Efficient Ways to Study/Learn College Math?

In summary, learning math concepts the "proper" way by visualizing the applications and solving problems with intuition can be a more efficient way to learn.
  • #1
Mathnomalous
83
5
Looking for efficient ways on how to properly learn algebra, calculus, and more advanced math branches necessary in engineering and science. At the moment, I follow the instructions taught in class and repeat them as necessary. Perhaps not a good approach since there are many ways to tackle math exercises and I don't feel I'm developing problem-solving skills beyond what I'm taught. I feel like a drone following directions while the people around me understand the concepts and how to branch off of those concepts.
 
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  • #2
Intuition comes after you do the 1,000th homework problem. Approximately.
 
  • #3
Do as many exercises as you can.
That's the only way...

When I first studied calculus, I didn't understood much of it.In fact, I felt like a robot. Don't feel worried if you haven't mastered all the concepts yet. You say you want this math for
applications in science and engineering. I understood Calculus concepts better when I started seeing these applications. That was when I started enjoying it.
 
  • #4
Thanks for the replies. Your advice generally falls in line with what my current math professor expressed to me. I can definitely vouch for doing as many exercises as one possibly can; that factor has helped me recognize patterns here and there in more difficult exercises. That should be good, no? Math seems to be all about patterns.
 
  • #5
Tinyboss said:
Intuition comes after you do the 1,000th homework problem. Approximately.
No, not really.

Or at least I really want to believe that there is a better way for people. I see them droning away solving problem after problem and afterwards they still lacks any form of deeper understanding.

I would say that the best way to learn it (Engineering maths) is something like this:
Learn the intuitive explanations. Understand the intuitive explanations. Visualize them. Try to visualize the problem before you do it, when you do it think in your intuitive terms what you are actually doing, then you should understand that it is all actually trivial. When you get to that point you are done.

Just hacking away at a lot of problems trying to get better at maths is like flapping around your arms randomly trying to get stronger arms.
 
  • #6
I agree you should also get some intuition. But calculus is not that intuitive for the beginner, so don't worry too much about it now. You may even understand the concepts, but many of them will only become natural to you after you've seen the applications. Since most calculus books I've seen focus on getting the answer right (and many teachers too), I think now you should focus in the methods (even though some of the most obscure ones are rarely used) and a bit of intuition (like the relation between integrals and area, how to find the formula for the volume of a cone/sphere using integrals, the relation between position, velocity, acceleration and derivatives, intuition about epsilons and deltas (for limits)). That amount of intuition should be enough for getting good grades and passing the course (unless you are in a really demanding course). Believe me, when you see the applications of it, your intuition will naturally develop (and you'll have many A-HA! moments).

This is also valid for other branches of mathematics: multivar calculus, linear algebra, differential equations... I've done that way, and it worked really nice.
 

1. How can I improve my understanding of college math concepts?

First and foremost, attend all lectures and actively participate in class discussions. Additionally, practice regularly by solving problems, reviewing notes, and seeking help from peers or professors when needed. Consider joining a study group or seeking tutoring services if you are struggling to understand certain concepts.

2. What are some efficient study strategies for college math?

Some effective study strategies for college math include creating a study schedule, breaking down complex concepts into smaller, manageable parts, and utilizing visualization techniques such as diagrams or graphs. It is also important to review material frequently rather than cramming before exams.

3. How can I retain the information I learn in college math?

One way to retain information in college math is to actively engage with the material rather than just passively reading or listening. This can include taking detailed notes, summarizing key concepts, and teaching the material to someone else. Additionally, practicing problems and explaining the steps to solve them can help solidify your understanding.

4. How can I stay motivated while studying college math?

Staying motivated while studying college math can be challenging, but setting specific and achievable goals can help. Break down larger goals into smaller, more manageable tasks and reward yourself after completing each one. It can also be helpful to remind yourself of the importance and relevance of the material to your overall academic and career goals.

5. What are some resources I can use to supplement my studying for college math?

There are many resources available to supplement your studying for college math, such as online tutorials, textbooks, practice problems, and video lectures. Your professor may also provide additional resources or recommend specific textbooks or websites. It can also be beneficial to seek help from a tutor or attend review sessions offered by your university.

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