Open Logic Project: An Open-Source, Collaborative Logic Text(openlogicproject.org)
openlogicproject.org
Open Logic Project: An Open-Source, Collaborative Logic Text
http://openlogicproject.org/
10 comments
Wow! Reading the table of contents, this seems like a pretty complete book. Most introductions to logic neglect the entire area of intuitionistic logic and proof theory so it's nice to see one that covers that along with the usual infinitarian stuff (FOL, model theory, computability, etc.)
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Thanks for the link. Definitely will be reading the book. I am going to university this fall. Of all the courses I will be taking this year. Proofs seem the most hardest. Is there any tips to tackle this?
The mindset necessary for proofs is very different from how most people learn mathematics. So long as you can get a small preview of that mindset, you'll be ahead of the game.
I'd suggest choosing a source which seems "too easy", or a curriculum which is "too short". It will be enough.
Additionally, as when learning anything mathematical, don't expect too much help from Wikipedia. Pedagogy often involves telling small lies to students at first, then clearing them up later. Wikipedia has a bias towards being correct, which means that the articles can't tell those small lies and the explanations are difficult for non-experts to understand.
Additionally, as when learning anything mathematical, don't expect too much help from Wikipedia. Pedagogy often involves telling small lies to students at first, then clearing them up later. Wikipedia has a bias towards being correct, which means that the articles can't tell those small lies and the explanations are difficult for non-experts to understand.
Congratulations on graduating high school. That's quite exciting, and I'm sure you'll love university.
The about page states that the book is for "an intermediate level (i.e., after an introductory formal logic course)." It'd be advisable to look elsewhere first if you don't have any exposure to propositional logic. For example, the first eight chapters of MIT's Mathematics for Computer Science textbook should be sufficient: https://courses.csail.mit.edu/6.042/spring17/mcs.pdf
The standard tip for reading mathematical texts is twofold: always try to come up with a proof before reading the one supplied in the text, and never ignore the problem sets. As Pólya famously put it, mathematics is not a spectator sport.
The about page states that the book is for "an intermediate level (i.e., after an introductory formal logic course)." It'd be advisable to look elsewhere first if you don't have any exposure to propositional logic. For example, the first eight chapters of MIT's Mathematics for Computer Science textbook should be sufficient: https://courses.csail.mit.edu/6.042/spring17/mcs.pdf
The standard tip for reading mathematical texts is twofold: always try to come up with a proof before reading the one supplied in the text, and never ignore the problem sets. As Pólya famously put it, mathematics is not a spectator sport.
For independent study a leaner approach might be best (the open logic textbook is meant to be remixed to form a course, so it includes a lot of material). I think Daniel Velleman's "How to Prove It" is a good textbook for learning to deal with proofs, plenty of exercises there and it has a more practical approach (it is intended for CS and math students). Volker Halbach's "The Logic Manual" is good, as is Restall's "Logic", although both are oriented to philosophy students.
EDIT: s/"How to Solve It"/"How to Prove It".
EDIT: s/"How to Solve It"/"How to Prove It".
To clarify:
Velleman wrote "How to Prove It": https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/...
Polya wrote "How to Solve It": https://www.amazon.com/How-Solve-Mathematical-Princeton-Scie...
Velleman wrote "How to Prove It": https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/...
Polya wrote "How to Solve It": https://www.amazon.com/How-Solve-Mathematical-Princeton-Scie...
Sorry, you are right (I actually have both in front of me... and Beeler's "How to Count"). Polya is also a nice read ;)
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They're very similar in the pattern of working out proofs.
That's what I remember over 30th years ago in intro to logic (philosophy course not math or comp-sci) being similar to my 9th grade geometry class proofs.
The skill to work on in an intro class is to make sentences out of the logic propositions and then work on making ordinary sentences into the logic notation.