NUMBERS AND SETS - 2020/1
Module code: MAT2051
This module introduces students to some aspects of number theory, combinatorics and set theory. It complements other pure mathematics modules by considering a variety of topics not encountered elsewhere.
FISHER David (Maths)
Number of Credits: 15
ECTS Credits: 7.5
Framework: FHEQ Level 5
JACs code: G130
Module cap (Maximum number of students): N/A
Prerequisites / Co-requisites
Indicative content includes:
Review of basics:Euclidean algorithm, prime factorization, congruences, Euler’s totient function.
Chinese Remainder Theorem, Fermat's Little Theorem, Wilson's Theorem.
Arithmetic functions. Möbius inversion.
Quadratic residues. Quadratic reciprocity. Euler's criterion. The Legendre symbol.
Simple Diophantine equations.
Recurrence relations, generating functions, partitions.
Binomial identities and their application to combinatorial problems.
Axioms of set theory. Relations on sets.Ordered sets.The axiom of choice.
Countability. Cardinal and ordinal numbers.
|Assessment type||Unit of assessment||Weighting|
|School-timetabled exam/test||CLASS TESTS (50 MINS)||20|
The assessment strategy is designed to provide students with the opportunity to demonstrate their ability to
construct and interpret mathematical arguments in the context of this module;
display subject knowledge by recalling key definitions and results;
apply the techniques learnt to both routine and unfamiliar problems.
Thus, the summative assessment for this module consists of:
One two-hour examination at the end of Semester 2, worth 80% of the module mark.
One class test, worth 20% of the module mark.
Formative assessment and feedback
Students receive written comments on their marked coursework assignments. Verbal feedback is provided in lectures and office hours.
- provide an insight into classical number theory and its applications, and to some elementary combinatorics
- introduce axiomatic set theory and investigate properties of infinite sets
- establish a basis for further study in pure mathematics and logic
|001||Demonstrate an awareness of some standard results and methods in number theory and set theory||K|
|002||Apply the basic techniques of number theory to congruences, arithmetic functions and public-key cryptography||KC|
|003||Calculate Legendre symbols using quadratic reciprocity||KC|
|004||Use binomial coefficients to solve simple problems in combinatorics||KC|
|005||Be familiar with the axioms of set theory, have a basic understanding of cardinal and ordinal numbers, know the axiom of choice and its equivalents||KC|
|006||Construct simple proofs similar to those encountered in the module.||KCT|
C - Cognitive/analytical
K - Subject knowledge
T - Transferable skills
P - Professional/Practical skills
Overall student workload
Independent Study Hours: 117
Lecture Hours: 33
Methods of Teaching / Learning
The learning and teaching strategy is designed to provide:
Knowledge of the theory and practice of the topics covered.
Experience of the methods used to interpret, understand and solve problems in these areas.
The learning and teaching methods include:
Three 50-minute lectures per week for eleven weeks, some being used as problem classes.
Online notes supplemented by additional examples in lectures.
Two unassessed coursework assignments, marked and returned.
Personal assistance given to individuals and small groups in office hours.
Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.
Programmes this module appears in
|Mathematics and Physics BSc (Hons)||2||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics and Physics MPhys||2||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics and Physics MMath||2||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics with Statistics MMath||2||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics with Statistics BSc (Hons)||2||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics BSc (Hons)||2||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics MMath||2||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics with Music BSc (Hons)||2||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Financial Mathematics BSc (Hons)||2||Optional||A weighted aggregate mark of 40% is required to pass the module|
Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2020/1 academic year.