Self-teaching: What topics do I learn first?

[operationsres]

I've become a bit obsessed with maths in the last month. I'm studying it in all my free time.

My knowledge is probably at the level of a 1st year student who just finished their 1st semester and did pretty well. I did 3 maths subjects at uni and aced them. However, I've forgotten quite a bit of it over the last 12 months, but have also re-learned a decent amount.

I've been starting my learning with analysis but I'm not sure it's the optimal way to start things off again.

Do you guys have any recommendations? I'm not sure what I should focus on first ... linear algebra, calculus, or the proof/limits side of analysis?

 

[cgk]

It might be helpful to self-learn useful auxiliary skills which are not directly taught in courses. This includes programming, writing technical articles, giving talks, applied math/comp.-sci techniques (say, geometric algebra, probability & statistics, local and global optimization) etc.

Mastery of such things can come in very handy later, and they form a skill axis orthogonal to your main academic skills. Additionally, some of them (e.g., programming) actually cannot be taught decently in courses beyond an elementary level, and are very suitable for self-learning at the same time.

 

[operationsres]

Thanks for the post. I'm co-authoring 3 applied econometrics/statistics papers at the moment so I'm fine on the programming/statistics front.

I'm interested in the more hardcore maths side.

 

[mathsman1963]

A good foundation for mathematical skills would be algebraic number theory. You can begin a study of this with nothing more than high school algebra yet many of its problems will test your ingenuity. My favourite book on this topic is Richard M Burton's Elementary Number Theory.

 

[Matrix0]

As a fellow scientist, I can understand your excitement and dedication towards learning math. It is great to see that you have a strong foundation in the subject from your previous university studies. When it comes to self-teaching, it can be overwhelming to decide where to start. My recommendation would be to focus on the fundamentals first. This can include topics such as algebra, trigonometry, and geometry. These concepts are the building blocks of advanced mathematics and having a strong understanding of them will make it easier for you to grasp more complex concepts later on.

Additionally, I would suggest revisiting the topics that you may have forgotten over the last 12 months. This will help refresh your memory and fill in any gaps in your knowledge. From there, you can move on to more advanced topics such as linear algebra, calculus, and analysis.

In terms of which specific topic to start with, it ultimately depends on your personal interests and goals. If you are interested in applications of math, then focusing on calculus and linear algebra would be beneficial. However, if you have a strong interest in the theoretical side of math, then starting with the proof and limits aspect of analysis may be more suitable.

Overall, my advice would be to start with the fundamentals, review any topics that you may have forgotten, and then move on to more advanced topics based on your interests and goals. Remember to also take breaks and not overwhelm yourself with too much information at once. Good luck with your self-teaching journey!