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Module MAU11002: Mathematics, Statistics and Computation II

Credit weighting (ECTS)

10 credits

Semester/term taught

Semester 2

Methods of Teaching and Student Learning
11 weeks; 8 hours per week, including 5 lectures, 2 tutorials and 1 computer practical.

2 lecturers from the School of Mathematics
1 lecturer from the School of Computer Science and Statistics
teaching assistants/demonstrators for tutorials and practicals

4 lectures + 2 tutorials per week will be taught by the School of Mathematics;
1 lecture + 1 computer practical per week will be taught by the School of Computer Science and Statistics

Lecturers

Dr. José Moreno (calculus)

Dr. Anthony Brown (linear algebra)

Dr. John McDonagh (statistics)

Learning Outcomes

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 functions, roots, trigonometric, exponential and logs and compositions of them;
find indefinite and definite integrals including the use of substitution and integration by parts;
solve simple maximisation/minimisation problems using the first derivative test and other applications including problems based on population dynamics and radioactive decay;
select the correct method from those covered in the module to solve wordy calculus problems, including 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 by Gauss-Jordan elimination;
calculate the determinant of a matrix and understand its connection to the existence of a matrix inverse; use Gauss-Jordan elimination to determine a matrix inverse;
determine the eigenvalues and eigenvectors of a matrix
determine the eigenvalues and eigenvectors of a matrix and link these quantities to population dynamics;
Understand the basic ideas of descriptive statistics, types of variables and measures of central tendency and spread.
Appreciate basic principles of counting to motivate an intuitive definition of probability and appreciate its axioms in a life science context.
Understand common discrete and continuous distributions and how these naturally arise in life science examples.
Understand how to take information from a data set in order to make inference about the population, appreciating the core ideas of sampling distributions, confidence intervals and the logic of hypothesis testing.
Have a basic understanding of the statistical software R including importing and exporting data, basic manipulation, analysing and graphing (visualisation) of data, loading and installing package extensions, and how to use help files and on-line resources to solve error queries or to achieve more niche capabilities.

Module Content

The module is divided into a maths and a statistics part, with maths further divided into calculus and linear algebra/discrete mathematics.

Mathematics:
a) Calculus:
3 lectures plus one tutorial per week. The syllabus is largely based on the text book [Stewart-Day], and will cover most of Chapters 1-6 along with the beginning of Chapter 7 on differential equations:

Functions and graphs. Lines, polynomials, rational functions, exponential and logarithmic functions, trigonometric functions and the unit circle.
Limits, continuity, average rate of change, first principles definition of derivative, basic rules for differentiation
Graphical interpretation of derivatives, optimization problems
Exponential and log functions. Growth and decay applications. semilog and log-log plots.
Integration (definite and indefinite). Techniques of substitution and integration by parts. Applications.
Differential equations and initial value problems, solving first order linear equations. Applications in biology or ecology.

b) Linear algebra/discrete mathematics:
1 lecture and 1 tutorial per week. The syllabus will cover parts of chapter 1 on sequences, limits of sequences and difference equations and then chapter 8 of [Stewart-Day] on linear algebra.
The syllabus is approximately:

Sequences, limits of sequences, difference equations, discrete time models
Vectors and matrices , matrix algebra
Inverse matrices, determinants
Systems of difference equations, systems of linear equations, eigenvalues and eigenvectors. Leslie matrices, matrix models

Statistics:
There will be 1 lecture per week and 1 computer practical. The syllabus will cover much of chapters 11-13 of [Stewart-Day] and use [Bekerman-et-al] as main reference for R in the computer practicals.
The syllabus is approximately: