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Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation.
152 pages, Paperback
First published March 5, 2010
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Displaying 1 - 30 of 33 reviews
March 12, 2016
Some clever tricks, although I'm not sure a book that has differential equations on page 4 qualifies as "street fighting" level (unless we're talking about the mean streets of Cambridge, MA).
August 22, 2020
Kind of pillow-fighting rather than street-fighting. Not much kicking and punching, rather a very primary training in modelling and estimation problems. Nothing much in it for a scientist or engineer.
January 1, 2016
This book gives examples of educated guessing and approximation methods to evaluate functions, or to obtain information on functions that are too hard to evaluate. As such, the book's target audience are physicists and engineers who frequently need to reason about complicated expressions for which they do not have closed form solutions. (The book is not so much aimed at mathematicians, as they are usually more concerned with analysing the structure of a problem, which is not what the book is about.)
Personally, I found some of the methods surprising, and a few of them were rather common sense. My favourites would be the dimensional analysis, the pictorial proofs, some of the methods about analogies and "taking out the big parts".
However, the history of approximation is a history written by the victors. All the approximations we learn about in physics which lead to great insights are only there because they were found to work a posteriori. We are not interested in approximations that do not work, and therefore you never read about them. With this book, it is the same. The tricks for approximations you find here are in there because they work in the particular examples. Unfortunately, it is a common theme with heuristics that there is no way of telling how well they generalise to other cases. Some of the techniques in this book also require a lot of previous knowledge about the problem, for example the application of the Navier-Stokes equation to estimate the drag on a falling paper cone.
Personally, I found some of the methods surprising, and a few of them were rather common sense. My favourites would be the dimensional analysis, the pictorial proofs, some of the methods about analogies and "taking out the big parts".
However, the history of approximation is a history written by the victors. All the approximations we learn about in physics which lead to great insights are only there because they were found to work a posteriori. We are not interested in approximations that do not work, and therefore you never read about them. With this book, it is the same. The tricks for approximations you find here are in there because they work in the particular examples. Unfortunately, it is a common theme with heuristics that there is no way of telling how well they generalise to other cases. Some of the techniques in this book also require a lot of previous knowledge about the problem, for example the application of the Navier-Stokes equation to estimate the drag on a falling paper cone.
January 13, 2018
thanks to this book, i'm going to punch the navier-stokes equations if i ever see them on the street
January 3, 2011
I wish I'd had this book in college. It explicates some quantitative methods (what one might call "physical intuition") that are similar to what I got from studying physics and mathematics at the undergraduate level; however, it unpacks these ideas in a way that standard texts (and, unfortunately, many courses) never do. There is some really nice, very "transferable" thinking here, and the tone is conversational. (To top it all off, Professor Mahajan has made the text available free online under MIT's OpenCourseWare license.)
The only drawback I saw was that (since much of the book presumes familiarity with first- or second-year collegiate math and physics content) there are a lot of nice ideas here that could transfer even further, but which the presentation might not make accessible to parts of its potential audience. So on the other hand, it's definitely got me thinking about how to draw out some of these ideas for middle- and high-school students who might otherwise be sliding into the chasm of "math isn't supposed to make sense".
The only drawback I saw was that (since much of the book presumes familiarity with first- or second-year collegiate math and physics content) there are a lot of nice ideas here that could transfer even further, but which the presentation might not make accessible to parts of its potential audience. So on the other hand, it's definitely got me thinking about how to draw out some of these ideas for middle- and high-school students who might otherwise be sliding into the chasm of "math isn't supposed to make sense".
July 10, 2019
Dimensional Analysis for guessing integrals blew my mind. Most of the rest of the book is competitive math tricks. Did not live up to the title, I gained little practical knowledge.
January 1, 2012
Not to brag, but I was a math whiz in high school and college, which is why I'm a fan of pop-math books that frame real world issues through the lens of numbers. Given the title of this book (and its subtitle "The Art of Educated Guessing and Opportunistic Problem Solving"), I was expecting something similar. I was surprised to find that instead of a pop-math book, this book is a straight-up math textbook. Mahajan teaches several new ways to approach mathematical problem-solving that tries to meld the theoretical with the practical, especially for situations that don't call for perfect precision. He even provides example problems to demonstrate his points and additional practice problems so that you can apply what you've just learned. This book is impossible for anyone who hasn't mastered calculus and basic Physics. The mathematician in me found this interesting; the reader in me realized I made a mistake in putting this on my 2012 Booklist. Recommended for mathematicians only.
February 1, 2016
"Most of us took mathematics courses from mathematicians—Bad Idea!"
October 28, 2018
Do not let the title fool you; this book is not for a commoner, this is hardcore mathematics.
Yes, it shows you how to cut corners in mathematics, but it does not shy away from formulae or regular invocations of calculus as something the reader is supposed to be intimately familiar with. This book is a college textbook and an excellent one - with examples, explanations, connections to physics and other STEM sciences. However, I would assume that anyone, who uses this type of advanced math, already thought about ways how to simplify the application of it and thus uses most of what is contained in the book.
Nevertheless, I recommend the book to especially college students or engineers to at least skim through. They will find some puzzles/exercises to test their wits on, and they might see some useful trick. Sanjoy certainly gave these corner-cutting tools some thought and presented them in depth and with an extensive discussion.
Sometimes the explanations seem more as a part of a supplementary course that relies on someone else to explain the mathematics themselves. Still, what I would certainly want to see in all math textbooks and deserves praise are the various and profound usage examples not only in physics but also in chemistry and other subjects.
Yes, it shows you how to cut corners in mathematics, but it does not shy away from formulae or regular invocations of calculus as something the reader is supposed to be intimately familiar with. This book is a college textbook and an excellent one - with examples, explanations, connections to physics and other STEM sciences. However, I would assume that anyone, who uses this type of advanced math, already thought about ways how to simplify the application of it and thus uses most of what is contained in the book.
Nevertheless, I recommend the book to especially college students or engineers to at least skim through. They will find some puzzles/exercises to test their wits on, and they might see some useful trick. Sanjoy certainly gave these corner-cutting tools some thought and presented them in depth and with an extensive discussion.
Sometimes the explanations seem more as a part of a supplementary course that relies on someone else to explain the mathematics themselves. Still, what I would certainly want to see in all math textbooks and deserves praise are the various and profound usage examples not only in physics but also in chemistry and other subjects.
February 4, 2018
I agree that it is very useful to be able to make back-of-the-envelope approximations to difficult problems, but some of the methods presented here are of questionable utility and are rather hard to justify.
I did like first few chapters which mainly dealt with dimensional analysis and integrals, but it seriously went downhill from there. What irritates me is when they so obviously stick a rabbit into a hat ("1/4 is close enough to 1/ 2pi") then expect you to be impressed when the rabbit pops out later ("our answer is, in fact, exact!!!!"). In essence, this book will teach you the art of reverse-engineered hand-wavy solutions.
It is definitely worth going through the first few chapters, but the rest deserved to be flicked-through at best.
I did like first few chapters which mainly dealt with dimensional analysis and integrals, but it seriously went downhill from there. What irritates me is when they so obviously stick a rabbit into a hat ("1/4 is close enough to 1/ 2pi") then expect you to be impressed when the rabbit pops out later ("our answer is, in fact, exact!!!!"). In essence, this book will teach you the art of reverse-engineered hand-wavy solutions.
It is definitely worth going through the first few chapters, but the rest deserved to be flicked-through at best.
February 4, 2020
The "street-fighting"-ness is illustrated in the context of math taught in 11th and 12th grades and in universities; specifically, using math problems (e.g., derivative operator, approximating summations) as opposed to real world problems. So, a reader will enjoy the book more if she is comfortable with math taught in high school and beyond, and is willing to work out the missing steps. Also, at times, the "street-fighting"-ness seemed way more elaborate and involved than the alternative.
Compared to book like "Math/Calculus Better Explained", I wish the book was more accessible by being more inefficient (i.e., being elaborate) in teaching efficient methods :)
Compared to book like "Math/Calculus Better Explained", I wish the book was more accessible by being more inefficient (i.e., being elaborate) in teaching efficient methods :)
March 18, 2023
I heard a lot of praise for this book, but reading it was rather underwhelming. Teaches people how to use some intuitive tricks for solving hard problems, but none of it seems novel. I feel like I might have enjoyed it before I'd already developed my own tricks for similar problems, but after a certain point, it just seems like most of the stuff in this book is trivial at best.
January 1, 2024
This book is very practical! I had used some of the tactics in this book to make a calculated guess and it feels like magic.
It should not guide mathematicians per se, but everyone with common sense also.
It should not guide mathematicians per se, but everyone with common sense also.
May 5, 2024
Great idea with somewhat weak execution. The idea of going through fast approaches, approximations, guesstimating is indeed very useful. I was hoping for more on Fermi problems (order of magnitude estimations) and similar.
March 15, 2022
made problem solving fun and easier
April 26, 2022
Great book. I think it has given me many new tools for solving problems where the closed-form solution is hard to find.
Read
August 22, 2022Won’t pretend I engaged as deeply as it deserved.
November 12, 2023
Interesting
I can get the general ideas or some of them although I would need a teacher and classmates to really work through it. If I even could then.
I can get the general ideas or some of them although I would need a teacher and classmates to really work through it. If I even could then.
January 30, 2024
It was okay.
1. Dimensional analysis + easy cases 2. Pictorial proofs 3. Lumping to solve equations 4. Relative errors
1. Dimensional analysis + easy cases 2. Pictorial proofs 3. Lumping to solve equations 4. Relative errors
July 19, 2023
This book was ok.
On the positive side, it gives a lot of examples and worked thought experiments to illustrate the principles being discussed in each section. I was familiar with some of the approaches (under different names) but there were enough new strategies (or new viewpoints on these) that it was worth the read.
On the negative side, I'll echo some comments from other reviewers that many of the techniques seem tailored to specific sorts of problems and it's unclear how generalizable they may be in other domains. Many of the cases required a fair amount of prior knowledge, as well, which made it harder for me to see the utility.
On the positive side, it gives a lot of examples and worked thought experiments to illustrate the principles being discussed in each section. I was familiar with some of the approaches (under different names) but there were enough new strategies (or new viewpoints on these) that it was worth the read.
On the negative side, I'll echo some comments from other reviewers that many of the techniques seem tailored to specific sorts of problems and it's unclear how generalizable they may be in other domains. Many of the cases required a fair amount of prior knowledge, as well, which made it harder for me to see the utility.
December 16, 2010
Tricks and techniques to guess "good enough" answers to complicated calculus problems. The math was beyond me, but I have enough of a math/physics background that I understood the basic ideas.
If I ever find myself in a situation where I'm dealing with complicated equations on a day-to-day basis, then this book is going to be sitting on my shelf. The techniques in this book are useful not only for getting quick, rough-estimate answers, but also show you how to better understand equations by looking at them in different ways. I've never been intuitive about math, and I've always had a hard time understanding the real-world meaning of any given equation. It would be invaluable to me to have a book that showed me how to, say, analyze which variable is most important, or how to think about an equation graphically, or how to draw useful analogies.
Highly recommended for calculus, physics, or engineering students, from first year to grad school. Also recommended for any professional who has to deal with complicated equations as part of their job.
If I ever find myself in a situation where I'm dealing with complicated equations on a day-to-day basis, then this book is going to be sitting on my shelf. The techniques in this book are useful not only for getting quick, rough-estimate answers, but also show you how to better understand equations by looking at them in different ways. I've never been intuitive about math, and I've always had a hard time understanding the real-world meaning of any given equation. It would be invaluable to me to have a book that showed me how to, say, analyze which variable is most important, or how to think about an equation graphically, or how to draw useful analogies.
Highly recommended for calculus, physics, or engineering students, from first year to grad school. Also recommended for any professional who has to deal with complicated equations as part of their job.
December 3, 2014
Great insight for students of physics and engineering. I would recommend young undergraduates to skim through the more intuitive parts (chapter 1 - dimensions, chapter 4 - pictorial proofs and the parts of other chapters that seem to catch your eyes) and read the rest as you advance in your studies. e.g., there's no good reason to read about guessing a Gaussian integral without ever using one or knowing it's properties.
April 25, 2016
Meh. Read it as an intro to the MIT OCW course that is nothing more that a read companion to this book.
Honestly it's quite interesting,but the tricks exposed in the book can hardly be applied outside of the context of the book itself. Other stuff it's just common sense. Anyway it's a good read for your amusement, but after reading it i'm not interested anymore in the course.
Honestly it's quite interesting,but the tricks exposed in the book can hardly be applied outside of the context of the book itself. Other stuff it's just common sense. Anyway it's a good read for your amusement, but after reading it i'm not interested anymore in the course.
August 28, 2015
Great read and very insightful. I highly recommend it. My only caveat is that it is not a book for math novices. If you aren't familiar with calculus, differential equations and statistics you may not find the book enjoyable.
September 18, 2021
I struggled myself through the book and completed most exercises (some of them left me clueless though). Overall it was a pretty frustrating experience. I’m happy thought that I didn’t give up, because the last chapter is a real gem in my opinion.
Want to read
May 3, 2010MIT prof, interesting ideas
Want to read
July 27, 2010recomended by boing boing
http://www.boingboing.net/2010/07/26/...
http://www.boingboing.net/2010/07/26/...
September 20, 2011
Some nice ideas and tricks but a lot of the time, it's really too much trickery. Unless you practice yourself in these tricks day-in-day-out, you will never get a grip on them.
November 13, 2014
Some really nice ideas and tricks,I like this book very much.
April 20, 2015
I skimmed this one. It codifies some things I already do, like dimensional analysis and order of magnitude estimation. I could see how this might make a good textbook for the right kind of course.
Displaying 1 - 30 of 33 reviews