Quick Note: LaTeX
May 1st, 2009 / No Comments » / by Chris
In learning how to use LaTeX for showing math formulas, I have found the online LaTeX Previewer extremely useful. You type in LaTeX, hit a button, and it shows you what it looks like.
Summations / Sigma Notation
May 1st, 2009 / 1 Comment » / by Chris
A few years ago I had a job interview with a company that ended up being pretty math focussed. I had been out of college for a while at the time, and on a day to day basis in doing software development I hadn’t had the opportunity to exercise a lot of the math that I had learned while in college. At some point in my life I had taken: Calc, Calc II, Linear Algebra, Discrete Math, and some others…but because I haven’t been using it, my math knowledge had kind of gone down the tubes.
So when I was asked a question about summations, I was kind of stumped. Now that I’ve started reading a algorithms text book, I’m running into summations all over again. In my search to re-learn them, I’ve found the following sites useful:
- Paul’s Online Math Notes – Prof. Paul Dawkins, of Lamar University, has a great math site, and has a good, short, re-introduction to summations here.
- PlanetMath’s Summation Page – PlanetMath has a good page on summations that goes a little more into detail on some summation properties and useful formulas
- Summation Formulas – Good outline of summation formulas
What I haven’t been able to find is a page explaining how the solutions for common summations is found, such as the one for a simple summation:
I’m not sure how that formula is reached, but I’m sure I’ll be trying to figure it out soon.
Update: Finally found a good description of the steps in solving the summation above, here’s my attempt at explaining it:
Byzantine Generals
April 30th, 2009 / No Comments » / by Chris
Article on the “Papers in Computer Science” blog about the Byzantine Generals problem. I like the summary on the blog of the problem, but I found the referenced paper a little hard to read at first, might just need to spend more time with it.
The Byzantine Generals problem is an exercise in fault tolerance and dealing with conflicting or even malicious behavior/messages in a distributed system.
Google’s BigTable
April 30th, 2009 / No Comments » / by Chris
Google’s BigTable is (was?) their approach to storing and accessing petabytes of data in a decentralized and highly-available way. At the most basic level it’s a properties system of keys and values, but goes way beyond that. It also provides mechanisms for spreading the data across thousands of machines while giving programmers an easy API for editing and reading data from the tables. Here’s their description of it:
Bigtable is a distributed storage system for managing structured data that is designed to scale to a very large size: petabytes of data across thousands of commodity servers. Many projects at Google store data in Bigtable, including web indexing, Google Earth, and Google Finance. These applications place very different demands on Bigtable, both in terms of data size (from URLs to web pages to satellite imagery) and latency requirements (from backend bulk processing to real-time data serving). Despite these varied demands, Bigtable has successfully provided a flexible, high-performance solution for all of these Google products. In this paper we describe the simple data model provided by Bigtable, which gives clients dynamic control over data layout and format, and we describe the design and implementation of Bigtable.
The paper isn’t too long (14 pages or so) and isn’t too hard to digest. You can read it here
First Post.
April 29th, 2009 / No Comments » / by Chris
I’ve been scouring the web off and on lately looking for interesting things to read. The kind of things that you’d book mark in a “Read Later” folder. Most of these things tend to be computer/programming related. I did a quick search on Google and Google Reader to see if I could find another blog out there that sort of cataloged these things, but I didn’t have any luck.
So I thought I’d start one.
This blog will generally be for posting links to, and maybe some reflection on, other peoples content: the kind of stuff I find interesting from a technical standpoint, stuff like papers and theory and whatnot. Stuff like white papers, pages on algorithms, articles about stuff I learned in college but have forgotten about, blog posts about some new take on software development process…really just about anything I think other programmers might find interesting to read about.
