### IA115-3-PS : Mathematical Methods and Statistics

This module provides an introduction to Statistics and Mathematics knowledge particularly in mechanics. The module is therefore taught in two parts: Statistics in the Autumn term and Mathematics in the Spring term. The topics in Statistics start from simple concepts such as data description and distribution, and then cover more advanced topics including discrete random and continuous variable, probability and probability distributions, and hypothesis testing. Students will be introduced to R software which is one of the most widely used statistical analysis software in the world. The topics in Mathematics include Numerical methods, Complex numbers and Mechanics which includes Newton's laws of motion, Moments of forces and the concept of Mechanical energy.

Aims

1. To provide students with a broad understanding from basic to advanced topics in Statistics and Mathematical skills with emphasis on Mechanics.
2. To give students the opportunity to engage actively with activities and class worksheets provided during lectures, labs and classes.
3. To enable students to develop their problem-solving skills by using relevant mathematical and statistical techniques.
4. To equip students with R software knowledge and develop an ability to gather and present the data appropriately.
5. To enable students to develop confidence in presenting solutions and findings to an audience with no specialist knowledge of Statistics and Mechanics.

Learning Outcomes

On successful completion of this module a student is expected to be able to:

1. Calculate and interpret simple summary statistics; measure of location, centre and dispersion.
2. Understand sampling, data presentation, interpretation and visualization.
3. Understand and apply probability rules.
4. Understand discrete and continuous probability distributions.
5. Understand and calculate hypothesis testing for continuous probability distributions.
6. Understand and use of R statistical package to analyse and interpret data.
7. Understand the basics of vector algebra, kinematic of motion and measurement system.
8. Understand and use Newton’s laws of motion, force, momentum and Moments of Forces.
9. Understand and do arithmetic with complex numbers and complex algebra.
10. Understand the basic techniques to use numerical method to solve equations.

Syllabus

Descriptive statistics: data collection and sampling methods; Measure of location, measure of dispersion. Stem and leaf plots, box plots and histograms, pie charts and time series.
Frequency distribution, estimating mean and variance from grouped frequency distribution.
Probability: relative frequencies and probability as a limit; simple and joint events, dependent and independent events. Venn diagrams, union and intersection of events; mutually exclusive events, general addition rule of probability.
Discrete and continuous random variables. Probability distributions: Binomial, geometric, Poison and Normal distribution, hypothesis testing and confidence intervals.
Basic techniques in numerical methods to approximate cubic, log and other equations.
Introduction to vector and vector quantities. Geometrical and algebraic Vector arithmetic and introduction to vector calculus.
Introduction to physical quantities in mechanics. Concepts of variables in motion, the measurement system and their conversion. Kinematics of linear motion. The relationship between distance, time, velocity and acceleration.
Introduction to Newton’s laws of motion. Concept of force, momentum and energy in mechanical systems. Concept and calculation of Moments of forces.
Introduction to complex numbers. Complex number representation on 2-D Cartesian plane. Complex number arithmetic.
Introduction to R package. Using R to calculate statistical quantities such as mean, standard deviation and producing graphs.

Assessment

A 90-minute in-class test (25% of coursework) – Takes place during Week 23
Assignment 500 words (25% of coursework) – Submit in week 26
A two-hour in-class test (50% of coursework) – Takes place during Week 35
A 2.5 hour-exam during the summer exam period. Questions are split 50:50 for Statistics, and Mathematics & Mechanics.

Non-assessed coursework

At the beginning of the Autumn Term students undergo a diagnostic test. Two weeks before each test there is a formative mock test followed by feedback.

40% coursework and 60% exam
Pass mark: 40%