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20cs700 [2020-09-03] – [Synopsis] Martin Ziegler20cs700 [2020-09-17] – [Synopsis] Martin Ziegler
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 ==== Synopsis ==== ==== Synopsis ====
-**0. Introduction & Motivation** ({{20cs700_.pdf|pdf}},{{20cs700_.ppt|ppt}}): \\+**0. Introduction & Motivation** ({{20cs700_.pdf|pdf}},{{20cs700_.ppt|ppt}},[[https://drive.google.com/file/d/1JQcoCtv6o9Yo3wTGCmTbkt2F8jV_egDm/|video]]): \\
 "Virtues" of Computer Science and Mathematics,  "Virtues" of Computer Science and Mathematics, 
 Abstract Data Types / Structures in Computer Science and Mathematics, Abstract Data Types / Structures in Computer Science and Mathematics,
 IEEE 754 / Floatingpoint Discretization Properties and Reliability, IEEE 754 / Floatingpoint Discretization Properties and Reliability,
 Numerical Folklore and Myths \\ Numerical Folklore and Myths \\
-**I. Recap on discrete Theory of Computation** ({{20cs700a.pdf|pdf}},{{20cs700a.ppt|ppt}}): \\ +**I. Recap on discrete Theory of Computation** ({{20cs700a.pdf|pdf}},{{20cs700a.ppt|ppt}},[[https://drive.google.com/file/d/1yuqN1sJ5GK9-sSrwVSaaYV0TmN-m0kR4/|video1]],[[https://drive.google.com/file/d/1B9dN6RNsuKLfGdmrjjfx6596K3wRVFe7|video2]]): \\ 
-Un-/Computability, Halting Problem, Semi-/Decidability, Reduction, WHILE model of computation, SMN property/Currying, Oracle computation \\ +Un-/Computability, Halting Problem, Semi-/Decidability, Reduction, WHILE model of computation, SMN property/Currying, Oracle computation, Limit Lemma, Arithmetic Hierarchy \\ 
-**II. Computability theory over the Reals**: \\ +**II. Computability theory over the Reals**:  \\ 
-real numbers: binary vs. approximation +a)   Computing Real Numbers: three equivalent notions, counter/examples, oracle-computable reals/limit Lemma ([[https://drive.google.com/file/d/1goACIp9v1Lva1m7tUx8E7_bS2xawIfUT|video]]) \\ 
-sequences, limits, rate of convergence +b)  Computing Real Sequences: semi-decidability / strong undecidability of equality, no computable sequence contains all computable reals  ([[https://drive.google.com/file/d/14TqLkBtmdQy5A-bLUDb0juOAmQKxcW-j|video]])\\ 
-qualitative stability: computability and continuity +c)  Computing Real Functions: closure under composition and restriction and sequences, necessarily continuous, computable Weierstrass Theorem ([[https://drive.google.com/file/d/1bD4sUmWErYefwmnXKibD08s04XPTDW6W|video]])\\ 
-real arithmetic, join, maximum, integral +d)  Advanced Un/Computility of Real Functions: uncomputable Argmin/Root Finding, uncomputable Derivative, uncomputable ODE, uncomputable, Wave Equation, compactness in Real Computation \\ 
-root finding, argmax, derivative +e)  Multi-Functions & Enrichment: generalized restriction, fundamental theorem of algebra, fuzzy sign, Archimedian property, linear algebra, analytic functions \\ 
-uncomputable wave equation +f)  Computing Real Operators: encoding continuous functions, encoding compact subsets \\
-analytic functions, discrete enrichment +
-multivaluedness, computability in linear algebra \\+
 **III. Computability on T0 spaces**: \\ **III. Computability on T0 spaces**: \\
 C[0;1] and computable Weierstrass Theorem C[0;1] and computable Weierstrass Theorem
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 2nd-order polynomial complexity theory 2nd-order polynomial complexity theory
 Weihrauch reductions Weihrauch reductions
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 ==== Test questions for self-assessment ==== ==== Test questions for self-assessment ====
 Mathematical background: Mathematical background: