Module overview
The module has two parts. The first part provides an introduction to the topic of operational research (OR). The key role of using models in OR to obtain solutions of practical problems arising in a variety of contexts is emphasised. Some classical problems are analysed and standard techniques for solving them are investigated.
The second part of the module covers computer programming and its use in solving certain types of mathematical problems. The computer programming language used is Python.
One of the pre-requisites for MATH2013
Linked modules
Pre-requisites: MATH1048 AND MATH1059
Aims and Objectives
Learning Outcomes
Learning Outcomes
Having successfully completed this module you will be able to:
- Formulate a mathematical model for certain types of practical problem
- Code simple mathematical algorithm in a programming language (Python), to analyze the computational behavior of such algorithms, and to describe them in writing.
- Appreciate the capabilities and limitations of OR techniques.
- Demonstrate knowledge and understanding of selected OR techniques
- Implement simple mathematical modeling and algorithms for to computational solutions of decision making problems.
Syllabus
Operational Research
- Linear programming (LP): assumptions, applications, geometry of LPs, graphical solution method, simplex method (single-phase and two-phase).
- Elements of integer programming modeling.
- Introduction to algorithms: definition and specification of algorithms; asymptotic estimates of their running times.
- Sorting algorithms.
- Shortest path algorithms for graphs with nonegative arc lengths.
Mathematical Computing
- Python: introduction, basic usage of the software used (either Jupyter notebooks or Spyder)
- Variables: Definition, naming conventions and using sensible names. Integer, float, strings, printing.
- Loops: Concept of iteration, using for and while loops, range function. Semantic whitespace in Python.
- Control flow: Logical statements and boolean variables. if/elif/else.
- Functions: Concept and procedural programming. Definition in Python: def and return keywords. Docstrings and help. Script files, import, packages.
- Data structures: Lists, tuples, dictionaries and sets. Vectors and arrays through numpy.
- LaTeX: Basic environments and sections. Packages such as amsmath. BibTeX and reference managers. Creating long documents.
- Excel: advanced data analysis and presentation. Linking to other packages (eg Python via xlrd and xlwt).
Learning and Teaching
Teaching and learning methods
Lectures, problem classes, computer workshops, private study.
| Type | Hours |
|---|---|
| Completion of assessment task | 60 |
| Lecture | 22 |
| Tutorial | 12 |
| Revision | 24 |
| Supervised time in studio/workshop | 20 |
| Preparation for scheduled sessions | 12 |
| Total study time | 150 |
Resources & Reading list
Textbooks
S.Dasgupta, C.H. Papadimirriou, U. Vazirani (2006). Algorithms. McGraw-Hill.
H.P. Langtangen (2016). A Primer on Scientific Programming with Python. Springer.
A.Saha (2015). Doing Math with Python. No Starch Press.
W.L. Winston (2004). Operations Research: Applications and Algorithms. Thomson Brooks/Cole.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Closed book Examination | 40% |
| Coursework | 40% |
| Coursework | 20% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Examination | 100% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
| Method | Percentage contribution |
|---|---|
| Examination | 100% |
Repeat Information
Repeat type: Internal & External