Module Details
| Module Code: |
MATH6056 |
| Title: |
Maths for Biological Sciences
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Long Title:
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Maths for Biological Sciences
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| NFQ Level: |
Fundamental |
| Valid From: |
Semester 1 - 2017/18 ( September 2017 ) |
| Field of Study: |
4610 - Mathematics
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| Module Description: |
An introduction to fundamental mathematical calculations and problem solving aimed at consolidating and developing student competence in the mathematical techniques which are central to the biological sciences.
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| Learning Outcomes |
| On successful completion of this module the learner will be able to: |
| # |
Learning Outcome Description |
| LO1 |
Perform a range of arithmetical calculations necessary for laboratory work in the biological sciences. |
| LO2 |
Manipulate a wide variety of algebraic expressions, transpose formulae, solve linear and quadratic equations, and solve systems of simultaneous equations. |
| LO3 |
Use the laws of indices and logarithms to solve related equations arising in applied problems. |
| LO4 |
Sketch graphs relating to quantities which are: in direct proportion and in inverse proportion; related linearly, exponentially or logarithmically. |
| LO5 |
Reduce equations to linear form and determine parameters from appropriate graphs. |
| LO6 |
Sketch a sinusoidal waveform and identify its salient characteristics. |
| LO7 |
Apply differentiation to problems regarding rate of change and optimization. |
| Dependencies |
Module Recommendations
This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named MTU module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s).
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Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list.
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| No incompatible modules listed |
Co-requisite Modules
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| No Co-requisite modules listed |
Requirements
This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section.
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| No requirements listed |
| Indicative Content |
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The Fundamentals of Arithmetic with Applications
SI units, prefixes, conversion of units. Ratio and proportion. Application to molarity, concentration. Scientific notation and significant figures. Approximation, error estimation, absolute, relative and relative percentage error.
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Basic Algebra
Order of operations (BODMAS rule). Algebraic manipulation and simplification to include the factorisation of reducible quadratics. Transposition of formulae. Solution of linear and quadratic equations. Simultaneous equations.
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Indices and Logarithms
The laws of indices. Logarithms and their use in the solution of indicial (exponential) equations.
Discussion of the number e and natural logarithms.
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Functions and Graphs
Function notation with particular emphasis on functions of one variable. Independent variable, dependent variable. Graphs of quantities which are in direct proportion and indirect proportion. Graphs of linear functions and quadratic functions. Exponential growth and exponential decay. Reduction of non-linear relations to linear form to allow for the estimation of parameters.
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Differentiation
Definition and graphical interpretation of the derivative. Differentiation of common functions using table look-up. Instantaneous rate of change. Maximum and minimum turning points of quadratic/cubic functions.
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Trigonometry
Angle measurement in degrees and radians. Conversion between degrees and radians and vice versa. Introduction of the trigonometric ratios via the unit circle. Solution of simple trigonometric equations. Graphing sine and cosine waveforms. Characteristics of a waveform: amplitude, period, frequency and phase.
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Module Content & Assessment
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| Assessment Breakdown | % |
|---|
| Coursework | 40.00% |
| End of Module Formal Examination | 60.00% |
Assessments
| End of Module Formal Examination |
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| Reassessment Requirement |
Repeat examination
Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.
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The University reserves the right to alter the nature and timings of assessment
Module Workload
| Workload: Full Time |
| Workload Type |
Contact Type |
Workload Description |
Frequency |
Average Weekly Learner Workload |
Hours |
| Lecture |
Contact |
Exposition of theory with illustrative concrete examples |
Every Week |
3.00 |
3 |
| Tutorial |
Contact |
Student problem solving under guidance of lecturer |
Every Week |
2.00 |
2 |
| Independent & Directed Learning (Non-contact) |
Non Contact |
Study of lecture material and exercise sheets |
Every Week |
2.00 |
2 |
| Total Hours |
7.00 |
| Total Weekly Learner Workload |
7.00 |
| Total Weekly Contact Hours |
5.00 |
| Workload: Part Time |
| Workload Type |
Contact Type |
Workload Description |
Frequency |
Average Weekly Learner Workload |
Hours |
| Lecture |
Contact |
Exposition of theory with illustrative concrete examples |
Every Week |
3.00 |
3 |
| Tutorial |
Contact |
Student problem solving under guidance of lecturer |
Every Week |
1.00 |
1 |
| Independent & Directed Learning (Non-contact) |
Non Contact |
Study of lecture material and exercise sheets |
Every Week |
3.00 |
3 |
| Total Hours |
7.00 |
| Total Weekly Learner Workload |
7.00 |
| Total Weekly Contact Hours |
4.00 |
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Module Resources
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| Recommended Book Resources |
|---|
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John Bird. (2014), Basic Engineering Mathematics, 6th. Elsevier Science Ltd, England, p.372, [ISBN: 9780415662789].
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Stroud, K.A.; Booth, Dexter J.. (2009), Foundation Mathematics, Palgrave MacMillan, England, p.752, [ISBN: 9780230579071].
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John Bird. (2014), Basic Engineering Mathematics [ebook], 6th. Elsevier Science Ltd, England, [ISBN: 9781315858845].
| | Supplementary Book Resources |
|---|
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Alicia Sevilla & Kay Somers. (2007), Quantitative Reasoning: Tools for Today's Informed Citizen, First. Key College Publishing, USA, p.613, [ISBN: 878-1-931914-90-1].
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COMAP. (2002), For All Practical Purposes: Mathematical Literacy in Today's World, Sixth. COMAP, USA, [ISBN: 978-0716738176].
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James F. Burkhart. (1999), Quantitative and qualitative reasoning skills, Second. Kendall/Hunt Publishing, USA, p.179, [ISBN: 978-0787263782].
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Donald Pierce, Don Pierce & Edward B. Wright. (1997), Mathematics for Life: A Foundation Course for Quantitative Literacy, Preliminary. Prentice Hall, [ISBN: 978-0134938592].
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Paul Monk and Lindsey J. Munro. Maths for chemistry, [ISBN: 978-0-19-954129-4].
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Frank H. Stephenson. Calculations for molecular biology and biotechnology, [ISBN: 978-0-12-375690-9].
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Applying maths in the chemical and biomolecular sciences: an example-based approach, [ISBN: 978-0-19-923091-4].
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Ehud Lamm, Ron Unger,. Biological Computation, [ISBN: 978-1-4200-8795-6].
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Philip R. Bevington, D. Keith Robinson. Data reduction and error analysis for the physical sciences, [ISBN: 978-0-07-119926-1].
| | Supplementary Article/Paper Resources |
|---|
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Mathematical Association of America. (2007), Calculation vs. Context,
| | Other Resources |
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Website, CIT Maths Online, available through Blackboard.
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Website, Franco Vivaldi. (2009), Essential Mathematics Web-book,
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Website, Eric Weisstein. Wolfram MathWorld,
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Website, Wolfram Alpha,
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Website, MathTutor,
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Website, MathCentre. MathCentre,
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Website, Khan Academy,
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