Module FOUN0331: NUMERICAL SKILLS AND RESEARCH METHODS FOR SCIENTISTS

Department: FOUNDATION YEAR [Queen's Campus, Stockton]

FOUN0331: NUMERICAL SKILLS AND RESEARCH METHODS FOR SCIENTISTS

Prerequisites

• None.

Corequisites

• None.

Excluded Combination of Modules

• Numerical Skills and Research Methods for Social Scientists (FOUN0321).

Aims

• To introduce and develop a bank of mathematical skills, which students can apply in a range of contexts.
• To introduce and develop understanding of basic statistical principles to provide a foundation for future study in the sciences.
• To develop students' learning skills.
• To develop a problem solving approach.
• To encourage students to develop confidence in their own abilities in maths.

Content

• Number: Arithmetic (+,-,x,/) directed whole numbers, fractions and decimals.
• Efficient accurate use of a calculator.
• Ratio, proportion (direct and inverse and using graphs).
• Percentages.
• Estimation, approximation and accuracy.
• Index notation (integer indices).
• vx and x??, surds and rational indices.
• Standard Index notation (a x 10m).
• Introduction to logarithms.
• Calculations using scientific formulae.
• Algebra: Symbols.
• Algebraic formulae, evaluation of terms.
• Formulation and solution of algebraic equations in one unknown.
• Use of brackets, collecting terms etc, algebraic expansion, elementary factorisations.
• Simultaneous linear equations in two unknowns.
• Functions as processes, concept of function, inverse function (simple cases).
• Graphs: Cartesian coordinates, linear graphs, the equation y=mx + c.
• Graphs from formulae, graph plotting, Rate of Change.
• Solving equations graphically.
• Exponential growth and decay.
• Mensuration: Measurement, length, area (triangles, quadrilaterals, circles), Volume.
• Angles, triangles, Pythagoras' theorem, Sine, Cosine and tangent for acute angles, Radians/degrees.
• Quadrilaterals, Symmetry, order of rotational symmetry.
• Statistics: Sampling - Distinctions between sample and population, Need for randomness in selecting a sample.
• Tabulation - Discrete/continuous data, Tally charts, frequency and grouped frequency tables, Class intervals and Implications of grouping.
• Representation - Bar Charts, Pie Charts, Histograms, Recognising visual misrepresentation.
• Measures of location - Mean and mode for raw data and frequency distribution, Median for raw data.
• Measures of Spread - Range, Quartiles, Inter-quartile range, Variance, standard deviation for raw data, frequency distribution.
• Correlation - Scatter diagrams +ve, -ve, or lack of correlation, line of best fit (by eye) through (x,y), interpolation and extrapolation.
• Probability - Venn diagrams.
• Range 0-1, impossible to certainty, Probabilities of equally likely events, Probability as a limit to relative frequency, Simple Addition and Multiplication of probabilities as appropriate, Tree diagrams.

Learning Outcomes

• By the end of the module the students will have acquired the skills to be able to:
• use a calculator appropriately in relation to problems faced.
• confidently manipulate items listed on the attached syllabus in a range of contexts.
• carry out a range of statistical procedures as listed on the attached syllabus.
• construct accurate graphs from data or calculation and analyse by interpolation or extrapolation and rate of change calculations.
• conduct a survey and analyse results statistically.

• By the end of the module the students will:
• be able to communicate effectively in writing
• be able to demonstrate problem solving skills
• have improved their own learning and performance
• be able to apply number both in the tackling of numerical problems and in the collecting, recording, interpreting and presenting of data

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Theory, initial concepts and techniques will be introduced during lectures.
• Much of the learning, understanding and consolidation will take place through the use of structured worksheets during tutorials and students' own time.
• Knowledge and ability to use and apply concepts and techniques will be tested in the module test.
• the end of the module exam.
• and in some pieces of work within the portfolio produced under invigilated conditions.
• Construction and analysis of graphs will also be consolidated and assessed by a task within the coursework portfolio.
• Design, implementation and statistical analysis of surveys will be consolidated and assessed through the independent production of a statistics project.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Students will be given self-testing units on a weekly basis.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University