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Proof techniques for IE

1CM57

About this course

Proof techniques:

  • What is a theorem or lemma?

  • How to formulate a theorem or lemma?

  • What is a proof?

  • Why do we prove?

  • What do we prove?

  • How do we prove?

  • Direct proof

  • Proof by induction

  • Proof by transposition

  • Proof by contradiction

  • Proof by exhaustion

  • Proof by construction

  • Nonconstructive proof

  • Probabilistic proof/sample path

  • Proof nor disproof

  • When is a proof finished?

  • Writing proofs

  • Evaluating proofs

Analysis:

  • To illustrate the different techniques topics like real numbers, axioms, rows, limits, continuity, differentiability, and convexity will be dealt with. Applicability to IE problems is touched upon.

Learning outcomes

PhD student

  • can formulate theorems
  • can distinguish several proof techniques
  • can apply these techniques in a basic setting
  • gains first insight in usefulness of different proof techniques in IE setting

Resources

Additional information

  • Credits
    ECTS 3
  • Level
    bachelor
If anything remains unclear, please check the FAQ of TU Eindhoven.

Offering(s)

  • Start date

    1 September 2024

    • Ends
      31 August 2025
    • Term *
      Block JAAR
    • Location
      Eindhoven
    • Instruction language
      English
    • Register between
      15 Jun, 00:00 - 31 Aug 2025
    Course is currently running
These offerings are valid for students of Utrecht University