How to self-study mathematics and understand it well?

In summary, the conversation discusses the topic of self-studying math, specifically applied mathematics. The speaker asks for advice on which topics to study after AP Calculus BC and which courses to take for an applied math degree. The expert suggests looking at the syllabus of applied math courses at major universities and mentions their own experience with related courses in physics. They also caution against skipping courses in order to get ahead.
  • #1
icecubebeast
66
3
I am taking AP Calculus BC and I want to self study math so that I can be good at it.
The field of mathematics I want to study is applied mathematics. What methods are good for studying math by myself and becoming good at it? Which topics should I study sequentially after learning AP Calculus BC? By topics I mean topics that are equivalent to university math courses.

Please don't say, "It depends on the university" but say which math courses that YOU took to get your applied math degree (masters 6 year).
 
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  • #2
There's the big three: Calculus, Linear Algebra and Differential Equations...

From there math branches out in many other areas.
 
  • #3
jedishrfu said:
There's the big three: Calculus, Linear Algebra and Differential Equations...

From there math branches out in many other areas.

Which areas? Can you be specific? How to self-study mathematics and understand it well?
 
  • #4
Calculus is taught in three parts differential, integral and multivariable. Linear Algebra is a one semester course and so is Differential Equations which usually covers ordinary differential equations not partial differential equations.

Check the site: http://mathispower4u.yolasite.com/

There are videos that that cover these three courses.
 
  • #5
jedishrfu said:
Calculus is taught in three parts differential, integral and multivariable. Linear Algebra is a one semester course and so is Differential Equations which usually covers ordinary differential equations not partial differential equations.

Check the site: http://mathispower4u.yolasite.com/

There are videos that that cover these three courses.

Can you please give me a course list and specifically which topics are based on and branch out from Calculus, Linear Algebra and Differential Equations? It is because I asked my teacher and there is complex analysis, differential geometry and many other topics that I don't know. So that's why I'm asking you to be specific.
 
  • #6
I can't answer your question as I don't have an MS or BS in Applied Math. I do have a BS in Physics which is close and I got that decades ago.

From my recollection the courses I took that were related to applied math:

Calculus 1, 2, 3
Linear Algebra
Differential Equations
Advanced Calculus
Boundary Value Problems
Tensor Analysis and Differential Geometry
Abstract Algebra
Topology
Group theory

And these physics courses

Classical Mechanics with Lagrangian and Hamiltonian forms
Electromagnetic Theory used Vector Analysis
Quantum Mechanics used Boundary Value Problems
General Relativity used Tensor Analysis and Differential Geometry

My suggestion to you is to look at the syllabus for Applied Math at several major universities and piece together a list and start studying it.

Be aware though that if you plan to skip some courses to "get ahead" you might regret it because your grades will be lower overall. I know I did this, I came in as a freshman and skipped Calculus 1 because I had learned the mechanics of it over the summer but didn't know the mathematical basis for it. I traveled farther mathematically by skipping a couple of others but then started taking some really tough courses with the proper background for doing proofs and it hurt my grades because I was getting Bs when I could have gotten As with less effort taking those courses I skipped and got no credit for.
 
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1. How can I motivate myself to self-study mathematics?

One way to motivate yourself is to set specific goals and break them down into smaller, achievable tasks. This will give you a sense of accomplishment and keep you motivated to continue studying. Additionally, finding a study buddy or joining a study group can provide accountability and make studying more enjoyable.

2. What resources should I use for self-studying mathematics?

There are many resources available for self-studying mathematics, such as textbooks, online courses, video lectures, and practice problems. It is important to find resources that align with your learning style and level of understanding. You may also want to consult with a math teacher or tutor for recommendations.

3. How can I effectively manage my time while self-studying mathematics?

To effectively manage your time, create a study schedule and stick to it. Prioritize difficult topics and allocate more time to them. Take breaks and use them to review what you have learned. It may also be helpful to track your progress and adjust your study schedule accordingly.

4. What strategies can I use to understand mathematical concepts better?

One strategy is to break down complex concepts into smaller parts and try to understand each part individually before putting them together. It can also be helpful to use visual aids, such as diagrams or graphs, to better understand abstract concepts. Additionally, practicing solving problems and explaining concepts to others can reinforce your understanding.

5. How can I test my understanding of math concepts while self-studying?

One way to test your understanding is by solving practice problems and checking your answers. You can also try teaching the concept to someone else and see if you can explain it clearly. Another option is to take online quizzes or practice tests to assess your knowledge and identify areas that need more review.

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