Title:  Essential Mathematical Skills 
Long Title:  Essential Mathematical Skills 
Field of Study: 
Mathematics

Valid From: 
Semester 1  2012/13 ( September 2012 ) 
Module Coordinator: 
David Goulding 
Module Author: 
AINE NI SHE 
Module Description: 
This module is about numeracy and basic algebraic competence. Its aim is to ensure that the firstyear student acquires proficiency across the spectrum of numerical and algebraic skills needed for the study of science and engineering subjects. Continuous assessment is based on the principle of no compromise on minimal standards for essential skills.

Learning Outcomes 
On successful completion of this module the learner will be able to: 
LO1 
Perform all manner of arithmetical calculations including those of an elementary statistical nature. 
LO2 
Use the laws of indices and logarithms to solve related equations arising in applied problems. 
LO3 
Manipulate a wide variety of algebraic expressions, transpose formulae and employ function notation effectively. 
LO4 
Sketch graphs relating to quantities which are: in direct proportion and in inverse proportion; related linearly, exponentially or logarithmically. 
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). 
No recommendations listed 
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 
Corequisites

No Co Requisites listed 
Module Content & Assessment
Indicative Content 
The Fundamentals of Arithmetic with Applications
The arithmetic of fractions. Decimal notation and calculations. Instruction on how to use a calculator. Ratio and proportion. Percentages. Tax calculations, simple and compound interest. Mensuration to include problems involving basic trigonometry. Approximation, error estimation, absolute, relative and relative percentage error. The calculation of statistical measures of location and dispersion to include arithmetic mean, median, mode, range, quartiles and standard deviation.

Indices and Logarithms
Indices with a discussion of scientific notation and orders of magnitude. Conversion of units. Logarithms and their use in the solution of indicial (exponential) equations.
Discussion of the number e and natural logarithms.

Basic Algebra
The laws of algebra expressed literally and illustrated both numerically and geometrically. Algebraic manipulation and simplification to include the factorisation of reducible quadratics. Transposition of formulae. Function notation with particular emphasis on functions of one variable.

Graphs
Graphs of quantities which are in direction proportion and indirect proportion. Graphs of simple linear, exponential and logarithmic functions. Reduction of nonlinear relations to linear form to allow for the estimation of parameters.

Assessment Breakdown  % 
Course Work  100.00% 
Course Work 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Short Answer Questions 
On the first portion of the indicative content described under heading one up to and including problems on mensuration. 
1 
20.0 
Week 4 
Short Answer Questions 
On the second portion of the indicative content described under heading one to include approximation/error analysis and calculations of a statistical nature. 
1 
20.0 
Week 6 
Short Answer Questions 
A general coverage of scientific notation, orders of magnitude and applied problems requiring a thorough knowledge of indices and logarithms for their solution. 
2 
20.0 
Week 8 
Short Answer Questions 
Algebraic manipulation and simplification, transposition of formulae and effective use of function notation. 
3 
20.0 
Week 10 
Short Answer Questions 
Plotting and analysis of graphs relating to quantities which
are: in direct proportion and in inverse proportion; related
linearly, exponentially or logarithmically. 
4 
20.0 
Sem End 
No End of Module Formal Examination 
Reassessment Requirement 
Repeat the module
The assessment of this module is inextricably linked to the delivery. The student must reattend the module in its entirety in order to be reassessed.

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 class tutor 
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 
This module has no Part Time workload. 
Module Resources
Recommended Book Resources 

 John Bird 2010, Basic Engineering Mathematics, Fourth Ed., Elsevier Science Ltd England [ISBN: 978 1856176972]
 Stroud, K.A.; Booth, Dexter J. 2009, Foundation Mathematics, Palgrave MacMillan England [ISBN: 9780230579071]
 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
 Website: Franco Vivaldi 2009, Essential Mathematics Webbook
 Website: Eric WeissteinWolfram MathWorld
 Website: Wolfram Alpha

Module Delivered in
