*GSCI0010 *Mathematics for Scientists

## Module Overview

This module is designed to provide students with the mathematics knowledge and skills required for a successful transition to degree-level study in disciplines related to the chemical and biological sciences. The material covered is at a level corresponding to pre-university qualifications such as ASlevel in the UK.

### Aims and Objectives

#### Module Aims

â€¢ Stimulate interest in and to promote the study of mathematical processes that will enhance the studentâ€™s studies in the sciences. â€¢ Develop understanding of mathematical techniques and their application through use of basic number, algebra, trigonometry, matrices, logarithms and calculus. â€¢ Extend the range of mathematical skills available to students and enable them to gain confidence in the use of mathematical techniques. â€¢ Prepare learners for application of mathematical techniques appropriate to their selected area of study in higher education.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

- recall, select and use knowledge of mathematical techniques appropriate to the study of the sciences;
- demonstrate knowledge and understanding of mathematical processes.

##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

- apply mathematical processes, skills and knowledge to some real scientific situations and to solve simple problems;
- interpret data and a variety of graphs and communicate information mathematically.

##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

- manage your own learning;
- apply mathematical methods to solve simple problems.

### Syllabus

Topic 1 :Revision Revision of numerical & algebraic skills Note: Numerical fractions, algebraic fractions, cancelling & crossmultiplication, transposition of formulae, indices and surds. Topic 2: Equations and Polynomials â€¢ set up and solve simple equations as well as linear simultaneous equations in two unknowns using substitution and elimination â€¢ set up and solve quadratic equations using factorisation and formula . Note: do not need to be able to use completing the square Topic 3: Indices and Logarithms â€¢ understand rational indices (positive, negative & zero) including indices expressed as fractions and use them to simplify algebraic expressions â€¢ be able to express a number in the form xÂ´10n â€¢ understand the relationship between indices and logs with special reference to log10 and loge (ln) â€¢ use the laws of logarithms to simplify expressions â€¢ be able to change the base of logs â€¢ be familiar with graphs of e x and e-x use logs to solve equations of the form ax = b and a 2x + ax + b = 0 Topic 4: Graphs â€¢ use coordinates to plot graphs of algebraic equations â€¢ find gradients and equations of straight lines â€¢ understand the relationship between gradients of parallel and perpendicular lines â€¢ plot graphs of pairs of equations Topic 5: Linear laws â€¢ use the equation of the straight line y = mx+ c in determining a linear law â€¢ determine non-linear laws reducible to linear form, such as y = ax 2 + b, y = Topic 6: Trigonometry â€¢ be aware of the 6 trigonometric functions, and use sin, cos and tan to solve problems in 2D and 3D â€¢ know forms of graphs for sin, cos and tan and understand the derivation of the positive and negative values â€¢ know the values of sin, cos and tan for common angles in the range 0o Â£x Â£ 360 o e.g. 0o, 30o, 45o,etc in surd form â€¢ be able to use the sine and cosine rules â€¢ know that area of triangle = Â½ bh = Â½ absinC â€¢ understand definition of a radian and be able to convert degreesÂ«radians â€¢ use formulae s = rq and A = Â½r 2q Topic 7: Statistics â€¢ promote understanding of statistical terms, the ways of gathering and displaying data as well as an awareness of bias â€¢ use analytical techniques to explain, justify and predict from data Topic 8: Matrices â€¢ add subtract and multiply matrices â€¢ identify null and identity matrices â€¢ evaluate determinant of 2x2 matrices â€¢ understand and use AA-1 = A -1A = I â€¢ formulate and solve linear simultaneous equations for 2 unknowns as matrix equations and solve using the inverse matrix method Topic 9: Differentiation â€¢ understand the gradient of a curve at a point as the limit of the gradients of a sequence of chords â€¢ Notes: should understand how to find derivatives of simple functions from first principles â€¢ use the derivative of x n, lnx, ex, sinx, cosx, tanx and constant multiples, sums/differences of these â€¢ find gradient of a curve at a point â€¢ find equation of tangent/normal to a curve at a point â€¢ use the product and quotient rules â€¢ use the chain rule to differentiate functions of the form f(g(x)) â€¢ understand that a derivative gives a rate of change â€¢ find the second derivative of a function â€¢ locate stationary points and distinguish between maxima and minima (by any method) Note: should know that not all stationary points are maxima or minima but don't need to know conditions for points of inflexion Topic 10: Integration â€¢ understand integration as the reverse of differentiation; integrate xn (including n = -1) ex sinx cosx sin2x together with sums/differences and constant multiples of these â€¢ use integration to find a region bounded by a curve and two ordinates or by two curves â€¢ use the trapezium rule and Simpson's rule to obtain approximate values for definite integrals â€¢ apply integration to find volumes of revolution about the x-axis

### Learning and Teaching

#### Teaching and learning methods

Teaching methods include: â€¢ lectures, to include worked examples and question/answer sessions; â€¢ ativities guided through work packs; â€¢ discussion and workshops. Learning activities include: â€¢ Lectures and group taught sessions; â€¢ individual work on examples, supported by tutor input, scussion and workshop sessions; â€¢ work pack activities and additional worksheets; â€¢ open book sessments to support learning in this module; . â€¢ private study and use of recommended text books; â€¢ resources hosted on the Virtual Learning Environment. Study Time allocation: â€¢ Contact Hours: 120 â€¢ Private Study hours: 180 â€¢ Total study time: 180 hours

Type | Hours |
---|---|

Supervised time in studio/workshop | 48 |

Preparation for scheduled sessions | 36 |

Follow-up work | 90 |

Lecture | 72 |

Wider reading or practice | 36 |

Revision | 18 |

Total study time | 300 |

#### Resources & Reading list

Anthony Croft and Robert Davison (5th). Foundation Maths.

### Assessment

#### Summative

Method | Percentage contribution |
---|---|

Examination (120 minutes) | 60% |

Examination (120 minutes) | 40% |

#### Referral

Method | Percentage contribution |
---|---|

Examination (120 minutes) | 60% |

Examination (120 minutes) | 40% |

#### Repeat Information

**Repeat type: Internal & External**