What is the MIT style of teaching calculus?

11 points by crypticlizard 7 years ago | 5 comments

I recently heard from a student at my college that the teacher I'll be taking for Integral Calculus mentions from time to time, "I teach Calculus the MIT style." Can anybody tell me what that means?

todd8 7 years ago |

I was a math major there. Each math professor had his own style for the smaller classes. There wasn't really a consistent teaching style for my classes except that they were challenging. Every student had to take a year of Calculus and a year of Physics and a semester of Chemistry among other general Institute requirements so the classes were very large, the teaching was top notch, and the problem sets were the first time most of the students had really been challenged at that level. Quizes and Exams were very hard.

However, first year Calculus is totally doable as long as you have a solid high school math background (polynomials, trig identities, etc). I recommend (and I'm not joking) buying the physical textbook and doing every problem--not every problem assigned--every problem in the book. This will take a few extra 8 hour days of work, but practice, practice, and more practice will make you faster and more able to do the test problems. You may not have a physical text book or you may not like the text in which case look for additional books to use. Schaum's Outlines for Calculus at various levels are good sources of problems to practice on and they have the answers to all problems in the back. Do every problem you can and get help to understand the one's that stump you. Do a few hundred more problems than your classmates and you can expect an A. Like golf, extensive practice will improve your test scores.

If you are unsure of your preparation for the course get Schaum's Outlines for the prerequisite course and do hundreds of review problems so you're ready for Calculus.

One other piece of trivial advice is to buy a ream or two of plain copier paper; loose paper always worked better than pads for me because it was less expensive and I could spread out my work. Write on only one side of each sheet, otherwise the flipping back and forth looking for some work you've already done is too distracting. Pages containing final answers to turn in for homework problems can be creased/folded along a vertical axis so they are easy to distinguish from the pages laid out for work on subsequent problems.

A 0.7mm mechanical pencil with a good sized eraser works well for lots of math (although some like yellow wood pencils). I learned to use ballpoint pens for math and engineering at MIT because crossing out is faster than erasing, but I believe that this is a minority opinion.

impendia 7 years ago | |

Great answer, and let me add one thing, if OP has the opportunity and desire to prepare in advance.

Usually the hardest thing about calculus is the precalculus. All sorts of algebra and trigonometry problems appear in the course of calculus problems, and if you can solve them reliably and quickly then you can concentrate on the calculus.

I'd recommend buying any precalculus book -- look for used copies of edition n-1 on Amazon, where n is the latest version - and doing the hardest exercises. These will be starred, and/or at the very end of the section. A great way to build up your chops.

dmlittle 7 years ago |

The only difference I know of is that "all of calculus"[1] is covered in 2 classes, 18.01 (single variable calculus) and 18.02 (multi variable calculus), instead of the more common Calc 1, 2 and 3. Each class also has different variations that covers the same material in a more in-depth theoretical manner (18.01 vs 18.012 and 18.02 vs 18.022). Other than that, the material covered is the same.

You can find the material for both calculus classes in OCW:

- https://ocw.mit.edu/courses/mathematics/18-01sc-single-varia...

- https://ocw.mit.edu/courses/mathematics/18-02sc-multivariabl...

[1] By "all of calculus" I mean the required calculus classes to get a degree. You can definitely take more theoretical or advanced classes.

Source: I'm an MIT alumni and I guess I took calculus the "MIT style" way

impendia 7 years ago |

As a math professor, I'd recommend contacting this professor, mentioning that you're going to take the class, and asking them. Along the lines of todd8's advice, you might ask for advice on how to best prepare.

These are the sorts of questions that professors tend to appreciate.

diehunde 7 years ago |

I don't know but there are calculus courses from MIT on youtube. That might give you a hint.