Cool statement about vector spaces

I found this cool quote that for now still blows my mind and seems cool although I am sure at a later point I will have a better grasp on things.

"A vector space that does not have a finite basis is called infinite dimensional. This is not an exotic property: many of the most important vector spaces, particularly spaces where the "vectors" are functions are infinite dimensional"

The parts that blew my mind were infinite dimensional not being an exotic property and the concept of functions as vectors. I am sure it will make more sense later.

Fields and Field extensions

huh \(\LaTeX\) what? So I am reading through the section on fields and field extensions but I have to admit it is blowing my mind and I have having a hard time following the signicance of what is going on.

\( x>3 \) One example they give is the extension from \(\mathbb{R}\)(real numbers, I don't have latex setup to do fancy letters here). The polynomial P(x) = x^2 +1 has no real root. The root is i which isn't contained in R. We adjoin i to R and we get a new field C(complex) of the form a+bi with a,b contained in R.

One of the parts that got me(although writing this post is helping me think it through) was the concept of adjoining. I originally assumed that it meant you added that item into the set comprising the field but that doesn't seem to be the case. Adjoining does the funky thing the you see normally with complex numbers. If you adjoin item x, then the field had members of the form a+bx.

Another example is the field Q(rationals) which you can adjoin (2)^1/2 or the square root of 2.

The members of the new field are now of the form a + b*(2)^(1/2).

As a side note that looks really ugly I need to figure how to do nice latex and mathematical symbols on here if I want this to keep dumping funky math on this blog.

Chord

So I was just thrown for a loop by the phrase
"the derivative of a function f at a point x is the limit of the
gradients of a sequence of chords of the graph off"

It makes much more sense once I hit wikipedia http://en.wikipedia.org/wiki/Chord_(geometry)

The chord is just the line between two points and the circle and in this case the derivitive at a point is gradient or slope of the line as the chord shortens till that line is ifinetly small and we are essential dealing with a point.

We also see the sequence of chords since this is the derivative of a function rather than a single point.

Makes sense, the vocab though threw me off for a bit.

Safari books online and Math

I have been interested in Safari books online for a number of years. I was first exposed during a summer internship in college. 

I was working remote doing some web development and I came accross a need to use regular expressions. My manager at the time recommeneded "Mastering Regular Expressions" by Friedl and wow that is a good book. I was living with my parents and their local library had a subscription to safari online so that with my library card I was able read this book. After going back to school I spent a number of years as a poor college student and couldn't justify the cost of safari online. 

Fortunately with a job change a few months ago I decided that regular daily investment in technical learning was a critical item in order for me to succeed in my software career.

I signed up and have been using safari online for several months now and find it very useful. In particular I have recently found "The princeton companion to mathematics" is available on safari. 

At my last job at National Instruments there was a strong culture of books group and I was able to attend part of a book group based on the abstract algebra book found here.

http://abstract.ups.edu/download.html

I thoroughly enjoyed it and I hope to deepen and broaden my mathematical knowledge. 

It is kinda funny as a kid I HATED math, it was repetitive and boring. I spent alot of effort(more on this another time) to take calculus in high school solely because it was required for Physics BC and I loved science.

Funny thing happened though. I loved calculus it was the first math course in which I felt that I was  learning things that broadened my mind and helped me understand the world. It wasn't repetitive but based on simple concepts that could be extrapolated to further ideas.

Anyway I want to deeply understand modern mathematics especially so I can help make sure that my children see the beauty of math rather than rote repetition. 

I will try and keep posting things here as I try and work my way through this thick and somewhat intimidating volume.

Learning security

Over the past few years I have begin to develop an interest in computer security and cryptography. I am going to attempt to document the process of learning for my benefit and others.

I have several tasks that I am currently working on to help this process.

Matasano crypto exercises- I first hard about this on hacker news and it rocks. I did the first set and a half a couple of months ago and then got rely busy so I haven't been able to make forward progress recently. Was doing them in Google go and that was fun

Enigma group challenges. I am user qianyilong. Currently I am still going through the basic skills ones.

Overthewire.org - I had a good friend who works in web security recommend these to me. Have played with several of them.

Coursera's cryptography 1 course - I am currently going through this but I found the class late and am so far behind that I don't think I can get credit but since I am doing this to learn I am OK with that.

At work a group of guys are doing a cryptography book group. The first half of the group if focusing on the abstract algebra background using the textbook from abstract.ups.edu

I am also following Bruce Schneier's  blog and cryptyo gram monthly email. I read his book applied cryptography cover to cover.

Things I am looking at

I just finished reading the basics of hacking and penetration testing by pat engebretson

I am reading Modern cryptanalysis by Christopher swenson

After reading the book on pen testing I am also looking into exploring
The owasp goat project as a learning opportunity.
Metasploit
Owasp zap
Many other tools that I have seen mentioned. I have created a little virtual machine security lab that I can use to try some of these things out.

So this post was long but this is the initial dump. I hope to update this blog near daily with my current status in learning.

他姓巴金斯

Sweet  found a Chinese copy of the hobbit.

Posting from my tablet

So is mostly just a test to see how easy it is to post from my android. I want to start treating this blog as an opportunity to intellectually stretch myself and updating from my tablet will make it easier I think.