Mathematical Methods and Statistics

The details

Requisites for this module

BSC N325 Actuarial Science (Including Foundation Year),

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 I1GF Data Science and Analytics (Including Foundation Year)

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 I1GF Data Science and Analytics (Including Foundation Year)

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.

-To provide students with a broad understanding from basic to advanced topics in Statistics and Mathematical skills with 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.

-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.

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.

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.

Formative assessment

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.

Summative assessment

Students will be required to submit a formative piece of writing during the term. This will not be graded, but feedback and guidance will be given as to how this could be improved in the future. The purpose of the formative assessment is to ensure that students become familiar with academic writing.

Coursework is comprised of two in-class tests and one assignment:

- in-class test 1 (25%)

- 500-word assignment (25%)

- in-class test 2 (50%)

2.5 hours exam during Summer Exam period. Questions are split 50:50 for Statistics, and Mathematics & Mechanics.

Reassessment strategy

Failed Exam:

Resit the exam which is re-aggregated with existing coursework mark to create a new module aggregate.

Failed Coursework:

Resubmit a piece of coursework (500 words) which is re-aggregated with existing exam mark to create a new module aggregate. The reassessment task will replace the coursework component and will enable the relevant learning outcomes to be met.

Failed Exam and Coursework:

Resit the exam and resubmit one piece of coursework (500 words) to be aggregated to create a new module aggregate.

- 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.

Formative assessment

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.

Summative assessment

Students will be required to submit a formative piece of writing during the term. This will not be graded, but feedback and guidance will be given as to how this could be improved in the future. The purpose of the formative assessment is to ensure that students become familiar with academic writing.

Coursework is comprised of two in-class tests and one assignment:

- in-class test 1 (25%)

- 500-word assignment (25%)

- in-class test 2 (50%)

2.5 hours exam during Summer Exam period. Questions are split 50:50 for Statistics, and Mathematics & Mechanics.

Reassessment strategy

Failed Exam:

Resit the exam which is re-aggregated with existing coursework mark to create a new module aggregate.

Failed Coursework:

Resubmit a piece of coursework (500 words) which is re-aggregated with existing exam mark to create a new module aggregate. The reassessment task will replace the coursework component and will enable the relevant learning outcomes to be met.

Failed Exam and Coursework:

Resit the exam and resubmit one piece of coursework (500 words) to be aggregated to create a new module aggregate.

In the Autumn Term, the module is delivered via a one-hour lecture; one-hour computer lab and one two-hour class in each week. In the Spring Term, the module is delivered via one-hour lecture; one-hour maths lab and a one two-hour class. The activities and class worksheets have a range of questions from basic level to strengthen students’ knowledge and more advanced level to challenge and intellectually stimulate more able students.
There are a total of twenty teaching weeks over the autumn and spring terms, with two weeks of revision lectures and classes in the summer term. All lecture notes and exercises are placed on Moodle for easy student access. ‘Listen Again’ is also used as part of learning support in which students can review the recordings at a later date.

This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.

Coursework / exam | Description | Deadline | Weighting |
---|---|---|---|

Coursework | In-class test 1 | 25% | |

Coursework | In-class test 2 | 50% | |

Coursework | Assignment | 25% | |

Exam | 210 minutes during Summer (Main Period) (Main) |

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

40% | 60% |

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

40% | 60% |

Module supervisor and teaching staff

Availability

No external examiner information available for this module.

Resources

Further information

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