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  6. MA1511: Set Theory

MA1511: SET THEORY (2025-2026)

Last modified: 19 Dec 2025 14:46


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 Aberdeen Sustained Study No
Co-ordinators
  • Dr Richard Hepworth

Qualification Prerequisites

  • Either Programme Level 1 or Programme Level 2

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

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

Syllabus

  • The algebra of sets.
  • Relations and functions.
  • Construction of the natural numbers.
  • Induction and strong induction.
  • Finite sets.
  • Construction of the integers.
  • Construction of the rational numbers.
  • Countability and uncountability.
  • Zorn's lemma.

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 31 August 2025 for 1st Term courses and 19 December 2025 for 2nd Term courses.

Summative Assessments

Design Project: Group

Assessment Type Summative Weighting 25
Assessment Weeks Feedback Weeks

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Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualApplyHave a working knowledge of basic logic.
ConceptualCreateBe able to give examples to illustrate the theorems from the course.
ConceptualUnderstandUnderstand Zorn's lemma.
ConceptualUnderstandUnderstand countability.
ConceptualUnderstandUnderstand functions between sets, and relations.
ConceptualUnderstandUnderstand the algebra of sets (including the empty set, intersection, union of sets).
ConceptualUnderstandUnderstand the natural numbers.
FactualRememberBe able to state the main definitions and theorems from the course.
ProceduralApplySolve problems, of varying levels of difficulty, on the material from the course.
ProceduralUnderstandDemonstrate knowledge and understanding of proof techniques from the course.

Homework

Assessment Type Summative Weighting 30
Assessment Weeks Feedback Weeks

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6 x Short Take-Home Assignments (5% each)
Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualApplyHave a working knowledge of basic logic.
ConceptualCreateBe able to give examples to illustrate the theorems from the course.
ConceptualUnderstandUnderstand the natural numbers.
ConceptualUnderstandUnderstand the algebra of sets (including the empty set, intersection, union of sets).
ConceptualUnderstandUnderstand functions between sets, and relations.
ProceduralApplySolve problems, of varying levels of difficulty, on the material from the course.
ProceduralUnderstandDemonstrate knowledge and understanding of proof techniques from the course.

Class Test

Assessment Type Summative Weighting 45
Assessment Weeks Feedback Weeks

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3 x Class Test (15% each)
Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualApplyHave a working knowledge of basic logic.
ConceptualUnderstandUnderstand the algebra of sets (including the empty set, intersection, union of sets).
ConceptualUnderstandUnderstand functions between sets, and relations.
ConceptualUnderstandUnderstand the natural numbers.
ProceduralApplySolve problems, of varying levels of difficulty, on the material from the course.
ProceduralUnderstandDemonstrate knowledge and understanding of proof techniques from the course.

Formative Assessment

There are no assessments for this course.

Resit Assessments

Reassessment

Assessment Type Summative Weighting
Assessment Weeks Feedback Weeks

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For each assessment, a corresponding reassessment will be offered. These have the following form:
• Homeworks: Reassessment consists of a new homework of the same form, assessing the same part of the course.
• Class Tests: Reassessment consists of a homework assessing the same part of the course.
• Group project: Reassessment consists of a solo project of a similar nature.
Each student is entitled to submit the reassessment(s) corresponding to any assessment(s) in which they received a score of E1 or less. Students may not submit reassessments corresponding to assessments in which they received a score of D3 or higher. Students are not obliged to submit all of the reassessments that they are entitled to. Scores for assessments where the student did not submit a reassessment, or was not entitled so submit a reassessment, are carried forward.
Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
ConceptualUnderstandUnderstand Zorn's lemma.
ConceptualApplyHave a working knowledge of basic logic.
ConceptualUnderstandUnderstand the algebra of sets (including the empty set, intersection, union of sets).
FactualRememberBe able to state the main definitions and theorems from the course.
ProceduralUnderstandDemonstrate knowledge and understanding of proof techniques from the course.
ConceptualUnderstandUnderstand countability.
ConceptualCreateBe able to give examples to illustrate the theorems from the course.
ConceptualUnderstandUnderstand functions between sets, and relations.
ConceptualUnderstandUnderstand the natural numbers.
ProceduralApplySolve problems, of varying levels of difficulty, on the material from the course.
 

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