Skip to main content

Module

MAS1701 : Logic, Sets and Counting

  • Offered for Year: 2020/21
  • Module Leader(s): Dr Alina Vdovina
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters
Semester 1 Credit Value: 10
ECTS Credits: 5.0

Aims

To present the notion and techniques of proof, illustrated by results in set theory and basic combinatorics. To stimulate logical thinking and to develop students' skills at constructing mathematical arguments.

Module summary

This module introduces the concept of proof in mathematics. Proof sets mathematics apart from other subjects: within mathematics we can prove statements are unambiguously true, rather than simply collecting evidence in support of statements as in other areas of science. The objects studied in this module are sets and functions between sets. Important techniques of proof presented will include proof by induction and proof by contradiction. The module will conclude with a variety of methods for counting the number of elements in sets.

Outline Of Syllabus

Logic and techniques of proof. Argument by contradiction and mathematical induction.

Sets and set operations.

Functions: composition of functions; injective and surjective functions.

Counting arguments for the number of elements in a set: sequences, permutations and combinations.

Teaching Methods

Module leaders are revising this content in light of the Covid 19 restrictions.
Revised and approved detail information will be available by 17 August.

Assessment Methods

Module leaders are revising this content in light of the Covid 19 restrictions.
Revised and approved detail information will be available by 17 August.

Reading Lists

Timetable