Module FOUD0701: Core Foundation Maths for Bioscientists

Department: Foundation Year (Durham)

FOUD0701: Core Foundation Maths for Bioscientists

Pre-requisites

Corequisites

Excluded Combinations

Aims

• To improve confidence in algebraic manipulation through the study of mathematical techniques and development of investigative skills.
• To introduce and develop a knowledge of logarithms and their uses.
• To introduce and develop a knowledge of trigonometry.
• To introduce and develop understanding of a range of standard techniques for differentiation and integration.
• To include trigonometric and logarithmic functions.
• To introduce and develop a bank of mathematical skills, which students can apply in a range of biological sciences contexts
• To introduce and develop understanding of basic statistical principles to provide a foundation for future study.

Content

• Quadratic equations, factorisation, graphs, quadratic formula.
• Trigonometry, sine, cosine, tangent.
• Sequences and Series , Arithmetic, geometric, use of sigma notation.
• Indices and Logarithms: laws, solution of equations.
• Reduction of a given relation to linear form, graphical determination of constants.
• Rate of change, increasing/decreasing functions, maxima and minima.
• Differentiation of: algebraic polynomials ,composite functions (chain rule), sum, product or quotient of two functions, trigonometric and exponential functions.
• Evaluation of integrals by using standard forms or partial fractions.
• Second derivatives of standard functions.
• Factor theorem.
• Percentage use
• Linear equations, Substitution and transposition of formulae
• Pythagoras' theorem
• Standard Index form
• Area and Volume, Symmetry
• Applications in scientific calculations
• Introduction to statistics: Mean. mode, median, standard deviation and histograms
• Proportional reasoning and Application of number to biomedical calculations

Learning Outcomes

• By the end of this module the student will have acquired the knowledge to be able to:
• confidently manipulate a range of algebraic expressions as needed in a variety of contexts.
• use logarithms to solve problems and to predict relationships from graphs.
• differentiate and integrate a number of different types of functions.

• By the end of this module the student will have acquired the skills to be able to:
• recall, select and use knowledge of appropriate integration and differentiation techniques as needed in a variety of contexts.
• confidently manipulate a range of algebraic expressions and use a range of techniques as required in problems appropriate to the syllabus.

• By the end of the module students will be able to:
• communicate effectively in writing.
• be able to apply number both in the tackling of numerical problems and in the collecting, recording, interpreting and presenting of data.
• be able to demonstrate problem solving skills.
• Invigilated test covers learning outcomes:SSK1. SSK2, SSK3, SSS1, SSS2, KS1, KS2, KS3, (ie everything)
• Class tests cover all above
• Coursework covers all above.

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 and seminars.
• Much of the learning, understanding and consolidation will take place through the use of structured exercise during seminar and tutorial sessions and students own time.
• Manipulative skills and ability to recall, select and apply mathematics including calculus will be assessed by an end of module test and a portfolio of tasks including some short invigilated tests and solutions to questions set on a weekly basis.
• Logarithms and prediction of relationships from graphs will be consolidated and assessed within a coursework task.
• In addition to obtaining an overall weighted mark of 50% or above, students must obtain a mark of 50% or above for the following element/s - Invigilated test.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment

Students will be given self testing units on a weekly basis. The module has variety form of assessment; portfolio tasks with a rapid marking turnaround fulfill a formative as well as summative role.