# MATH06072 2019 Mathematics for Science 3

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**Description**

Further development of mathematical techniques necessary for scientists

### Learning Outcomes

*On completion of this module the learner will/should be able to;*

**1.**

Use the laws of logarithms to solve complex equations, analyse exponential data and plots

**2.**

Use exponents to perform population analysis and determine the half life and cell doubling times of natural growth and decay.

**3.**

Perform probability calculations of single and multiple events and use normal distribution to determine biological probabilities.

**4.**

Perform calculations with simple matrices, solve systems of simultaneous equations using matrix methods.

**5.**

Evaluate integral calculus problems and determine the area under various curves

### Teaching and Learning Strategies

This module will be delivered full time. This will include 2 live lectures per week supported by online VLE (Moodle) based notes, videos and associated quizzes.

These lectures are augmented by 2 x 1 hr "Maths practicals" where students can work on the online quizzes and written problems in an informal setting with one or more tutors present to provide assistance and feedback.

### Module Assessment Strategies

Students are required to achieve 100% in each online Quiz before the deadline. (Summative)

Students complete 1 CA tests based on these online Quiz. (Summative)

Students complete 8 written worksheets into their Journal. (Summative)

Attendance at all Maths practicals is recorded and the Journal mark is multiplied by this value.

### Repeat Assessments

Repeat Continuous Assessment and/or Final Exam

### Module Dependencies

**Prerequisites**

**Co-requisites**

**Incompatibles**

### Indicative Syllabus

**Use the laws of logarithms to solve complex equations, analyse exponential data and plots**

- Convert powers to logs and vice versa
- Solve complex log equations
- Use the laws of logs
- Determine the nature of exponential curves
- Use semi log paper to plot exponential curves
- Analyse exponential data to determine its base equation.

**Use exponents to perform population analysis and determine the half life and cell doubling times of natural growth and decay.**

- Growth and decay functions and curves
- Half life & cell doubling times calculations
- Carbon dating

**Perform probability calculations of single and multiple events and use normal distribution to determine biological probabilities.**

- Probability theory
- Independent and dependent events
- Mutually exclusive/complementary events
- AND OR NOT rules of probability
- Marginal and conditional probabilities
- Probability trees
- Standard Normal distributions and Z scores
- Calculations finding the probability and percentile values using normal distribution tables

**Perform calculations with simple matrices, solve systems of simultaneous equations using matrix methods. **

- Order of a matrix
- Addition, subtraction and multiplication of matrices
- Transpose and inverse of a matrix
- Using matrix inverses to solve systems of linear equations
- Using matrix row operations to solve systems of linear equations

**Evaluate integral calculus problems and determine the area under various curves **

- Indefinite integrals and the constant of integration
- Boundary conditions and definite integrals
- Using the rules of integrals
- Evaluating integral expressions
- Determining the area under a curve

### Coursework & Assessment Breakdown

**Coursework & Continuous Assessment**

**End of Semester / Year Formal Exam**

### Coursework Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
---|---|---|---|---|---|---|

1 | Moodle quizzes | Continuous Assessment | Assessment | 10 % | OnGoing | 1,2,3,4,5 |

2 | CA Test | Continuous Assessment | Assessment | 15 % | Week 9 | 1,2,3,4 |

3 | Journal | Continuous Assessment | Written Report | 15 % | OnGoing | 1,2,3,4,5 |

### End of Semester / Year Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
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1 | Final exam. | Final Exam | Closed Book Exam | 60 % | End of Semester | 1,2,3,4,5 |

### Full Time Mode Workload

Type | Location | Description | Hours | Frequency | Avg Workload |
---|---|---|---|---|---|

Lecture | Tiered Classroom | Lecture | 2 | Weekly | 2.00 |

Tutorial | Computer Laboratory | Maths Practical | 1 | Weekly | 1.00 |

Independent Learning | Not Specified | Self Study | 4 | Weekly | 4.00 |

### Required & Recommended Book List

**Required Reading**

2012-09-06

*Maths for Science*OUP Oxford

ISBN 0199644969 ISBN-13 9780199644964

Maths for Science overturns the misconception that maths is a daunting, theory-filled subject by providing a confidence-boosting overview of essential mathematical skills and techniques. Written in a clear, straightforward style, with examples and practice problems throughout, it is the ideal guide for all science students.

### Module Resources

**Non ISBN Literary Resources**

None

**Journal Resources**

None

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**Additional Information**

None