Math

Arithmetic and later Mathematics were my best subjects in School, both in terms of my interest and the marks I received. Grade 9 Mathematics especially stands out as the whole year was dedicated to Geometry, a personal favourite.

University Mathematics was a different story. My troubles began with Math 120, the only course during First Year that ended in December 1970, taught by a Prof who was hard to understand and covered little, if any, of the material on the exam. The results of the final exam taught me an important lesson: read the textbook; just listening to the Prof is not good enough. It was the only university course that I ever failed, though I made up for it by studying the text book for two weeks and scoring a 90% on the Supplemental Exam written in indoor temperatures approaching 100ºF in August 1971.

Calculus was another story. High School had left me with no reason to be alarmed about the subject, having completely covered the subject of Differentiation and even got a good start on Integration. Despite three full years of Integration in UBC Math courses, I never was able to master that part of Calculus, but somehow managed to pass all three courses.

The third of those three courses was a classic case of False Advertising. Discrete Random Processes was the name of that Third Year Math course. Within the first of the eight months of the course, Discrete Random Processes were completely covered and we moved on to Continuous Random Processes, which is based on Integration. That surprise turn of events occurred just days after the deadline to switch courses.

Then a pair of happy coincidences happened. The Vancouver Bus Drivers went to strike and Vancouver got a lot of snow that year. The Professor’s sports car immediately got stuck when there was any snow on the road and he could not take a bus, so he was invariably very late for his 8:30 a.m. class, my dreaded Third Year Math course.

The Prof felt so bad about being late so often that he gave me a passing mark on my final exam even though all of the questions required a numeric answer, and I wrote essays for each question explaining how I would figure out the answer if I knew the formula and could do the Integration required, which I did not and could not.

Not that Mathematics did not play an important role in my UBC education. It was Math 140 that first introduced me to computers and convinced me to switch my Major to Computer Science. Linear Programming was the title of the course and involved finding the best solution to The Traveling Salesman Problem and other situations with a large number of potential solutions. A modern, but much more complex, equivalent is faced by worldwide Courier companies: how to minimize the distance traveled by all of its vehicles while doing all of its pickups and deliveries each day. There are millions, perhaps billions, of ways to Route the fleet of vehicles.

Another excellent UBC Math course was Arrays and Matrices. It has helped immensely over the years as they are also powerful concepts in Computer Programming.

I found that the most useful Mathematics at UBC though was taught in Computer Science classes or learned from doing projects for these courses. Including:

  • Arithmetic in Number Bases besides 10, most notably 8 (Octal), 16 (Hexadecimal) and 2 (Binary), which was essential for analyzing Computer Memory Dumps of running programs;
  • Boolean Logic, to get the correct sequence of NOT, AND and OR in a complex IF statement;
  • How to calculate the day of the week for any date between 1900 and 2099;
  • The existence of fairly accurate methods of estimating the value of types of Mathematics that cannot be done directly on a computer.

The Math course I must regret not taking was Statistics and Probability. I actually pushed quite hard to take it in Second Year but could not get approval to take one extra Unit over the standard 15 Units of coursework per year. Thanks to my initial failure, discussed above, of a Math course in First Year.

The one Math course that I am glad I did not take was the only undergraduate course that UBC offered in Geometry, my favourite, as mentioned above. A friend took it, even though he had not taken any Geometry in High School, thanks to a move between Quebec and Ontario school systems. After a brief review of Planar Geometry, this course spent the rest of the year on Geometry on a spherical surface. You would think that, given that the Earth is a Sphere, this would be useful, but Surveying and all other practical applications use Planar Geometry.