By the end of the course the student should be able to:
Be able to apply correctly the notion of divisibility to prove basic theorems concerning the divisibility of integer numbers.
Be able to apply correctly the Division Algorithm to calculate the greatest common divisor of two given numbers and its application to the resolution of Diophantine equations.
Be able to apply correctly the notions pertaining to modular arithmetic to prove basic theorems and its applications to elementary hashing functions and its use in cryptography, the use of modular arithmetic in daily activities such as check digits in area such as banking, and universal product codes.
Be able to apply the notion of prime number and make use of the Fundamental Theorem of Arithmetic in the calculation of number factorization and calculus of the greatest common divisor and least common multiple of some given numbers.
Be able to apply computer arithmetic with large numbers and its application in cryptography in particular the RSA algorithm.
Be able to do basic matrix operations (addition, subtraction, multiplication, transpose, and power) and the application of matrices to cryptography and graphs.
Recursive algorithms and, in particular, in the resolution of recurrence relations of linear homogeneous with constant coefficients and some of its applications.
Apply correctly counting principle in the resolution of combinations and permutations.
Apply correctly the Pigeon Principle and the Binomial Theorem in the resolution of combinations and diverse application where calculation of estimate may be necessary.
Know the basic terminology of graph and recognize special types of graphs as well as how to represent these different types of graphs and know some of their basic applications.
Able to calculate Euler and Hamilton path in a given graphs.
Able to calculate the shortest-path in a given weighted graph.
Be able to traverse binary trees using the schemes of preorder, inorder, and postorder.
Be able to write a given infix arithmetic expression in Postfix notation
Be able to evaluate an arithmetic expression in Postfix notation.
Be able to find the binary tree representation of a given expression in Postfix notation.
Be able to find a spanning tree in a simple graph and some of the application of spanning trees in computer science.
Be able to recognize basic types of phrase-structured grammars and the language generated by these grammars.
Be able to find the top-down derivation tree of a sentence in the language generated by a grammar.
Know if a given string is in the language generated by regular set
Be able to find the equivalent finite state machine of a given phrase-structured grammar.
Created a station on
pandora based only on the JJ Cale song "Travelin' Light." Listened to it all day today. A lot of the tunes I have been soaking in lately are just too digital and beat-driven. Listening to bald monkeys banging on stuff and howling has been nice. As the summer grains funnel down to nothing in the top half of the hourglass, that's when commitment becomes a flock of geese in my rotary engines... that is to say that I start building this two column list, on one side being the things I'd like to be doing and on the other side the things that I will be doing instead. It's easy for me to hear this sort of complaint from someone else and then say "well, make the necessary changes..." All of these pesky goals, hopes, and dreams are coming to unexpected fruition with the momentum of an intergalactic 50-ton monolith. Not really enough free spirit left to even climb to the front seat and make changes at this point. I'll poke my head out of the executive porthole when the humidity has become more reasonable and the leaves begin to change. I hope you're there to share a hot cider and a hike at that juncture. Knit me a scarf, I don't care about the color scheme.
Not deceased yet. Undergoing major surgery. Potential loss of personalized content, to be replaced with buzzwords, jargon, and marketspeak. Lust for life downgraded to desire for nicer sofa and new sunglasses. Let's call it a lifestyle lift. Working on starting a corporation with friends to exploit and extort the people and the planet. Seriously you guys. Got promoted at the 9-5 to something a lot more challenging and related to my computing interests. School gets officially hard starting at the end of August. Insurance premium raised on account of me backing my new car into a PARKED EFFING CAR. All sports on hold due to bulging disc except swimming and walking. Is walking a sport? It is when you sit on your duff as much as I do. About to become an expert on patio furniture and storage buildings, just you wait. Feeling gimpy and unstoppable at the same time. See you at Karaoke.
There was a problem with the way I imported the blog from my server to the google hosted version. It broke all my image links. I had to export it and do a global search and replace on the xml file and re-upload it. In short, this means all of the old posts are now illustrated beautifully again. Hey - thanks for being such a great blog reader. I mean it. Without you, I would probably pull out my own fingernails and feed them to a sea turtle.