

Amir Alexander Author Of Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World

From my list on the power and wonder of mathematics.

Why am I passionate about this?

I have written four books (so far) about the surprising ways mathematics pervades human culture, religion, and even politics. The five books I recommend here, each in its own way, shows how mathematics is very much a part of our lives, even if we don’t always notice it. Thanks to books like these, you do not have to be a mathematician to appreciate how this seemingly abstract field shapes our very human world.

Amir's book list on the power and wonder of mathematics

Amir Alexander Why did Amir love this book?

That Steven Strogatz, Cornell Professor and longtime New York Times columnist, is unsurpassed as an expositor of mathematics, goes without saying. No one can make the abstract and technical appear simple and intuitive like Strogatz. In Infinite Powers he takes on the Calculus -- the central pillar of modern mathematics that is also the bane of many a high-school student. It is an immensely powerful field, and at its core is a concept that is both counter-intuitive and paradoxical: the infinite.

The roots of the calculus, we learn, go back to the ancient Greeks, whose notions of the infinite were put to powerful mathematical use by Archimedes. Strogatz continues with Galielo’s dynamics and Kepler’s laws of planetary motion, before reaching the turning point: The discovery of the Calculus by Newton and Leibniz. This leads straight to a discussion of differential equations, which are responsible for so much of what makes…

By Steven Strogatz,

Why should I read it?

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

What is this book about?

From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus—how it works and why it makes our lives immeasurably better. 
 
Without calculus, we wouldn’t have cell phones, TV, GPS, or ultrasound. We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket.

Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down-to-earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real-world problems,…


Book cover of Alex Through the Looking-Glass

David Acheson Author Of The Wonder Book of Geometry: A Mathematical Story

From my list on mathematics for the general reader.

Why am I passionate about this?

I am an applied mathematician at Oxford University, and author of the bestseller 1089 and All That, which has now been translated into 13 languages. In 1992 I discovered a strange mathematical theorem – loosely related to the Indian Rope Trick - which eventually featured on BBC television. My books and public lectures are now aimed at bringing mainstream mathematics to the general public in new and exciting ways.

David's book list on mathematics for the general reader

David Acheson Why did David love this book?

This is a sequel to Alex Bellos's bestseller Alex's Adventures in Numberland, but more focused on applications of mathematics to the real world, especially through physics. Many of these were known to me, particularly when they involved calculus, but I greatly enjoyed Alex's distinctive and novel way of putting across sophisticated ideas, in part by interspersing them with personal interviews with mathematicians of all kinds.  

By Alex Bellos,

Why should I read it?

1 author picked Alex Through the Looking-Glass as one of their favorite books, and they share why you should read it.

What is this book about?

From triangles, rotations and power laws, to fractals, cones and curves, bestselling author Alex Bellos takes you on a journey of mathematical discovery with his signature wit, engaging stories and limitless enthusiasm. As he narrates a series of eye-opening encounters with lively personalities all over the world, Alex demonstrates how numbers have come to be our friends, are fascinating and extremely accessible, and how they have changed our world.

He turns even the dreaded calculus into an easy-to-grasp mathematical exposition, and sifts through over 30,000 survey submissions to reveal the world's favourite number. In Germany, he meets the engineer who…


Book cover of A Calculus of Suffering: Pain, Professionalism and Anesthesia in Nineteenth-Century America

David Healy Author Of Children of the Cure: Missing Data, Lost Lives and Antidepressants

From my list on how medicine should be.

Why am I passionate about this?

I’ve been researching treatment harms for 3 decades and founded RxISK.org in 2012, now an important site for people to report these harms. They’ve been reporting in their thousands often in personal accounts that feature health service gaslighting. During these years, our treatments have become a leading cause of mortality and morbidity, the time it takes to recognize harms has been getting longer, and our medication burdens heavier. We have a health crisis that parallels the climate crisis. Both Green parties and Greta Thunberg’s generation are turning a blind eye to the health chemicals central to this. We need to understand what is going wrong and turn it around.   

David's book list on how medicine should be

David Healy Why did David love this book?

Most of us figure doing evil, even if good results, is not ethical but without this, there would be no medicine. Martin Pernick covers the discovery of anesthesia and the ethical dilemmas this new ability to save lives by poisoning people posed. Anesthesia is a technique and techniques are amoral. How do we ensure they enhance rather than diminish us? How do we avoid seduction into a sleep during which we can be cosmetically enhanced? Is there a limit to how many drugs we give children to manage their behaviour – just because we can? Treating and stopping are not the same as not treating. Pernick doesn’t tell us how to manage this calculus, but he makes us aware modern life involves more of a calculus than we might have thought.   

By Martin S. Pernick,

Why should I read it?

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

What is this book about?

Analyzes the impact of anesthesia on nineteenth-century medicine, discusses the advantages and disadvantages of anesthesia, and explains how rules for its use were developed


Book cover of Strategy: An Introduction to Game Theory

Felix Munoz-Garcia Author Of Game Theory: An Introduction with Step-by-Step Examples

From my list on learning Game Theory.

Why am I passionate about this?

I am a Professor of Economics at Washington State University. My research focuses on applying Game Theory and Industrial Organization models to polluting industries and other regulated markets. I analyze how firms strategically respond to environmental regulation, including their output and pricing decisions, their investments in clean technologies, and merger decisions, both under complete and incomplete information contexts.

Felix's book list on learning Game Theory

Felix Munoz-Garcia Why did Felix love this book?

This book is a short introduction to undergraduate-level Game Theory, with a special focus on basic games of complete information and contracts.

It avoids jargon, notation, or formal definitions but emphasizes economic intuition and offers many examples in each chapter. Some chapters require a good math background, making the book a good fit for students who already took at least one course in algebra and calculus.

By Joel Watson,

Why should I read it?

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

What is this book about?

Joel Watson has refined his successful text to make it even more student-friendly. A number of sections have been added, and numerous chapters have been substantially revised. Dozens of new exercises have been added, along with solutions to selected exercises. Chapters are short and focused, with just the right amount of mathematical content and end-of-chapter exercises. New passages walk students through tricky topics.


Book cover of Mathematics for the Million: How to Master the Magic of Numbers

David Acheson Author Of The Wonder Book of Geometry: A Mathematical Story

From my list on mathematics for the general reader.

Why am I passionate about this?

I am an applied mathematician at Oxford University, and author of the bestseller 1089 and All That, which has now been translated into 13 languages. In 1992 I discovered a strange mathematical theorem – loosely related to the Indian Rope Trick - which eventually featured on BBC television. My books and public lectures are now aimed at bringing mainstream mathematics to the general public in new and exciting ways.

David's book list on mathematics for the general reader

David Acheson Why did David love this book?

This book has haunted me for years. For what is it, exactly, that gives it such enduring popularity? After all, it was first published in 1936, yet is still in print today. In his autobiography, Hogben remarks on the importance of eye-catching illustrations but speculates that its success may instead be because the book contains – most unusually for a 'popular' work – exercises and answers, making it more suitable for self-teaching. Whatever the real answer, his book must surely have something to teach anyone – like myself – who aspires to bring mainstream mathematics to life for the general public.

By Lancelot Hogben,

Why should I read it?

1 author picked Mathematics for the Million as one of their favorite books, and they share why you should read it.

What is this book about?

Explains mathematics from counting to calculus in the light of man's changing social achievements.


Book cover of Microeconomics

Ana Espinola-Arredondo Author Of Intermediate Microeconomic Theory: Tools and Step-by-Step Examples

From my list on getting into microeconomics.

Why am I passionate about this?

When understanding the interactions in our economy, it is critical to recognize all participants in this complex system. I’m passionate about microeconomics because it provides me with a different perspective to examine the world around me. I use my microeconomic glasses and I enjoy rationalizing the daily interactions and predicting the potential outcomes.

Ana's book list on getting into microeconomics

Ana Espinola-Arredondo Why did Ana love this book?

This is a widely used book in introduction to microeconomics courses in colleges around the world, from the Nobel Prize winner Paul Krugman.

The book assumes no algebra or calculus, other than elementary arithmetic, thus being appropriate for students from different backgrounds.

Each chapter is well motivated with real-life problems and data, followed by a basic, intuitive, explanation of how microeconomics helps us model and understand the tradeoff that individuals or firms face in that setting.

Highly recommended for students with little math background.

By Paul Krugman, Robin Wells,

Why should I read it?

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

What is this book about?

When it comes to explaining current economic conditions, there is no economist readers trust more than New York Times columnist and Nobel laureate Paul Krugman.  Term after term, Krugman is earning that same level of trust in the classroom, with more and more instructors introducing students to the fundamental principles of economics via Krugman’s signature storytelling style. The new Third Edition of Paul Krugman and Robin Wells’s Economics is their most accomplished yet—extensively updated to offer new examples and stories, new case studies from the business world, and expert coverage of the ongoing financial crisis. Watch a video interview of…


Book cover of Book of Proof

Michael Anthony Lewis Author Of Social Workers Count: Numbers and Social Issues

From my list on quant geeks.

Why am I passionate about this?

I've had a long-time interest in two things: mathematics and social issues. This is why I got degrees in social work (Masters) and sociology (PhD) and eventually focused on the quantitative aspects of these two areas. Social Workers Count gave me the chance to marry these two interests by showing the role mathematics can play in illuminating a number of pressing social issues.

Michael's book list on quant geeks

Michael Anthony Lewis Why did Michael love this book?

Many people associate mathematics with calculating things or plugging numbers into formulas to get answers to a multitude of problems.

But this isn't how mathematicians view their discipline. They see mathematics as more about starting with definitions of key mathematical concepts, stating axioms about these concepts, and proving things about them. For those interested in going from calculating and plug and chug mathematics to "real" mathematics, Richard Hammack's book is a terrific place to start.

The book covers a number of topics that cut across all of pure and applied mathematics, topics such as sets, relations, and functions. But the heart of the book is focused on how mathematicians go about proving things. If one wants a glimpse of how mathematicians really work, go out and get this book immediately.  

By Richard Hammack,

Why should I read it?

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

What is this book about?

This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions, calculus…


Book cover of Chases and Escapes: The Mathematics of Pursuit and Evasion

Pramod Ganapathi Author Of Mathematical and Algorithmic Puzzles

From my list on mathematical and algorithmic puzzles.

Why am I passionate about this?

I am a Research Assistant Professor of Computer Science at Stony Brook University learning/teaching/researching mathematics/algorithms/puzzles. In these fields, I have published a book, published 15+ papers in conferences/journals, been granted a US patent, won two Outstanding Paper Awards, taught 10+ courses in 25+ offerings, and have supervised 90+ master's/bachelor students. I am a puzzle addict involved in this field for 25 years and puzzles are my religion/God. Puzzles are the main form of supreme energy in this universe that can consistently give me infinite peace.

Pramod's book list on mathematical and algorithmic puzzles

Pramod Ganapathi Why did Pramod love this book?

This book is full of beautiful puzzles on a mathematical topic called pursuit evasion. Its author Paul Nahin has written tens of books in physics and mathematics.

Nahin's writing can be described as a captivating reading experience pulling readers into his world like a whirlpool. His appreciation of mathematics, physics, and the people who discover them is unmatchable. It seems like the physics of motion and the mathematics of calculus is inseparable, as can be witnessed in the book.

The calculus used in this book is heavy. Nevertheless, Nahin makes his readers fall in love with this big beast. Almost every puzzle in this book is aesthetically beautiful and gives readers a deep sense of satisfaction. My favorites include Lady in the Lake, and Lion and Man.

By Paul J. Nahin,

Why should I read it?

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

What is this book about?

We all played tag when we were kids. What most of us don't realize is that this simple chase game is in fact an application of pursuit theory, and that the same principles of games like tag, dodgeball, and hide-and-seek are also at play in military strategy, high-seas chases by the Coast Guard, and even romantic pursuits. In Chases and Escapes, Paul Nahin gives us the first complete history of this fascinating area of mathematics, from its classical analytical beginnings to the present day. Drawing on game theory, geometry, linear algebra, target-tracking algorithms, and much more, Nahin also offers an…


Book cover of Teaching and Learning Algebra

David Acheson Author Of The Wonder Book of Geometry: A Mathematical Story

From my list on mathematics for the general reader.

Why am I passionate about this?

I am an applied mathematician at Oxford University, and author of the bestseller 1089 and All That, which has now been translated into 13 languages. In 1992 I discovered a strange mathematical theorem – loosely related to the Indian Rope Trick - which eventually featured on BBC television. My books and public lectures are now aimed at bringing mainstream mathematics to the general public in new and exciting ways.

David's book list on mathematics for the general reader

David Acheson Why did David love this book?

This may seem an odd choice, but as a maths popularizer I need to know all that I can about why some people find the main elements of the subject so difficult. I found Doug French's book exceptionally helpful in this respect, even though it is aimed principally at high school teachers. This is partly because he focuses throughout on the most important mathematical ideas and difficulties. Moreover, the scope is wider than the title suggests, for he also ventures imaginatively into both geometry and calculus.

By Doug French,

Why should I read it?

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

What is this book about?

Continuum has repackaged some of its key academic backlist titles to make them available at a more affordable price. These reissues will have new ISBNs, distinctive jackets and strong branding. They cover a range of subject areas that have a continuing student sale and make great supplementary reading more accessible. A comprehensive, authoritative and constructive guide to teaching algebra.


Book cover of La Dame d'Esprit: A Biography of Marquise Du Châtelet

Karen Offen Author Of Debating the Woman Question in the French Third Republic, 1870-1920

From my list on remarkable French women.

Why am I passionate about this?

I have always been fascinated by France and things French. In graduate school, no women’s history was on our required reading lists. As a young woman, though, entering a professional field in which women were few on the ground, much less studied, I became an avid reader of biographies of achieving women – partly to learn how they were able to surmount (or not) the obstacles that confronted them in a male-dominated world. The five stellar biographies of French women I present here are products of the newer work in retrieving women’s histories. They are deeply researched and engagingly written. They confirm the saying that “truth is stranger than fiction.”

Karen's book list on remarkable French women

Karen Offen Why did Karen love this book?

This splendid biography traces the life and times of the Marquise Du Châtelet, born in Paris in December 1706, who became one of the most erudite women of her époque. For fifteen years she was the companion to Voltaire, the best-known of the French philosophes. She mastered calculus and translated Newton’s Principia, in addition to carrying on an active social life and raising several children. She died at the age of 42, following the birth of a daughter conceived with another lover. The author explains her subject’s life course as “from a life of frivolity to a life of the mind.” It’s a great read.

By Judith Zinsser,

Why should I read it?

1 author picked La Dame d'Esprit as one of their favorite books, and they share why you should read it.

What is this book about?

Documents the life of the French Enlightenment-era intellectual, from her aristocratic youth and controversial choice to become the mistress of Voltaire to her mathematical and scientific achievements and work as a translator of Newton.