An Introduction to Logic

(lectures: 2 hours per week)

 

The course covers the main principles of logic. How to understand the structure of scientific reasoning?

How to distuinguish the different kinds of arguments? How to use logic in problem solving?

Module 1. (Week 1 – Week 6) is about Classical Propositional Logic, a syllabus is here

Module 2. (Week 7 – Week 13) is about Modern Logic: Theory and Applications, a syllabus is here

 

Topics:

1.   Introduction: syntax and semantics.

2.   Reasoning. Solving logical puzzles.   slides

3.   Propositions. Logical equivalence.   slides

4.   Logical operators. Negation, conjunction, disjunction.    slides

5.   Truth tables. Venn diagrams. Logic and set theory.   slides

6.   Midterm exam: logical puzzles..   Sample Test          Solutions for Sample Test
      Midterm Test   (as it should have be)
      Scores

7.   First order logic.   slides

8.   Deductive and inductive reasoning.     slides

9.   Axiomatic theories.     slides

10. Gödel's incompleteness theorems.     slides

11. Logical and statistical inference.

12. Paradoxes and fallacies.     slides

13. Final exam: a comprehensive test.     Sample Test

 

 

Basic readings:

 

Herrick, Paul: The Many Worlds of Logic (second edition) Oxford University Press, 1999.

 

Smullyan, Raymond M.: What Is the Name of This Book?  Prentice-Hall, 1978.

 

Further readings:

 

Hofstadter, Douglas R.: Gödel, Escher, Bach. Random House, 1979.

 

Davis, Philip J. — Hersh, Reuben: The Mathematical Experience. Birkhauser, Study Edition, 1992.

 

Rényi, Alfréd: Dialogues on Mathematics. Holden-Day, 1967.

 

Székely, J. Gábor: Paradoxes in Probability Theory and Mathematical Statistics. Springer, 2002.

 

Waner, S. - Costenoble, S. R.: Introduction to Logic (online version)  

 

 

Evaluation:

 

50% : written test in logical puzzles

50% : written exam in theory of logic
Grading info is here