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MAU11002 Mathematics, statistics and computation

Module Code	MAU11002
Module Title	Mathematics, statistics and computation
Semester taught	Semester 2
ECTS Credits	10
Module Lecturers	Prof. Anthony Brown (calculus) Prof. Marvin Anas Hahn (discrete) Prof. John McDonagh (statistics)
Module Prerequisites	N/A

This module is examined in a 3-hour examination at the end of Semester 2.
The mathematics part of the module contributes 70% towards the overall mark (with 50% based on the exam and 20% based on the tutorials).
The statistics part of the module contributes 30% towards the overall mark (based on a final assignment at the end of the semester).

11 weeks of teaching with 5 lectures, 2 tutorials and 1 computer practical per week.

On successful completion of this module, students will be able to

Use graphs of functions in the context of derivatives and integrals.
Compute derivatives and equations of tangent lines for graphs of standard functions including rational, trigonometric, exponential and logarithmic functions.
Compute definite and indefinite integrals using substitution and integration by parts.
Solve maximisation/minimisation problems using the first derivative test and other applied problems based on population dynamics and radioactive decay.
Algebraically manipulate matrices by addition and multiplication and use Leslie matrices to determine population growth.
Solve systems of linear equations using Gauss-Jordan elimination.
Calculate the determinant of a square matrix and use Gauss-Jordan elimination to determine a matrix inverse.
Find the eigenvalues and the eigenvectors of a given square matrix.
Learn the basic ideas of descriptive statistics, types of variables and measures of central tendency and spread.
Recognise common discrete and continuous distributions and how these naturally arise in life science examples.
Extract information from a data set and make inference about a population using ideas of sampling distributions, confidence intervals and hypothesis testing.
Carry out basic tasks using the statistical software R such as importing, exporting and manipulating data, analysing and graphing data, loading and installing package extensions, as well as using help files and online resources to either solve error queries or achieve more niche capabilities.

Calculus part: functions and graphs, limits, continuity, definition of derivative, rules of differentiation, graphical interpretation of derivatives, optimisation problems, growth and decay applications, semilog and log-log plots, techniques of integration, differential equations and initial value problems.
Discrete part: limits of sequences, difference equations, discrete time models, vectors and matrices, inverse matrices, determinants, systems of difference equations, systems of linear equations, eigenvalues and eigenvectors, Leslie matrices, matrix models.
Statistics part: numerical and graphical descriptions of data, relationships and linear regression, samples and inference, conditional probability and Bayes' rule, discrete and continuous random variables, sampling distribution, confidence intervals, hypothesis testing.