If you were asked to build a modern math syllabus what will you include?

Question

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.

mikewarot · Accepted Answer

There'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.

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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.

defterGoose · Answer

Set 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.

gus_massa · Answer

I'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 · Answer

Gilbert 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.

jstx1 · Answer

The 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?

tomcam · Answer

Stats

Normille · Answer

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