Math is great! discussion
Welcome!

Don't worry about discussions being difficult. I'm a middle school math teacher and that's where most of my math reading falls, level wise.
Feel free to share anything else you've read or discovered online. =)


cheers,
Matt

Are you going into elementary ed, Ashley? I taught 5th grade for 3 years before I switched this year to middle school math.


A lot of problems are not as easy as multiplication. The Traveling Salesman Problem (TSP) is a classic example of a problem that does not seem to be polynomial. Suppose you have to visit n cities, in any order, but you want to take the shortest trip that will pass through all n. How do you decide what route to take? There are (essentially) n! routes, and n! grows faster than any fixed power of n, so, unless we can be clever and figure out a way to not have to check all n! possible routes, this is not a "polynomial time" problem. (I've read that one can actually solve this in "n^2 2^n" time, which is much better than n!, but still far from polynomial.)
As for that NP business, consider if someone told you they had the best route connecting n cities. Could you verify that this was indeed the best route without simply solving the problem for yourself? Compared to the factoring problem: while coming up with factors for a given large number n, if someone claims that n factors as n=ab, it can be checked easily simply by multiplying a times b. So, it seems factoring and the TSP are problems of different sorts.
I've never investigated these types of problems myself, except for a computer science course or two many years ago. And while number theory is my thing, I've never found cryptography to be very appealing. But these are very interesting questions, nonetheless.
cheers,
Matt

You must have went to one of those fancy colleges!
:P
Speaking of cryptography, guess what book I'm currently reviewing: http://www.goodreads.com/book/show/15...

Reviewing, eh? That's cool. Personally, I think cryptography is "a pretty flower, that smells bad." That is, nice math, but applied to problems that seem quite un-fun, and at least a little ugly.
But, as long as you like it...
cheers,
Matt

Like doctormatt, I have a PhD in mathematics. (We attended the same fancy university, where we specialized in number theory and volleyball.)
I have a mathematics shelf here:
http://www.goodreads.com/review/list/...
which I will try to add to.

If you're mainly interested in the RSA encryption scheme, you should be able to get whatever you want from the RSA website. If you're also interested in the "information theory" behind encryption schemes in general, then you'd probably like Katz and Lindell's book. It's a fairly complete presentation of the ideas behind public-key cryptography.

I don't usually read math related books, but there is one, I havn't really made it all the way through, but what I have read so far has been useful. It is called Rapid Math Tricks and Tips. You spend 30 days learning 2 tricks a day and then you will have a ton of useful tricks at hand(or at head I should say, because you would remember the tricks.)

Feel free to keep sharing stuff with us and jump into any conversations. We're small, but we have a good time.









Do you like the math in Chemistry? I thought Chemistry was tons of fun!




Here is an interesting link for all of you other novices out there. It has a great learning plan for theoretical physics (all free and online), which I am sure everyone knows is comprised of a lot of math. http://www.phys.uu.nl/~thooft/theoris...
Enjoy!

One of the best series of books about math is The World of Mathematics: A Four-Volume Set, which is a collection of essays about various aspects of math. I think my folks got it for me when I was in high school.
As for fiction, here are ones I like, and I hope others can add to this list.
Uncle Petros and Goldbach's Conjecture: A Novel of Mathematical Obsession by Apostolos Doxiadis
The Indian Clerk by David Leavitt
I haven't read these but plan to soon.
The Housekeeper and the Professor by Yoko Ogawa
Logicomix: An Epic Search for Truth by Apostolos Doxiadis

My name is Claire and i'm living in London, UK (originally from Gold Coast, QLD, Australia)
I have recently been priming my math skills for an interview for a certificate I hopefully get in to!
I haven't done maths for quite a while but now I am getting back into it, the challenge is quite good.
^ Vicki, is it good being a programmer? It's a career I am currently considering, all my programmer friends say it is hard, but worth it.



;-)








I've gone back to school in my old age of 28, at least I feel old compared to others. I'm majoring in Applied Mathematics. My interests so far are Electromagnetism and Vector Analysis (especially Vector Calculus and I want to do more work with representing divergence and curl using linear algebra techniques).
Anyway, I've only been studying math for a couple years now, but I've gone through all the Calculus tracks, learned how to program in Mathematica, took Differential Equations, went through Linear Algebra, at least those are all the ones I really liked. I get to take Complex Analysis next semester and I can't wait, because I feel like that's one of the things missing from my world of math!
This semester I'm taking Mathematical Physics, Electromagnetism I, Mathematical Analysis, and Discrete Structures. And I am currently teaching myself how to program in LabVIEW for a new research job I got at my University.
I love reading about anything math related. I read all my text books and read a lot of fun outside reading books. There's so much cool stuff to learn!!


I've been 'lurking' on this group for a few months now and your post inpired me to respond (though a bit delayed).
Congratulations on going back to school. I wish you luck.
I've enjoyed reading all the posts. It looks like this group has a very diverse membership. That is great to see.
I apologize for the long post. Guess I should have posted sooner ;)
Personally, I love math. I took it in university but I don't use it for my work. I do tutor high school math on a regular basis. I especially love vector calculus and linear algebra. I'd like to try Mathematica some day. Maybe if I ever go back to school and can get a student copy. For now I mostly use a pen and paper :)
About ten years ago I was afraid that my math skills were dwindling as I'd been out of school for over ten years and was working as a programmer that didn't involve much math. I started reviewing my university books and then started learning tensor calculus. It inspired me. I then tried to get into differential forms, quanterions and finally discovered geometric algebra (GA).
I have tried to understand the different approaches by looking at things like divergence and curl and Electromagnatism.
There was an interesting paper I read on using differential forms (DF) as a pedigogical approach to teaching Electromagnetic theory. I think that GA also has the same advantages. However, both appoaches can seem a bit strange. Further, I think there is still an advantage to looking at it the conventional way with vector analysis as well as DF or GA. But it is all really exciting because it all adds insight and helps us understand things better.
My learning seems to go in spurts. I am not good at doing it on a daily basis so I often find myself reviewing and catching up. But it is all for fun.
I'm curious if you or anyone else has had any exposure to Geometric Algebra or Geometric Calculus.
-- warning -- shameless plug alert --
For those unfamiliar with Geometric Algebra this is my understanding (which you should take with a grain of salt as I am self taught and may have led myself astray :). GA is a way to represent higher dimentional object beyond vectors in a consistent and systematic way that allows for standard mathematical operation like addition, multiplication and division and exponents. Something that you cannot do with vectors (there is the cross product and dot product but that is not true multiplication). GA is really just a form of clifford algebra that has a simpler syntax like vector calculus but I think that it is much more powerful than vector calculus. Dr. David Hestenes of Arizona State University has been a huge force behind GA and now it seems to me that the University of Cambridge is really behind it now too. Alas, I have yet to see any courses at my local university.
Books mentioned in this topic
Uncle Petros and Goldbach's Conjecture: A Novel of Mathematical Obsession (other topics)The Indian Clerk (other topics)
Mathemagic: Magic, Puzzles and Games with Numbers (other topics)
Flatland: A Romance of Many Dimensions (other topics)
The World of Mathematics: A Four-Volume Set (other topics)
More...
Authors mentioned in this topic
David Leavitt (other topics)Apostolos Doxiadis (other topics)
Yōko Ogawa (other topics)
Keith Devlin (other topics)
Go ahead and introduce yourself (and add some good books while you're at it)!
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I'm Nicole and I teach 7th grade math in California. I've got a BS in architectural engineering and enjoy reading about math. I find it truly fascinating, and look forward to discussing it. I am not, however, a mathematician, so don't get too technical on me. =)