# Description

# Advanced Mathematics

Module title | Advanced Mathematics |
---|---|

Module code | INT0045 |

Academic year | 2021/2 |

Credits | 20 |

Module staff | Robin Patrick Dixon (Convenor) |

Duration: Term | 1 | 2 | 3 |
---|---|---|---|

Duration: Weeks | 10 |

Number students taking module (anticipated) | 50 |
---|

## Description - summary of the module content

### Module description

How can you record and manipulate the quantities of different goods in your company warehouse? How can you find out whether your rival company is telling the truth about their products without taking them all to pieces? How high will your fireworks go before they turn and fall back onto the amazed onlookers? How does changing one small thing affect all the other things dependent on it? What is the trajectory of an asteroid escaping from orbit? You can answer all these questions if you study the mathematics taught in this module!

**Pre-requisite modules: INT0007 Foundation Mathematics**

## Module aims - intentions of the module

This module aims to provide a foundation in mathematics for students who intend to follow a degree programme in the areas of Economics, Mathematics, Psychology, Engineering, Science or related disciplines. It builds on the knowledge and skills developed in Foundation Mathematics. Students will be expected to manage their time successfully in order to complete a series of coursework and other tasks.

## Intended Learning Outcomes (ILOs)

### ILO: Module-specific skills

On successfully completing the module you will be able to...

- 1. Use scientific mathematical notation
- 2. Manipulate algebraic expressions and functions
- 3. Demonstrate understanding of and apply mathematical techniques in calculus and statistics
- 4. Recognise and construct graphs from algebraic, logarithmic and exponential functions
- 5. Use some statistical techniques to describe and analyse data

### ILO: Discipline-specific skills

On successfully completing the module you will be able to...

- 6. Demonstrate understanding of mathematical principles required in business and scientific disciplines
- 7. Construct and solve mathematical models representing situations in the business and scientific worlds
- 8. Use the results of calculations to make predictions and interpret answers
- 9. Describe and interpret sets of data using statistical analysis

### ILO: Personal and key skills

On successfully completing the module you will be able to...

- 10. Interpret and analyse data

## Syllabus plan

### Syllabus plan

- Estimation, absolute and relative answers.
- Algebra. Algebraic fractions: cancelling, adding, subtracting, multiplying, and dividing. Partial fractions. The modulus function. Simultaneous equations, 1 linear and 1 quadratic. Inequalities. Division of a polynomial by a linear orquadratic polynomial. The factor theorem. The remainder theorem. Binomial expansion of (1+
*x*)^{n }and (*a+bx*)^{n}, where*n*isan integer or a fraction. - Vectors. Addition, Modulus, Scalar Product, Angle between vectors, Equation of line, Vector Product.
- Function notation:
*y**=**f**(**x**).*Curve sketching of quadratic and cubic functions. Application of simple transformations on the graph*y*=*f**(**x**)*. Domain and range. Composite Functions. - Matrices. Addition, Subtraction, Multiplication of up to 3x3 matrices. Inverse of 2x2 matrix. Using matrices to solve simulations equations.
- Co-ordinate geometry. Sketching curves given by Cartesian equations. Asymptotes.
- Differentiation. e
^{x}, In*x*. The chain rule, the product rule, the quotient rule. Connected rates of change. - Integration of exponentials, log functions. Integration: by substitution, by parts, of rational functions using partial fractions.
- Probability. Random variables. The probability function.
- Statistics. The binomial distribution. Hypothesis testing using the normal distribution.

## Learning and teaching

### Learning activities and teaching methods (given in hours of study time)

Scheduled Learning and Teaching Activities | Guided independent study | Placement / study abroad |
---|---|---|

60 | 140 | 0 |

### Details of learning activities and teaching methods

Category | Hours of study time | Description |
---|---|---|

Scheduled Learning and Teaching activities (synchronous) | 60 | Small group lessons, including lectures, examples, practice and use of computing techniques |

Guided independent study | 140 | Study of written notes, practise examples, using resources supplies on ELE and other on-line learning material |

## Assessment

### Formative assessment

Form of assessment | Size of the assessment (eg length / duration) | ILOs assessed | Feedback method |
---|---|---|---|

Practice online final exam quiz | 2 hours | 1-10 | Verbal and answers on ELE |

### Summative assessment (% of credit)

Coursework | Written exams | Practical exams |
---|---|---|

30 | 70 | 0 |

### Details of summative assessment

Form of assessment | % of credit | Size of the assessment (eg length / duration) | ILOs assessed | Feedback method |
---|---|---|---|---|

Coursework assignments | 30 | Several (usually 5) online Computer Marked Assessments each taking approximately 3 hours | 1-10 | Online feedback immediately after submission |

Final Examination (open book) | 70 | 2 hours online quiz | 1-10 | Written feedback on formal submission |

## Re-assessment

### Details of re-assessment (where required by referral or deferral)

Original form of assessment | Form of re-assessment | ILOs re-assessed | Timescale for re-assessment |
---|---|---|---|

Examination | Examination (2 hour online quiz) | 1-10 | Next assessment opportunity |

### Re-assessment notes

Deferral – if you miss an assessment for reasons judged legitimate by the Mitigation Committee, the applicable assessment will normally be deferred. See ‘Details of reassessment’ for the form that assessment usually takes. When deferral occurs there is ordinarily no change to the overall weighting of that assessment.

Referral – if you have failed the module overall (i.e. a final overall module mark of less than 40%) you will be required to take a re-sit exam. Only your performance in this exam will count towards your final module grade. A grade of 40% will be awarded if the examination is passed.

## Resources

### Indicative learning resources - Basic reading

Hanrahan, V., Matthews, J., Porkess, R. & Secker, P. (2004). *MEI AS Pure Mathematics C1 and C2: MEI Structured Mathematics* (3^{rd} Ed.). London: Hodder Murray.

Berry, C., Hanrahan, V., Porkess, R., Secker, P.(2004). *MEI A2 Pure Mathematics C3 and C4: MEI Structured Mathematics* (3^{rd} Ed.). London: Hodder Murray.

Eccles, A., Francis, B., Graham, A.,& Porkess, R. (2004). *MEI Statistics 1: MEI Structured Mathematics* (3^{rd} Ed.). London: Hodder Murray.

Eccles, A., Francis, B., Green, N.,& Porkess, R. (2004). *MEI Statistics 2: MEI Structured Mathematics* (3^{rd} Ed.). London: Hodder Murray.

Berry, C., Martin, D., & Heard, T., (2004). *MEI AS Further Pure Mathematics FP1*:* MEI Structured Mathematics* (3^{rd} Ed.). London: Hodder Murray.

### Indicative learning resources - Web based and electronic resources

ELE – http://vle.exeter.ac.uk/course/view.php?id=8184

Module has an active ELE page

### Indicative learning resources - Other resources

Pledger, K., Attwood, G., MacPherson, A., Moran, B., Petran, J. & Wilkins, D. (2004). *Core Mathematics 1: Heinemann Modular Mathematics*. Oxford: Heinemann Educational.

Pledger, K., Attwood, G., MacPherson, A., Moran, B., Petran, J., Staley, G. & Wilkins, D. (2004). *Core Mathematics 2: Heinemann Modular Mathematics*. Oxford: Heinemann Educational.

Pledger, K., Attwood, G., MacPherson, A., Moran, B., Petran, J., Staley, G. & Wilkins, D. (2004). *Core Mathematics 3: Heinemann Modular Mathematics.* Oxford: Heinemann Educational.

Attwood, G., Dyer, G. & Skipworth, G. (2000). *Statistics 1: Heinemann Modular Mathematics*. Oxford: Heinemann Educational.

### Key words search

Mathematics, Foundation Mathematics, Foundation Statistics

Credit value | 20 |
---|---|

Module ECTS | 10 |

Module pre-requisites | Foundation Maths |

Module co-requisites | None |

NQF level (module) | 3 |

Available as distance learning? | Yes |

Origin date | 20/08/2019 |

Last revision date | 27/07/2021 |