During the first lecture, the last example is extremely hard to understand. Fortunately, it won’t be tested.
Then it will introduce some basic concepts like:
Statement: a sentence that is True or False. Proposition: claim that requires a proof. Theorem: Strong proposition. Lemma: Weak proposition. Corollary: Follows immediately from a proposition. Axiom: A given truth.
Then the course covers number theory and so on. Let’s take a look at what math 145 (snew) does:
- Logic and Proof (with many axioms introduced)
- Rings, Fields, Orders and Induction (pmath 347/348)
- Complex Numbers (pmath 352)
- Cardinality
- Factorization of Integers
- Congruence and Modular Arithmetic
- Cryptography (co 487)
- Factorization in Rings (pmath 347)
- Various Topics in Number Theory (pmath 340/440/441)
So this is pretty much a super set of math 135 in all aspects.
I don’t have much well-typed notes. Course notes together with lectures should be enough.
