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When learning Calc, I always appreciated anyone who could teach the main points without slipping into formal textbook descriptions and terminology. The more advanced one gets in Math, (eg, your teacher or professor with an advanced Math degree), the more they tend to do it, even of they try not to.

I like this text - reminds me of "the complete idiot's guide to calculus" which I used as a companion to my Calc textbook (Stewart) when learning. Not sure I would have faired as well without it.

https://www.amazon.com/Complete-Idiots-Guide-Calculus/dp/002...

It gives a great and sometimes humorous understanding, which formed a nice framework when I moved on to Vector Calc, Differential Equations, etc later on. At that point in your math career, you can't (or shouldn't try to) rely on mindless algorithms/processes to solve problems like you may have in high school. You've got to understand what you're doing.

Ps, I doubt many on HN really needed to hear that, but it may be a useful note for somebody.

⬐ zamalek

> appreciated anyone who could teach the main points without slipping into formal textbook descriptions and terminology

This is why I can't impart knowledge at all. I get too technical. When I'm in a mentorship position, I need to be pair programming, and I need to be hands off the keyboard. Getting me to explain anything is a fruitless exercise.

And that's fine: not everyone has to be destined to be a teacher. It is important to know that you are not (if you are not), and to thoroughly appreciate those who are.

⬐ hdjjhhvvhga

> not everyone has to be destined to be a teacher. It is important to know that you are not (if you are not), and to thoroughly appreciate those who are.

Well, this should be understood, but it's not. Especially in the current academic setup the professors - experts in the field - should have the skill to transmit their knowledge to students. Unfortunately, many spectacularly fail. They'd better focus on research and leave the job of teaching to more able individuals.

My pet peeve is linear algebra. You can present it in an extremely boring way, and this is what most professors do. It's like they wanted to make this fascinating subject as repulsive as possible. Maybe you could get away with it 50 years ago, but now we have all the tools and areas of application that make teaching linear algebra in the old way a crime.

⬐ katzgrau

Linear Algebra was another one I had a tough time with until I found the right "teacher."

Gilbert Strang's MIT Open Courseware series to the rescue. He wrote the textbook I was using and was also pretty entertaining. My college professor made the concepts sound terribly complicated, but Strange made them highly approachable and interesting.

⬐ hdjjhhvvhga

Some quotes from his "Notes on Group Work":

> I am convinced by the experience of others: It is good for students to work in small groups. There are so many reports about the success of this idea that it has to be accepted as valuable. It will be implemented in different ways, and the comments from Ithaca about group projects are representative:

> "The approach changed the students' attitudes toward mathematics. The projects engage the curiosity of the good students and challenge them, but this does not come at the expense of average and weaker students. In fact, cooperative work with good, motivated students bolsters the others.'

> "A common fear about groups is that one student may do nothing but still get the same grade as the members who did all the work. This has not been a great problem . . . (others say the same). Students experience cooperative learning. They talk to each other about mathematical ideas and they form friendships with other mathematics students."

> I personally believe that we too often lose sight of the human part of learning mathematics.

⬐ hdjjhhvvhga

This is a very important point. Because of the "curse of knowledge", at a certain point you are unable to communicate the subject you're expert in to beginners. That's why one of the best ways to study is with your peers: the one who gets it first has the best chances to transmit their aha moment to their colleagues.

It's difficult because to get to the level of a beginner you need to force yourselves to make many oversimplifications, moreover, you have to deliberately be imprecise otherwise people won't understand you. But some people do have this talent: even though they are experts, they still can transmit their knowledge at various levels of difficulty. Keith Devlin is one. Feynman of course.