Quantitative Methods
Lecture 1
Introduction,
sets and mathematical language
•INM/BAKVM

Outline of the lecture



Syllabus (short version)
•1. Motivational introduction, history of mathematics
•2. Algebraic Expressions
•3. Equations and Inequalities
•4. Matrix calculus
•5. Determinants
•6. Systems of linear algebraic equations
•7. Sequences, limits of sequences
•8. Basic functions of one real variable
•9. Limits of functions of one real variable
•10. Differential calculus of functions of one real variable
•11. Using differential calculus of functions of one real variable
•12. Integral calculus of functions of one variable and its applications
•13. Application of differential and integral calculus in economics and management

Outline of the lecture



Mathematical language
•Simple propositions
•Logical conjunctions
•Some useful equivalences
•Sylogism

Mathematical language



Mathematical language



Mathematical language



Mathematical language



Mathematical language



Mathematical language



Some equivalences I



Some equivalences II



Some equivalences III



Some equivalences IV



Sylogism
Example:
  —  Socrates is a man.
  —  A man is mortal.
Conclude that:
  —  Socrates is mortal.

Sets and
set operations
•Sets
•The empty set
•Set operations
•Some useful equalities

Sets



Sets



Sets



The empty set



Set operations



Set operations



Set operations



Set inclusion



Set operations



Mathematical language: Quantifiers



Mathematical language: Quantifiers



De Morgan’s Laws I



Number domains



Number domains



Number domains