Registry

Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Mathematics for Scientists II
Module Code	MS223
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Niamh O'Sullivan Semester 2: Niamh O'Sullivan Autumn: Niamh O'Sullivan
Module Teacher	Niamh O'Sullivan
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

The aim of this module is 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. Students will learn how mathematics can be used as a tool for solving scientific problems and a language for communicating information. This is a know-how and skills module. Students will participate in the following learning activities: Lectures: Students will attend two one-hour lectures per week. These lectures are designed to introduce learners to the mathematical principles and problem solving techniques that underpin this module. Tutorials: Each student will attend one one-hour tutorial per week. Problem sheets based on lecture content are distributed to the students and they are strongly advised to attempt all tutorial questions in advance of the tutorial.Reading: Students are expected to fully utilise the textbooks recommended.

Learning Outcomes

1. Demonstrate an understanding of concepts by use of examples or counterexamples.
2. Apply the rules of probability and assign probabilities to events.
3. Know how to obtain expectations of discrete and continuous random variables.
4. Use the normal and student t-distributions to test statistical hypotheses and to compute confidence intervals.
5. Perform the calculations that arise when the calculus of several variables is used to solve problems.

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	24	Two lectures per week
Independent learning	64	Study over 16 weeks-including exam preiod
Examination	2	End of Semester Exam
Tutorial	10	Weekly Tutorial
Directed learning	25	Solving Tutorial questions
Total Workload: 125

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

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.
Basic combinatorics, 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 problems..

Assessment Breakdown
Continuous Assessment	30%	Examination Weight	70%

Course Work Breakdown
Type	Description	% of total	Assessment Date
In Class Test	Short Test	15%	Week 25
In Class Test	Short Test	15%	Sem 2 End

Reassessment Requirement
Resit arrangements are explained by the following categories; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
This module is category 3

Indicative Reading List