Title:  Maths for Biological Sciences 
Long Title:  Maths for Biological Sciences 
Field of Study: 
Mathematics

Valid From: 
Semester 1  2017/18 ( September 2017 ) 
Module Coordinator: 
Brigid Lucey 
Module Author: 
AINE NI SHE 
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. 
Learning Outcomes 
On successful completion of this module the learner will be able to: 
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. 
Prerequisite learning 
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 CIT module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s). 

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. 
No incompatible modules listed 
Corequisite Modules

No Corequisite 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.

No requirements listed 
Module Content & Assessment
Indicative Content 
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.

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.

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.

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 nonlinear relations to linear form to allow for the estimation of parameters.

Differentiation
Definition and graphical interpretation of the derivative. Differentiation of common functions using table lookup. Instantaneous rate of change. Maximum and minimum turning points of quadratic/cubic functions.

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.

Assessment Breakdown  % 
Course Work  40.00% 
End of Module Formal Examination  60.00% 
Course Work 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Short Answer Questions 
Inclass test 
1,2 
20.0 
Week 5 
Short Answer Questions 
Inclass test 
2,3,4 
20.0 
Week 9 
End of Module Formal Examination 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Formal Exam 
EndofSemester Final Examination 
1,2,3,4,5,6,7 
60.0 
EndofSemester 
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.

The institute reserves the right to alter the nature and timings of assessment
Module Workload
Workload: Full Time 
Workload Type 
Workload Description 
Hours 
Frequency 
Average Weekly Learner Workload 
Lecture 
Exposition of theory with illustrative concrete examples 
3.0 
Every Week 
3.00 
Tutorial 
Student problem solving under guidance of lecturer 
2.0 
Every Week 
2.00 
Independent & Directed Learning (Noncontact) 
Study of lecture material and exercise sheets 
2.0 
Every Week 
2.00 
Total Hours 
7.00 
Total Weekly Learner Workload 
7.00 
Total Weekly Contact Hours 
5.00 
Workload: Part Time 
Workload Type 
Workload Description 
Hours 
Frequency 
Average Weekly Learner Workload 
Lecture 
Exposition of theory with illustrative concrete examples 
3.0 
Every Week 
3.00 
Tutorial 
Student problem solving under guidance of lecturer 
1.0 
Every Week 
1.00 
Independent & Directed Learning (Noncontact) 
Study of lecture material and exercise sheets 
3.0 
Every Week 
3.00 
Total Hours 
7.00 
Total Weekly Learner Workload 
7.00 
Total Weekly Contact Hours 
4.00 
Module Resources
Recommended Book Resources 

 John Bird 2014, Basic Engineering Mathematics, 6th Ed., Elsevier Science Ltd England [ISBN: 9780415662789]
 Stroud, K.A.; Booth, Dexter J. 2009, Foundation Mathematics, Palgrave MacMillan England [ISBN: 9780230579071]
 John Bird 2014, Basic Engineering Mathematics [ebook], 6th Ed., Elsevier Science Ltd England [ISBN: 9781315858845]
 Supplementary Book Resources 

 Alicia Sevilla & Kay Somers 2007, Quantitative Reasoning: Tools for Today's Informed Citizen, First Ed., Key College Publishing USA [ISBN: 8781931914901]
 COMAP 2002, For All Practical Purposes: Mathematical Literacy in Today's World, Sixth Ed., COMAP USA [ISBN: 9780716738176]
 James F. Burkhart 1999, Quantitative and qualitative reasoning skills, Second Ed., Kendall/Hunt Publishing USA [ISBN: 9780787263782]
 Donald Pierce, Don Pierce & Edward B. Wright 1997, Mathematics for Life: A Foundation Course for Quantitative Literacy, Preliminary Ed., Prentice Hall [ISBN: 9780134938592]
 Paul Monk and Lindsey J. Munro, Maths for chemistry [ISBN: 9780199541294]
 Frank H. Stephenson, Calculations for molecular biology and biotechnology [ISBN: 9780123756909]
 Applying maths in the chemical and biomolecular sciences: an examplebased approach [ISBN: 9780199230914]
 Ehud Lamm, Ron Unger,, Biological Computation [ISBN: 9781420087956]
 Philip R. Bevington, D. Keith Robinson, Data reduction and error analysis for the physical sciences [ISBN: 9780071199261]
 Supplementary Article/Paper Resources 

 Mathematical Association of America 2007, Calculation vs. Context
 Other Resources 

 Website: CIT Maths Online, available through Blackboard
 Website: Franco Vivaldi 2009, Essential Mathematics Webbook
 Website: Eric WeissteinWolfram MathWorld
 Website: Wolfram Alpha
 Website: MathTutor
 Website: MathCentreMathCentre
 Website: Khan Academy

Module Delivered in
