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On Learning Some Math

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On Learning Some Math AbacusWell-nighOn Learning Some Math Oct 25, 2015 In late May, I left my startup job to study math. I had been working at the startup for the past eighth months, having started in mid-September of the year before. I was one of their two backend engineers, teaming up with a remote developer in China to build out the backend for the company’s product, an iPhone game. They hired me considering I aced their coding test, and I ended up stuff directly responsible for the majority of the company’s client-serving backend. It was demanding, it pushed me, I liked it. I was moreover starting out as a part-time student in Columbia’s QMSS program, in their data science concentration. It was supposed to be a challenging track – I was warned that most students waif out. It sounded exciting. I knew my math preliminaries was relatively weak – one semester of calculus, plus discrete math. I had been fully out of school for two years at that point, so I thought I’d take it slowly and sign up for two classes. Probability and Statistics. Social Science Theory and Methods. Plus the new startup job, and the non-profit I help run. Nothing could go wrong with this plan. I am occasionally naive. The year was rough. 80-hour-weeks-every-week rough. I waif into a calculus-based statistics undertow without really knowing that much calculus. I’m pretty sure that the first time I had to unquestionably solve an integral, it was a double. Things are coming at us pretty fast. The midterm stereotype is less than 40%. I contemplate the philosophy of the letter “F”. I hustle and struggle and put in the time. Random variables, probability distributions. Independence, expectation. Samples, confidence, hypotheses. I get good at breaking big problems into smaller ones. Things come together. Everything starts to make sense. I get an A. It was encouraging. Thanks, Professor Cunningham. I didn’t like the Theories and Methods course. Mostly considering the professor thought he was too important to scarecrow preparing his lectures. I match his effort. Get an A-. By a point. I decide that’s fair. Social science is stepping into the preliminaries for me anyway. I sign up for Data Visualization in the Spring. Only one class, plus a unstudied once-weekly seminar. I am hoping for a slightly increasingly relaxed semester. Went in to data visualization the first day and immediately realized that matriculation was not worth the money. I only had a few semesters of grad school, and I wasn’t going to be wasting time. I transfer into Machine Learning. It seems the semester will be slightly less relaxed. My visitor is geting tired of my wonk activities. I didn’t particularly think it was their merchantry what I did without hours. I was exchanging ~50 hours a week of diligent labor for an 80k salary, which I thought was unquestionably pretty fair. I am pulling a lot of weight. They do not invest in my professional development. They are not interested in my thoughts on the product. They suggest that I start coming in on weekends. I know I have the smallest probity stake out of anyone there. There is no opportunity for growth. They are not making a strong case. I am wondering what lessons I should be taking yonder from this. I contemplate the increasing presence of Millenials in the workforce. I missed the first ML lecture, due to same schedule switch. I walk in fifteen minutes late to the second lecture, having gotten lost trying to find the room. I take a seat near the back, finding a spot next to a rebellious-looking kid straight out of hipster Brooklyn. I get out my notebook (an extra-large unlined Moleskine, my signature), and a pencil. I squint at the workbench and the first thing I see is some sort of upside-down triangle. The professor is talking well-nigh gradients and projections. I have no idea what is going on. For a few minutes I strongly consider walking out. I stick it out. I basically understand what is going on. The professor is very good. I can visualize shapes in three-dimensional space. I know how to square things. I wifely down. The kid next to me is funny and interesting. I end up really liking Machine Learning. It is like stuff in wizard school. There are many interesting ways to turn data into variegated data that is somewhat increasingly actionable. I use special symbols to make knowledge towards out of thin air. Hyperplanes. Prediction. Kernels. Boosting. I am very pleased with the whole thing. I get flipside A. I am heartened. Thanks, Paisley. I am starting to think that this math and computer thing is important and that I should start doing increasingly of it. My visitor is reaching the same conclusion. We part ways in May, a wifely and towardly separation. I had managed to imbricate most of the year’s tuition as well as replenish most of my savings, so I was feeling well-appointed financially. I hands had five months rent just lying around. I finger free. I decide it’s time to learn math properly. Hustling through two semesters of grad school was fine, but I want to unquestionably be good at this. I needed to know what things were, and how they worked. I wanted to learn the math that I could have learned in college, if I had been a bit increasingly mature. I thought when to the Berkeley undergraduate math sequence, specifically the lower-division requirements. 1A: Differential Calculus. 1B: Integral Calculus. 53: Multivariable Calculus. 54: Linear Algebra and Differential Equations, 55: Discrete Math. I decide that I want all of it. I had taken 1A as a freshman, driven by a unrepealable exploratory impulse that was later weakened by the pre-law GPA-protecting pragmatism. I took Math 55 as a senior, as one of the “hard classes” for my Cognitive Science major. Up until this year, I had had a fear of math as something which I would not hands be good at. I had been lazy well-nigh math in upper school; I hadn’t yet seen the point. I get to it. I plan to go to school full-time in the September. It is late May. I have well-nigh three months. I need to build a foundation. I am not interested in paying for undergraduate classes. A formal undertow would moreover be far too slow. I’ve heard of the internet. I’m motivated. I start at Khan Academy. Their streamlined towage politely suggests I review some precalculus. I am disheartened but resolved. I had copied my friend Stephen’s math homework all throughout 11th grade. Khan Academy is correct. Salman Khan walks me from the Unit Sphere all the way through Integral Calculus. Triangles, sinusoids, Taylor series, implicit derivation, integration by parts, ramified numbers, the works. I am embarassed at first – I am learning material stuff taught to upper schoolers ten years my junior. But this is the path. I take every test, solve every problem that comes my way. (I shoehorn to skipping the test for L’Hospital’s rule). Thanks, Sal. The whole thing takes well-nigh a month. I finish everything through single-variable calculus in late June. I decide to start multivariable. I uncork looking at Khan Academy’s offerings, but find them underdeveloped. It is time for something increasingly traditional. Enter MIT OpenCourseWare. MIT foresaw the MOOC revolution at least ten years early, having started putting lectures and undertow materials online since 1999. Browsing the web for multivariable calculus courses, I find a series of videos of the unshortened set of lectures of MIT 18.02, Multivariable Calculus, taught in Fall 2007 by Denis Auroux. This is right. I am worldly-wise to work through 2-3 lectures per day. A 50-minute lecture takes me well-nigh 2-3 hours to digest. I do not skip days, although on weekends I go a bit easy. I am very happy well-nigh multivariable calculus. Vectors make sense, as do their gradients. Level sets. Divergence. Flux. Curl. I get used to drawing in three dimensions. I do a lot of integrals. All of a sudden there are theorems. I yank a lot of shapes. I like the way the pencil taps versus the notebook when I am solving equations quickly. I develop unrepealable writing flourishes. Denis Auroux is a funny lecturer. I like theorems. I protract to take all the tests. I take my time with them. I enjoy them. I do pretty well. Thanks, Denis. I finish in well-nigh three weeks. It’s time for Linear Algebra. I squint online then and end up when at MIT OCW, this time at Gilbert Strang’s 18.06, recorded Fall 1999. I love linear algebra. I love Gilbert Strang. I felt transported to that classroom in 1999, learning well-nigh vector spaces and orthogonality and rank. The relationships between the various mathematical objects are rich and profound. Machine Learning is making increasingly sense. I am intrigued by the properties of determinants. I protract to process 2-3 lectures per day. In early August, I fly when to California for five weeks: Three in Santa Monica, two in Oakland, one in Black Rock City. Not a bad itinerary. My time in Santa Monica is spent riding my bike, hanging out with my parents, and finding eigenvectors. It is exceedingly pleasant. Gilbert Strang is an wondrous lecturer. I multiply a lot of matrices. “Again,” I tell myself, starting on a practice problem. “Again. Again.” I develop intuitions. By the time I get to Oakland, I have only three lectures and the final left to take. I find it markedly increasingly difficult to focus once I victorious – the excitement, reunions with friends, the venture of stuff when in the Bay, proves distracting. I struggle to focus, but sooner do power through and finish. I spend six hours on the final, sitting in a coffee shop on Telegraph Avenue. Again, I do well. Thanks, Gilbert. I want to take a moment and unclose the debt owed to these three men, and the teams which organized and published their content. The education I received would not have been possible ten years ago; someone in my position would have faced significantly greater obstacles. I finger a closeness to them, as though I had truly been their student. Thanks. I get when to Brooklyn just in time for the second day of school. My first matriculation is Advanced Machine Learning. The first lecture: a “calibration quiz” meant to prune the matriculation lanugo to size. I am anxious. This matriculation is important to me. I get in. The next installment begins. Comments Please enable JavaScript to view the comments powered by Disqus. Abacus Abacus kronovet@gmail.com kronosapiens kronosapiens I'm Daniel Kronovet, a data scientist living in Tel Aviv.