Discrete Mathematics I (ex Discrete Structures and Logic I)

Professor: Evanthia Papadopoulou
Assistant: Maksym Zavershynskyi
Assistant: Sandeep Kumar Dey

Tipo di corso: Lecture
Valore in crediti ECTS: 6
Riferimenti bibliografici sul sito della biblioteca (CoRe)

Academic year 2012/13 - Fall semester

Objectives
This course will introduce the student to logic and to the idea that one can use logical techniques to "prove" mathematical statements. To some extent most students have already "proved" mathematical statements by mechanically manipulating algebraic equations in order to arrive at an answer. For example, proving that a quadratic equation has particular roots. But students are probably unaware that logic is at work underneath the manipulations. In this course, logic and its descriptive power will be explored, and then used to construct more complicated proofs about abstract objects like sets, relations and functions. The student will learn how to structure and execute a logically correct mathematical proof and to analyze proofs written by others.

Contents
Deduction, propositional logic, predicate logic, quantified logic, induction, recursion, sets and set operations, relations, functions, proof techniques.

Teaching mode
Lecture and exercises

References
How to Prove It: A Structured Approach (2nd Ed), Daniel J. Velleman.