Mathematics In 10 Lessons The Grand Tour Pdf

Open Preview

See a Problem?

We'd love your help. Let us know what's wrong with this preview of Mathematics in 10 Lessons by Jerry P. King.

Thanks for telling us about the problem.

Friend Reviews

To see what your friends thought of this book, please sign up.

Community Reviews

· 33 ratings · 6 reviews

Start your review of Mathematics in 10 Lessons: The Grand Tour

Dec 20, 2009 Jeff rated it really liked it

Jerry P. King has written two math books for general audiences The Art of Mathematics and this one. In the later, he lays out a fairly sophisticated argument for why mathematics is an art that requires an aesthetic theory to evaluate. It is a great book that has really impacted the way that I think about, teach, and do math.

King makes an argument that this book is a complement to the first as it is meant to share the beauty of mathematics. He argues that it is a grand tour of math that is meant

King makes an argument that this book is a complement to the first as it is meant to share the beauty of mathematics. He argues that it is a grand tour of math that is meant for poets to get a feel of why math is more related to the work of writing poetry than it is to the work of doing science. Because this book's intended audience is folks on the humanities side of C.P. Snow's two worlds of the humanities and the sciences, you would think that it is easily accessible to the literary crowd. In fact on the back of the book, there is a quote from another math professor that says "no prior knowledge of mathematics is assumed or expected." However that is not to say that this book isn't difficult. King starts with a few basic principles and builds the large complex abstract world of mathematics from there.

It is a book that I read cover to cover and have learned immensely from. However, it is also a book that requires a slower engagement with opportunities to revisit. I loved it and do think there is beauty here. However, I love it because I love the patterns that emerge from studying math. I'm not sure that someone that comes from far on the humanities side of the intellectual divide would be willing to engage in the long hard engagement that learning this math requires. That said, I didn't understand everything here, and I'm not sure how much time I'm willing to revisit the work.

Overall though, King has written a book that with some work beautifully illustrates how math can be created from just a small bit of raw material,namely a few basic axioms and an understanding of formal logic. Pick it up and have fun!

...more

King intended this book to be "math for non-mathematicians," people who went through math in school, didn't like it, and otherwise never wanted to see it again. He said he wrote it for those who majored in liberal arts. I'd say he only partly succeeded in doing this. He seemed to think he could accomplish this by occasionally telling an interesting story about math, emphasizing its elegance, and how mathematicians think it's beautiful, and sometimes quoting a piece of classical literature. I thi King intended this book to be "math for non-mathematicians," people who went through math in school, didn't like it, and otherwise never wanted to see it again. He said he wrote it for those who majored in liberal arts. I'd say he only partly succeeded in doing this. He seemed to think he could accomplish this by occasionally telling an interesting story about math, emphasizing its elegance, and how mathematicians think it's beautiful, and sometimes quoting a piece of classical literature. I think his approach needed more work, particularly in his presentation of the math itself. He showed some promise in the beginning of the book, giving me one or two "a-ha" moments that were really rewarding. He did it by illustrating the same concept a couple different ways, using different representations. As the book progressed, though, he increasingly went away from this approach, and towards what I'd call a "typical math book" (though, with the aforementioned quotes mixed in, and there are quite a few more proofs than your typical math book). Of the lessons that took that approach, I really appreciated what he presented about fractions (rational numbers). He answered some basic questions about them that had been bugging me for years, like *why* when you divide two fractions, you invert and multiply.

True to the title, the book takes you through a series of lessons that cover the basic mathematics that every mathematician knows in their bones.

In general, what I appreciated about the book is that I can tell he went through the effort to fill in holes in the math education that most people receive when they go through school; what your math classes did not teach you about math, but which if you knew it, would help you understand the concepts better.

Given that, I have some complaints. One is that there are times when he holds your hand, but there are many other times when he doesn't. He repeatedly skipped steps that made me think, "Wait, how did he get that?" Sometimes if I thought through the intermediate steps myself, I could get why he did it, but other times, I just felt stumped. There were several times where I wondered if he did this intentionally, like he wanted you to think about why he did what he did, as a way of goading you to think mathematically. As someone whose "math-fu" is weak, this approach was not encouraging. I think he needed to take more care with the learning curve. My second complaint is that he had a bunch of typos in the book. In most books, this would just be annoying, but with a subject that depends heavily on using a vocabulary that is new to the reader, and which leans heavily on a symbolic language to explain things, this matters a lot! There were times when I was confused by an expression, and I wondered whether I didn't understand an underlying concept, and needed to review it, or whether King just screwed up in the typesetting. Third, he often refers back to concepts, either directly, or indirectly, that he covered 10, 20, 30 pages earlier, but rather than reprise the concept where he's talking about it, he expects you to either remember what he talked about earlier, or to remember where it is in the book, and go back and review it yourself. He only explains concepts once. For this reason, I think it would behoove the reader to take notes. I did that a little, but I think it would've helped me to do that more.

King takes an easy approach to having the reader do exercises. In the beginning of the book, he sets up exercises for readers to do as proofs, but beyond the first chapter, you'll often see him put forward a proposition that he does not close, and then say, "This is left as an exercise for the reader." He doesn't set up anything. He leaves that to you, if you want to do it. You can keep reading, which I did quite a bit.

I was hoping that this book would give me a good grounding in understanding math as mathematicians understand it. I don't think it accomplished that. It was, however, very effective in helping me understand a couple areas of math much better than I used to, and for that, it was worth reading.

...more

Feb 24, 2016 Scott rated it liked it

Good, but my main criticism is the proof reading was terrible, the book was filled with typos – bad enough just for prose, but really deadly for the equations, it's no help at all when you're trying to figure out what's going on and what's on the page is incorrect to begin with.

Nov 06, 2014 Russell rated it really liked it

Imagine a whirlwind tour of the seven world wonders, with just enough history to provide some context and spark interest in the reader, and decent sketch of the basic qualities of the wonder in question. That's what this book was like. And it was surprisingly well done.

The author makes some silly claims, like math leads to Truth, which it doesn't, it leads to a well ordered and logically sound system and, when done correctly, a consistent system. With a proper mathematical system we can gain insight into the workings of reality, but Truth? No, such a thing lies beyond human made constructs. Ask two different philosophers about it and you'll get a dozen answers!

But that's a minor point, the rest of the book is focused on the author's core subject: mathematics. And you'll get it by the pageful. This is a book that not only does a solid job going over the big ten the author had identified but also acts a reference book. A rare combination indeed.

This is a keeper.

...more

I read about this book in Science News. It is an attempt by a mathematician to explain the beauty of mathematics to those who did not study physical sciences and may have a limited math background.

I was hoping my teenagers, who are in Advanced Math in school, might find some interested bits that would show them the interesting parts of mathematics, beyond the rote exercises they do in school. But it's way too advanced for middle schoolers.

I read about this book in Science News. It is an attempt by a mathematician to explain the beauty of mathematics to those who did not study physical sciences and may have a limited math background.

...more