## 1000-level modules

MT1001 Introductory Mathematics

MT1002 Mathematics

MT1003 Pure and Applied Mathematics

MT1007 Statistics in Practice

MT1010 Topics in Mathematics: Problem-solving Techniques

MT1901 Topics in Contemporary Mathematics (Evening degree programme only)

#### MT1001 Introductory Mathematics

Credits | 20.0 |
---|---|

Semester | 1 |

Academic year | 2018/9 |

Timetable | 9.00 am |

Description | This module is designed to give students a secure base in elementary calculus to allow them to tackle the mathematics needed in other sciences. Students wishing to do more mathematics will be given a good foundation from which they can proceed to MT1002. Some of the work covered is a revision and reinforcement of material in the Scottish Highers and many A-Level syllabuses. |

Prerequisites | Higher or A-Level Mathematics (A/S level Mathematics with approval of Head of School). |

Antirequisites | MT1003, CS1010. Students may not take MT1001 and EC1003 at the same time, but they may take MT1001 in first year and EC1003 in second year |

Lectures and tutorials | 5 lectures (weeks 1 - 10), 1 tutorial and 1 laboratory (weeks 2 -11). |

Assessment | Written Examination = 90% (2-hour final exam = 70%, 2 class tests = 10% each), Coursework = 10% |

Module coordinator | Dr C V Tran |

Lecturer | Dr C V Tran, Dr T Coleman, Dr P Pagano, Dr P Syntelis |

#### MT1002 Mathematics

Credits | 20.0 |
---|---|

Semester | Both |

Academic year | 2018/9 |

Timetable | 9.00 am |

Description | This module is designed to introduce students to the ideas, methods and techniques which they will need for applying mathematics in the physical sciences or for taking the study of mathematics further. It aims to extend and enhance their skills in algebraic manipulation and in differential and integral calculus, to develop their geometric insight and their understanding of limiting processes, and to introduce them to complex numbers and matrices. |

Prerequisites | MT1001 or B at Advanced Higher Mathematics or B at A-Level Mathematics. |

Antirequisites | |

Lectures and tutorials | 5 lectures (weeks 1 - 10), 1 tutorial and 1 laboratory (weeks 2 - 11). |

Assessment | Written Examination = 90% (2-hour final exam = 70%, 2 class tests = 10% each), Coursework = 10% |

Module coordinator | Dr A Naughton (S1), Prof C M Roney-Dougal (S2) |

Lecturer | Dr A Naughton, Dr R K Scott, Prof L Olsen, Prof K J Falconer (S1); Prof C M Roney-Dougal, Dr T Coleman, Dr A Wright, Dr A Naughton (S2) |

#### Syllabus

- Revision of integration techniques, hyperbolic functions and applications to integration;
- Limits of functions, l’Hospital’s rule;
- Complex numbers: their arithmetic, Argand diagram, modulus-argument form, de Moivre’s theorem, powers and roots, geometric and trigonometric applications;
- Differential equations: first order separable, first order linear, second order with constant coefficients both homogeneous and inhomogeneous;
- Matrices, determinants and linear equations: basic matrix operations, inverses including by row operations, determinants and their properties, solutions of systems of linear equations, including degenerate cases;
- Vectors: Vector operations, including scalar and vector product, geometrical applications including equations of lines and planes;
- Proof: the need for precision in mathematics, basic types of proof, including induction;
- Sequences and series: convergence of sequences, convergence of series, geometric series, tests for convergence, power series, Taylor-Maclaurin series, including standard examples (exp, sine, etc.).

#### Reading list

- E. Kreyszig,
*Advanced Engineering Mathematics*(John Wiley, 2011). [This book covers much more material than just this module and will be useful for many level 2 modules.] - Robert A. Adams,
*Calculus - A Complete Course (6th Edition)*(Prentice Hall, 2006). - E. W. Swokowski, M. Olinick, D. Pence,
*Calculus (6th Edition)*(Addison Wesley, 2003). [This book is out of print, but is in the library and may be available second-hand.] - K. E. Hirst
*Numbers, Sequences and Series*, (Edward Arnold, 1995). - K. E .Hirst
*Vectors in 2 and 3 Dimensions*, (Edward Arnold, 1995).

#### MT1003 Pure and Applied Mathematics

Credits | 20.0 |
---|---|

Semester | 2 |

Academic year | 2018/9 |

Timetable | 9.00 am |

Description | The aim of this module is to provide students with a taste of both pure and applied mathematics, to give them insight into areas available for study in later years and to provide them with the opportunity to broaden their mathematical experience. |

Prerequisites | MT1002 |

Antirequisites | |

Lectures and tutorials | 5 lectures (weeks 1 - 10), 1 tutorial and 1 laboratory (weeks 2 - 11). |

Assessment | Written Examination = 90% (2-hour final exam = 70%, 2 class tests = 10% each), Coursework = 10% |

Module coordinator | Dr A P Naughton |

Lecturer | Dr A P Naughton, Dr A L Wilmot-Smith, Dr C Bleak |

#### Syllabus

- Functions and Relations.
- Natural numbers and integers. Elementary number theory.
- Rational numbers, irrational numbers, real numbers.
- Groups. Permutations and geometric symmetries,subgroups.
- Graphs. Hamiltonian and Eulerian paths, planarity, trees.
- Discrete and continuous descriptions.
- Simple continuous mathematical models applied to mechanical, thermal and biological problems. Autonomous systems.
- Solution of difference equations with applications to economics and population dynamics. The logistic and related equations. Chaos.
- Difference equations as iterative methods for solving algebraic equations.
- Numerical solution of initial value problems using simple difference schemes.

#### Reading list

*Advanced Engineering Mathematics*E Kreyszig; Wiley; 2001*Calculus*, R A Adams; Pearson; 2002.*Calculus (6th Edition)*E W Swokowski, M Olinick, D Pence; PWS; 1994.

#### MT1007 Statistics in Practice

Credits | 20.0 |
---|---|

Semester | 2 |

Academic year | 2018/9 |

Timetable | 11.00 am |

Description | This module provides an introduction to statistical reasoning, elementary but powerful statistical methodologies, and real world applications of statistics. Case studies, such as building an optimal stock portfolio, and data vignettes are used throughout the module to motivate and demonstrate the principles. Students get hands-on experience exploring data for patterns and interesting anomalies as well as experience using modern statistical software to fit statistical models to data. |

Prerequisites | An A grade at GCSE/Grade 1 at Standard Grade Mathematics or a C grade at AS level/Higher Mathematics. |

Antirequisites | |

Lectures and tutorials | 4 lectures (weeks 1 - 10), 1 tutorial and 1 laboratory (weeks 2 - 11). |

Assessment | 2-hour Written Examination = 50%, Coursework = 50% |

Module coordinator | Dr M L Burt |

Lecturer | Dr M L Burt, Dr C G Paxton, TBC |

#### MT1010 Topics in Mathematics: Problem-solving Techniques

Credits | 10.0 |
---|---|

Semester | 1 |

Academic year | 2018/9 |

Timetable | 10.00 am Mon (odd weeks), Wed and Fri |

Description | This module introduces some important basic concepts in mathematics and also explores problem-solving in the context of these topics. It is intended to strengthen the mathematical skills of an undergraduate entering on the Fast Track route into the MMath degree programme. |

Prerequisites | Admission onto the Fast Track MMath degree programme |

Antirequisites | |

Lectures and tutorials | 1.5-hour lecture, 1 practical and 1 tutorial (x 10 weeks) |

Assessment | 1.5-hour Written Examination = 50%, Coursework = 50% |

Module coordinator | Dr V Popov |

Lecturer | Dr V M Popov, Dr R K Scott, Prof N Ruskuc |

This module is taken only by students on the Fast Track route through the MMath degree programme.

#### Syllabus

The syllabus splits into five blocks, each consisting of two weeks, covering:

- Divisibility properties of integers, the Euclidean Algorithm;
- Polynomials, their roots and divisibility properties;
- Sequences and convergence (iterative schemes, Newton's Method, Euler Algorithm);
- Euclidean geometry (possible topics including conic sections, equations of parabolae, ellipses, etc.);
- Combinatorics and probability.

Block 5 will tie in with the material that students are covering during the semester in MT2504.

#### Reading list

- David M. Burton,
*Elementary Number Theory*, Allyn & Bacon, 1976 - Erwin Kreyszig,
*Advanced Engineering Mathematics*, Wiley, 2011 - Earl W. Smokowski, Michael Olinick & Dennis Pence,
*Calculus*, PWS Pub. Co., 1994 - Sheldon Ross,
*A First Course in Probability*, Pearson, 2014

#### ID1003 Great Ideas 1

Credits | 20.0 |
---|---|

Semester | 1 |

Academic year | 2018/9 |

Timetable | 1.00 pm Mon, 1.00 pm Tue, 1.00 pm Thu |

Description | The aim of this module is to trace some of the major intellectual and societal threads in the development of modern civilisation: the 'canon' of modern thought. The module is in three sections. Part 1 is "Arguments and Facts" and explores the fundamentals of logic, analysis and reasoning. Part 2. "Rhetoric, Debate and Understanding" will explore how argument can be used to cajole, convert, persuade and entertain and emphasise the importance in understanding another person's position. Part 3 "Applying Analysis" takes the learning and skills of the previous sections and applies them to some of the great texts and artworks of western civilisation. |

Prerequisites | |

Antirequisites | |

Lectures and tutorials | 2 to 3 lectures and 1 tutorial. |

Assessment | 2-hour Written Examination = 50%, Coursework = 50% |

Module coordinator | Dr C Paxton |

Lecturer | Team taught |

#### MT1901 Topics in Contemporary Mathematics

Credits | 20.0 |
---|---|

Semester | 1 |

Academic year | TBD |

Timetable | Next available TBD |

Description | This module will introduce areas of contemporary mathematics and statistics at a basic level. Topics may include chaos and fractals, the golden ratio, mathematical modelling of populations and analysis of the resulting equations. The statistical component will consider how to graph data, and will introduce probability, odds and betting, basic descriptive statistics and uncertainty and risk. The topics will be illustrated by simple examples and day-to-day situations. |

Prerequisites | Entry to the Evening Degree programme. Basic algebraic manipulation, but not any knowledge of calculus, will be assumed. (Maths Standard Grade (Credit level) or Maths GCSE (Higher tier) would provide sufficient algebraic background.) |

Antirequisites | |

Lectures and tutorials | 1 x 3-hour session (lecture plus tutorial). |

Assessment | Coursework = 100% |

Module coordinator | TBC |

Lecturer | TBC |

This module runs in alternate years.

#### Syllabus

- Recurrence relations and applications, Fibonacci numbers;
- Newton’s mathematics;
- Fractals, chaos, Julia sets and the Mandelbrot set;
- Modern statistics, looking at data, basic probability;
- Statistical inference and hypothesis testing.

#### Assumed knowledge

Basic algebraic manipulation, but not any knowledge of calculus, will be assumed. (Maths Standard Grade (Credit level) or Maths GCSE (Higher tier) would provide sufficient algebraic background.) This material will be reviewed in the first session.

#### Reading list

- Stephen B. Maurer & Anthony Ralston,
*Discrete Algorithmic Mathematics*(Addison-Wesley, 1991) [Chapter 5, p366-437]. - Richard Johnsonbaugh,
*Discrete Mathematics*(Pearson, 2005) [Chapter 7.1-7.2, pp279-304]. - Kenneth H. Rosen,
*Discrete Mathematics and Its Applications*, (McGraw-Hill, 1999) [Chapter 5.1-5.2, pp308-332]. - Louis Trenchard More,
*Isaac Newton*(Scribners 1934). - Kenneth Falconer,
*Fractals – A Very Short Introduction*(Oxford UP, 2013). - H.-O. Peitgen, H Jürgens & D Saupe,
*Chaos and Fractals*(Springer-Verlag, 1992). - Ian Stewart,
*Does God Play Dice?*(Penguin, 1990). - M. Blastland & A. Dilnot,
*The Tiger that Isn't: Seeing Through a World of Numbers*(Profile Books, 2007). - D. Huff,
*How to Lie with Statistics*(Penguin, 1991). - David Salsburg,
*The Lady Tasting Tea?: how statistics revolutionized science in the twentieth century*(Henry Holt, 2002).