Download 2013/14 - ECM1707 - Probability and Discrete Mathematics Module

2013/14 - ECM1707 - Probability and Discrete Mathematics
Module Title
Probability and Discrete
Mathematics
Credit Value:
15
Module Code
ECM1707
Module Convener:
Dr Ana Rodrigues
(Coordinator)
DURATION: TERM
1
2
3
DURATION: Weeks
0
11 weeks
0
Number of Students Taking Module (anticipated)
212
DESCRIPTION - summary of the module content
Discrete mathematics is concerned with quantities, which vary discretely, as opposed to the continuous variables you have
encountered in calculus. Therefore, on this module, you will be concerned with counting rather than measuring. For example, you will
learn how to enumerate permutations and combinations of objects satisfying specified conditions. This example provides a link to
probability theory, where we determine the probability of each outcome of a combinatorial experiment by expressing the number of
different ways that outcome can be realised as a fraction of all the possibilities. But probability also uses continuous mathematics for
cases where the possible outcomes of an experiment form a continuous range. This module will provide you with the basic concepts
and tools needed for the study of discrete mathematics and probability. As such, it forms an essential part of a rounded mathematical
education, and in particular it is a prerequisite for the modules in the statistics stream within the mathematics syllabus.
Prerequisite module: ECM1706 or equivalent
AIMS - intentions of the module
The aim of this module is to introduce you to some basic topics in discrete mathematics and to the elementary concepts of probability,
including random variables and common probability distributions. In general, the module aims to provide you with some basic, essential
knowledge relevant to all mathematical studies. In particular, it aims to provide a foundation for further study in statistics or stochastic
processes.
INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)
On successful completion of this module you should be able to:
Module Specific Skills and Knowledge:
1 demonstrate a sound understanding of selected essential topics in discrete mathematics and of basic probability theory, including the
ability to apply those concepts in tackling an appropriate range of problems.
Discipline Specific Skills and Knowledge:
2 show sufficient knowledge of fundamental mathematical concepts, manipulations and results, including relevant finite and infinite
summations.
Date of Last Revision: January 20th 2014
2013/14 - ECM1707 - Probability and Discrete Mathematics
Personal and Key Transferable/ Employment Skills and Knowledge:
3 reason using abstract ideas, formulate and solve problems and communicate reasoning and solutions effectively in writing;
4 use learning resources appropriately;
5 exhibit self management and time management skills.
SYLLABUS PLAN - summary of the structure and academic content of the module)
- review of set theory and standard notation;
- review of sums of standard finite and infinite series;
- counting principles;
- methods of proof;
- probability;
- random variables;
- discrete probability distributions;
- discrete bivariate and multivariate distributions;
- continuous random variables: the exponential, gamma, uniform and normal distributions, expectations and moments;
- continuous bivariate and multivariate distributions: joint, marginal and conditional distributions, conditional expectation and variance,
covariance and independence;
- distributions of functions of random variables, linear combinations of random variables, the central limit theorem, approximations to
the binomial and Poisson distributions; distributions derived from the normal distribution.
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled
Learning &
Teaching Activities
49.00
Date of Last Revision: January 20th 2014
Guided
Independent Study
101.00
Placement / Study
Abroad
0.00
2013/14 - ECM1707 - Probability and Discrete Mathematics
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category
Hours of study time
Description
Scheduled learning and teaching activities
33
Lectures
Scheduled learning and teaching activities
5
Problem class
Guided independent study
10
Coursework
Guided independent study
91
Guided independent study
ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment
Size of Assessment (e.g.
duration/length)
ILOs Assessed
Feedback Method
Fortnightly exercise
10 hours
1-4
Tutorial
SUMMATIVE ASSESSMENT (% of credit)
Coursework
20
Written Exams
80
Practical Exams
Form of Assessment
% of Credit
Size of Assessment
(e.g. duration/length)
ILOs Assessed
Feedback Method
Written exam – closed
book
80
2 hours
1-4
In accordance with
CEMPS policy
Coursework – based on
questions submitted for
formative assessment
20
10 hours
1-5
Tutorial/seminar/written
DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment
Form of Re-assessment
ILOs Re-assessed
Time Scale for
Re-reassessment
All above
Written exam (100%)
All
August Ref/Def period
RE-ASSESSMENT NOTES
Referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being
awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the
deferred examination mark combined with the original coursework mark.
RESOURCES
Date of Last Revision: January 20th 2014
2013/14 - ECM1707 - Probability and Discrete Mathematics
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener
ELE – http://vle.exeter.ac.uk
Reading list for this module:
Author
Title
McColl, J
Edition
Probability
CREDIT VALUE
15
PRE-REQUISITE MODULES
ECM1706
CO-REQUISITE MODULES
None
NQF LEVEL (FHEQ)
Publisher
Year
ISBN
Arnold
1995
0000340614269
ECTS VALUE
7.5
1 (NQF Level 4)
AVAILABLE AS DISTANCE
LEARNING
No
ORIGIN DATE
Monday 19 November 2012
LAST REVISION DATE
Monday 20 January 2014
KEY WORDS SEARCH
Probability; discrete mathematics; probability distributions; continuous and discrete random
variables; moment generating function.
Date of Last Revision: January 20th 2014