## IA115-3-FY-CO:

Mathematical Methods and Statistics

## Key module for

BSC LG18 Economics and Mathematics (Including Foundation Year),

BSC L1G8 Economics with Mathematics (Including Foundation Year),

BSC GN18 Finance and Mathematics (Including Foundation Year),

BSC G104 Mathematics (Including Foundation Year),

BSC 9K18 Statistics (Including Foundation Year),

BSC G1G8 Mathematics with Computing (Including Foundation Year),

BSC G1F5 Mathematics with Physics (Including Foundation Year),

BSC I1GF Data Science and Analytics (Including Foundation Year)

## Module description

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 variables, 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 include Newton's laws of motion, Moments of forces and the concept of Mechanical energy.

## Module aims

The aims of this module are:

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

## Module learning outcomes

By the end of this module, students will be expected to be able to:

- Calculate and interpret simple summary statistics; the measure of location, centre and dispersion.
- Understand sampling, data presentation, interpretation and visualization.
- Understand and apply probability rules.
- Understand discrete and continuous probability distributions.
- Understand and calculate hypothesis testing for continuous probability distributions.
- Understand and use of R statistical package to analyse and interpret data.
- Understand the basics of vector algebra, kinematics of motion and measurement systems.
- Understand and use Newton’s laws of motion, force, momentum and Moments of Forces.
- Understand and do arithmetic with complex numbers and complex algebra.
- Understand the basic techniques to use numerical methods to solve equations.

**Skills for your professional life (Transferable Skills)**

By the end of this module, students will have practised the following transferrable skills:

- 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. The probability distributions you learn in this module are indeed models to fit our observation of real data and understand the probabilistic nature of the phenomena under study.
- Application of Mathematics: Mathematics is not just a hobby with numbers. Learning the application of Mathematics in Mechanics in this module is a valuable skill that can be equally valid in many other fields including data science where Mathematics is applied to real-world problems.
- Using graphs to solve hard problems: in numerical methods, you learn how to approximate a solution which otherwise cannot be solved by analytic Mathematics.
- IT skills: you can learn how to use technology for productive, accurate and speedy statistical analysis in the R platform. R is widely sued in business communities as well as scientific and engineering disciplines. Using statistical methods in the old style is tedious and unproductive. Learning R is a great skill you can use in your future studies as well as in your work career. Further, by using NUMBAS you learn how to use software to get instant results from your problem-solving activity. This is also a vital tool in many applications and environments where extensive Mathematics is used.
- 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.

## Module information

*Syllabus*

- Descriptive statistics: data collection and sampling methods; Measure of location, the 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 the 2-D Cartesian plane. Complex number arithmetic.
- Introduction to R package. Using R to calculate statistical quantities, manipulating data frames, calculating probabilities and visualising data using various graphs.

## Learning and teaching methods

This module will be delivered via:

- One 1-hour lecture per week.
- One 2-hour class per week.
- One 1-hour lab session per week.

The lab session will be the R-statistical tool for statistics in the first term and NUMBAS on Moodle for the topics in the second term).

Teaching and learning on Essex Pathways modules offers students the ability to develop the foundation knowledge, skills, and competencies to study at the 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.

All lecture notes, classwork exercises and lab exercises are placed on Moodle prior to the teaching events for easy student access. Lecture notes will be enhanced by audio input for each lecture slide to make it easier to follow the topics on the slide. Students are expected to complete the lab exercises using the R-statistical tool (free to download and install) in term one, and on NUMBAS in Moodle in term two, in their own individual study time. Support for this is provided via email and through Academic Support Hours.

## Bibliography

## Assessment items, weightings and deadlines

Coursework / exam | Description | Deadline | Coursework weighting |
---|---|---|---|

Coursework | IA115 In-person, Open Book (restricted) Test 1 | 33% | |

Coursework | IA115 In-person, Open Book (restricted) Test 2 | 33% | |

Coursework | IA115 - R Lab Work | 17% | |

Coursework | IA115 - NUMBAS Lab Work | 17% | |

Exam | Main exam: In-Person, Open Book (Restricted), 150 minutes during Summer (Main Period) | ||

Exam | Reassessment Main exam: In-Person, Open Book (Restricted), 150 minutes during September (Reassessment Period) |

### Additional coursework information

*Formative assessment*

- Students engage in-class activities, and lab exercises with R-Statistics for Statistics in the first term and NUMBAS for Mechanics and other topics in term two. Students get feedback in class and lab sessions, as well as via emails and one-to-one meetings where necessary.

*Summative assessment*

- In-person, open book (restricted) test 1 (1.5 hours) - this will be given in week 9 and will cover only topics in Statistics. Test 1 covers all topics up to and including the topics in week 8.
- R lab work - throughout term 1, you will practice on the R platform. Every week you learn how to use R to carry out simple tasks in Statistics. You are awarded 10% for completing the tasks in the labs.
- In-person, open book (restricted) test 2 (2 hours) - this will be given in week 23 and will include only topics covered in term two up to and including the topics in week 22.
- NUMBAS lab work (10%) - every week, throughout term 2 you will tackle and complete tasks in the labs on the NUMBAS platform. You are awarded 10% for completing the tasks in the lab.
- In-person, open book (restricted) 2.5 hrs exam - all topics from both terms 1 and 2 will be covered in the exam except for questions in the R platform.

*Reassessment strategy*

- Failed exam - Resit the exam which is re-aggregated with the existing coursework mark to create a new module mark.
- Failed coursework - Resit the exam, which counts as coursework, and resubmit R lab work. The weighting will be divided 90:10 between the resit exam and R lab work to create a new coursework mark. This mark is then re-aggregated with the existing exam mark to create a new module mark. The reassessment task will enable the relevant learning outcomes to be met.
- Failed exam and coursework - Resit the exam and resubmit R lab work. The weighting will be divided 90:10 between the resit exam and R lab work to create a new module mark.

### Exam format definitions

**Remote, open book:**Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.**In-person, open book:**Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.**In-person, open book (restricted):**The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.**In-person, closed book:**The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

### Overall assessment

Coursework | Exam |
---|---|

60% | 40% |

### Reassessment

Coursework | Exam |
---|---|

60% | 40% |

## External examiner

**67**hours,

**64 (95.5%)**hours available to students:

**0**hours not recorded due to service coverage or fault;

**3**hours not recorded due to opt-out by lecturer(s), module, or event type.

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