Introduction to Set Theory

{| An introductory course from the School of Mathematics
 * bgcolor="#E6CFDD" style="border:1px solid #cfcfcf;padding:1em;padding-top:0.5em;padding-bottom:0em;"| Introduction to Set Theory
 * bgcolor="#E6CFDD" style="border:1px solid #cfcfcf;padding:1em;padding-top:0.5em;padding-bottom:0em;"| Introduction to Set Theory


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This course aims to provide a thorough introduction to the subject of set theory. We will cover the following: Set-theoretical paradoxes and means of avoiding them. Sets, relations, functions, order and well-order. Proof by transfinite induction and definitions by transfinite recursion. Cardinal and ordinal numbers and their arithmetic. Construction of the real numbers. Axiom of choice and its consequences.

Course requirements
The following knowledge is required or desirable on commencement of study of this course:
 * knowledge of basic Pure Mathematics
 * knowledge of formal proofs

Course outline
This is an approximate depiction of the course:
 * Propositional Logic
 * Axiomatic Approach
 * Unions and Intersections
 * Algebra of Sets
 * Ordered Pairs
 * Relations
 * Functions
 * Ordering Relations
 * Cardinal Arithmetic
 * Partial, Linear Orderings
 * Well Orderings
 * Comparison Theorem for Well Orderings
 * Isomorphisms
 * Transfinite Recursion Theorem
 * Replacement Axioms
 * Epsilon-Images
 * Ordinals
 * Ordinal Numbers
 * Ordinal Arithmetic

Lecture series

 * Lecture 1 Propositional Logic
 * Lecture 2 not available yet

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