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I have always thought that, regardless of major subject, a really good college education should include a good one or two semester course in world history. The emphasis should not be on who won which war. It should start with an estimate of prehistory based on archaeology and cultural anthropology. It should include changes in agriculture, industry, religion, sociology, and political philosophy.
Another essential course is the mechanical and electrical, but not the modern, semesters of the introductory physics course for engineers and science majors. A prerequisite is the book "Quick Calculus" by Kleppner and Ramsey. The useless bag of tricks in a typical two semester calculus course is not needed.
It is so likely that a college graduate will end up in a career that he did not major in, that he should prepare for this by taking introductory courses in as many fields as possible. Presumably algebra, trigonometry, geometry, biology, chemistry and physics were learned in high school. Linear algebra, probability and statistics, and numerical methods should be taken in college. Also, introductory courses in geology, computer programming, business and finance, economics, government, philosophy, and cultural anthropology, as a minum, should be taken in college. Attractive options are extra courses in business, social ballroom dancing, music appreciation, introductory courses in electrical engineering, mechanical engineering, civil engineering and agriculture.
I majored in physics, but could not get a job in physics. I got a job in electronic engineering, and had to learn it on the job. The only parts of my physics education that helped me were the mechanical and electrical parts of the introductory physics course. This would not have been enough had I not read the book "Dynamical Analogies" by Olson which described the analogies between mechanical quantities and electrical circuit quantities. Thus displacement=charge, velocity=current, force=voltage, mass=inductor, spring=capacitor, shock absorber=resistor, dry friction=two zener diodes back to back to back, lever=transformer, valve=transistor. The first and most useful circuit analyis technique I taught myself was two port models. Also essential, I skimmed a book on linear systems theory.
The math courses that helped directly were algebra, trigonometry, calculus only as far as what is covered in "quick calculus", and linear algebra. I was helped indirectly by a math course in advanced calculus, not because it taught me calculus, but because it taught me careful thinking. The point is, introductory courses were useful, advanced courses were not, except for advanced caluculus. One advanced course that would have helped that I did not take was matrix calculus. I gather that the same subject matter is more commonly taught as differential geometry but with different notation, a different emphasis and a different set of applications in mind. But unfortunately I did not take either.
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