Independently Learning Mathematics

In summary, the person is independently learning mathematics and is currently studying calculus through M. Spivak and R. Courant's books. They have no formal education in higher mathematics and are in their early twenties. They plan on finishing these books and then moving on to other works on analysis and constructive mathematics. They are feeling overwhelmed and unsure if their approach is correct. They have received advice to start with a basic calculus book before moving on to more advanced topics. They are currently looking into resources on how to become a pure mathematician or statistician.
  • #1

EOB

2
0
I realize it's a very broad statement to say that I'm independently learning mathematics because I am definitely not learning all of mathematics. I am currently studying the calculus and of right now via M. Spivak and have also been consulting R. Courant's Differential and Integral Calculus, vol 1.

I have zero formal education in the calculus or any other higher mathematics for that matter. I am now in my early twenties and beginning a "formal" learning of mathematics on my own. I was planning on finishing at least one of the aforementioned works on the calculus and then finish reading the following works regarding analysis. The books that I have planned on consulting regarding this endeavor are Analysis 1 & 2 by Einar Hille and Foundations of Modern Analysis by Jean Dieudonne (I do have copies of all of the works that are listed in this query.)

When I'm finished with those works I am hoping that this will give me sufficient preparation to finish reading E. Bishop's Foundations of Constructive Mathematics and A.A. Markov's The Theory of Algorithms. Regarding all of the previously mentioned titles, I have read parts of them and I believe that I have been reading them in an "incorrect" order. I'm feeling overwhelmed as to whether or not my approach is "correct" because minus the works on the calculus alone, I comprehend very little of the other works listed. Thus far all of the aforementioned works have taxed my mental faculties to such an extent that I could no longer pursue the reading of some of them because I do not have the required background to understand much of the content contained within them and I do not want to develop a lack of appreciation of the information that these books contain if I were to continue reading them without really understanding what is being discussed. Any advice on how I should learn formal mathematics and whether the order in which I am currently studying in order to ultimately study constructive mathematics is the "right" way/a way that will allow for that goal to actualize will be greatly appreciated. Thank you for your time/thoughts/recommendations. :)

Regards,

EOB
 
Physics news on Phys.org
  • #2
As someone who self studies math/physics (admittedly, not in a highly disciplined fashion, unfortunately!) I can tell you right off the bat that you are expecting too much of yourself, too quickly. By starting off that advanced, you are building on a shaky foundation and may be liable to get discouraged and give up. Or worse yet, misunderstand topics and have it come back later to haunt you (not good if you're trying to prove something logically!)

Spivak is a great book and it helped me tremendously when I took real analysis in college, but this was only after a few years of building up to it. Start with a basic calculus book used in college calculus (the 9th edition of Finney and Thomas is an excellent and cheap book) and work through it methodically and carefully - the "brute force" computation not only enhances what is going on in proofs, it builds problem solving skills. Then, afterwards, go to the more elegant formulations of calculus!

Hopefully this helps a little!
 
  • #4
CJ2116 and IGU:

Your advice falls on ears that are not deaf and I thank both of your very much for your recommendations. I'm currently perusing the information contained in the redirect link provided by IGU. I thank you both for your time and your recommendations!
 
  • #5


I can understand your desire to independently learn mathematics and your determination to work through difficult texts. It is important to have a strong foundation in calculus before moving on to more advanced topics, so it is good that you are consulting multiple texts and seeking advice on the best way to approach your studies.

My advice would be to focus on one text at a time, starting with the one that you find the most approachable and building your understanding from there. This may require going back and reviewing some concepts from earlier texts, but it will ultimately make your learning more efficient and effective. It is also helpful to supplement your reading with practice problems and seek out resources such as online tutorials or study groups to help clarify any difficult concepts.

Additionally, it is important to have a clear goal in mind for why you are studying mathematics and what you hope to achieve. This will help guide your learning and keep you motivated. Constructive mathematics is a fascinating area, but it may be helpful to have a solid understanding of more foundational concepts in analysis before diving into it.

Remember, learning mathematics is a journey and it takes time, patience, and perseverance. Don't be discouraged if you encounter difficulties or feel overwhelmed at times. Seek out help and keep pushing forward towards your goal. Good luck on your mathematical journey!
 

1. What is independent learning in mathematics?

Independent learning in mathematics refers to the process of acquiring knowledge and skills in mathematics without direct instruction or guidance from a teacher or tutor. It involves taking responsibility for one's own learning and setting goals, managing time, and seeking resources to enhance understanding and problem-solving abilities.

2. How can one effectively learn mathematics independently?

To effectively learn mathematics independently, one must first have a strong foundation in basic mathematical concepts. This can be achieved through practice and repetition, as well as seeking help from online resources or textbooks. It is also important to set goals and create a study plan, prioritize understanding over memorization, and regularly review and self-assess progress.

3. What are some resources for independent learning in mathematics?

There are various resources available for independent learning in mathematics, such as online tutorials, practice problems, textbooks, and educational websites. Many universities also offer open courseware or online courses in mathematics that can be accessed for free. Additionally, joining study groups or seeking help from a tutor or mentor can also be beneficial.

4. Can anyone learn mathematics independently?

Yes, anyone can learn mathematics independently with dedication and perseverance. It may be more challenging for some individuals, but with the right resources and strategies, anyone can develop their mathematical skills and understanding.

5. What are the benefits of learning mathematics independently?

Learning mathematics independently can improve critical thinking, problem-solving, and analytical skills. It also allows individuals to learn at their own pace and explore topics of interest beyond the curriculum. Additionally, it can build self-confidence and self-motivation, as well as prepare individuals for future academic and career pursuits.

Suggested for: Independently Learning Mathematics

Replies
3
Views
766
Replies
10
Views
2K
Replies
6
Views
1K
Replies
2
Views
889
Replies
13
Views
958
Replies
6
Views
2K
Replies
7
Views
1K
Replies
9
Views
963
Back
Top