Self studying math topics over the summer

In summary: Some other sources you may want to check out are "Calculus: A New Approach" by Stewart and White or "A First Course in Linear Algebra" by Freeman and Tukey. Some other sources you may want to check out are "Calculus: A New Approach" by Stewart and White or "A First Course in Linear Algebra" by Freeman and Tukey.
  • #1
glen37
15
0
this year I finished calculus BC, which is the equivalent of calc 1 and 2. I feel as though I've completely mastered the material and I'm ready to start moving on before I enter university next year. The next math classes I'd be taking would be differential equations, calc 3 (multivariable calculus) and linear algebra and I'm looking to get a head start on them over the summer since math is what I really want to do. I don't want to buy any textbooks for them so does anyone know good online resources for these subjects?

also I feel focusing on all this calculus business may be boring at times over the summer so I'm open to any other mathematical subjects that are interesting and I can delve into at any pace I want.

anyone have ideas? these are some interesting lectures I'm looking at right now but I really want to have a strong foundation in these topics.

http://www.academicearth.org/courses/linear-algebra
http://www.academicearth.org/courses/differential-equations
http://www.academicearth.org/courses/multivariable-calculus-1
 
Physics news on Phys.org
  • #2
I don't know about the other two, but I've watched some of Gilbert Strang's linear algebra lectures and they're quite good. My first exposure to linear algebra was a summer class (can it already be 20 years ago?) that used Strang's "Linear Algebra and Its Applications" as the text, which I enjoyed at the time:

https://www.amazon.com/dp/0030105676/?tag=pfamazon01-20

I see that the online course includes three quizzes and the final exam, but I don't see any homework problems. (But check out the final exam: "closed book, ten wonderful problems.") You will probably want to find a good source of problems if you want to gain any mastery over the material. I don't know any good online sources offhand, but if you have access to a decent library you can always borrow Strang's book.
 
Last edited by a moderator:
  • #3
I feel as though I've completely mastered the material

You haven't completely mastered Calculus until you can do most, if not all, of Spivak's problems.
 
  • #4
thrill3rnit3 said:
You haven't completely mastered Calculus until you can do most, if not all, of Spivak's problems.

This sounds like a good idea and I think I'll actually work through this book. Are there solutions?

Are there books similar to spivak for the other topics I listed that build up a strong foundation and focus on proofs? I'm really looking to prepare myself for undergraduate studies in math.
 
  • #5


I would first like to congratulate you on your dedication and enthusiasm for self-studying math over the summer. Math is a fundamental subject in many scientific fields and having a strong foundation in it will definitely benefit you in your future studies.

In terms of online resources, there are many great websites and platforms that offer free or low-cost courses and lectures on differential equations, calc 3, and linear algebra. Some popular ones include Khan Academy, Coursera, and edX. These websites offer a variety of courses from top universities and instructors, and often have interactive exercises and quizzes to help reinforce your learning.

In addition to these specific math topics, I would also suggest exploring other branches of mathematics such as discrete mathematics, abstract algebra, and number theory. These subjects may not be directly related to the math classes you will be taking in university, but they will broaden your understanding and appreciation for the field.

Lastly, I would encourage you to also take breaks and explore other interests during your summer self-study. While it is important to have a strong foundation in math, it is also important to have a well-rounded education and pursue other interests. Who knows, you may find a new passion or connection between math and another subject area.

Overall, I applaud your proactive approach to learning and wish you all the best in your summer self-study and future studies in mathematics. Keep up the hard work and curiosity!
 

1. What are the benefits of self studying math topics over the summer?

Self studying math topics over the summer can have numerous benefits, such as improving critical thinking and problem-solving skills, building a strong foundation for future math courses, and gaining a deeper understanding of the subject material. It also allows for a more flexible and personalized learning experience.

2. How should I structure my self study for optimal results?

The best way to structure your self study for math topics over the summer is to set specific goals and create a schedule. Make sure to review any prerequisite material before diving into new topics, and practice regularly to reinforce your understanding. It can also be helpful to seek out additional resources, such as textbooks or online tutorials.

3. Can self studying math topics over the summer replace traditional classroom learning?

Self studying math topics over the summer can be a valuable supplement to traditional classroom learning, but it should not be seen as a replacement. While self studying allows for a more personalized and independent approach, it is still important to have access to a teacher or tutor for guidance and clarification.

4. How do I stay motivated and focused while self studying math topics over the summer?

Staying motivated and focused while self studying math topics over the summer can be challenging, but there are a few strategies that can help. Setting achievable goals, rewarding yourself for progress, and taking breaks when needed can all help maintain motivation. Additionally, finding a study partner or joining a study group can provide accountability and support.

5. Are there any specific math topics that are particularly beneficial to self study over the summer?

While any math topic can be beneficial to self study over the summer, some may be more suitable than others. Algebra, geometry, and calculus are all foundational topics that are important to have a strong understanding of. Additionally, statistics and probability can be useful for a wide range of fields and can also be self studied effectively. Ultimately, the best topic to self study will depend on your individual goals and interests.

Similar threads

  • STEM Academic Advising
Replies
1
Views
847
  • STEM Academic Advising
Replies
7
Views
1K
  • STEM Academic Advising
Replies
11
Views
1K
Replies
7
Views
809
  • STEM Academic Advising
Replies
10
Views
2K
  • STEM Academic Advising
Replies
14
Views
1K
  • STEM Academic Advising
Replies
3
Views
1K
  • STEM Academic Advising
Replies
8
Views
716
  • STEM Academic Advising
Replies
2
Views
696
  • STEM Academic Advising
Replies
7
Views
1K
Back
Top