Module Code - Title:

MA4603 - SCIENCE MATHEMATICS 3

Year Last Offered:

2025/6

Hours Per Week:

Lecture

2

Lab

0

Tutorial

1

Other

0

Private

7

Credits

6

Grading Type:

N

Prerequisite Modules:

Rationale and Purpose of the Module:

To introduce students to the fundamental ideas of uncertainty through probability. To introduce students to the most widely used statistical distributions and applications thereof. To lay a good foundation for the stream of statistically oriented modules in the fourth year. To introduce statistical inference through the concepts of estimation and hypothesis testing. To introduce students to a modern statistical software package (e.g. MINITAB), and motivate the practice of statistics through the analysis of real data and case studies.

Syllabus:

Variables:continuous and discrete; Representation of variables: frequency tables, histograms, bar charts, etc; Reduction of variables: measures of location and dispersion, mean, variance, range, median, quartiles, etc; Introduction to the fundamentals of probability; Experiments, sample spaces, events; Laws of probability: addition and multiplication, conditional probability (sensitivity and specificity); Introduction to random variables; probability density functions; Special distributions:binomial, normal; Statistical inference: point and interval estimates, standard error of an estimator, hypothesis testing, one and two-tailed tests; One and two sample problems for the mean, variance and proportion; Relationships between quantitative variables:PearsonÆs correlation coefficient; Regression analysis.

Learning Outcomes:

Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)

On successful completion of this module, students should be able to: -Classify data according to type and scale of measurement and distinguish between populations and samples. -Summarise data using graphical and numerical methods -Calculate probabilities based on the application of commonly used distributions e.g. the Normal, Binomial, Poisson and exponential distributions -Construct confidence intervals and test hypotheses about population means, proportions and variances. -Describe, quantify the strength of and model the relationship between two quantitative variables.

Affective (Attitudes and Values)

None

Psychomotor (Physical Skills)

None

How the Module will be Taught and what will be the Learning Experiences of the Students:

Normal lecture and tutorial mode of delivery. Examples used should be appropriate and relevant as far as practicable.

Research Findings Incorporated in to the Syllabus (If Relevant):

Prime Texts:

Wild, C.J., Seber, G.A.F. (2000) Chance Encounters ¿ a first course in data analysis and inference , Wiley

Other Relevant Texts:

McClave, J.T., Dietrich, D.H., and Sincich, T. (1997) Statistics, (7th ed.) , Prentice Hall.

Moore, D.S., and McCabe, G.P. (1998) Introduction to the practice of statistics (3rd Ed.) , Freeman

Chatfield, C. (1981) Statistics for technology", (2nd ed.) , Penguin.

Cheremisinoff, Nicholas P. (1987) Practical statistics for engineers and scientists , Technomic

Scheaffer, Richard L, and McClave, James, T. (1990) Probability and statistics for engineers , PWS-Kent.

Programme(s) in which this Module is Offered:

Semester(s) Module is Offered:

Module Leader:

james.a.sweeney@ul.ie