Independent branch of Mathematics?

[1mmorta1]

I have done well in undergraduate mathematics, and would like to do some self study in something more advanced and stimulating.

I am interested in concepts such as number theory and set theory, or any type of mathematics that can be used to study systems of information, behavior...anything beyond your "daily" mathematical calculations.

The problem is that I've noticed I often don't understand some of the basic concepts in advanced mathematics books. I recognize that this just means I have more learning to do before I can begin studies in those areas :)

My question is if there are any advanced areas of mathematics that are self-contained, that I could study from the ground up without having to understand some of the more advanced undergrad subjects. (i.e. can I study [insert branch here] without mastering lie groups, or having taking coursework on mathematical proofs, and so on and so on)

I am certainly not mathematicaly incompetent, but I'm also not a graduate student. I was thinking perhaps number theory or game theory could be prime candidates, but don't want to purchase any materials only to find out they are beyond me.

Does anyone have any recommendations?

(This question may need to be moved from this thread, I wasn't sure where the best place to post it would be)

 

[mathman]

Number theory is probably your best bet. Game theory might need calculus. If you have had calculus, there is much more open.

 

[Bacle]

I think combinatorics is also a pretty good bet.

 

[1mmorta1]

Thank you guys. Calculus won't be a problem :) Wow, there is an awful lot to combinatorics.

 

[CellCoree]

I would like to say that mathematics is a vast and ever-growing field, with many different branches that can be considered independent. Number theory and set theory are just two examples of these branches, and they can definitely be used to study systems of information and behavior beyond basic calculations. However, it is important to note that all areas of mathematics are interconnected and build upon each other, so it is always beneficial to have a strong foundation in the basics before delving into advanced topics.

That being said, there are certainly areas of mathematics that are more self-contained and can be studied without a deep understanding of other advanced topics. Number theory and game theory are good examples of this, as they have their own set of principles and concepts that can be studied independently. However, it is still important to have a solid understanding of mathematical proofs and logic, as these are fundamental skills in any advanced area of mathematics.

If you are interested in self-studying these topics, I would recommend starting with some introductory textbooks or online courses to build a strong foundation before moving on to more advanced materials. It is also helpful to have a mentor or someone knowledgeable in the field to guide you and answer any questions you may have.

In summary, while there are certainly independent branches of mathematics, it is always beneficial to have a strong understanding of the basics before diving into advanced topics. With dedication and hard work, you can certainly self-study and excel in these areas. Good luck in your studies!