The art of educated guessing

Course objectives

The aim of the course is to introduce the basic concepts of mathematical modeling and estimation techniques. The phenomena we want to model are usually too complex and therefore it is necessary to introduce some approximations and estimates in the process.

Estimation is used by everyone in the first approximation of a solution. Just as it is used by engineers, it is also used by physicists, mathematicians, economists and all other people in everyday life.

Assessment is most powerful when used in combination with more complex modeling techniques.

The course is problem-oriented, and the emphasis will be on the innovative use of new techniques and their application in solving specific problems.

Enrolment requirements and/or entry competences required for the course

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Learning outcomes at the level of the programme to which the course contributes

  • Apply specific knowledge and skills from selected disciplines constituting cognitive science.
  • Participate in data-driven innovation projects and apply appropriate data science tools.
  • Initiate and sustain innovation activities in an interdisciplinary team.
  • Employ diverse disciplinary tools in exploring and describing the nature of cognitive processes.
  • Critically evaluate cognitive science findings and synthesize information to be employed in a collaborative professional environment.
  • Apply interdisciplinary approach in examining phenomena pertaining to cognition.

Course content (syllabus)

  1. Introduction to the idea of mathematical modeling.
  2. Divide and conquer reasoning.
  3. Use abstraction to organize complexity.
  4. Invariants.
  5. Symmetry and conservation laws.
  6. Proportional reasoning.
  7. Introduction to dimensions and dimensional analysis.
  8. For how long to cook a turkey and other applications of dimensional analysis.
  9. Dimensional analysis in learning theory.
  10. Approximation techniques. Estimating integrals and derivatives in mathematical models.
  11. Pictorial proofs.
  12. Introduction to probability.
  13. Random walks.
  14. Reasoning by analogy.
  15. Understanding complex phenomena.

Student responsibilities

Class attendance. Independent assignments. Midterm exam and final exam.

Required literature

  • S. Mahajan, Street-fighting Mathematics: The art of educated guessing and opportunistic problem solving, The MIT Press 2010
  • S. Mahajan, The Art of Insight in Science and Engineering, The MIT Press 2014

Optional literature

  • A. Zee, Fly by Night Physics: How Physicist use the backs of envelopes, Princeton University Press 2020