Here are 100 books that Mathematical Writing fans have personally recommended if you like
Mathematical Writing.
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Though I’ve coached endurance athletes to world championships, I’m an expert on not working out. It’s what you do when you’re not training that matters most! All the books on this list teach habits that help you relax about things that don’t matter while guiding you to define what does matter and explaining ways to most efficiently focus your energies there. This jibes with my work as a yoga teacher: we seek to find the right application of effort, and to layer in ease wherever possible. I don’t think it’s stretching too much to call each book on the list both a work of philosophy and also a deeply practical life manual.
I think about this book every day, even though it was written almost 25 years ago, and the edition I read explained how to manage your paper file folders! (One of my most-used apps, the to-do manager Things, is built on this system.)
I love how much time this book has saved me as I juggle running several businesses, staying active in my hobbies, and running a household. Allen’s approach to capturing your ideas and then deciding how to organize them so that you can keep track of what needs your attention is both simple and really profound.
For athletes who need to be as efficient as possible to reserve time and energy for training, this book is a lifesaver.
The book Lifehack calls "The Bible of business and personal productivity."
"A completely revised and updated edition of the blockbuster bestseller from 'the personal productivity guru'"-Fast Company
Since it was first published almost fifteen years ago, David Allen's Getting Things Done has become one of the most influential business books of its era, and the ultimate book on personal organization. "GTD" is now shorthand for an entire way of approaching professional and personal tasks, and has spawned an entire culture of websites, organizational tools, seminars, and offshoots.
Allen has rewritten the book from start to finish, tweaking his classic text…
I am a Reader in the Mathematics Education Centre at Loughborough University in the UK. I have always loved mathematics and, when I became a PhD student and started teaching, I realized that how people think about mathematics is fascinating too. I am particularly interested in demystifying the transition to proof-based undergraduate mathematics. I believe that much of effective learning is not about inherent genius but about understanding how theoretical mathematics works and what research tells us about good study strategies. That is what these books, collectively, are about.
This book provides a systematic account of how to understand and structure mathematical proofs. Its approach is almost entirely syntactic, which is the opposite of how I naturally think – I tend to generate arguments based on examples, diagrams, and conceptual understanding. But that difference, for me, is precisely what makes this book so valuable. Solow gives a no-nonsense, practical, almost algorithmic approach to interpreting logical language and to tackling the associated reasoning. His book thereby provides the best answer I know of to the “How do I start?” problem so often encountered when students begin constructing proofs.
This text makes a great supplement and provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs. The approach is to categorize, identify, and explain (at the student's level) the various techniques that are used repeatedly in all proofs, regardless of the subject in which the proofs arise. How to Read and Do Proofs also explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique consciously, based on the form of the…
I am a Reader in the Mathematics Education Centre at Loughborough University in the UK. I have always loved mathematics and, when I became a PhD student and started teaching, I realized that how people think about mathematics is fascinating too. I am particularly interested in demystifying the transition to proof-based undergraduate mathematics. I believe that much of effective learning is not about inherent genius but about understanding how theoretical mathematics works and what research tells us about good study strategies. That is what these books, collectively, are about.
Many undergraduate mathematics books – even those aimed at new students – are dense, technical, and difficult to read at any sort of speed. This is a natural feature of books in a deductive science, but it can be very discouraging, even for dedicated students. Houston’s book covers many ideas useful at the transition to proof-based mathematics, and he has worked extensively and attentively with students at that stage. Consequently, his book maintains high mathematical integrity and has lots of useful exercises while also being an unusually friendly read.
Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many…
I am a Reader in the Mathematics Education Centre at Loughborough University in the UK. I have always loved mathematics and, when I became a PhD student and started teaching, I realized that how people think about mathematics is fascinating too. I am particularly interested in demystifying the transition to proof-based undergraduate mathematics. I believe that much of effective learning is not about inherent genius but about understanding how theoretical mathematics works and what research tells us about good study strategies. That is what these books, collectively, are about.
Research in cognitive psychology has revealed a lot about human learning and how to make it more effective. Most mathematics students – and indeed their professors – know very little about this research or how to apply it. Weinstein and Sumeracki’s book explains how psychologists generate evidence on learning, gives a basic account of human cognitive processing, explains some strategies for effective learning, and gives tips for applying them. It is not about mathematics and it certainly will not make advanced mathematics simple, but I think that we would all have an easier time if we were more aware of some common misunderstandings about learning and effective ways to improve it.
Educational practice does not, for the most part, rely on research findings. Instead, there's a preference for relying on our intuitions about what's best for learning. But relying on intuition may be a bad idea for teachers and learners alike.
This accessible guide helps teachers to integrate effective, research-backed strategies for learning into their classroom practice. The book explores exactly what constitutes good evidence for effective learning and teaching strategies, how to make evidence-based judgments instead of relying on intuition, and how to apply findings from cognitive psychology directly to the classroom.
Including real-life examples and case studies, FAQs, and…
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…
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 +…
I have devoted my entire career to mathematics, and have a life filled with meaning and purpose through my roles as an educator, researcher, and consultant. I teach at the Vancouver campus of Northeastern University and am the owner and principal of Hoshino Math Services, a boutique math consulting firm.
The author explains the importance of abstraction in logic, demonstrating its three main components: paths made of long chains of logic, packages made of a collection of concepts structured into a new compound unit, and pivots to build bridges to previously disconnected places.
Eugenia Cheng does an excellent job of abstracting principles of logic to better understand challenging real-world societal issues such as affirmative action and cancer screening. I found it quite compelling to understand how and why she came to her positions on various issues, through her axiom that "avoiding false negatives is more important than avoiding false positives." I appreciated the expertise by which she weaved numerous hard topics, in both mathematics and social justice, into a coherent and compelling narrative.
How both logical and emotional reasoning can help us live better in our post-truth world
In a world where fake news stories change election outcomes, has rationality become futile? In The Art of Logic in an Illogical World, Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life. Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do?…
I've been teaching math and physics for more than 20 years as a private tutor. During this time, I experimented with different ways to explain concepts to make them easy to understand. I'm a big fan of using concept maps to show the connections between concepts and teaching topics in an integrated manner, including prerequisites and applications. While researching the material for my book, I read dozens of linear algebra textbooks and watched hundreds of videos, looking for the best ways to explain complicated concepts intuitively. I've tried to distill the essential ideas of linear algebra in my book and prepared this list to highlight the books I learned from.
In my opinion, Prof. Axler's book is the best way to learn the formal proofs of linear algebra theorems.
My undergraduate studies were in engineering, so I never learned the proofs. This is why I chose this book to solidify my understanding of the material; it didn't disappoint! Already, in the first few chapters, I learned new things about concepts that I thought I understood.
The book contains numerous exercises which were essential for the learning process. I went through the exercises with a group of friends, which helped me stay motivated. It wasn't easy, but all the time I invested in the proofs was rewarded by a solid understanding of the material.
I highly recommend this book as a second book on linear algebra.
This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra.
The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have…
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.
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.
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…
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.
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.
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.
