Mastering Math: Tips for Understanding and Learning on the Fly

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Learning advanced math concepts during lectures can be challenging, especially when notation and derivations seem overwhelming. Many students find that they struggle to grasp material in real-time, often needing to revisit textbooks and examples afterward. A common strategy for improvement is to prepare by reading the material before class, which helps reinforce understanding and allows students to follow along more effectively. Engaging with problems and practicing techniques outside of class is also crucial, as it builds familiarity with the methods used by instructors. Some students note that while lectures may not serve as the primary learning tool, they are valuable for clarifying doubts and solidifying knowledge. This approach is particularly beneficial for those transitioning to more rigorous university courses, where the pace and complexity increase significantly. Emphasizing preparation and practice can lead to greater confidence and success in mastering mathematical concepts.
Poop-Loops
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Ok, bad pun.

But since like Calculus in High-School (err... 3 years ago?) I've had trouble learning math "on the fly", i.e. as it is being taught by the teacher. All the notation and derivation flies over my head during class and I have to do it myself later by reading the book and doing examples. That's a waste of time. Is there a way I can "pick up" the math while it's being taught? Some way of thinking or something? How did you learn to do it?

By the way, I've already taken multivariable calc, linear algebra, and Diff EQ's (ODE's), so I'm kind of late in asking this, I think...
 
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Read the material before you go to class.
 
In your case it seems like you just need practice. The way demonstrations are conducted and the toolbox of "tricks" used in solving problems is not infinite, and after a while, you know them all and its easier (possible!) to follow what the teacher's doing as he is doing it.

But for now, the best thing you can do imo is what you're already doing, i.e. re-do step by step what is done in the book and by the teacher.
 
I agree with reading and learning the material before class. The majority of the learning does not take place in class. Class is just a way to see if you can follow the line of though, as well as making notes to some people. Although that means more time for study, sometimes, depending on who you are, it can be successful.
 
I don't look at lecture as a way of learning the material per se; I view it as a way of re-enforcing what I've already learned on my own by studying the book and working problems (lots of problems if necessary). I use lecture to clarify anything I may be confused about and solidify the things I'm fairly confident with. I find this to be the most efficient and (more importantly) effective way of learning math.
 
Poop-Loops said:
...I've had trouble learning math "on the fly", i.e. as it is being taught by the teacher. All the notation and derivation flies over my head during class and I have to do it myself later by reading the book and doing examples.

I have this exact same problem.
 
It's not a problem, it's a natural part of the learning process of advanced math/physics.
 
Well I feel really stupid when the people around me answer the professor is asking (i.e. "What goes in the denominator?", "Which is a series for...?", etc.) and I'm just stumped.

In my physics classes, I can understand it when the prof is doing something conceptual, i.e. explaining a problem like a PV chart or something, where it's not really math intensive, it's conceptually intensive. Then the notation is no longer a barrier for me.

I'll read before class, then. This is my first quarter at a university (went from a community college), and the classes are a lot harder, but I'll be damned if I'm going to fail.
 

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