One significant problem with studying mathematics or related topics is that, throughout all your years of education, nobody ever actually taught you how to study it! In my continuing quest to improve my own learning abilities, I have come across some great resources. Some of those I will mention here in future posts, but most of my summaries of the most useful concepts I am posting on my other blog, which you can find at
Even though the blog is seemingly aimed at a second-level course, I still urge you to check it out. All the concepts and techniques I discuss there are ones I use every day as a professional mathematician.
There are some great free resources listed on this course page: http://www.cs.cmu.edu/~odonnell/complexity/
Unfortunately, not all the links work, and not all the resources are free, but you might still find something of value.
One of the most famous problems in all of mathematics (and our courses) has had a movie made about it. The official website at http://www.travellingsalesmanmovie.com/ has more details.
The following link has a large list of videos online for you to watch. Some have optimisation as the focus, whilst others are just good lectures about somewhat related subjects, such as quantum computation and complexity.
Also take notice of the links on the side – there are many more interesting pages to visit.
The following link takes you to an animated explanation of Dijkstra’s algorithm. If at first it doesn’t load, just load again:
The next link has some demos of various algorithms, including Dijsktra and Ford-Fulkerson:
If you have access to Mathematica, you should take a look at
From Lance Fortnow comes “The Golden Ticket: P, NP and the Search for the Impossible”:
“The P-NP problem is the most important open problem in computer science, if not all of mathematics. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives.”
It can be bought for the Kindle at Amazon.com. It seems to be available through the Exclusive Books website as a hardcopy, but it is quite expensive. I would suggest rather buying the Kindle edition and reading it with a Kindle reading app on your PC, if you don’t own a Kindle.
The author has a complexity blog at http://blog.computationalcomplexity.org/.
Update: It is more reasonably priced on Kalahari.com than on the Exclusive Books site (like most books).