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XX10190: Programming and discrete mathematics

Follow this link for further information on academic years Academic Year: 2019/0
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 12      [equivalent to 24 CATS credits]
Further information on notional study hours Notional Study Hours: 240
Further information on unit levels Level: Certificate (FHEQ level 4)
Further information on teaching periods Period:
Academic Year
Further information on unit assessment Assessment Summary: CW 50%, EX 50%
Further information on unit assessment Assessment Detail:
  • Coursework 1 (CW 25%)
  • Coursework 2 (CW 25%)
  • Examination 1 (EX 20%)
  • Examination 2 (EX 30%)
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: You must have A Level Mathematics grade A or equivalent in order to take this unit.
Further information on descriptions Description: Aims:
To teach generic programming skills and a range of topics in discrete mathematics which are connected to computation.

Learning Outcomes:
After taking this unit, the student should be able to:
* Apply the basic principles of programming in studying problems in discrete mathematics.
* Make proper use of data structures in the applications context.
* Demonstrate understanding of a range of mathematical topics which relate to computation, such as modular arithmetic, elementary graph theory and elementary computational number theory and their applications.
* Analyse the complexity of simple algorithms
* Explain the use of some famous algorithms such as the Fast Fourier Transform.
* Use the MATLAB programming environment.

Skills:
Numeracy T/F A
Problem Solving T/F A
Information Technology T/F A

Content:
The role of computing in mathematics
Matlab programming environment: Editing, importing and exporting data, getting help, functionality, graphics and mathematical applications.
Control structures for programming: Pseudocode, selection statements, repetition statements. Elementary logic in programming.
Elementary mathematical applications: e.g. summing series.
Data types: integers, real and complex numbers. Binary representation. Arrays, user-defined data structures.
Procedures, types of variables, parameter passing, scope of functions, functions as arguments. Applications, e.g. to modular arithmetic.
Graphs, trees, sorting and searching: applications.
Complexity of algorithms, order of an algorithm, examples of algorithms with logarithmic, polynomial and exponential order. Proofs by induction.
Recursion and its relation to induction.
Mathematical applications of recursion, e.g. Pascal's triangle, Euclid's algorithm, computing fractals.
Matrices and matrix operations. Applications, e.g. Fibonacci numbers, modelling networks.
Object-oriented programming. The object oriented paradigm, defining classes in Matlab, encapsulation. Examples from graphics.
Software development. The difficulty of formal proof, and the importance of testing. "black box" versus "white box" testing. Test coverage, and its importance in Matlab.
Cryptography, RSA. Error correcting codes.
Digital signal processing and FFT.
Further information on programme availabilityProgramme availability:

XX10190 is Compulsory on the following programmes:

Department of Mathematical Sciences
  • USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 1)
  • USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 1)
  • USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 1)
  • USMA-AFB13 : BSc(Hons) Mathematics (Year 1)
  • USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 1)
  • USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 1)
  • USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 1)
  • USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 1)
  • USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 1)
  • USMA-AFB05 : BSc(Hons) Statistics (Year 1)
  • USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 1)
  • USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 1)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 1)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 1)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 1)

Notes: