Introduction to Mathematical Thinking

Introduction to Mathematical Thinking

Keith J. Devlin / Aug 22, 2019

Introduction to Mathematical Thinking In the twenty first century everyone can benefit from being able to think mathematically This is not the same as doing math The latter usually involves the application of formulas procedures and sy

  • Title: Introduction to Mathematical Thinking
  • Author: Keith J. Devlin
  • ISBN: 9780615653631
  • Page: 364
  • Format: Paperback
  • In the twenty first century, everyone can benefit from being able to think mathematically This is not the same as doing math The latter usually involves the application of formulas, procedures, and symbolic manipulations mathematical thinking is a powerful way of thinking about things in the world logically, analytically, quantitatively, and with precision It is nIn the twenty first century, everyone can benefit from being able to think mathematically This is not the same as doing math The latter usually involves the application of formulas, procedures, and symbolic manipulations mathematical thinking is a powerful way of thinking about things in the world logically, analytically, quantitatively, and with precision It is not a natural way of thinking, but it can be learned Mathematicians, scientists, and engineers need to do math, and it takes many years of college level education to learn all that is required Mathematical thinking is valuable to everyone, and can be mastered in about six weeks by anyone who has completed high school mathematics Mathematical thinking does not have to be about mathematics at all, but parts of mathematics provide the ideal target domain to learn how to think that way, and that is the approach taken by this short but valuable book The book is written primarily for first and second year students of science, technology, engineering, and mathematics STEM at colleges and universities, and for high school students intending to study a STEM subject at university Many students encounter difficulty going from high school math to college level mathematics Even if they did well at math in school, most are knocked off course for a while by the shift in emphasis, from the K 12 focus on mastering procedures to the mathematical thinking characteristic of much university mathematics Though the majority survive the transition, many do not To help them make the shift, colleges and universities often have a transition course This book could serve as a textbook or a supplementary source for such a course Because of the widespread applicability of mathematical thinking, however, the book has been kept short and written in an engaging style, to make it accessible to anyone who seeks to extend and improve their analytic thinking skills Going beyond a basic grasp of analytic thinking that everyone can benefit from, the STEM student who truly masters mathematical thinking will find that college level mathematics goes from being confusing, frustrating, and at times seemingly impossible, to making sense and being hard but doable Dr Keith Devlin is a professional mathematician at Stanford University and the author of 31 previous books and over 80 research papers His books have earned him many awards, including the Pythagoras Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award He is known to millions of NPR listeners as the Math Guy on Weekend Edition with Scott Simon He writes a popular monthly blog Devlin s Angle for the Mathematical Association of America, another blog under the name profkeithdevlin , and also blogs on various topics for the Huffington Post.

    Table of mathematical symbols by introduction date The following table lists many specialized symbols commonly used in mathematics, ordered by their introduction date. Introduction to Mathematical Thinking Coursera Learn Introduction to Mathematical Thinking from Stanford University Learn how to think the way mathematicians do a powerful cognitive process developed over thousands of years Mathematical thinking is not the same as doing mathematics at A Mathematical Introduction to Robotic Manipulation A Mathematical Introduction to Robotic Manipulation Richard M Murray California Institute of Technology Zexiang Li Hong Kong University of Science and Technology Grade Introduction Common Core State Standards Grade Introduction Print this page In Grade , instructional time should focus on four critical areas developing understanding of and applying proportional relationships developing understanding of operations with rational numbers and working with expressions and linear equations solving problems involving scale drawings and informal geometric constructions, and working High School Geometry Introduction Common Core State High School Geometry Introduction Print this page An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts interpreting a schematic drawing, estimating the amount of wood needed to frame a sloping roof, rendering computer graphics, or designing a sewing pattern for the most efficient use of material. INTRODUCTION TO THE SPECIAL FUNCTIONS OF INTRODUCTION TO THE SPECIAL FUNCTIONS OF MATHEMATICAL PHYSICS with applications to the physical and applied sciences John Michael Finn April , Mathematical Methods for Physicists A concise introduction Mathematical Methods for Physicists A concise introduction This text is designed for an intermediate level, two semester undergraduate course in mathematical physics. Course Descriptions Mathematical Sciences Caltech Engineering and Applied Science Computing Mathematical Sciences Mathematical Biology I An Introduction, Third Edition Preface to the Third Edition In the thirteen years since the rst edition of this book appeared the growth of mathe matical biology and the diversity of applications has been astonishing. An Introduction to Mathematical Modelling Matemtica MathematicalModelling Introduction This book is based on a course given to rst year students doing Calculus in the University ofWestern Australia s Department ofMathematics and

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    About "Keith J. Devlin"

      • Keith J. Devlin

        Dr Keith Devlin is a co founder and Executive Director of the university s H STAR institute, a Consulting Professor in the Department of Mathematics, a co founder of the Stanford Media X research network, and a Senior Researcher at CSLI He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences He also works on the design of information reasoning systems for intelligence analysis Other research interests include theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition He has written 26 books and over 80 published research articles Recipient of the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award He is the Math Guy on National Public Radio.


    186 Comments

    1. Didn't complete all of the exercises since many of them are nearly the same as the MMOC Devlin teaches through Coursera, and some of them took longer than I had time for (I'll be revisiting, this was a pretty cursory read). Renders poorly on the kindle but very instructive nonetheless.



    2. This would work very well if you're about to start a university degree that supposed you did some "higher" mathematics in high school and you need an introduction, or a refresher - you'll learn what all of those Greek symbols do (university-level notation), you'll learn about the kind of precise language you need, how to structure proofs, types of proofs, etc. The language is the best part. It's never particularly dry or boring, Devlin knows how to structure what he wants to convey. However, mos [...]


    3. This was basically a retread of the Coursera course, and while I still really really love the preface to this book with its overview of the difference between school mathematics and actual Mathematics, the details of how to come to an attitude of puzzling over math and logic problems didn't really make for a readable book.


    4. I've been reading this book while taking Dr. Devlin's Coursera class of the same name. I have greatly enjoyed both the textbook and the online course. If you have any interest in mathematics, I recommend both the course and this textbook.


    5. Great way to jump into mathematical concepts that many people didn't learn in school. I used it as a way to catch up on understanding some of the basics of computer science-oriented math and it helped tremendously. Includes exercises but no answers, which really makes it sort of frustrating to do them because it can feel like a waste of time and there are other meatier books with more problem sets.


    6. This is a book you shouldn't only read but live with it for however long it takes you grasp the content. This includes thinking deeply about almost every sentence, solve or at least try to solve every exercise, even if it costs you many hours of your life. If I follow my own advice I am far from done with the book but intend to start again right away.


    7. A good and accessible introduction to mathematical reasoning, with exercises to test your comprehension. It covers logic and mathematical proof, and does not require much previous mathematical knowledge, so it is accessible to lay readers as well as people studying maths at school or university.


    8. EINFÜHRUNG IN DIE FORMALE LOGIK»You won't learn much new math from this book. But by acquiring the ability to think like a mathematician, you will be able to master new math quickly«Stanford-Mathematiker & Wissenschaftspopularisierer Devlin erklärt in diesem Heft das neuere, begriffliche (also das Wesen der Sache ergründende/auf sich selbst reflektierende) Denken moderner Hochschulmathematik, das der rechnenden, prozedurenfolgenden Sekundarschule abginge (wie Mathematikern Jahrhunderte [...]


    9. This was nice - Prof. Devlin throws in some humor, history, and down-to-earth language into this "introduction" to mathematical thinking. I'd say it certainly would work better if used in a class (e.g. a course complementary text) because although for the already initiated the proofs that are given are "basic" -- for those who are truly starting their journey into mathematical thinking it will still be tough and would benefit from the advice of a teacher (for some of the practice problems, for e [...]


    10. The introductory essay on math is great, I got a great deal of insights out of that. The rest was nice, but I was too bored by the time I got through the major half of the book, having learned proofs and other things beforehand. I certainly am not with the camp who thinks a proofs class should be required before taking any math-major course class (e.g. Abstract Algebra, Real Analysis, etc.) . But that is just me, coming from a rich pre-university background, having exposed myself to some interes [...]


    11. Lousy introduction to formal logic. If you have at lest a basic understanding of the term such as disjunction, conjunction, implication or equivalence, this book is going to be a waste of time. I have deep respect for Keith Devlin. My experience with his other books has been pleasing at least. This, however, I either misunderstood or is not really something worth reading thouroughly.


    12. The first chapter of this short book is a terrific explanation of the value of math and why it matters. As a proponent of the rethinking of education in general and the needs of a changing economy in particular, I found that Devlin really understood what too many people do not. The rest of the book is good, too, but that whole first section was what really piqued my interest!


    13. One of my (multi) NY resolutions is to study the math pretty much from scratch and this is a good first book - the material is pretty simple though even if you took math in college it still going to be a workout.


    14. Most problems at the latter end of the book were too technical for readers who have no background in higher maths. And this is supposed to be 'Intro to mathematical thinking'. The outline is good to follow though, so you can take it from there.




    15. It's a good book especially for non-mathematician to learn the essence of mathematics.The author described in depth how the framework of mathematical thinking deal with every day related matters.


    16. It tends to reaffirm the status quo by suggesting ways to be better equipped to handle it. Not what I expected from Devlin, who had been a proponent for reform.




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