I’m currently in the process of writing a mathematics book aimed at the high school level. The idea is to introduce high school students (or anyone with a basic background in mathematics, really) to the wonder of mathematics through hands-on problem-solving in topics not usually encountered in high school. Feel free to read any of the drafts linked below and (if you feel so inclined) to provide me with feedback. (If you intend to provide feedback, you probably want to first read this short note to test readers.)
The following chapters are available in draft form:
- Preface/Chapter 0: Boolean Algebra, draft #2 (June 24, 2007)
- Chapter 1: Problem-Solving and Proof, draft #1 (June 24, 2007)
- Chapter 2: Numbers, draft #1 (June 24, 2007)
Planned (possible) topics for future chapters include:
- Functions and Sequences
- Fibonacci Numbers and the Golden Ratio
- Number Theory
- Combinatorics
- Complex Numbers and Beyond
- Sets and Infinity
- Group Theory
- Graph Theory
- Computation
February 22, 2008 at 4:14 am |
I think it would be nice (especially for some more computationally intensive sections like group theory) to have sample code that could be used in Sage to solve some problems that would be (nearly) impossible to do by hand. e.g. RSA enctyption with large keys. For that reason I would like to point you to Sage: http://sagemath.org which, in case you don’t know, is a Free/OSS CAS that ties many different systems together in one easy to use package.
Sage allows for sharing “notebooks” and uses jsmath to get decent typesetting of formulas. You could create a companion notebook for a chapter, or even publish the entire book as Sage notebooks. I know they are looking for a bunch of examples and introduction stuff that I think this book would be perfect for. There are a number of people on the Sage project who are interested in teaching Math to High School/early undergraduate students, and would appreciate your help. Lots of others are interested in research of course…
Anyway, I just thought you might be interested since I would have loved both Sage and a book like this when I was in High School. I now have my Master’s
-Ivan
February 23, 2008 at 2:52 pm |
“It can seem somewhat non-intuitive that A =) B is true when A is false.
The idea is that A =) B only says what happens when A is true; when A
is false, you certainly can’t say that A =) B is false (even though it may
not be true in any really meaningful sense). As an example, suppose your
friend says, \If it rains tomorrow, I will stay inside.” If your friend goes out
to splash in the puddles during a downpour the next day, then they lied,
no question about it. But suppose the next day dawns bright and sunny,
and your friend goes outside. Did they lie? Well . . . no. Your friend didn’t
say what they would do if it didn’t rain, so their statement was vacuously
true.”
It may be just me but I do not think it is obvious that you are talking about both F T -> T and F F -> F.
I think it would help to say actually state you are talking about F T -> T and F F ->F and then say if its sunny and if your friend stays in or goes out will not be a lie. Your rain example is good but needs to be tied to both statements.
I think for many its not just having having A as False but the having F F turn up T that causes confusion.
March 8, 2008 at 12:05 pm |
It’s Discrete Math. A good book is Suzanne Epp’s Discrete Math with Applications. I dunno if it’s taught in some high-schools. Most high-school students are stuck with calculus. There are questions whether Discrete Math should be taught separately from its applications.
February 4, 2009 at 8:38 am |
While skimming chapter0-pre2.pdf, I came to the footnote which says
“Unless Australia has just been made up as a part of a giant conspiracy. I mean have you ever been to Australia? . . . Are you sure it was really Australia?”
This is absurd, I live in Australia.
March 16, 2009 at 6:40 pm |
This reminds me of the sentiments expressed at the following places:
http://steve-yegge.blogspot.com/2006/03/math-for-programmers.html
http://stackoverflow.com/questions/52176/what-are-the-core-mathematical-concepts-a-good-developer-should-know
+1 for writing about the math that got left behind
July 11, 2009 at 2:14 am |
I enjoyed reading your drafts very much! I can’t wait for the final version to come out.
As a high school student myself, I can affirm to your comparison of real math to school math. Unfortunately, I’m not sure that many highschoolers will read this book. :( I’m the only guy in my grade that (publicly) reads books like this, and any attempt to explain my obsession or convince them to read a book like yours is often met with failure.
Keep on writing!
July 11, 2009 at 9:03 am |
Thanks Sam! I haven’t worked on this in a while but I still intend to finish the project at some point. Knowing that people are reading and enjoying what I have so far is encouraging, so thanks for leaving a comment.
Keep on reading!