2020 Math Skills Seminar
Section outline
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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).
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zoom registration link Link/URL
Please register for the zoom sessions via this link before the first lecture.
Once you registered you will obtain a confirmation email. The email contains your personal link to the zoom sessions and the passcode. You need to use this link to participate in the lectures.
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Q&A Forum
Questions by the students will be answered by the teacher (or other students)
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propositions, negation, conjunction, disjunction, exclusive or, conditional, logical equivalence
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Quiz 1 Test
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different ways how to express implication in English, converse, inverse, contrapositive, biconditional, proving equivalence, De Morgan laws, propositional functions
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Quiz 2 Test
Note: you win points by answering correctly, but you can also lose points by answering incorrectly (your total points will never be below 0). This means that if you are unsure, you are better off not answering instead of guessing.
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proof by contrapositive, universal and existential quantification, bound and free variables, scope of a quantification
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Quiz 3 Test
Note: you win points by answering correctly, but you can also lose points by answering incorrectly (your total points will never be below 0). This means that if you are unsure, you are better off not answering instead of guessing.
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composing quantified propositions, nested quantification, scope of a quantifier, unique quantification, De Morgan laws for quantification
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Quiz 4 Test
Note: you win points by answering correctly, but you can also lose points by answering incorrectly (your total points will never be below 0). This means that if you are unsure, you are better off not answering instead of guessing.
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translating mathematical statements into quantified propositions, repetition: expressing restrictions on the domain using propositions
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Quiz 5 Test
Note: you win points by answering correctly, but you can also lose points by answering incorrectly (your total points will never be below 0). This means that if you are unsure, you are better off not answering instead of guessing.
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Terminology: theorem, lemma, corollary, conjecture, axiom; direct proof and indirect proof by contrapositive of implications
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Quiz 6 Test
Note: you win points by answering correctly, but you can also lose points by answering incorrectly (your total points will never be below 0). This means that if you are unsure, you are better off not answering instead of guessing.
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proof by contradiction, proof of equivalence, exhaustive proof, proof by cases, without loss of generality
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Quiz 7 Test
Note: you win points by answering correctly, but you can also lose points by answering incorrectly (your total points will never be below 0). This means that if you are unsure, you are better off not answering instead of guessing.
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Cantor's Theorem (proof by contradiction), the Four Colour Theorem (exhaustive proof)
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Quiz 8 Test
Note: you win points by answering correctly, but you can also lose points by answering incorrectly (your total points will never be below 0). This means that if you are unsure, you are better off not answering instead of guessing.
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without loss of generality, constructive and non-constructive existence proofs (winning strategy for Chomp), pigeonhole principle
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Quiz 9 Test
Note: you win points by answering correctly, but you can also lose points by answering incorrectly (your total points will never be below 0). This means that if you are unsure, you are better off not answering instead of guessing.
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generalized pigeonhole principle and applications
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Quiz 10 Test
Note: you win points by answering correctly, but you can also lose points by answering incorrectly (your total points will never be below 0). This means that if you are unsure, you are better off not answering instead of guessing.
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Erdös-Szekeres theorem, Ramsey theorem, induction
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Quiz 11 Test
Note: you win points by answering correctly, but you can also lose points by answering incorrectly (your total points will never be below 0). This means that if you are unsure, you are better off not answering instead of guessing.
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wrong induction "proofs", strong induction
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Quiz 12 Test
Note: you win points by answering correctly, but you can also lose points by answering incorrectly (your total points will never be below 0). This means that if you are unsure, you are better off not answering instead of guessing.
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fundamental theorem of arithmetic, Fibonacci numbers, proof by picture
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Quiz 13 Test
Note: you win points by answering correctly, but you can also lose points by answering incorrectly (your total points will never be below 0). This means that if you are unsure, you are better off not answering instead of guessing.
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Quiz 14 Test
Note: you win points by answering correctly, but you can also lose points by answering incorrectly (your total points will never be below 0). This means that if you are unsure, you are better off not answering instead of guessing.
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