Learning Advanced Math During a Break

In summary, the speaker has taken several math courses including algebra, trigonometry, and calculus, and plans on reviewing those subjects during their break. They are also interested in learning a new topic such as discrete math or set theory, and are open to book recommendations. The speaker suggests books for calculus, linear algebra, discrete math, and set theory, and also mentions the possibility of exploring abstract algebra.
  • #1
Miike012
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The courses I've taken are algebra, trig, calculus 1 and 2 with analy. geometry and elementary linear algebra. Now that I have a three month break I plan on reviewing calc 1 and 2, and linear algebra. I would also like to learn a new topic but I don't know what subjects would be in my range of experience. I was thinking discrete math or set theory. Would those topics be difficult to learn on my own? Suggestions on other topics are welcomed.
 
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  • #2
No, it wouldn't be that difficult to learn on your own. Would you like book recommendations for the topics you listed??

Calculus: Now that you already know the basic calculus, I think Spivak is well within the range of your abilities.
https://www.amazon.com/dp/0914098918/?tag=pfamazon01-20

Linear algebra: Try Friedberg or Lang.
https://www.amazon.com/dp/0130084514/?tag=pfamazon01-20
https://www.amazon.com/dp/1441930817/?tag=pfamazon01-20

Discrete math: I learned the topic from Grimaldi's book and it was quite good. The book by Knuth is also quite popular.
https://www.amazon.com/dp/0201726343/?tag=pfamazon01-20
https://www.amazon.com/dp/0201558025/?tag=pfamazon01-20

Set theory: You probably mean a basic proof book. I think Velleman covers quite a lot of set theory so that would be a good first book.
https://www.amazon.com/dp/0521675995/?tag=pfamazon01-20

As for other topics. You might want to look at abstract algebra. A decent first book is Pinter: https://www.amazon.com/dp/0486474178/?tag=pfamazon01-20
 
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Related to Learning Advanced Math During a Break

1. How can I effectively learn advanced math during a break?

There are a few strategies you can use to effectively learn advanced math during a break. First, make a plan and set achievable goals for yourself. This will help you stay organized and motivated. Second, try to practice regularly and consistently, even if it's just for a short amount of time each day. Third, make use of online resources and tools, such as video tutorials, practice problems, and online forums for asking questions and getting help. Finally, consider seeking out a tutor or joining a study group to supplement your learning.

2. Is it possible to learn advanced math on my own during a break?

Yes, it is possible to learn advanced math on your own during a break. However, it may require more discipline and self-motivation compared to learning in a traditional classroom setting. It's important to have a strong foundation in the basics of math and to seek out resources and support when needed. Don't be afraid to reach out for help or clarification if you encounter difficulties.

3. How much time should I dedicate to learning advanced math during a break?

The amount of time you should dedicate to learning advanced math during a break will depend on your personal goals and schedule. It's important to find a balance between studying and taking breaks to avoid burnout. Aim for at least 30 minutes to an hour of focused studying each day, but adjust this time as needed to fit your schedule and learning pace.

4. What are some ways to make learning advanced math during a break more interesting?

There are a few ways you can make learning advanced math during a break more interesting. One way is to try to relate the concepts to real-life situations or applications. This can help make the material more relevant and engaging. Another way is to mix up your study methods by incorporating visual aids, hands-on activities, or games into your learning. Additionally, taking breaks and switching up your study environment can help prevent boredom and keep your mind fresh.

5. Can learning advanced math during a break improve my overall math skills?

Yes, learning advanced math during a break can definitely improve your overall math skills. By challenging yourself with more complex concepts, you can strengthen your critical thinking, problem-solving, and analytical skills. These skills can then be applied to other areas of math and even in other subjects or real-life situations. Additionally, learning advanced math can also boost your confidence and build a stronger foundation for future math courses or career opportunities.

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