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Ask HN: If you were asked to build a modern math syllabus what will you include?
Mathematics and Computer Science are inter-mingled. Both must learn areas of either. It is indeed important to learn programming to learn about modern proof assistants. Similarly to work in fields like graphics, ML computer science students must learn areas of math like linear algebra, probability, etc.
If you were asked to design a general math curriculum at university level which subjects will you make compulsory and in what order? Keeping in mind that when a student goes out after learning this curriculum, they can easily pick up new areas when needed.
- Normille 5y agoThe S
- debanjan16 5y agoThe what?
- Normille 5y agoThe S. It's MATHS with an S. Short for mathematics. You don't drop the plural indicator when you contract a word... ... unless you're an English language mangling American!
- debanjan16 5y agoHaha! Got it. No I am not American. It was a mistake.
- jstx1 5y agoThe question implies that things could be somehow improved or modernised. Pick the current curriculum of some good university like MIT for example - what do you think is wrong or missing from it?
- gus_massa 5y agoI'd like to delay integration by parts until the third year of the degree in Physics or Math, when the student must learn advanced electromagnetism or partial differential equations. For a degree in Medicine or Architecture it's probably skipable. I'd use the extra time for more exercises of integration by substitution (but not the weird ones) and to understand what the substitution means and how it works. Integration with substitution is an important topic for all degrees with a mathematical base.
- krasotkin 5y agoGilbert Strang advocates for more emphasis on linear algebra over calculus. Linear algebra is incredibly powerful stuff without even adding a computer into the consideration. The overlap here is so cool to me. Finite Elements, PDEs, and all sorts of engineering methods/tools live in the space where computer science and linear algebra overlap.
- duped 5y agoHow do you teach PDEs without calculus?
- sgillen 5y agoI think the idea is to teach less calculus, not no calculus.
- krasotkin 5y agoDefinitely not without calculus! I'm imagining an approach focusing on numerical methods that would have students working on problem sets in computer labs e.g. a first problem set might include simulating a 1-D heat equation using the finite difference method.
- defterGoose 5y agoSet theory and the basics of Modern Algebra should be taught in tandem with Type theory/objects. I feel like I "learned how to learn" quantum mechanics from Stanford's intro Java/CS curriculum. Abstraction as a subject would open a lot of mental doors for people in disparate areas of STEM I think.
- shoo 5y agoif you regard pure math as "the real thing" when it comes to mathematics, then it is a shame in my country that the first exposure that students have to this is in 2nd year of university studies, if they opt in to analysis & abstract algebra. primary school, high school and the more applied university classes drill rote learning and ability to compute, but don't teach ability to work with abstractions, unpack definitions, extend definitions to new settings, search for, present and critique proofs. from the perspective of wanting to share the beauty of pure math with a wider audience, it'd be great to introduce earlier (at least optionally). on another hand, introducing widely applicable tools for conducting and evaluating experiments would probably be far more useful to the world -- i'd be tempted to chuck out or defer a lot of early rote learning of trig, calculus, integration and replace them with probability, statistics, causal inference, experimental design. or at least offer both as different streams. arguably, this would be more useful to a lot more people than concentrating on pure math.
- mikewarot 5y agoThere's a very practical skill that doesn't appear to be taught in school. Someone, somewhere along the line needs to teach how to make back of the envelope estimates of answers to problems. You should be able to leverage what you already know and get within an order of magnitude of the correct answer. Ideally this would be something you could teach right after multiplication and division in grade school, then keep repeating through the rest of education. Teaching it at University is better than never. ---- Example: One day on the way home from work, passing a large Digital Billboard in Chicago, my friend wondered how much an Ad on one of them would cost. I did this math: Estimate the size of the billboard... 10x4 meters It has to be as bright as the sun to be seen during the day, which is 1000 watts/meter^2 Power for the sign 40,000 watts Losses for electronics, etc. 50% Total power 40kw / 0.5 --> 80kw Cost per kwh - $0.10 Cost per hour to run the sign $8.00 Cost of ownership factor x2 Cost of profit for owner x2 Cost per hour to rent (bulk) $32 Hours/month 730 (round up to 1000) Cost per month $32,000 - retail Fact - 6 to 8 ads usually rotate on a sign, costs are $1200 to $15,000 per month depending on site and market. Thus the revenue from a board ranges from $7200 to $120,000 per month. It turned out that my estimate was in the ballpark. Everyone should be able to do something like that by the time they get to University.
- jonjacky 5y agoMIT Open Courseware: Street-Fighting Mathematics "This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. ..." https://ocw.mit.edu/courses/mathematics/18-098-street-fighting-mathematics-january-iap-2008/ https://ocw.mit.edu/courses/mathematics/18-098-street-fighti...
- debanjan16 5y agoThis is something I have read people do. Napkin mathematics they call it. Richard Hamming has a chapter in the book The Art of Doing Science and Engineering. I want to learn it. This helps a lot in guessing what the results should be before we go on proving/deriving it. A hunch. A spidey sense. I like it.
- tomcam 5y agoStats