This course provides a very brief overview of fundamental mathematical concepts such as propositional and predicate logic, set theory, the number system, and proof techniques.
Students will be able to at the end of the course :
- Recognize the logical structure underlying simple puzzles
- Have the ability to manipulate logical expressions
- Describe the relationship between logic and set theory.
- Differentiate between natural, integer, rational, real, and complex numbers.
- Recognize various basic proof techniques
1. (A) Introduction
- Overview and motivation of the topics to be treated in the course.
(B) Propositional logic
- The building blocks
- Basic operations
- De Morgan's laws
- The Lady or the Tiger?
(C) Predicate logic, set theory, and functions
- Predicate logic
- Predicate logic and set notation
- Functions and their graphs
- Onto and one-to-one
2. (A) Numbers
- The natural numbers
- The other numbers
(C) Final test