Introductory description

FP041-15 Scientific Programming and Mathematical Modelling

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

1. Introduction to data science and scientific programming in Python
   What is data science?
   Introduction to Python
   The use of Python for data scientist
   Variables and data types
   Operation and function
   Python data science libraries: numpy, panda, matplotlib

2. Introduction to Mathematical Modelling
   Different types of model
   Mathematical model
   Applications and classifications of mathematical model
   Limitations of mathematical model
   4 stages of mathematical modelling
   Applying mathematical modelling to provide insights and predictions to real world problems

3. Modelling using functions and structured data
   Mathematical expression, equations, and functions
   Understanding the difference between equations and functions
   Recognizing functions from relations, graph, structured data, and word problem
   Constructing a linear function from structured data and word problem
   System of linear model

4. Basics of descriptive and inferential analysis
   Empirical data and statistics
   Using measures of central tendency and measures of spread to summarize and describe data
   Population and samples
   Using interval estimates and hypothesis testing to make inferences about the population from which the sample is drawn
   P-value and confidence interval
   Limitations of descriptive and inferential statistics

5. Statistics fundamentals with Python
   Importing data sets to analyse in Python (datasets, csv files, and excel spreadsheet)
   Using describe and summarize function in python to do descriptive analysis
   Illustrate data using data visualization tools
   Using statistical functions in Python for measures of central tendency and spread
   Measures of correlations between pairs of data

6. Modelling with linear regression
   Introduction to simple linear regression
   Dependent and independent variables
   Coefficient estimate
   Using Ordinary Least Square method to estimate the values of the coefficients
   Making predictions with simple linear regression

7. Big data analytics with python
   What is big data?
   Importing and analysing large data sets in Python
   Model development
   Preparing data for linear regression in Python
   Using python to build a linear regression model from large data sets.
   Making predictions based on the model developed.

Learning outcomes

By the end of the module, students should be able to:

• Critically observe a real-world problem and applying the 4-stages of mathematical modelling (building, analysing, validating, and applying) to provide insights and predictions.
• Demonstrate understanding of basic mathematical concepts in data science, relating to linear function, descriptive analysis, inferential analysis, and linear regression.
• Utilize Python to prepare data for analysis, perform simple data analysis, create meaningful data visualization, and make prediction from data.
• Produce a rigorous analytical report which considers a broad range of mathematical and statistical methods to describe, analyse, extrapolate, and apply big data.

Indicative reading list

Bender, E.A., 2012. An introduction to mathematical modeling. Courier Corporation.

Hill, C., 2016. Learning scientific programming with Python. Cambridge University Press.

Langtangen, H.P. and Langtangen, H.P., 2009. A primer on scientific programming with Python (Vol. 2). Berlin, Germany: Springer.

View reading list on Talis Aspire

Interdisciplinary

This module has links between Mathematics, Data Science, and Computer Science.

Subject specific skills

Mathematical Skills

Analytical Skills

Problem-solving skills

Investigative Skills

IT Skills

Transferable skills

Mathematical Skills

Analytical Skills

Problem-solving skills

Communication Skills

Investigative Skills

IT Skills