MATH 135 - Intro to proof

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.

Carmen’s notes

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