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…
It is April 1st, 2038. Day 60 of China's blockade of the rebel island of Taiwan.
The US government has agreed to provide Taiwan with a weapons system so advanced that it can disrupt the balance of power in the region. But what pilot would be crazy enough to run…
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.
Mia Lark is running out of options. There is only one way to change the score: the fantasy planet Revivium.
Armed with the powerful magic in the helm and the friendly AI, Hex that goes with it, Mia throws caution out the window. It’s time to find the main guildhall…
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…
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.
Steve Strogatz is our generation’s poet laureate of math. I could not put this book down because, although I use math daily, I was amazed at how Strogatz connects everything to everyday experience. Just one example: Hardly anyone gets told about “group theory” in high school because it’s “too advanced”—but here we find it beautifully illustrated with the problem of flipping your mattress twice a year.
This book will help you have your own ideas by opening your eyes to a world of things that just make better sense through the lens of careful analysis, the interplay of the visual and the symbolic, and (just enough) abstraction.
Award-winning Steven Strogatz, one of the foremost popularisers of maths, has written a witty and fascinating account of maths' most compelling ideas and how, so often, they are an integral part of everyday life.
Maths is everywhere, often where we don't even realise. Award-winning professor Steven Strogatz acts as our guide as he takes us on a tour of numbers that - unbeknownst to the unitiated - connect pop culture, literature, art, philosophy, current affairs, business and even every day life. In The Joy of X, Strogatz explains the great ideas of maths - from negative numbers to calculus, fat…
Winner of the 2024 New Mexico - Arizona Book Award.
In this deeply researched novel of America's most celebrated outlaw, Mark Warren sheds light on the human side of Billy the Kid and reveals the intimate stories of the lesser-known players in his legendary life of crime. Warren's fictional composer…
I'm a British writer, (though I now live and work in California) and a Stanford professor who is passionate about helping everyone know they have endless potential and that math is a subject of creativity, connections, and beautiful ideas. I spend time battling against math elitism, systemic racism, and the other barriers that have stopped women and people of color from going forward in STEM. I am the cofounder of youcubed, a site that inspires millions of educators and their students, with creative mathematics and mindset messages. I've also made a math app, designed to help students feel good about struggling, called Struggly.com. I love to write books that help people develop their mathematical superpowers!
This is a beautiful book filled with glossy color photos, that would be a lovely gift for any girl or woman interested in mathematics, or really, any human.
Inside the book are the “rebel women” who have specialized in mathematics (and yes it seems you still need to be a rebel to succeed in this male-dominated field). I learned so much about the mathematics the women studied and created, as well as the ways they battled for recognition to be able to contribute to mathematics.
The book is filled with powerful and creative mathematics produced by inspirational women.
From rocket scientists to code breakers, discover the incredibly inspiring stories of more than 30 women who fought through the obstacles, shattered the stereotypes, and embraced their STEM passions.
Prepare to be inspired. With more than 200 photos and original interviews with several of the amazing women covered, Power in Numbers: The Rebel Women of Mathematics is a full-color volume that takes aim at the forgotten influence of women on the development of mathematics over the last two millennia.
Each biography reveals the amazing life of a different female mathematician, from her childhood and early influences, to the obstacles she…
If you want to know what conducting an orchestra is like, you ask a conductor. If you want to know what being a mathematician is like, you ask a mathematician. I have been studying, researching, and teaching mathematics (mainly at Cambridge but also in France and elsewhere) for a lifetime and loved (almost) every moment of it. In the words of Constance Reid, `Mathematicians are people who devote their lives to what seems to me a wonderful kind of play.'
This book is out of print, but I include it in the hope that some public-spirited publisher may be persuaded to reissue this large-format picture book. It was the first book on mathematics that I read at about the age of ten and it contained precisely what I needed to show me that this was a subject with a history and a use. (Nor am I the only mathematician to have this experience.)
As an adult, I found the same author’s Mathematics for the Million a bit crass and utilitarian but I pardon him everything for a wonderful first experience.
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.
This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.
Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been…
I'm a British writer, (though I now live and work in California) and a Stanford professor who is passionate about helping everyone know they have endless potential and that math is a subject of creativity, connections, and beautiful ideas. I spend time battling against math elitism, systemic racism, and the other barriers that have stopped women and people of color from going forward in STEM. I am the cofounder of youcubed, a site that inspires millions of educators and their students, with creative mathematics and mindset messages. I've also made a math app, designed to help students feel good about struggling, called Struggly.com. I love to write books that help people develop their mathematical superpowers!
I love all of Eugenia’s books, she is a cool mathematician working to educate the public about real mathematics – a subject of deep explorations and connected ideas.
Eugenia shares the creativity in mathematics, and the importance of pushing against boundaries, including the gender boundaries that often stop girls and women going forward in STEM. Her playful use of mathematical ideas to disrupt the myths of narrow and inequitable mathematics and the dominance of men in the field, is so fascinating, especially for those of us perturbed by the inequities in STEM.
This is a great book for those who would like to love mathematics a little more than they do now.
One of the world’s most creative mathematicians offers a new way to look at math—focusing on questions, not answers
Where do we learn math: From rules in a textbook? From logic and deduction? Not really, according to mathematician Eugenia Cheng: we learn it from human curiosity—most importantly, from asking questions. This may come as a surprise to those who think that math is about finding the one right answer, or those who were told that the “dumb” question they asked just proved they were bad at math. But Cheng shows why people who ask questions like “Why does 1 +…
Ramon Ramirez’s Dog is a collection of essays written over the years about the adventures and misadventures, mostly outside but occasionally inside the diplomatic career of a U.S. ambassador. Common threads weaving the stories together are a desire for a life well-lived, balancing career with family and friends, keeping physically…
I have worked in scientific research and teaching for over 30 years, and maintained a love of art and music as well, but am saddened when I hear statements, especially from high-school pupils, that ‘there is no room for creativity or imagination in science.’ Like all working scientists, I know that imagination is the most important faculty for a scientist. The Poetry and Music of Science is my project to tease out the creative threads in the scientific process, and also to find the buried pathways that link science with the arts and humanities. The journey of discovery has been full of surprises and delights for me.
Visual representations are not the only pathway to creative acts in art and science, but they are responsible for large territories of creativity – including, and surprisingly, the mathematical. Arthur Miller shows how ‘seeing the unseen’ becomes possible from atoms to the conservation of energy in science, and from modernism to cubism in art. The book itself is as visually striking as its contents and helped me to think through why the visual metaphor – ‘Oh, I see!’ – becomes the standard description of the moment of insight.
Here, distinguished science historian Arthur I. Miller delves into the connections between modern art and modern physics. He takes us on a wide-ranging study to demonstrate that scientists and artists have a common aim: a visual interpretation of both the visible and invisible aspects of nature. Along the way, we encounter the philosophy of mind and language, cognitive science and neurophysiology in our search for the origins and meaning of visual imagery. At a time when the media are overeager to portray science as a godless, dehumanising exercise undermining the very fabric of society, this sixth book by Professor Miller…
