Registry

Module Specifications

Archived Version 2009 - 2010

Module Title	Mathematics for Scientists II
Module Code	MS223
School	School of Mathematical Sciences
Online Module Resources
Module Co-ordinator	Dr Niamh O'Sullivan	Office Number	X135
Level	2	Credit Rating	5
Pre-requisite	None
Co-requisite	None

Module Aims

To give a thorough grounding in probability, statistics and calculus of several variables as required for the successful understanding and solution of problems in science.
To understand how mathematics can be used as a tool for solving scientific problems and a language for communicating information.

Learning Outcomes

To improve mathematical skills and knowledge essential in science.
To develop skills in deductive reasoning and communication of scientific results.

Indicative Time Allowances
	Hours
Lectures	24
Tutorials	12
Laboratories	0
Seminars	0
Independent Learning Time	39

Total	75
Placements
Assignments

NOTE

Assume that a 5 credit module load represents approximately 75 hours' work, which includes all teaching, in-course assignments, laboratory work or other specialised training and an estimated private learning time associated with the module.

Indicative Syllabus

Sets: Definitions; set operations; set identities. Russell''s paradox.

Probability: Random experiments; axioms of probability; independent events; conditional probability; Bayes'' theorem.

Random variables and probability densities: Discrete and continuous random variables; characteristics of random variables; probability distributions and densities.

Some important probability densities: How to count; the binomial, Poisson, Pascal and normal distributions.

Statistical inference: Point estimates and confidence intervals; the central limit theorem; hypothesis tests.

Vector calculus and functions of several variables: Vectors; scalar and cross product; applications. Scalar and vector fields; partial derivatives; div, grad and curl; surfaces; optimization