Here are 100 books that Conceptual Mathematics fans have personally recommended if you like
Conceptual Mathematics.
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I hate nothing more than feeling uncertain about my views on an important topic. That’s why I cherish tools for thought that help me cut through the various confusions to which humans are prone. The sharpest tool we’ve got is modern symbolic logic, as it has been developed since the late 19th century. I’ve loved symbolic logic since I took my first logic class in college. I’ve been teaching Intro Logic for over twenty years at Princeton University, and I’ve published several papers and books that employ logic to try to gain clarity on philosophical issues.
A true gem in the realm of symbolic logic textbooks, this book stands out for its crystal-clear explanations and elegant English prose. It’s my top recommendation for anyone coming from a humanities background or returning to academia after a break.
Tomassi’s writing makes symbolic logic both accessible and engaging.
Bringing elementary logic out of the academic darkness into the light of day, Paul Tomassi makes logic fully accessible for anyone attempting to come to grips with the complexities of this challenging subject. Including student-friendly exercises, illustrations, summaries and a glossary of terms, Logic introduces and explains:
* The Theory of Validity * The Language of Propositional Logic * Proof-Theory for Propositional Logic * Formal Semantics for Propositional Logic including the Truth-Tree Method * The Language of Quantificational Logic including the Theory of Descriptions.
Logic is an ideal textbook for any logic student: perfect for revision, staying on top of…
The dragons of Yuro have been hunted to extinction.
On a small, isolated island, in a reclusive forest, lives bandit leader Marani and her brother Jacks. With their outlaw band they rob from the rich to feed themselves, raiding carriages and dodging the occasional vindictive…
I hate nothing more than feeling uncertain about my views on an important topic. That’s why I cherish tools for thought that help me cut through the various confusions to which humans are prone. The sharpest tool we’ve got is modern symbolic logic, as it has been developed since the late 19th century. I’ve loved symbolic logic since I took my first logic class in college. I’ve been teaching Intro Logic for over twenty years at Princeton University, and I’ve published several papers and books that employ logic to try to gain clarity on philosophical issues.
One of my teachers once described this as "the best book with the most misleading title." Despite the title, it’s not about physics—it’s about the symbolic reasoning that underpins theoretical physics.
If you’re looking for a fast-paced overview of the mathematical tools used in cutting-edge physics, this book is unparalleled.
Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the "whys" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle physics, and astrophysics.
I hate nothing more than feeling uncertain about my views on an important topic. That’s why I cherish tools for thought that help me cut through the various confusions to which humans are prone. The sharpest tool we’ve got is modern symbolic logic, as it has been developed since the late 19th century. I’ve loved symbolic logic since I took my first logic class in college. I’ve been teaching Intro Logic for over twenty years at Princeton University, and I’ve published several papers and books that employ logic to try to gain clarity on philosophical issues.
Although I’m not a programmer, I couldn’t leave programming—a quintessential example of symbolic reasoning—off this list. For someone like me, with a background in mathematics and philosophy, this book provides a concrete look at how abstract reasoning can be applied in programming.
For programmers, it’s an engaging introduction to category theory. This is a brilliant example of interdisciplinary thinking at its best.
When Annie Thornton, midwife and apprentice witch, falls through time to a 15th-century Yorkshire village with her telepathic cat, Rosamund, she befriends Will and Jack, two soldiers returning from the French Wars. Mistress Meg, Annie’s ancestral aunt living in the 15th century, is…
As a kid I read every popular math book I could lay my hands on. When I became a mathematician I wanted to do more than teaching and research. I wanted to tell everyone what a wonderful and vital subject math is. I started writing popular math books, and soon was up to my neck in radio, TV, news media, magazines... For 12 years I wrote the mathematical Recreations Column for Scientific American. I was only the second mathematician in 170 years to deliver the Royal Institution Christmas Lectures, on TV with a live tiger. The University changed my job description: half research, half ‘outreach’. I had my dream job.
Mathematicians are constantly baffled by the public’s lack of awareness, not just of what mathematics does, but what it is. Today’s technological society functions only because of a vast range of mathematical concepts, techniques, and discoveries, which go far beyond elementary arithmetic and algebra. This was one of the first books to tackle these misunderstandings head on. It does so by examining not just the math and what it’s used for, but the social structures, the ‘conditions of civilization’ that have brought us to this curious state: utterly dependent on math, almost universally unaware that we are.
"A passionate plea against the use of formal mathematical reasoning as a method for solving mankind's problems. . . . An antidote to the Cartesian view that mathematical and scientific knowledge will suffice to solve the central problems of human existence." — The New York Times "These cogitations can and should be read by every literate person." — Science Books and Films "A warning against being seduced or intimidated by mathematics into accepting bad science, bad policies, and bad personal decisions." — Philadelphia Inquirer Rationalist philosopher and mathematician René Descartes visualized a world unified by mathematics, in which all intellectual…
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.
This is one of the first books in the entire puzzles literature that gave multiple detailed solutions to several beautiful mathematical puzzles.
Some of today's most famous puzzles were either popularized or introduced in this book. For example, truck in the desert, start of the snow, the rookie electrician, hole in a sphere, captivating problem in navigation, the hunter and his dog, the counterfeit coin, and common birthdays.
This book with its multiple-solutions feature taught me that we should never stop searching for more solutions as there can always be a better solution. Furthermore, when 1- or 2-paragraph solutions were the norm, this book illustrated the beauty of having multi-page detailed solutions.
Interestingly, this book is a crowd-written book as most of the puzzles and solutions presented in this book are contributed by readers of a magazine. This implies that it is possible to write great crowd-written books.
For two decades, an international readership of workers in applied mathematics submitted their favorite puzzles to a mid-twentieth-century column, The Graham Dial. This original collection features 100 of the publication's very best problems, with themes ranging from logic and engineering situations to number theory and geometry. Each problem was specifically selected for its widely differing modes of solution, and most include several methods of solution plus assessments of their efficacy. In checking their solutions against the book's, readers may find that their interest in the puzzles increases. The search for an answer can develop into a challenge to improve upon…
Lilli Botchis, PhD, is a psycho-spiritual counselor, educator, and vibrational medicine developer with four decades of experience in advanced body/soul wellness and the development of higher consciousness. Her expertise includes botanicals, gems, color, flower essences, bio-energy therapies, and holographic soul readings. Lilli is an alchemist, mystic, and translator of Nature’s language as it speaks to our soul. A brilliant researcher in the field of consciousness, she understands the interconnectedness of Nature and the human being and is known as an extraordinary emissary of the natural world. Lilli has been inducted into the Sovereign Order of St. John of Jerusalem, Knights Hospitaller. Many seek her out for her visionary insights and compassionate wisdom.
According to Michael Schneider, "The universe may be a mystery, but it's no secret." This book is a comprehensive yet simple visual guide to understanding the hidden meaning in the mathematical composition of all physical form. It is fun and fascinating to discover the sacred geometry visible throughout nature, in flowers, crystals, plants, shells, and the human body. You don't have to be a mathematician to see the beauty and symmetry of these patterns in every expression of God's creation, once revealed.
Discover how mathematical sequences abound in our natural world in this definitive exploration of the geography of the cosmos
You need not be a philosopher or a botanist, and certainly not a mathematician, to enjoy the bounty of the world around us. But is there some sort of order, a pattern, to the things that we see in the sky, on the ground, at the beach? In A Beginner's Guide to Constructing the Universe, Michael Schneider, an education writer and computer consultant, combines science, philosophy, art, and common sense to reaffirm what the ancients observed: that a consistent language of…
Chasing Light is a lyrical meditation on grief, memory, and the fragile beauty of everyday life. At its core, it is a story of resilience, forgiveness, and the transformational power of human connection. It sheds light on the overlooked realities of homelessness and addiction, while emphasizing the importance of compassion…
Philosophy’s core questions have always obsessed me: What is real? What makes life worth living? Can knowledge be made secure? In graduate school at the University of Virginia I was drawn to mathematically formalized approaches to such questions, especially those of C. S. Peirce and Alain Badiou. More recently, alongside colleagues at Endicott College’s Center for Diagrammatic and Computational Philosophy and GCAS College Dublin I have explored applications of diagrammatic logic, category theory, game theory, and homotopy type theory to such problems as abductive inference and artificial intelligence. Philosophers committed to the perennial questions have much to gain today from studying the new methods and results of contemporary mathematics.
The Univalent Foundations program in foundations of mathematics launched by Voevodsky and others in the past decade and a half has contributed to a promising new paradigm unifying computation, mathematics, logic, and proof theory.
Understanding the core elements of this research program, Homotopy Type Theory, is essential for contemporary philosophers who want to engage directly with current developments in mathematics and computer science.
Corfield is a well-established name in philosophy of mathematics, and this book is the best introduction to Homotopy Type Theory for philosophers.
Working within themes and problematics that will be familiar to philosophers with a basic background in logic, Corfield covers the elementary constructions of homotopy types from a logical point of view and provides plenty of provocative suggestions for how these formal tools might reinvigorate philosophical research today.
"The old logic put thought in fetters, while the new logic gives it wings."
For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory.
Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New…
My name is Susan Marie Chapman and I am an award-winning Children’s Book Author. I have written over fourteen children’s books. I grew up on a farm surrounded by animals and nature and my seven sisters and brothers. Wow!! My goal is to get as many books into the hands of children that I possibly can. You see, reading books, especially picture books, is a way for a child to see the world through the pictures and words of a book. It creates imagination and excitement and fun and questions which lead to answers which makes you smarter. So read, read, read, until you run out of books, which will never happen.
What child isn’t curious about the night sky and all the stars that live up there? Did you know that the Sun is a giant star? This book is full of fun facts, not just about stars but about our planet. It helps to put things into perspective, so to speak. It talks about gravity and how many miles away the moon is from the earth. I think kids will learn a lot from reading this book and will even be able to impress their friends with all of their newly acquired knowledge. Did you know the earth looks green because it’s covered in 3,000,000,000,000 trees?? I love this book because learning new things is fun and this book is all about fun. I felt very smart after reading this book.
A Boston Globe–Horn Book Honor Book * Winner of the Mathical Book Prize
Perfect for curious children, classrooms eager for STEM content, and readers who have devoured Ada Twist, Scientist and How Much Is a Million?
Did you know that the earth is covered in three trillion trees? And that seven billion people weigh about the same as ten quadrillion ants? Our world is full of constantly changing numbers, from a hundred billion trillion stars in space to thirty-seven billion rabbits on Earth. Can you imagine that many of anything?
The playful illustrations from New York Times–bestselling artist Isabel Greenberg…
Philosophy’s core questions have always obsessed me: What is real? What makes life worth living? Can knowledge be made secure? In graduate school at the University of Virginia I was drawn to mathematically formalized approaches to such questions, especially those of C. S. Peirce and Alain Badiou. More recently, alongside colleagues at Endicott College’s Center for Diagrammatic and Computational Philosophy and GCAS College Dublin I have explored applications of diagrammatic logic, category theory, game theory, and homotopy type theory to such problems as abductive inference and artificial intelligence. Philosophers committed to the perennial questions have much to gain today from studying the new methods and results of contemporary mathematics.
Far too many math books are written in a style so terse and ungenerous that all but the most mathematically gifted readers hardly have a fair chance of understanding.
On the other hand, the discursive style of much philosophy of mathematics gains readability at the expense of formal rigor. Button and Walsh strike the perfect balance in this exceptionally rich introduction to model theory from a distinctively philosophical perspective.
There’s no getting around the fact that the mathematics of model theory is hard going. But this book works through all the relevant proofs in clear and detailed terms (no lazy “we leave this as an exercise for the reader”), and the authors are always careful to motivate each section with well-chosen philosophical concerns right up front.
Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of…
Portrait of an Artist as a Young Woman
by
Alexis Krasilovsky,
Kate from Jules et Jim meets I Love Dick.
A young woman filmmaker’s journey of self-discovery, set against a backdrop of the sexual liberation movement of the 1970s and 1980s. In Portrait of an Artist as a Young Woman, we follow Ana Fried as she faces the ultimate…
Philosophy’s core questions have always obsessed me: What is real? What makes life worth living? Can knowledge be made secure? In graduate school at the University of Virginia I was drawn to mathematically formalized approaches to such questions, especially those of C. S. Peirce and Alain Badiou. More recently, alongside colleagues at Endicott College’s Center for Diagrammatic and Computational Philosophy and GCAS College Dublin I have explored applications of diagrammatic logic, category theory, game theory, and homotopy type theory to such problems as abductive inference and artificial intelligence. Philosophers committed to the perennial questions have much to gain today from studying the new methods and results of contemporary mathematics.
From a strictly philosophical perspective, the emergence of category theory as a unifying paradigm rivaling set theory is probably the most important development in mathematics in the last half-century.
But for philosophers without a lot of mathematical background, learning even its rudiments can be daunting. Among many introductory texts (Lawvere and Schanuel, Awodey, Riehl, Spivak), Cheng’s book stands out as perhaps the friendliest and most accessible.
She does not forego rigor, but she isn’t afraid to put aside precise formalism when necessary for intuition and clearer understanding. Her book takes the reader from mathematical beginnings through category theory’s core constructions to glimpses of higher-order categories (one of Cheng’s areas of expertise).
A mathematically novice philosopher who wants to understand the basics of category theory couldn’t do better.
Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes and help you develop your own thinking, with no formal mathematical background needed. The book brings abstract mathematical ideas down to earth using examples of social justice, current events, and everyday life - from privilege to COVID-19 to driving routes. The journey begins with the ideas and workings of abstract mathematics, after which you will gently climb toward more technical material,…