Module Directory

This module introduces Statistics and some useful Mathematical applications and techniques such as mechanics, Numerical Methods and Complex numbers. 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 and continuous random variables, probability and probability distributions, and hypothesis testing. Students will be introduced to the R software package which is one of the most widely used statistical analysis tools in the world.

The module aims are:

1. To provide students with a broad understanding from basic to advanced topics in Statistics and Mathematical skills with emphasis on broad applicability.


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 and tools.


4. To equip students with R software knowledge and enable them to develop an ability to use and analyse data appropriately.


5. To enable students to develop confidence in presenting solutions and findings to an audience with no specialist knowledge of Statistics and Mathematics.

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 R statistical package to analyse and interpret data.


7. Understand the basics of trigonometry and its applications to vector algebra and use this to study basic classical mechanics and measurement systems.


8. Understand sequences and series and evaluating finite summations (including arithmetic and geometric progressions), and the binomial theorem.


9. Understand and use Newton’s laws of motion and forces


10. Understand and do arithmetic with complex numbers and complex algebra.


11. Understand the basic techniques to use numerical methods for solving equations.

Skills for your professional life (Transferable Skills)

By completing this module, you will be able to transfer your skills in numerous areas as follows:

a) Statistical analysis and modelling: this is extremely useful in many disciplines, including science, engineering and business. In the real world, we need to collect data, and making sense of data requires Statistical techniques. This helps to understand the underlying causes and relationships, model the data and make correct decisions. Probability distributions that you learn in this module are models to fit measured real data and understand the probabilistic nature of the phenomena under study.

b) Application of Mathematics: learning how to apply mathematics to a wide array of real-world problems and situations in this module is a valuable skill in many other fields including data science.

c) Using graphs to solve hard problems: in numerical methods, you learn how to approximate a solution which otherwise cannot be solved by analytic Mathematics.

d) IT skills: you can learn how to use technology for productive, accurate and speedy statistical analysis using the R platform. R is widely used in business communities as well as scientific and engineering disciplines, as it is simpler and more accurate than performing statistical methods on large data sets by hand. Learning R is a great skill you can use in your future studies as well as in your work career. Further, by using NUMBAS (as you also do in the IA112/IA126 modules) you learn how to use software to get instant results from your problem-solving activities. This is also a vital tool in many applications and environments where extensive Mathematics is used.

e) Logical approach: doing advanced topics in Statistics and Mathematics helps you develop additional skills in planning, analysing, and learning methodical and logical approaches to problem-solving. These skills are transferrable to many areas of your future studies and work.

Syllabus

1. Descriptive statistics: data collection and sampling methods; Measures of location, measures of dispersion. Visualisation of data, including plots such as stem and leaf plots, box plots and histograms, pie charts and time series.


2. Frequency distributions, estimating mean and variance from grouped frequency distributions.


3. Probability: relative frequencies and probability as a limit; simple and joint events, dependent and independent events. Venn diagrams, the Union and Intersection of events; mutually exclusive events, general addition rule of probability.


4. Discrete and continuous random variables. Probability distributions: Binomial, geometric, Poisson and Normal distributions, hypothesis testing.


5. Basic techniques in numerical methods to approximate solutions to equations.


6. Introduction to vector and vector quantities. Geometrical and algebraic Vector arithmetic.


7. Introduction to physical quantities in Mechanics. Concepts of variables in motion, the measurement systems, and their conversion. Kinematics of linear motion. The relationship between distance, time, velocity and acceleration.


8. Introduction to Newton’s laws of motion. Concept of force in mechanical systems. Calculation with force diagrams.


9. Introduction to complex numbers. Complex number representation on 2-D Cartesian plane. Complex number arithmetic. Complex numbers as solutions to quadratic equations.


10. Introduction to R package. Manipulating data frames, vectorisation, and basic statistics.

 Teaching and learning on Essex Pathways modules offers students the ability to develop the foundational knowledge, skills, and competences to study at undergraduate level, through a curriculum that is purposely designed to provide an exceptional learning experience. All teaching, learning and assessment materials will be available via Moodle in a consistent and user-friendly manner.

The module is delivered via 1 x 1-hour lecture, 1 x 2-hour class and 1 x 1-hour lab (this will be a mixture of RStudio and Numbas). All lecture notes, classwork exercises and lab exercises are placed on Moodle prior to the teaching events for easy students’ access. Lecture notes will be available in PowerPoint format. Lectures are also available on the Listen Again website (see the module guide on Moodle). Students are expected to complete the lab exercises in labs and/or in their own individual study time. Extra support for this is provided via email and through academic support hours.