Pure Mathematics study - question

[heff001]

I am planning to study the following pure mathematics areas (on my own) and wanted to know if this is the best sequence:

1- Formal Logic
2 -Philosophical Logic
3- Sentential Logic
4- Predicate Logic
5- Symbolic Logic

6 -Set Theory

7 -Pure Mathematics (Intro, Pure Math I and II and Hardy) - not sure if this belongs here? Should I begin here?

8 -Abstract AlgebraI do not want to study applied / discrete mathematics. My background is computer science.

 

[Svein]

I am planning to study the following pure mathematics areas (on my own) and wanted to know if this is the best sequence:

1- Formal Logic
2 -Philosophical Logic
3- Sentential Logic
4- Predicate Logic
5- Symbolic Logic

6 -Set Theory

7 -Pure Mathematics (Intro, Pure Math I and II and Hardy) - not sure if this belongs here? Should I begin here?

8 -Abstract AlgebraI do not want to study applied / discrete mathematics. My background is computer science.

You could do it that way - if you want to end up hopelessly confused. If you want to study mathematical logic, Predicate logic is easiest and closest to computer science. The next level is first-order logic, but I do not recommend that until after a season or two of Pure Mathematics Intro. I would also defer set theory and abstract algebra until after that intro.

 

[micromass]

I would suggest:

1) Introduction to proofs, for example using the book of proof: http://www.people.vcu.edu/~rhammack/BookOfProof/

2) Abstract Algebra, for example using Pinter: https://www.amazon.com/dp/0486474178/?tag=pfamazon01-20

3) Introduction to foundational mathematics, for example using Stillwell: https://www.amazon.com/dp/3319015761/?tag=pfamazon01-20

Then you can go on to study mathematical logic and axiomatic set theory.

Please do no hesitate to contact me with further questions or guidance!

 

[nomadreid]

For a soft but good introduction to set theory, I would suggest Halmos' "Naive Set Theory". Google it, and you have the choice between a free but poor pdf copy or a respectable paid copy; but a lot of libraries have it.

 

[mathman]

When I was getting my math education, I was never exposed to your steps 1-5. Mine started (after calculus, etc.) with 6 (set theory).

 

[heff001]

Thanks to all...

Why is Set Theory a topic to wait on after studying Pure Math? I am an IT Data Architect where relational theory is based on set theory. The theory of relational databases is built upon the mathematical theory of sets.

 

[micromass]

Thanks to all...

Why is Set Theory a topic to wait on after studying Pure Math? I am an IT Data Architect where relational theory is based on set theory. The theory of relational databases is built upon the mathematical theory of sets.

OK, you didn't specify that you wanted to obtain a background in set theory in order to understand relational databases. From your post, I gathered that you were interested in mathematical logic and axiomatic set theory.
First of all, I want to say that when I studied relational databases, I never found my knowledge of set theory very useful, but maybe I didn't go very deep into it. I think it would be good for you to go through a basic proof book such as Velleman: https://www.amazon.com/dp/0521675995/?tag=pfamazon01-20 That should be enough background for everything to do with relational databases.