Registry
Module Specifications
Archived Version 2015 - 2016
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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. | |||||||||||||||||||||||||||||||||||||||||
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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. | |||||||||||||||||||||||||||||||||||||||||
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 |
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Indicative Content and
Learning Activities SetsDefinitions, set operations; set identities. Russell's paradox.ProbabilityRandom experiments; axioms of probability; independent events; conditional probability; Bayes' theoremRandom variables and probability densitiesDiscrete and continuous random variables; characteristics of random variables; probability distributions and densities.Some important probability densitiesBasic combinatorics, the binomial, Poisson, Pascal and normal distributions.Statistical inferencePoint estimates and confidence intervals; the central limit theorem; hypothesis tests.Vector calculus and functions of several variablesVectors; scalar and cross product; applications. Scalar and vector fields; partial derivatives; div, grad and curl; surfaces; optimization problems. | |||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources None | |||||||||||||||||||||||||||||||||||||||||
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