## Weekly outline

• ### General

This is the webpage of the English version of the course taught by Andreas Feldmann, which takes place on Mondays at 14:00 to 15:30. Please only register for this course and sign up for the zoom sessions below if you are registered for the English version of the Mathematical Skills seminar held by Andreas Feldmann in SIS (see link below).

• zoom registration link URL
• Q&A Forum
• lecture notes File
• ### Oct 5

propositions, negation, conjunction, disjunction, exclusive or, conditional, logical equivalence

• Quiz 1
• ### Oct 12

different ways how to express implication in English, converse, inverse, contrapositive, biconditional, proving equivalence, De Morgan laws, propositional functions

• Quiz 2
• ### Oct 19

proof by contrapositive, universal and existential quantification, bound and free variables, scope of a quantification

• Quiz 3
• ### Oct 26

composing quantified propositions, nested quantification, scope of a quantifier, unique quantification, De Morgan laws for quantification

• Quiz 4
• ### Nov 2

translating mathematical statements into quantified propositions, repetition: expressing restrictions on the domain using propositions

• Quiz 5
• ### Nov 9

Terminology: theorem, lemma, corollary, conjecture, axiom; direct proof and indirect proof by contrapositive of implications

• Quiz 6
• ### Nov 16

proof by contradiction, proof of equivalence, exhaustive proof, proof by cases, without loss of generality

• Quiz 7
• ### Nov 23

Cantor's Theorem (proof by contradiction), the Four Colour Theorem (exhaustive proof)

• Quiz 8
• ### Nov 30

without loss of generality, constructive and non-constructive existence proofs (winning strategy for Chomp), pigeonhole principle

• Quiz 9
• ### Dec 7

generalized pigeonhole principle and applications

• Quiz 10
• ### Dec 14

Erdös-Szekeres theorem, Ramsey theorem, induction

• Quiz 11
• ### Dec 21

wrong induction "proofs", strong induction

• Quiz 12
• ### Jan 4

fundamental theorem of arithmetic, Fibonacci numbers, proof by picture

• Quiz 13
• • Quiz 14