What are the prerequisites for studying advanced mathematics?

[DrPhoton]

Ok Forum
I was interested in studying some advanced math but I was lost as to where to start from so here are the things I'd like to learn
1-Number theory
2-Set theory
3-Group theory
4-Linear Algebra
5-Abstract Algebra
6-Topology

atm I am learning Calculus II but I'd like to do more ..
So I'd like you guys to list the Prerequisites Of each of these topics and/or list them in the order that they should be learned and if you could name the top 5 books for each of these topics or link me to the books in the books forum . I'd appreciate it .

P.s if someone has already posted a thread which is more or less similar please let me know.
Thanks
DR.PHOTON

 

[cochemuacos]

Im not familiar with all the math you listed, but i believe i can give you some info about a few of them.

In essence you don't need any prerequisites for set theory, but you should be confortable doing proofs. Same goes for topology, but it might help if you already know advance calc, it will "make more sense".

Finally, for linear algebra, you olnly need basic high school algebra and I recommend learning the rigourus part of it, the one which involve proofs. Is't a nice way to learn and develop your proof skills. Maybe gat a copy of https://www.amazon.com/Linear-Algebra-Edition-Stephen-Friedberg/dp/0130084514/ref=sr_1_2?ie=UTF8&qid=1363233494&sr=8-2&keywords=friedberg after that, you may try abstract and group theory. In my opinion you should begin with linear algebra. good luck

 

[Sankaku]

While there are many different paths you can take through mathematics, my advice is to cover some basics before getting too ambitious:

- Do some very basic set theory before anything else (this is often taught as part of other courses).

- Do linear algebra before abstract algebra (group theory is part of abstract algebra).

- Also, do linear algebra before multivariable calculus (and differential equations).

- Do some real analysis before topology.

Elementary number theory can be done with some simple set theory and proof skills, but what mathematicians consider full-on number theory requires advanced tools from abstract algebra.

As you can guess from above, I would recommend starting with some basic set theory and linear algebra. Linear algebra is as foundational as calculus (if not more so for pure mathematics). There are lots of good books discussed in the book forum.

 

[halo31]

id basically do this. You need to learn how to write proofs first and the best way to do that is get a book that does just that.. Id recommend the one by Peter J Eccles. It's a very nice introduction to proofs. From there learning linear algebra and number theory can readily be done. I'd say friedburg is quite advanced and very easy to get lost with. A more gentler approach would be learning linear algebra at a notch below such as from a book like David Poole's linear algebra book. Then Id recommend Axler's linear algebra done right over any other book. I had a great time with that book and not to mention he introduces determinants at the very end which I say is brilliant. For number theory there are lots of books on it all with a different taste. There are plenty of great books on number theory such as the one by Gareth Jones and Thomas Koshy. From here you can jump straight into abstract algebra ( gallian is my choice) and then basic analysis ( protter or ross are great books). From here you will have built up a good core and you can basically move on to areas of math you would like to learn about. Good luck!

 

[DrPhoton]

id basically do this. You need to learn how to write proofs first and the best way to do that is get a book that does just that.. Id recommend the one by Peter J Eccles. It's a very nice introduction to proofs. From there learning linear algebra and number theory can readily be done. I'd say friedburg is quite advanced and very easy to get lost with. A more gentler approach would be learning linear algebra at a notch below such as from a book like David Poole's linear algebra book. Then Id recommend Axler's linear algebra done right over any other book. I had a great time with that book and not to mention he introduces determinants at the very end which I say is brilliant. For number theory there are lots of books on it all with a different taste. There are plenty of great books on number theory such as the one by Gareth Jones and Thomas Koshy. From here you can jump straight into abstract algebra ( gallian is my choice) and then basic analysis ( protter or ross are great books). From here you will have built up a good core and you can basically move on to areas of math you would like to learn about. Good luck!

While there are many different paths you can take through mathematics, my advice is to cover some basics before getting too ambitious:

- Do some very basic set theory before anything else (this is often taught as part of other courses).

- Do linear algebra before abstract algebra (group theory is part of abstract algebra).

- Also, do linear algebra before multivariable calculus (and differential equations).

- Do some real analysis before topology.

Elementary number theory can be done with some simple set theory and proof skills, but what mathematicians consider full-on number theory requires advanced tools from abstract algebra.

As you can guess from above, I would recommend starting with some basic set theory and linear algebra. Linear algebra is as foundational as calculus (if not more so for pure mathematics). There are lots of good books discussed in the book forum.

Im not familiar with all the math you listed, but i believe i can give you some info about a few of them.

In essence you don't need any prerequisites for set theory, but you should be confortable doing proofs. Same goes for topology, but it might help if you already know advance calc, it will "make more sense".

Finally, for linear algebra, you olnly need basic high school algebra and I recommend learning the rigourus part of it, the one which involve proofs. Is't a nice way to learn and develop your proof skills. Maybe gat a copy of https://www.amazon.com/Linear-Algebra-Edition-Stephen-Friedberg/dp/0130084514/ref=sr_1_2?ie=UTF8&qid=1363233494&sr=8-2&keywords=friedberg after that, you may try abstract and group theory. In my opinion you should begin with linear algebra. good luck

Thank you so much (: