Here are 100 books that How to Read and Do Proofs fans have personally recommended if you like
How to Read and Do Proofs.
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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.
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.
Mathematics requires accurate calculation, and students sometimes think that getting the right answer is enough. But mathematics is also about valid logical arguments, and the demand for clear communication increases through an undergraduate degree. Students, therefore, need to learn to write professionally, with attention to general issues like good grammar, and mathematics-specific issues like accuracy in notation, precision in logical language, and structure in extended arguments. Vivaldi’s book has a great many examples and exercises, and students could benefit from studying it systematically or from dipping into it occasionally and reflecting on small ways to improve.
This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student.
The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a…
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…
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.
The Four Color Problem was one of the most baffling questions in mathematics for over 120 years. First posed in 1852, it asks whether every map can be colored with four colors, or fewer, so that regions adjacent along a boundary have different colors. The answer (yes) was finally obtained in 1976, with massive computer assistance. This method was initially controversial, but the result is now firmly established. This highly readable account, with full-color illustrations, opens up the history and the personalities who tackled this topological enigma, as well as making the mathematics comprehensible. The path to the final solution is littered with blunders and mistakes, but also illustrates how mathematicians can join forces across the generations to chip away at a problem until it cracks wide open.
On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history--one that would confound thousands of puzzlers for more than a century. This is the amazing story of how the "map problem" was solved. The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little…
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.
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.
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…
Bertrand Russell wrote that: “Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.” I agree. Math is, however, a human thing, all tangled up with the nature of human personality and the history of our civilizations. Well-written biographies of great mathematicians put that “stern perfection” in a proper human context.
Gödel (1906-1978) is, like Newton, an unpromising subject for biography. He was antisocial and mentally unstable. His obsessive fear of being poisoned led eventually to him starving himself to death.
Rebecca Goldstein is a professor of philosophy with a deep interest in logic and the foundations of mathematical truth – the applecart that Gödel overturned in 1931 with his tremendous paper on the incompleteness of axiomatic systems. She is also an experienced novelist. This combination makes her just the right person to construct a gripping story out of Gödel’s weirdness and world-shaking importance.
Probing the life and work of Kurt Goedel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning-and brought him to the edge of madness.
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.
Anany Levitin introduced me to algorithmics – my second love (my first love is mathematics), through his legendary algorithmics textbook. He was one of my superheroes in my young adult life and he got me addicted to algorithms. His book is my favorite because it is beautifully organized based on design techniques, well-written, and uses nice puzzles to teach algorithms.
Levitin went much deeper and wrote this book on algorithmic puzzles. This book is the first mainstream book in the puzzle literature that taught beautiful algorithmic puzzles via various algorithm technique techniques. Levitin claimed several mathematical puzzles as algorithmic focusing on aspects of the solutions that are automatable.
Elegant puzzles (with extensive references) in this book that I have enjoyed include missionaries and cannibals, bridge crossing, circle of lights, MU puzzle, turning on a light bulb, chameleons, poisoned wine, game of life, twelve coins, fifteen puzzle, hats with numbers, and…
Algorithmic puzzles are puzzles involving well-defined procedures for solving problems. This book will provide an enjoyable and accessible introduction to algorithmic puzzles that will develop the reader's algorithmic thinking.
The first part of this book is a tutorial on algorithm design strategies and analysis techniques. Algorithm design strategies - exhaustive search, backtracking, divide-and-conquer and a few others - are general approaches to designing step-by-step instructions for solving problems. Analysis techniques are methods for investigating such procedures to answer questions about the ultimate result of the procedure or how many steps are executed before the procedure stops. The discussion is an…
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.
Peter Winkler is famous for his collections of counterintuitive puzzles. Thousands of people, including me, have spent many sleepless nights trying to understand the mysteries in these puzzles, for which, I am forever grateful.
Haunting puzzles in the book include hats and infinity, all right or all wrong, comparing numbers version 1/2, wild guess, laser gun, precarious picture, names in boxes, sleeping beauty, and dot-town exodus.
Most puzzle books exclude counterintuitive puzzles for unknown reasons. So, many people incorrectly assume that counterintuitive puzzles are majorly found in paradoxes. Peter Winkler in this book shows that counterintuition can come from either puzzles or solutions or both, and they need not come from paradoxes alone.
Finally, reading Winkler's statements is an absolute delight due to its enjoyable and entertaining nature.
Research in mathematics is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing mathematics. Mathematical Puzzles makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem.
Features
A collection of the world's best mathematical puzzles
Each chapter features a technique for solving mathematical puzzles, examples, and finally a genuine theorem of mathematics that features that technique in its proof
Puzzles that are entertaining, mystifying, paradoxical, and satisfying; they are not…
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…