radioactve_piano's review against another edition
3.0
It's only been three and a half years since I've been in an upper-level math class, and yet, I felt like a dunce at many points in this book.
Granted, that may have been due to Nahin's decidedly engineer-fascinated-by-math style of writing (that style does exist, I swear; I grew up with my dad teaching me math in a way that can only be described as filtered through an engineer's mind); aside from my dad, the people I spoke math with were all mathematicians.
I should have read this when I first received it as a gift if I wanted to fully grasp all of the equations. As it was, despite my degree in math and the insanely slow pace I took reading this, the lack of constant use of many equations and theorems shown in the book meant I recognized the name and the general idea, but was totally lost on some of his executions.
Granted, that may have been due to Nahin's decidedly engineer-fascinated-by-math style of writing (that style does exist, I swear; I grew up with my dad teaching me math in a way that can only be described as filtered through an engineer's mind); aside from my dad, the people I spoke math with were all mathematicians.
I should have read this when I first received it as a gift if I wanted to fully grasp all of the equations. As it was, despite my degree in math and the insanely slow pace I took reading this, the lack of constant use of many equations and theorems shown in the book meant I recognized the name and the general idea, but was totally lost on some of his executions.
peacefixation's review against another edition
3.0
I held on for the first few chapters but this ended up being quite a difficult read and I had to skim over most of the math. Despite that, it was a very interesting read and I learned a lot about sqrt(-1). I hope to return in a month or so for another go, with a pen and paper close at hand!
trask0730's review against another edition
A pretty good book! I did myself a favor and avoided doing lots of hard math myself haha (I figured I will have plenty of that in the years to come). That being said, I loved learning the historical context of one of my favorite subjects within mathematics!
mathstalio's review against another edition
2.0
I read this with the thought that it would be a history of imaginary numbers (it was) and their applications (ehhhh). The author starts out with an intro that says any student who has taken high school calculus should be able to follow the math of the book. Definitely not. I mean, I could have followed the included calculations but I chose not to because it was simply unnecessary to show the entire derivation of formulas. Tell me ABOUT them and where they came from. That's what I was hoping this book would be. Maybe it's unfair to judge a book on what you wanted it to be, but. Here we are. Too calculation heavy, I wanted more history and DESCRIPTIONS of applications. Although I did learn enough to be able to give my students a bit more background on complex numbers when we get to them.
brettt's review
2.0
Of all the people who probably hide their heads at the goofs they have made, the person who named "imaginary" numbers is probably among them as far as the field of mathematics is concerned.
So-called "imaginary" numbers describe the square roots of negative numbers, which are impossible to calculate using plain integers. The square root of 1, for example, is 1 because 1x1=1. But the square root of -1 seems impossible to figure, because the only way to get to -1 is to multiply two different numbers together. A negative number multiplied by another negative number leaves a positive number, not a negative one. At some point, mathematicians decided that there would be a square root of -1, and it would just be a 1 that was on another "axis" than the regular positive-negative line. But since the number didn't seem to have any real-world analogue like positive and negative numbers did, it somehow got hung with the tag, "imaginary." So today we say that the square root of negative 1 is i. The square root of -4 is 2i, and so on.
Retired electrical engineering professor Paul Nahin outlines some of the development of i through the history of mathematics in An Imaginary Tale. Some early cultures refused to acknowledge the existence of a quantity that could be squared to form a negative number, and even into the Renaissance and enlightenment years the so-called "imaginary" numbers were considered at best unimportant. They were not useful except in specialized cases and it seemed even mathematicians had reservations about dealing with numbers that didn't represent any real quantity.
Today, i and its counterparts find widespread use in many areas of math, and the only reservations that seem to continue deal mostly with the use of the word "imaginary." Nahin explores how important i is in many fields of engineering, especially his own. This part of the book -- about the latter two-thirds -- is heavily laden with equations and formulas and is going to be beyond most non-mathematician or non-engineer readers. He probably would have had to lengthen the book considerably to bring that subject matter within the grasp of the lay reader, but that doesn't make the string of equations and engineering language any easier to navigate.
Original available here.
So-called "imaginary" numbers describe the square roots of negative numbers, which are impossible to calculate using plain integers. The square root of 1, for example, is 1 because 1x1=1. But the square root of -1 seems impossible to figure, because the only way to get to -1 is to multiply two different numbers together. A negative number multiplied by another negative number leaves a positive number, not a negative one. At some point, mathematicians decided that there would be a square root of -1, and it would just be a 1 that was on another "axis" than the regular positive-negative line. But since the number didn't seem to have any real-world analogue like positive and negative numbers did, it somehow got hung with the tag, "imaginary." So today we say that the square root of negative 1 is i. The square root of -4 is 2i, and so on.
Retired electrical engineering professor Paul Nahin outlines some of the development of i through the history of mathematics in An Imaginary Tale. Some early cultures refused to acknowledge the existence of a quantity that could be squared to form a negative number, and even into the Renaissance and enlightenment years the so-called "imaginary" numbers were considered at best unimportant. They were not useful except in specialized cases and it seemed even mathematicians had reservations about dealing with numbers that didn't represent any real quantity.
Today, i and its counterparts find widespread use in many areas of math, and the only reservations that seem to continue deal mostly with the use of the word "imaginary." Nahin explores how important i is in many fields of engineering, especially his own. This part of the book -- about the latter two-thirds -- is heavily laden with equations and formulas and is going to be beyond most non-mathematician or non-engineer readers. He probably would have had to lengthen the book considerably to bring that subject matter within the grasp of the lay reader, but that doesn't make the string of equations and engineering language any easier to navigate.
Original available here.
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