As I get deeper into AI, I realize that there was a math class I never had which would have been incredibly valuable as an undergrad. ??This class should have been day 1 of my undergrad, perhaps repeated every year, and certainly addressed for 20-30 min of each math course I took. ??That class would simply be a survey of mathematics, or maybe just, math from 10 000 feet.
As I dig deeper into unsupervised learning approaches, the solutions combine statistics with calculus and also require algebra to resolve. ??The intuition for many of the solutions comes from graph theory and geometry. ??Practical approaches require computational mathematics, statistics again (for estimations and acceptable error), and signal processing. ??Finally, truly practical applications often require computational resources and data stores that are enabled by (to be grossly general) computer science while delivering them on schedule and in a maintainable state is software engineering. ??
I disliked most of my math classes through college. ??Many of my professors were very poor teachers which was compounded by their poor command of the English language. ??The courses were poorly organized, exams poorly written, and notoriously hard to study for. ??As an example, my Stats 231 (stats 2 for math majors) final exam was worth up to 80% of my mark, but marked out of just 38. ??It was written by another prof, and required the cumulative learnings from stats 1 and stats 2, but advertised as not retesting material from stats 1. ??A very unpleasant experience at the time, but quite successful at failing at least 10% of the class, which is about right. ??(For reference, I started with somewhere in the neighborhood of 1000 students in my major, and somewhere around 600 graduated.)
I feel that keeping the bigger picture in view — applications of the math we were learning, or maybe starting with 1-day intro to AI or other advanced topics and just point out the math needed to go into them — would have been immensely valuable.
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