#274 overall
18.006 Calculus Revisited
MIT OpenCourseWare
2 recommenders · 2 threads · recommended in 2 years, 2012–2017 · score 1.8
A single-variable calculus course from MIT OpenCourseWare, taught by Herbert Gross, that revisits calculus concepts with an emphasis on building intuition alongside rigour. The lectures were originally recorded in 1973 and are republished on OCW.
Commenters call it one of the best calculus lectures they have seen and cite it as an example of building intuition without sacrificing rigour.
Mathematicsintermediatefreevideo lectures#calculus#single variable#intuition#rigour#herbert gross#mit ocw
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20062026
Herbert Gross MIT Calculus Revisited - is one of best lectures I have seen, and it is recorded way back in 1973.
I think you are talking about a different thing than I do. I have nothing against demanding some rigour in reasoning very early on in mathematics courses, what I am concerned about is the purely formal presentation of mathematical concepts, especially those that were first discovered by studying physical or geometrical situation and which naturally arise in such contexts. For example, is the formal epsilon-delta definition of a limit the best way to begin a calculus course? Yes, this is logically one of the basic building blocks of the theory, but what value does it have pedagogically for a beginning student? It is known that learning happens to a large degree via associating new concepts with ones already known, what can such a definition be associated with? This is carried out to extremes some times, I've seen introductory calculus books replacing sentences in natural language with formal-logic apparatus like quantifiers etc. and advertising it as some great pedagogical improvement.
Those are in my opinion excellent examples of courses developing intuition without sacrificing rigour:
http://ocw.mit.edu/resources/res-18-006-calculus-revisited-s...
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
I also love the books by Richard Courant for how they manage to explain the concepts in crystal-clear English writing, present both the applications and the theory, building up the rigour gradually.