david_reads_books's review against another edition
4.0
Actually, this book is over my head. Tons of very well laid-out math on complex topics. To read this book you should have a mathematical background equivalent to what a beginning third year college undergraduate in an engineering or physics program of study would have completed. So, done with Calculus, Differential Equations, Linear Algebra, Probability/Statistics. And you need to LIKE your Math!
The math on page 22 has the Cayley-Hamilton theorem, alpha and beta characters both super and sub-scripted, matrices of sin and cos terms, the Identity matrix, and De Moivre's Theorem. On this same page are phrases like: "not hard to establish", "simply take it as plausible", "refer to any good book on linear algebra", "all we have left to do", "a straightforward task", "equations are easy to solve for", "I'll let you do the algebra to confirm", "actually easily handled", "actually don't have to worry about that particular problem"
While I like math, and I'm an EE/Physics person, I am out-of-shape for this intensity level of math. I fully read ch 1, and then skimmed the rest of the book. The final 22 pages on Euler paint a nice bio. The author describes this book as a "second half" to his 1998 publication: [b:An Imaginary Tale: The Story of the Square Root of Minus One|357209|An Imaginary Tale The Story of the Square Root of Minus One|Paul J. Nahin|https://i.gr-assets.com/images/S/compressed.photo.goodreads.com/books/1348774169l/357209._SY75_.jpg|347370] Maybe I'll go and try to read that book first.
1)Complex Numbers (matrices, 2D vectors, complex indeed!)
2)Vector Trips
3)Irrationality of pi^2
4)Fourier Series
5)Fourier Integrals
6)Electronics and sqrt(-1)
Euler: The Man and the Mathematical Physicist
The math on page 22 has the Cayley-Hamilton theorem, alpha and beta characters both super and sub-scripted, matrices of sin and cos terms, the Identity matrix, and De Moivre's Theorem. On this same page are phrases like: "not hard to establish", "simply take it as plausible", "refer to any good book on linear algebra", "all we have left to do", "a straightforward task", "equations are easy to solve for", "I'll let you do the algebra to confirm", "actually easily handled", "actually don't have to worry about that particular problem"
While I like math, and I'm an EE/Physics person, I am out-of-shape for this intensity level of math. I fully read ch 1, and then skimmed the rest of the book. The final 22 pages on Euler paint a nice bio. The author describes this book as a "second half" to his 1998 publication: [b:An Imaginary Tale: The Story of the Square Root of Minus One|357209|An Imaginary Tale The Story of the Square Root of Minus One|Paul J. Nahin|https://i.gr-assets.com/images/S/compressed.photo.goodreads.com/books/1348774169l/357209._SY75_.jpg|347370] Maybe I'll go and try to read that book first.
1)Complex Numbers (matrices, 2D vectors, complex indeed!)
2)Vector Trips
3)Irrationality of pi^2
4)Fourier Series
5)Fourier Integrals
6)Electronics and sqrt(-1)
Euler: The Man and the Mathematical Physicist
blackoxford's review against another edition
4.0
Better than Prozac
Euler’s formula is arguably the most beautiful construction in mathematics. It shows how, with unparalleled elegance, five incommensurables universes of numbers are related to one another. Nahin makes the argument wonderfully and shows how the identity’s simple beauty is just as much use as ornament, solving a variety of mathematical problems in novel ways. Although not directed toward mathematicians, the book does require some competence in trigonometry, calculus, and elementary numerical analysis, probably obtained through study in engineering or physics. If you can handle it, I think you’ll find it comforting just how consistent, coherent and stable mathematics can be in a rapidly changing world.
Euler’s formula is arguably the most beautiful construction in mathematics. It shows how, with unparalleled elegance, five incommensurables universes of numbers are related to one another. Nahin makes the argument wonderfully and shows how the identity’s simple beauty is just as much use as ornament, solving a variety of mathematical problems in novel ways. Although not directed toward mathematicians, the book does require some competence in trigonometry, calculus, and elementary numerical analysis, probably obtained through study in engineering or physics. If you can handle it, I think you’ll find it comforting just how consistent, coherent and stable mathematics can be in a rapidly changing world.
sdoire's review
3.0
I picked this one up thinking it would be a math history book (and because it had a great cover!), but it turned out to be more of a math book. Which would have been fine if I had ever taken advanced number theory or electrical engineering courses, but I hadn't. Still, I broke out my calculus textbook and followed along as best I could. Probably absorbed 60% of it. When writing prose instead of formulas, the author is witty and engaging. I'd like to read a pure history of math book by him.
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