Self-Study Plan: Advancing Math and Physics for a College Freshman

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In summary, a freshman in a community college, second semester, graduated high school 4 years ago and is currently taking calc 3, differential equations (no partial), and linear algebra. He is waiting for the semester to end so he can take exams and has all the free time he could want. He wants to use this time to learn math and physics as fast as he can, but is not sure which order to follow. He should start with calculus on manifolds and real analysis, and then move on to abstract algebra, probability theory, and set theory/logic.
  • #1
MetalManuel
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Currently a freshman in a community college, second semester. Graduated high school 4 years ago, so when I came to school again it was weird. I had taken ap calc in high school, so I went into calc 2 and calc physics 1 and got A's quite easily.

It boosted my ego and now I think I am some sort of genius haha. I want to challenge myself and see how fast I can learn math and physics. I am in calc 3, differential equations (no partial), and linear algebra right now. I finished learning the course work last month for the semester so now I am waiting for the semester to end (waiting for the time to come for exams).

I have all this free time now, but I want to use it to go ahead and teach myself math and physics as fast and as high as I can, but I am not sure which order I should follow.

In what order should I teach myself math and physics, all the way to the advanced grad work? I know em is next for physics, but I am not sure what math would go with it.
 
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  • #2
Calc physics 2 is intro E&M as you know. Based on the info in your post, you certainly have covered enough calculus to do freshman E&M. I'd start reading ahead on that material.

When you make it through that, the next topic would be sophomore level modern physics. You should be able to easily figure out what modern physics book your school uses, and read ahead from that.

Be careful not to burn out before your exams!
 
  • #3
What mathematics goes with each physics course past EM? Math and physics go hand in hand, so I feel like you didn't give me the whole story.
 
  • #4
Only for mathematics:

I think you may be ready for "Calculus on Manifolds" by Spivak. Or some real analysis.
After this would follow topology and differential geometry.

Other math that you could look at, but which aren't immediately useful are abstract algebra, probability theory and set theory/logic. You can start any of these at any time. But if physics is your goal, then these aren't immediately useful...
 
  • #5
Thanks, physics is my goal, but i feel I should be strong at math as well even if they aren't directly related. Differential geometry sounds fun.
 

FAQ: Self-Study Plan: Advancing Math and Physics for a College Freshman

How can a self-study plan help a college freshman advance in math and physics?

A self-study plan allows a college freshman to take control of their own learning and progress at their own pace. By following a structured plan, students can focus on areas they struggle with and spend more time on topics they find challenging. This can help them gain a deeper understanding of math and physics concepts and improve their skills in these subjects.

What should be included in a self-study plan for math and physics?

A self-study plan should include a list of topics to cover, resources such as textbooks and online materials, and a schedule for studying and practicing. It should also include goals and objectives, as well as a way to track progress and make adjustments as needed.

Is a self-study plan suitable for all levels of math and physics?

Yes, a self-study plan can be tailored to fit the needs of students at any level. It can be used to review basic concepts or to tackle more advanced topics. The key is to create a plan that is challenging but achievable for the individual student.

How much time should be dedicated to self-studying math and physics?

The amount of time needed for self-study will vary for each student and will depend on their goals and current level of understanding. However, it is recommended to dedicate at least 2-3 hours per week for each subject. Consistency is key, so it is important to establish a routine and stick to it.

Can a self-study plan replace traditional classroom learning?

No, a self-study plan should not be seen as a replacement for traditional classroom learning, but rather as a supplement. It is important for students to have access to a teacher or tutor for support and to have opportunities for hands-on practice and application of concepts. A self-study plan can enhance and reinforce what is learned in the classroom.

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