Historical and Philosophical Foundations for Mathematics, Writing a Math Book

[Caramon]

Hello,
Recently I've been attempting to put together a brief book on mathematics. The first section is short and introductory as I lead up into calculus. I kind of feel bad that I skipped over conics, geometric series, permutations and combinations, transformations of functions, and so many other topics... but I assume anyone who would be reading at this level already knows that and is possibly looking for a brief recap or some additional insight.

I'm by no means a professional mathematician and am finishing my undergraduate in Astrophysics so I am not a math major either. Please let me know if any information is erroneous or does not make sense, and all feedback is appreciated!

Here it is for download:
http://www.freefilehosting.net/historicalandphilosophicalfoundationsformathematics"

Thank you!

 

[discrete*]

I'd be happy to give your book a look-through, but I'm not downloading it from that site. If you want, post a link to a PDF or a more secure source.

 

[micromass]

Why not put the document on scribd? www.scribd.com
It's a very reliable site!

 

[Caramon]

http://www.scribd.com/full/48917837?access_key=key-1zqu8eb024hjc626vuez

There we go. Sorry, I just uploaded it to a random file hosting site... not trying to give people a virus or something, its like a 50kb word document X:

 

[pantechc70]

I found it very interesting you should update the thread when you add more to it. I would add a section on the basic formulas/equations in algebra II and Geometry. It really goes well with the recap you mentioned in your first post: Like Area,Perimeter and Volume for basic shapes. You could also go into detail on how these formulas were discovered.

 

[chiro]

A couple of suggestions

When talking about calculus, you could explain the motivation of trying to find different measures (like length, area, volume etc) in cases where you don't have straight lines: so basically its the generalization of linear problems to non-linear problems.

If you ever get into topics of certain mathematical structures (like say groups, vector spaces and so on), you could probably state the motivation for these is purely to find properties of these systems which are valuable since a lot of these abstract entities exist in many scenarios in different forms.

I guess if you are talking about orthogonality, you could mention that the importance of orthogonality whether it relates to vectors in euclidean geometry, or functions in Fourier transforms, is that essentially every item is essentially "independent" of every other item and modifying the value of one item (like say in a vector) won't change the others. So in essence orthogonality is an organized way to "decompose" any system into independent entities. This kind of "atomic analysis" let's you find ways to break down systems into simpler systems, and as a tool in science, you can see why it is particularly important.