Skip to Main Content
It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results.

Elements of Set Theory and Mathematical logic: Course Contents (MAT 102)

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects

Course Outline

Set theory:

Sets, subsets, operations with sets:

union,intersection, difference, symmetric difference,

Cartesian product and disjoint union.

Functions: graph of a function.

Composition; injections,

surjections, bijections, inverse function.

Computing cardinals:

Cardinality of Cartesian product, union.

Cardinality of all functions from a set to another  set.  

Cardinality  of  all  injective,  surjective 

bijective functions from a set to another set.

Infinite sets, finite sets.

Countable sets,

properties, examples (Z, Q).

R is not countable. R, RxR, RxRxR have the same cardinal.

Operations with cardinal numbers.

Cantor-Bernstein theorem.


Equivalence relations,

partitions, quotient set; examples,

parallelism, similarity of triangles.

Order relations, min, max, inf, sup; linear order.

Examples: N, Z, R, P(A). Well ordered sets and induction.

Inductively ordered sets and Zorn’s lemma.

Mathematical logic:

Propositional Calculus.

Truth tables. Predicate Calculus.

E Books

Text Books

Related Books

Ask help

Google books

Google Book Search