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Mathematical Modelling with Professional Skills - PHY00024C
Related modules
Pre-requisite modules
- None
Co-requisite modules
- None
Prohibited combinations
Module will run
| Occurrence | Teaching cycle |
|---|---|
| A | Autumn Term 2021-22 to Summer Term 2021-22 |
Module aims
The aim of this module is to illustrate the general principles in constructing models by simple examples, and practice. The level of mathematics used will be modest, and some new simple mathematical techniques will be introduced to extend the range of models that can be studied. Some of the ideas will be implemented using spreadsheets but no computer programming is required. The examples will be drawn mainly from physics. Problems encountered in the real- world will also be discussed. Also it includes a general introduction to the subject, basic IT skills, report writing, use of information resources, experimental techniques, problem solving and computer programming. This will be achieved through a mix of activities, including laboratories, workshops, lectures, programming classes and small group teaching.
Introductory Python Programming
This course introduces problem solving using computers, using Python as the programming language. The most difficult aspect of programming is designing a step-by- step recipe (algorithm) to solve a given problem. This kind of logical problem solving is a useful skill which is highly valued in research and in the commercial world, and which all physicists should learn through practice. Once an algorithm has been designed, it must be implemented in a programming language, which for this course is Python. Python is a modern language which is freely available for Windows, Linux/Unix and Mac OS with extensive documentation, tutorials and extensions available online. It is easy to learn but very powerful, and is increasingly being used commercially and in scientific research. Students will learn how to create programs in the Python language to solve physics problems and then visualise the results in 2D and 3D. The emphasis is on problem solving, and teaching skills which students can then apply to other areas of their study.
Module learning outcomes
- Explain the basic philosophy of mathematical modelling
- Use dimensional analysis to propose a simple mathematical form for a model
- Use the results of experiments to provide values for parameters in the model
- Optimise the parameter values in the model
- Create a model using network analysis
- Derive a mathematical form and solve using calculus-based methods
Module content
Mathematical Modelling Syllabus
- Modelling Principles
- Dimensional analysis and Dimensional similarity
- Fitting and Interpolation
- Optimisation
- Networks
- Difference equations and differential equations
- Numerical Integration
- Stochastic methods
Professional Skills Syllabus
- Induction Activities: Introduction to communication skills, study skills, career planning, personal development planning (3 hour lecture). Library: tour of the JB Morrell library (1 hour) and information retrieval exercises. A basic introduction to IT (web, e-mail, etc) and use of Office applications for scientific presentation (3 hours of computer sessions).
- Statistics: Five lectures on basic concepts in probability and statistics, with weekly coursework problems. Covers the notion of probability and binomial, Poisson, and normal probability distributions.
Introduction to Experimental Laboratory
- Three short workshops on experimental measurement techniques, plotting scientific data, and recording data and analysing errors.
- A core experiment to be presented in a formal report (see First Year Laboratory Handbook for full details).
- Scientific report writing: An introduction to writing scientific reports (1-hour workshop).
- Problem solving skills: Small group discussions with your supervisor, to help develop “thinking-like- a-physicist” skills such as order of magnitude estimations, dimensional analysis, applying differential equations, and curve sketching and interpretation (5 x 1-hour tutorials).
Introductory Python Programming Syllabus
- Problem solving strategies and algorithm development
- Computer programming fundamentals and Python
- Looping with for..in and while loops
- Control using if, elif and else
- Getting input from the user, and printing results
- Debugging and testing methods
- Pythons module system and importing libraries
- Defining functions and using built-in mathematical functions
- Using Visual Python to produce animations of mechanics simulations
Assessment
| Task | Length | % of module mark |
|---|---|---|
| Essay/coursework Induction and laboratory activities |
N/A | 5 |
| Essay/coursework Laboratory Reports |
N/A | 10 |
| Essay/coursework Mathematical Modelling Assignment |
N/A | 10 |
| Essay/coursework Python Assignments totalling: |
N/A | 20 |
| Essay/coursework Statistics |
N/A | 5 |
| Essay/coursework York Strengths |
N/A | 5 |
| Online Exam - 24 hrs (Centrally scheduled) Mathematical Modelling Exam |
8 hours | 40 |
| Practical Laboratory Notebooks |
N/A | 5 |
Special assessment rules
None
Reassessment
| Task | Length | % of module mark |
|---|---|---|
| Essay/coursework Induction and laboratory activities |
N/A | 5 |
| Essay/coursework Laboratory Reports |
N/A | 10 |
| Essay/coursework Mathematical Modelling Assignment |
N/A | 10 |
| Essay/coursework Python Assignments totalling: |
N/A | 20 |
| Essay/coursework Statistics |
N/A | 5 |
| Essay/coursework York Strengths |
N/A | 5 |
| Online Exam - 24 hrs (Centrally scheduled) Mathematical Modelling Exam |
8 hours | 40 |
| Practical Laboratory Notebooks |
N/A | 5 |
Module feedback
Our policy on how you receive feedback for formative and summative purposes is contained in our Department Handbook.
Indicative reading
First course in mathematical modelling (3rd ed) by F P Giordano, D Weir and W P Fox. (Brooks- Cole, 2002)***
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