Searching for an Algorithm - Week of Oct 22

Now that we have covered algorithms in class I have started to think of a problem which I could try to develop an algorithm for.  I worked through the paper folding exercise given and got some practice working with the patterns and trying different approaches to the same problem.  What I liked in particular about the paper folding algorithm was that it mapped a natural number n to a pattern.  That one single number can contain not only the number of up folds and down folds, but the order that these folds appeared in as well, that really impressed upon me how powerful algorithms can be and given on of these 'recipes' how much information can be stored in a single number.

A problem that I would like to solve myself goes as follows:

I want to arrange bottle caps into pyramids.  I will start by making an equilateral  triangle of bottle caps with side length n (where n is some natural number of bottles caps, it would be tough to use a fraction of one or a negative number of caps) then I will make another such triangle with side length n-1, then stack this smaller triangle onto the larger one, and repeat until I get a triangle of side 1 on the top (not much of a triangle I know but none the less).  I want to know if I start with a side of n caps, how many bottle caps will it take to finish the pyramid.

I will probably try and solve in by considering the total number of bottle caps in each level and then add the levels.  Maybe I could come up with equations analogous to area and volume for the triangles and pyramids respectively.  Also I could make a chart of different values of n and the corresponding values for the total number of caps and even some other values might be helpful.  I will work on this here and there and see if I am any nearer to a solution next week.

Theo

Post Term Test - Week of October 15th

With the first term test in the rear view it feels like we are really in the thick of things now.  The test didn't have any questions that I felt were unfair or unreasonably difficult.  Much to my surprise I froze on the binary multiplication, it wasn't that it was in base 2 (that as I've said I am fairly comfortable with) but I forgot how column multiplication works!  I'm sure I could have worked it out but for the time constraint.  An hour goes by pretty quick when your writing a test and I felt that even another 15 minutes would have given me a chance to review my answers and catch anything I missed.  All in all though it was a fair test and I can't complain. I am going to put a little more emphasis on this weeks tutorial exercise this week than I have in the past.  By working on it tonight I can get a feel for wether or not I will be able to finish the exercise and grasp the concepts in the one hour of the tutorial on wednesday or wether I will need to commit more time to it.  I think that becoming more comfortable with the tutorial exercises will better prepare me for the next term test.

Theo

Base 2, DrRacket... and SLOG? - Week of October 8th

This blog is a first for me so I am not sure exactly what I am supposed to say to whom, so I will start by introducing myself.  My name is Theo and will be keeping a course log (or SLOG if you prefer, I don't) for CSC 104.  I am a first year student in math and physics just to give some perspective.

I'm kicking myself for letting this assignment sneak up on (and past) me, as I am working on this a day late.  The biggest pitfall for the one day a week class has been letting myself forget about it until the day of.  I have decided to put a reminder in my calendar to check the course website at least one other time during the week.

So far the course content has been manageable.  The history covered in lectures in interesting though I am glad it is kept brief.  Fortunately I have seen fields in base 2 in my Math courses already so this is one less thing to worry about.  If I have any advice for people who are struggling with the idea, it would be to consider the similarities with base 10 (regular every day numbers), the two really aren't as different as they seem at first.

DrRacket on the other hand has been a small but very real source of stress for me.  The tough thing for me is to remember the different functions and how they work with each other.  For instance, rotating an image counter-clock wise was simple and given in the tutorial exercises, but trying to remember how to rotate an image by degrees was a fruitless endeavour. Armed with only the word rotate, an image, and some number of degrees, I tried a variety of different combinations with no success.  To remedy this I will be making more use of the picturing programs pdf.  As if that were not frustrating enough, DrRacket (and I suppose programming in general) is so incredibly pedantic that nothing seems to work on the first try, and rarely the second.  One redeeming value however is receiving an error message that tells you what it is that is not working.  That is a luxury I do appreciate.

This brings to an end my first weekly log for the course, hopefully I don't get drilled too badly for being a little late with my first entry.  Good luck to everyone with the test tomorrow!

Theo