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Note that this schedule will be updated frequently in the course of the semester!
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Lecture 1: January 16 Introduction, general remarks, administrative points. Early history of mathematics. |
Lecture 2: January 18 The origins of mathematics: Egypt, Babylonia, Greece |
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Lecture 3: January 23 Early mathematics. Proof that the square root of 2 is irrational. |
Lecture 4: January 25 Proof that there are infinitely many primes. Mathematical notation. |
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Lecture 5: January 30 The notion of proof: deductive validity. |
Lecture 6: February 1 More about arguments: possibility, objectiveness, forms of arguments, inductive/deductive reasoning. |
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Lecture 7: February 6 (Early course evaluations). Proofs by contradiction. |
Lecture 8: February 8 Definitions. |
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Lecture 9: February 13
(Early course evaluation results). Axiomatic theories. |
Lecture 10: February 15
Consistency and independence. |
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Lecture 11: February 20
Axiomatizations of geometry. Axiomatizations of number theory. |
Lecture 12: February 22
Philosophical and mathematical limitations of axiomatizations. |
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Lecture 13: February 27
Let's Make a Deal problem. Axioms of Probability. |
Lecture 14: March 1
Review. Bring your own questions! |
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Midterm, March 6
Midterm exam |
March 8
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Lecture 15: March 13
Conditional probability. Bayes' Theorem. Deductive solution to the problem. |
Lecture 16: March 15
Another application of probability theory. |
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Lecture 17: March 20
Aristotle's syllogisms. Terminology |
Lecture 18: March 22
Propositional logic |
March 27
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March 29
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Lecture 19: April 3
More propositional logic: Knights & Knaves, Natural Deduction |
Lecture 20: April 5
Quantifiers. |
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Lecture 21: April 10
Non-classical logics. Mathematical Induction (I) |
Lecture 22: April 12
Deadline: Essay topic has to be approved. Mathematical Induction (II) |
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Lecture 23: April 17
Set Theory. Functions. |
Lecture 24: April 19
Deadline: Essay outline has to be handed in. Cardinality of N, Z, Q. |
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Lecture 25: April 24
Cardinality of R. |
Lecture 26: April 26
Deadline:Essay due. Philosophy of mathematics |
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May 1
Bring your own questions! |
May 3
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