Regardless of the philosophical debate on whether mathematics is discovered or invented, it remains a deeply creative field. Everything in mathematics is constructed from the ground up, from a very small set of assumptions. No matter if the interest is towards an application or for a purely theoretical construct, the journey is the same. The only limitation in this exploration is the truth: we cannot stray away from a path of truthful statements.
Just as in a novel, the author builds a world with certain rules which cannot be violated afterwards, the mathematics has its rules for ensuring we remain on a path that leads to truth. Logic is the field which looks deep into the rules of the mathematics, establishing what can be done and cannot be done.
Logical Options: An introduction to classical and alternative logics presents a tour of various logics, building an understanding of the various possible logical systems, along with their capabilities and limitations.
Chapter 1: Classical Propositional Logic
1.1: Introductory Remarks
1.1.1
1.2: Propositional Logic
1.2.1: 1, 2a 1.2.2: 1 1.2.3: 1, 2(1.1, 1.2), 3a 1.2.4: 1, 5a 1.2.5
1.3: Trees for Classical Propositional Logic
1.3.1: 1a, 2a, 3a
1.4: Metatheorems
1.4.1
1.5: Other Proof Methods
1.5.1 1.5.2 1(some of them), 2 1.5.3 1.5.4 1.5.5
Chapter 2: Classical Predicate Logic
2.2 Tree Rules for Classical Predicate Logic
2.2.1 (Trees = fun)
2.3 Predicate Languages and Their Intepretations
2.3.1
2.4 Set Theory
nothing (= all trivial stuff)
2.5 Interpretations of Languages for Predicate Logic
2.5.1
2.6 Validity, Satisfiability, and Models
2.6.1
2.7 Correctness and Adequacy
2.7.1 2.7.2