3 ms·

> As part of the first semester you take linear algebra and analysis, starting out with the basics of formal logic There is not enough time to learn the basics

> As part of the first semester you take linear algebra and analysis, starting out with the basics of formal logic There is not enough time to learn the basics of formal logic and linear algebra and/or analysis in a single class, but I think what you’re referring to is an introduction to proof techniques like induction, modus tollens, quantifiers, etc. Every math and computer science department in the US that I’ve ever heard of teaches these topics, but I wouldn’t call it a formal logic class.

constantcrying 3y ago
For me basic formal logics means learning the symbols (conjunction, disjunction, implication, equivalency, not, etc.) and the rules of inference to maniuplate these symbols and using these rules to prove new things. How can you teach analysis without that anyway. It is absolutely essential for set theory and how would you e.g. define the reals (in a "proper" math course, not engineering) without a good understanding of set theory? If you don't believe me, here is a link to the contents of a first semester engineering math course from some german technical university: https://page.math.tu-berlin.de/~joswig/teaching/notes/Joswig-LineareAlgebra-08_09.pdf https://page.math.tu-berlin.de/~joswig/teaching/notes/Joswig... The symbols should be enough to tell you what the contents are.
- Tainnor 3y ago
  > For me basic formal logics means learning the symbols (conjunction, disjunction, implication, equivalency, not, etc.) and the rules of inference to maniuplate these symbols and using these rules to prove new things. That's really only baby logic. Which, probably, is what will be sufficient for most mathematician most of the time. A real first introduction to formal logic would introduce an actual formal proof system and go at least as far as proving completeness of first order logic.
  - constantcrying 3y ago
    >That's really only baby logic. Instead of (literally) infantalizing the name, you could also call it basic formal logic.
    - Tainnor 3y ago
      I don't want to quibble about names (and I wasn't the person to come up with the term "baby logic"), but the point is that just introducing a couple of connectives and proof strategies doesn't even constitute the basics of what mathematical logic really is about. Which btw I'm perfectly fine with, most people don't need more than that. If you do want to study logic formally, the basics start with well-formed formulas, signatures, etc. I guess what you call it doesn't matter a lot, but the discussion seems to have started with the assertion that most students, even in mathematics, never really learn formal logic, and I would agree with that (under my definition of "formal logic"), while also agreeing with you that you can't pursue a degree in maths without knowing how induction works or what a bijection is. But still, most people don't need to know exactly how to formalise induction and that it's actually (in its full form) a second-order axiom.
- l33t233372 3y ago
  That level of logic taught to every mathematics and computer science student, and it’s really not what I was thought others in this thread were talking about.

constantcrying 3y ago

For me basic formal logics means learning the symbols (conjunction, disjunction, implication, equivalency, not, etc.) and the rules of inference to maniuplate these symbols and using these rules to prove new things. How can you teach analysis without that anyway. It is absolutely essential for set theory and how would you e.g. define the reals (in a "proper" math course, not engineering) without a good understanding of set theory? If you don't believe me, here is a link to the contents of a first semester engineering math course from some german technical university: https://page.math.tu-berlin.de/~joswig/teaching/notes/Joswig-LineareAlgebra-08_09.pdf https://page.math.tu-berlin.de/~joswig/teaching/notes/Joswig... The symbols should be enough to tell you what the contents are.

Tainnor 3y ago
> For me basic formal logics means learning the symbols (conjunction, disjunction, implication, equivalency, not, etc.) and the rules of inference to maniuplate these symbols and using these rules to prove new things. That's really only baby logic. Which, probably, is what will be sufficient for most mathematician most of the time. A real first introduction to formal logic would introduce an actual formal proof system and go at least as far as proving completeness of first order logic.
- constantcrying 3y ago
  >That's really only baby logic. Instead of (literally) infantalizing the name, you could also call it basic formal logic.
  - Tainnor 3y ago
    I don't want to quibble about names (and I wasn't the person to come up with the term "baby logic"), but the point is that just introducing a couple of connectives and proof strategies doesn't even constitute the basics of what mathematical logic really is about. Which btw I'm perfectly fine with, most people don't need more than that. If you do want to study logic formally, the basics start with well-formed formulas, signatures, etc. I guess what you call it doesn't matter a lot, but the discussion seems to have started with the assertion that most students, even in mathematics, never really learn formal logic, and I would agree with that (under my definition of "formal logic"), while also agreeing with you that you can't pursue a degree in maths without knowing how induction works or what a bijection is. But still, most people don't need to know exactly how to formalise induction and that it's actually (in its full form) a second-order axiom.
l33t233372 3y ago
That level of logic taught to every mathematics and computer science student, and it’s really not what I was thought others in this thread were talking about.