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  6. MA1511: SET THEORY

MA1511: SET THEORY (2014-2015)

Last modified: 28 Jun 2018 10:27


Course Overview

Set theory was introduced by Cantor in 1872, who was attempting to understand the concept of "infinity" which defied the mathematical world since the Greeks. Set Theory is fundamental to modern mathematics - any mathematical theory must be formulated within the framework of set theory, or else it is deemed invalid. It is the alphabet of mathematics.

In this course we will study naive set theory. Fundamental object such as the natural numbers and the real numbers will be constructed. Structures such as partial orders and functions will be studied. And of course, we will explore infinite sets.



Course Details

Study Type Undergraduate Level 1
Term Second Term Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Dr Assaf Libman

What courses & programmes must have been taken before this course?

None.

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

Course Aims: The aim of this course is to make the students familiar the fundamental background necessary to understand all the later courses in mathematics. Main Learning Outcomes: The students should learn and get the working knowlegde of the material described in the Content section. Content: * Truth tables, examples of proofs; * sets, subsets, union, intersection, power set etc; * relations, linear and partial orders; * equivalence relation; * functions, images, preimages etc., bijections, cardinality; * construction of the natural numbers, integers, rational and real numbers; * countable and uncountable sets; * mathematical induction; * the axiom of choice and Zorn's lemma; Optional topics: * well ordered sets, ordinals; Schroeder-Bernstein's theorem; * transfinite induction and well ordering theorem; * Propositional logic - completeness and compactness.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

1st Attempt: 1 two hour written examination (70%) in course assessment (30%) Resit: 1 two hour written examination (100%)

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials.

Course Learning Outcomes

None.
 

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