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Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks

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These simple math secrets and tricks will forever change how you look at the world of numbers. Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculat These simple math secrets and tricks will forever change how you look at the world of numbers. Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun. Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school. Also available as an eBook


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These simple math secrets and tricks will forever change how you look at the world of numbers. Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculat These simple math secrets and tricks will forever change how you look at the world of numbers. Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun. Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school. Also available as an eBook

30 review for Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks

  1. 5 out of 5

    Roy Lotz

    Some years ago, on a whim, I picked up Moonwalking with Einstein by Joshua Foer. In that book, the author—a hitherto unremarkable journalist—details how he learned memory techniques that allowed him to recall hundreds of digits of pi, to learn the names of dozens of strangers in minutes, and to memorize the order of an entire deck of cards in the amount of time it takes me to tie my shoes. I was completely captivated. The idea that someone could so radically augment his mental prowess using anci Some years ago, on a whim, I picked up Moonwalking with Einstein by Joshua Foer. In that book, the author—a hitherto unremarkable journalist—details how he learned memory techniques that allowed him to recall hundreds of digits of pi, to learn the names of dozens of strangers in minutes, and to memorize the order of an entire deck of cards in the amount of time it takes me to tie my shoes. I was completely captivated. The idea that someone could so radically augment his mental prowess using ancient techniques appealed deeply to me. Soon I set about teaching myself some of these methods. The most famous and powerful is the so-called ‘memory palace’: converting information into images, and then placing these images in a familiar space. Using this method, I was able to memorize well over one hundred digits of pi. I even managed to learn the order of a few decks of cards. This was impressive in itself, and a testament to the efficacy of these techniques. Even so, learning the techniques was itself time-consuming, and without significant practice I was sluggish both in committing to memory and recalling information. You cannot become a memory athlete without significant practice. What was worse, these systems only really worked with certain types of information. The technique for memorizing cards, for example, was useless when it came to remembering German vocabulary. So, after a few weeks, I gave it up. I bought this book during my brief memory-trick craze, but my enthusiasm had worn off before I began it. Thus it languished on my shelves for many years—until now. Though this book is technically co-authored, it seems obvious that Arthur Benjamin was the driving force behind it. Michael Shermer, the founder of the Skeptics Society, contributed an afterword in which he argues (unpersuasively) that these mathematical tricks and techniques somehow aid in being skeptical—though a quick-calculating conspiracy theorist strikes me as perfectly plausible. Benjamin, meanwhile, contributes the real meat of the book: ways to speed up mental calculation. He himself is a master of these techniques, which he uses for a sort of numerical magic show (there are many clips online). Benjamin has done a wonderful job in compiling this little handbook. The mathematical tools are simple, easy to use, and effective. I had become so reliant on the calculator in my phone that it was a relief and, if you can believe it, a real pleasure to return to doing sums and products myself. The world of numbers can be unexpectedly fascinating, revealing unusual patterns, connections, and symmetries. I must admit, however, that I mostly skipped the last section on large multiplication problems, since the amount of practice required to properly execute them exceeded my interest in being a human calculator. Benjamin’s feats in calculation, like Foer’s feats in memorization, show what the simple human brain can do when aided with techniques and training—achieving abilities so uncanny that it can seen like magic to the uninitiated. To me, this fact alone is cause for hopefulness, since it reveals to us the transformative power of expertise.

  2. 5 out of 5

    Onna

    I LOVE this book! It's a nerd's dream come true for me. I checked it out from the library and had it for at least two months. It pained me to give it back. I'm going to buy it soon as I get money. These tricks are so wonderful, it's a wonder they didn't use these in school. I loved the Pi part. I can recite Pi to a hundred digits now! Always been a goal of mine too. I was content with knowing it for 20 digits, but this made it super easy to know it to a hundred. Then the figuring out the weekday I LOVE this book! It's a nerd's dream come true for me. I checked it out from the library and had it for at least two months. It pained me to give it back. I'm going to buy it soon as I get money. These tricks are so wonderful, it's a wonder they didn't use these in school. I loved the Pi part. I can recite Pi to a hundred digits now! Always been a goal of mine too. I was content with knowing it for 20 digits, but this made it super easy to know it to a hundred. Then the figuring out the weekday when you have a date. Awesome! The multiplying is really neat too. As you can tell I just LOVE this book! I'm cheesing writing this. lol! Go read it. If you only read one part, I suggest the Pi bit. :)

  3. 5 out of 5

    Nick

    This book helped me to re-build a fresh perspective on doing math in my head. He builds on a central idea of breaking down seemingly complex computations into simple, manageable ones. He then gives you new ways of seeing numbers such that, once these various patterns become familiar, you are able to employ tricks to getting the math done quickly. One of his first examples is how to square a two-digit number that ends in 5. "... you need to remember only two things. 1. The answer begins by multipl This book helped me to re-build a fresh perspective on doing math in my head. He builds on a central idea of breaking down seemingly complex computations into simple, manageable ones. He then gives you new ways of seeing numbers such that, once these various patterns become familiar, you are able to employ tricks to getting the math done quickly. One of his first examples is how to square a two-digit number that ends in 5. "... you need to remember only two things. 1. The answer begins by multiplying the first digit by the next higher digit. 2. The answer ends in 25. For example, to square the number 35, we simply multiply the first digit (3) by the next higher digit (4), then attach 25. Since 3 × 4 = 12, the answer is 1225. Therefore, 35 × 35 = 1225."

  4. 4 out of 5

    Phil Sykora

    Foreword by Bill Nye? BILL NYE?!? Watching him was definitely the greatest time I had in science class. Knowing that he advocates this book (or was bought out to support it) is pretty much worthy of my attention. No question there is definitely useful (to the point of being necessary) information in this book. In the first chapter (ironically Chapter 0), I was introduced to a smorgasbord of various tricks that became immediately useful: the rule of multiplying 11s, squaring numbers that end in 5, m Foreword by Bill Nye? BILL NYE?!? Watching him was definitely the greatest time I had in science class. Knowing that he advocates this book (or was bought out to support it) is pretty much worthy of my attention. No question there is definitely useful (to the point of being necessary) information in this book. In the first chapter (ironically Chapter 0), I was introduced to a smorgasbord of various tricks that became immediately useful: the rule of multiplying 11s, squaring numbers that end in 5, multiplying two digit numbers with the same first digit and second digits that sum to 10 (which, I admit was a little bit harder to have explained but as soon as I got it, it became ridiculously valuable). Beyond that, I learned how to do pretty much all math in my head. Squaring any two digit number above 30 was something I thought was reserved for savants (like the guy from Pi). I feel nerdy as hell for praising the book this much but it really is that good. You might not want to be bogged down with explanations of how to square three digit numbers in your head but I would recommend anyone to read Chapter 0, then see how they like it, or evaluate if it's going to be useful to them.

  5. 4 out of 5

    Jeremy

    As a nerd who is desperate for attention but also very lazy, this book was a godsend! Arthur Benjamin's mental math tips are very easy to learn, yet still appear impressive to the casual observer. Towards the end of the book, there are some real showstoppers, but even if one only gets halfway through the tricks, you could still impress people at a party (a very lame party).

  6. 5 out of 5

    Mike Shultz

    I slowed down about half way through this book and was ready to give it 3 stars. In some cases I had discovered a fair number of the tricks on my own, or had learned them elsewhere. The processes described were sometimes just brute mathematics, requiring you compute, then hold numbers in your head and compute again. However, the second half had some cool techniques that I didn't know, and while 4 or 5-digit multiplication problems are just plain difficult (as the author admits), 3 and 4 digit sq I slowed down about half way through this book and was ready to give it 3 stars. In some cases I had discovered a fair number of the tricks on my own, or had learned them elsewhere. The processes described were sometimes just brute mathematics, requiring you compute, then hold numbers in your head and compute again. However, the second half had some cool techniques that I didn't know, and while 4 or 5-digit multiplication problems are just plain difficult (as the author admits), 3 and 4 digit squares are more doable than I would've thought, and (perfect) cube roots of numbers with up to 6 digits are so easy it's fun. With the neat mathematical "magic tricks" at the end to cap it off, this book was back up to 4 stars for me.

  7. 5 out of 5

    Tom

    Two stars really isn't a fair rating. Had some fun adding and subtracting and then multiplying 3 digit numbers in my head. But as the problems get more complex, my limitations became apparent. Couldn't read through the entire book. When I couldn't do what the book was suggesting, just gave up. So no - reading this book wont suddenly make you a math genius. There are some interesting stories with interesting perspectives, but not enough to inspire the me to practice the "tricks" and yes I expect th Two stars really isn't a fair rating. Had some fun adding and subtracting and then multiplying 3 digit numbers in my head. But as the problems get more complex, my limitations became apparent. Couldn't read through the entire book. When I couldn't do what the book was suggesting, just gave up. So no - reading this book wont suddenly make you a math genius. There are some interesting stories with interesting perspectives, but not enough to inspire the me to practice the "tricks" and yes I expect the average person will need to practice. So in fairness the 2 stars represents the bitterness I felt upon failing to become an overnight mathemagician...but who knows, maybe you can do it!

  8. 4 out of 5

    Mars

    The author is enthusiastic, but somehow this enthusiasm doesn't transmit to the reader. The tricks work, but I am incredibly bored by this book regardless. (might have worked better with real-life examples, but I for one am hard-pressed to think of a good real-life reason to multiply a pair of two-digit numbers in your head)

  9. 4 out of 5

    Natalya

    "Special thanks to NATALYA ST. CLAIR for typesetting the initial draft, which was partly supported by a grant from the Mellon Foundation." :D

  10. 5 out of 5

    Kevin M

    Fantastic book! If you love math, or would just like to be able to struggle less with it, this book is a great tool. One caveat however: don't expect magically easy math abilities. Benjamin shows you the tools to make mental math problems exponentially easier, but at the end of the day you still need to calculate! Now with that out of the way, can you calculate squares and square roots in your head? For two, three-no-five digit numbers? This book will show you the ways of these and many other fa Fantastic book! If you love math, or would just like to be able to struggle less with it, this book is a great tool. One caveat however: don't expect magically easy math abilities. Benjamin shows you the tools to make mental math problems exponentially easier, but at the end of the day you still need to calculate! Now with that out of the way, can you calculate squares and square roots in your head? For two, three-no-five digit numbers? This book will show you the ways of these and many other fantastic mathematical prestidigitation techniques. Calculate the day of the week of any calendar date? Check. Estimate square roots to many decimal places? Check. Memorize Pi to hundreds of digits? Check. Use mod sums to check your answers? Check (digit)! Bottom line: get this book if you want to nerd out and work your math muscles.

  11. 5 out of 5

    Lance Greenfield

    I really liked this book, and its accompanying video CD. The author is full of enthusiasm and the mathematical tricks are really worth learning, and so simple. I enjoyed teaching some of the tricks to my grandson, who, in turn, enjoyed showing them off to his friends and teachers at school. I'd recommend this book to everyone. A lot of fun!

  12. 5 out of 5

    Jeff Yoak

    I tremendously enjoyed both the book and the video course. I was familiar with Benjamin both from other courses and from his mental math tricks. Not only did I improve a lot just from watching, but I picked up some really neat new tricks that I know I can get with practice. Lots of fun.

  13. 5 out of 5

    Deborah

    An entertaining math book! Seriously. Easy to read and easy to understand strategies for improving number sense. I think my kids might also like how the author frames the equations as tricks or illusions. Of course, with my short memory, I had to buy a copy so I can refer back to it. Sorry library.

  14. 4 out of 5

    Samantha

    Helped me so much to make math easier. I shocked my friends into thinking I was a super genius and with this books helps I won't stop. I put it down because after a while it was starting to bore me but after a few months you can pick back up again.

  15. 4 out of 5

    Jessica

    I already knew/used a few of these tricks, but some were new and pretty smart. And there's nothing nerdier than doing math in you head on the train, so that was fun.

  16. 4 out of 5

    Justice Mansour

    The first third of this book should be mandatory for all math and elementary educators. Gets a little unnecessary after that, but it was still a good read.

  17. 4 out of 5

    Matt

    Some things in here I have no interest in mastering, but there are some neat tricks worth some study!

  18. 5 out of 5

    Colin

    This was good. I learned some cool ways to do quick math, along with some ways that I can amaze my students.

  19. 4 out of 5

    Benjamin Bastian

    I absolutely loved this lecture! The professor who taught it was, in my opinion, phenomenal. The secrets of mental math are, I find, very intriguing.

  20. 4 out of 5

    Vanessa

    I watched the "video" book from the library. Fun parlor tricks, but these methods still take lots of practice and memorizing. Definitely a few things for multiplying multi-digit factors I will use going forward but some, like Vedic division, I'll never use.

  21. 5 out of 5

    Msalem

    Starts out interesting. Loses its spark about four chapters in.

  22. 4 out of 5

    Leo

    This book was quite helpful for my uses but leaves many topics uncovered. I used the book to prep for various interviews where I need to do math in my head FAST and without paper. This book was an excellent start. I would say that it is too brief to be exhaustive so I'd recommend consulting other materials if you're trying to learn mental math for a serious goal. What the book does provide is a solid introduction into doing math in your head and if you get through it, you will probably end up wan This book was quite helpful for my uses but leaves many topics uncovered. I used the book to prep for various interviews where I need to do math in my head FAST and without paper. This book was an excellent start. I would say that it is too brief to be exhaustive so I'd recommend consulting other materials if you're trying to learn mental math for a serious goal. What the book does provide is a solid introduction into doing math in your head and if you get through it, you will probably end up wanting to learn more. For example, it teaches vedic division (on paper) but there are many more vedic concepts to learn than that. Note that the book stresses flexibility in how you look at numbers and if nothing else, will teach you to look at a math problem in several ways. I ended up skipping a couple of the chapters that deal with very advanced multiplication (the pacing of the book leaves something to be desired.) and the Major System (you essentially memorize images as a peg system that makes long calculations easier to not forget as you're doing another step). Great read overall - just make sure you know why you are reading it!

  23. 5 out of 5

    Liz

    I skimmed this book extremely fast so probably not quite fair to give it a rating. I learned several things I never knew about math. Just the chapter on multiplication in less than 5 minutes helped me understand the math curriculum theories for my sons' elementary school better than I've received from any teacher or the principal. However, it is a hard core book on math so how exciting could that really be? And it's not really a book to read, but more to work through. So I was not motivated to w I skimmed this book extremely fast so probably not quite fair to give it a rating. I learned several things I never knew about math. Just the chapter on multiplication in less than 5 minutes helped me understand the math curriculum theories for my sons' elementary school better than I've received from any teacher or the principal. However, it is a hard core book on math so how exciting could that really be? And it's not really a book to read, but more to work through. So I was not motivated to wander or take it too seriously right now. I'd highly recommend it as another alternative source for those looking to become solid math teachers and/or parents home-schooling their children. If you are a crazy parent trying to go above & beyond public school, this might be a good assignment to give your middle/high schooler over summer... but who does that really?

  24. 4 out of 5

    Emil Petersen

    This is potent stuff. The first chapters were much like my own way of doing calculations in my head, and so I was lulled into saying to myself "this is not that hard". By the last few chapters my face practically melted. Most of us can recognize when we meet the threshold of our mental abilities, and I met mine when doing larger multiplications. All these calculations requires quite a few balls in the air and it is a whole other level multiplying two 5-digit numbers on stage in front of an audie This is potent stuff. The first chapters were much like my own way of doing calculations in my head, and so I was lulled into saying to myself "this is not that hard". By the last few chapters my face practically melted. Most of us can recognize when we meet the threshold of our mental abilities, and I met mine when doing larger multiplications. All these calculations requires quite a few balls in the air and it is a whole other level multiplying two 5-digit numbers on stage in front of an audience, as Arthur Benjamin. He says that we all can learn these (truly impressive) methods for calculation, but I'd like to add that you're not going to succeed just by leafing his book through; it takes A LOT of practice. .. And why the hell have I not learned this in school??

  25. 4 out of 5

    Jackie Fowler

    There were enough interesting math shortcuts in this book to keep my interest, especially those dealing with multiplication tricks, squaring, finding divisors (and why those tricks work), and figuring out any day of the week in the Gregorian Calendar. But, there were also many parts that just weren't feasible to me. Only certain people, like the author, are capable of doing all the mental tricks he covers. Some math problems were just too much to do with paper and pencil, and I'm a math person! There were enough interesting math shortcuts in this book to keep my interest, especially those dealing with multiplication tricks, squaring, finding divisors (and why those tricks work), and figuring out any day of the week in the Gregorian Calendar. But, there were also many parts that just weren't feasible to me. Only certain people, like the author, are capable of doing all the mental tricks he covers. Some math problems were just too much to do with paper and pencil, and I'm a math person! The other cricism I have is of the last chapter, the epilogue. It doesn't seem related to the rest of the book.

  26. 4 out of 5

    William Schram

    Contains techniques for lightning fast mental calculation and other things for elementary mathematics and random tricks. For instance, it includes the phonetic memory system for recalling numbers and a way to calculate dates in your head. The techniques listed in the book are a bit counter intuitive, but they work pretty well. The book also contains problems for you to do on your own in order for you to go and improve your abilities at this particular skill. Also contained within are biographies Contains techniques for lightning fast mental calculation and other things for elementary mathematics and random tricks. For instance, it includes the phonetic memory system for recalling numbers and a way to calculate dates in your head. The techniques listed in the book are a bit counter intuitive, but they work pretty well. The book also contains problems for you to do on your own in order for you to go and improve your abilities at this particular skill. Also contained within are biographies of other historical lightning calculators and random bits of trivia which makes this book pretty interesting.

  27. 5 out of 5

    Mohammed Almahfoudh

    The author of this book calls himself a mathemagician. He combines his love to both math and magic in this book. The book introduces creative , simple and easy ways for doing algebra. When reading this book, I realized that I was already using some of the methods introduced in the book. I have to say that even though I am not a math lover, I really enjoyed reading this book and practicing its creative calculations methods. One final note, after you're done with reading the book, check out the re The author of this book calls himself a mathemagician. He combines his love to both math and magic in this book. The book introduces creative , simple and easy ways for doing algebra. When reading this book, I realized that I was already using some of the methods introduced in the book. I have to say that even though I am not a math lover, I really enjoyed reading this book and practicing its creative calculations methods. One final note, after you're done with reading the book, check out the references at the end.

  28. 4 out of 5

    Franco Arda

    I'm neither interested in squaring three-digit numbers in my head nor in doing mathematical magic. I'm only interested in practical mental math. I did buy this book for chapter 5; *** Good Enough; The Art of 'Guesstimation' ***. I've been doing guesstimations for many years intuitively, not very structured. This fine chapter teaches beginners the art of guesstimation while experts can go back to the basics and hone their skills while they might discover something new ... I did do so with approxi I'm neither interested in squaring three-digit numbers in my head nor in doing mathematical magic. I'm only interested in practical mental math. I did buy this book for chapter 5; *** Good Enough; The Art of 'Guesstimation' ***. I've been doing guesstimations for many years intuitively, not very structured. This fine chapter teaches beginners the art of guesstimation while experts can go back to the basics and hone their skills while they might discover something new ... I did do so with approximating years needed for trippling an investment given interest rates of X% p.a.

  29. 5 out of 5

    Haghia lubis

    The first few chapters is commonly educated during my primary school, although the later chapters are much more complicated. Perhaps asian schools with all the kumon and other math's concept has already taught this early on, since asian's are mostly well known with their math capability. yet, it is still refreshing and helpful on a much advanced level, though i don't think the later chapter shall help me much in my daily live.

  30. 4 out of 5

    Robert

    Entertaining, no doubt. I think this is most useful for younger readers who aren't married to the way they were taught to do math in school. For anyone who loves math, you should read this book. It will help you understand better how numbers relate to each other and why. It adds perspective. I'd recommend this book if math is something you really find interesting, or you want to look smarter than you are.

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