Pure Mathematics study - question

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Discussion Overview

The discussion revolves around the optimal sequence for studying various areas of pure mathematics, particularly focusing on logic, set theory, and abstract algebra. Participants share their personal experiences and recommendations for self-study paths, emphasizing foundational topics and their relevance to different backgrounds, such as computer science and data architecture.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant proposes a sequence starting with formal logic and moving through various types of logic before addressing set theory and abstract algebra.
  • Another participant suggests that starting with an introduction to proofs might be more beneficial before delving into abstract algebra and foundational mathematics.
  • A different viewpoint emphasizes the importance of set theory, questioning why it should be postponed until after studying pure mathematics.
  • Some participants express that their own educational paths did not include the initial steps of logic proposed by others, indicating variability in educational approaches.
  • One participant mentions that their experience with relational databases did not require a deep understanding of set theory, suggesting that practical applications may differ from theoretical study.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best sequence for studying pure mathematics. There are multiple competing views on the order of topics and the necessity of certain foundational subjects, particularly regarding the timing of set theory in relation to other areas.

Contextual Notes

Some participants highlight the dependence of their recommendations on personal educational experiences and specific career applications, which may not universally apply to all learners. There is also mention of differing interpretations of what foundational knowledge is necessary for understanding relational databases.

Who May Find This Useful

This discussion may be useful for individuals interested in self-studying pure mathematics, particularly those with backgrounds in computer science or data architecture, as well as those seeking guidance on the sequence of mathematical topics to study.

heff001
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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.
 
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heff001 said:
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.
 
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!
 
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.
 
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).
 
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.
 
heff001 said:
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.
 
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