# Mathematics MMath

University of LiverpoolChiedi il prezzo

## Informazioni importanti

Tipologia | Bachelor's degree |

Luogo | Liverpool (Inghilterra) |

- Bachelor's degree
- Liverpool (Inghilterra)

If you enjoyed studying Mathematics at school and would like to study the subject in more depth, you should consider G100 or G101. G100 provides an excellent foundation for a wide range of careers. Students who opt for the four-year MMath programme are well placed to embark on a PhD or to take a research post in industry after graduation. In the first two years of these programmes, you will study a range of topics covering important areas of both Pure and Applied Mathematics – no assumptions are made about whether or not you have previously studied Mechanics or Statistics, or have previous experience of the use of computers. Year One modules introduce fundamental ideas and also reinforce A level work. Subsequently, you can either specialise or continue to study abroad range of topics. For both of these programmes, you will take at least two modules of Pure Mathematics and two of Applied Mathematics in Year Two. Department Key Facts Number of first year students197 Year One undergraduates in 2015 Graduate prospects89.1% of our graduates are employed or in further study within six months of graduating (Destination of Leavers from Higher Education 2012/13) National Student Survey87% of our students agree staff are good at explaining things (National Student Survey 2015) Why this subject? Take the first steps towards a brilliant career. Employers tell us that, alongside key problem solving skills, they want strong communication skills and the ability to work in a team – so we have ensured that these are integral to our Mathematics programmes. As a result, we have an excellent graduate employment record. About a third of graduates become business and finance professionals; but there is a whole...

Inizio | Luogo |
---|---|

15 set 2018 |
LiverpoolChatham Street, L69 7ZH, Merseyside, Inghilterra Visualizza mappa |

Inizio |
15 set 2018 |

Luogo |
LiverpoolChatham Street, L69 7ZH, Merseyside, Inghilterra Visualizza mappa |

## Cosa impari in questo corso?

Credit | Basic | IT | Basic IT training | ||||||

Basic IT | Statistics | Mathematics | Mechanics | ||||||

Calculus | Algebra | Geometry | Project | ||||||

systems | GCSE Mathematics | Skills and Training | systems | ||||||

Credit | IT | systems | IT |

## Programma

You will take the modules:

(a) Calculus I

(b) Introduction to Linear Algebra

(c) Calculus II

(d) Numbers and Sets

(e) Dynamic Modelling

(f) Introduction to Statistics

You have the choice of:

(g) Mathematical IT Skills

or

(i) Introduction to Programming in Java

and

(h) Numbers, Groups and Codes

or

(j) Introduction to Databases

You will have to take (i) and (j) if you want to take Computer Science modules in your second year.

Tutorials for foundation modules (a and c) are in groups of about six students.

- Calculus I (MATH101)
**Level**1**Credit level**15**Semester**First Semester**Exam:Coursework weighting**80:20**Aims**1. To introduce the basic ideas of differential and integral calculus, to develop the basic skills required to work with them and to apply these skills to a range of problems.

2. To introduce some of the fundamental concepts and techniques of real analysis, including limits and continuity.

3. To introduce the notions of sequences and series and of their convergence.

**Learning Outcomes**After completing the module students should be able to:

· differentiate and integrate a wide range of functions;

· sketch graphs and solve problems involving optimisation and mensuration;

· understand the notions of sequence and series and apply a range of tests to determine if a series is convergent.

- Calculus Ii (MATH102)
**Level**1**Credit level**15**Semester**Second Semester**Exam:Coursework weighting**80:20**Aims**· To discuss local behaviour of functions using Taylor’s theorem.

· To introduce multivariable calculus including partial differentiation, gradient, extremum values and double integrals.

**Learning Outcomes**After completing the module, students should be able to:

· use Taylor series to obtain local approximations to functions;

· obtain partial derivatives and use them in several applications such as, error analysis, stationary points change of variables;

· evaluate double integrals using Cartesian and polar co-ordinates.

- Introduction To Linear Algebra (MATH103)
**Level**1**Credit level**15**Semester**First Semester**Exam:Coursework weighting**80:20**Aims**- To develop techniques of complex numbers and linear algebra, including equation solving, matrix arithmetic and the computation of eigenvalues and eigenvectors.
- To develop geometrical intuition in 2 and 3 dimensions.
- To introduce students to the concept of subspace in a concrete situation.
- To provide a foundation for the study of linear problems both within mathematics and in other subjects.

**Learning Outcomes**After completing the module students should be ableto:

- manipulate complex numbers and solve simple equations involving them
- solve arbitrary systems of linear equations;
- understand and use matrix arithmetic, including the computation of matrix inverses;
- compute and use determinants;
- understand and use vector methods in the geometry of 2 and 3 dimensions;
- calculate eigenvalues and eigenvectors and, if time permits, apply these calculations to the geometry of conics and quadrics.

- Numbers, Groups and Codes (MATH142)
**Level**1**Credit level**15**Semester**Second Semester**Exam:Coursework weighting**90:10**Aims**· To provide an introduction to rigorous reasoning in axiomatic systems exemplified by the framework of group theory.

· To give an appreciation of the utility and power of group theory as the study of symmetries.

· To introduce public-key cryptosystems as used in the transmission of confidential data, and also error-correcting codes used to ensure that transmission of data is accurate. Both of these ideas are illustrations of the application of algebraic techniques.

**Learning Outcomes**After completing this module the student should be able to:

1. Use the division algorithm to construct the greatest common divisor of a pair of positive integers;

2. Solve linear congruences and find the inverse of an integer modulo a given integer;

3. Code and decode messages using the public-key method;

4. Manipulate permutations with confidence;

5. Decide when a given set is a group under a specified operation and give formal axiomatic proofs;

6. Understand the concept of a subgroup and use Lagrange''s theorem;

7. Understand the concept of a group action, an orbit and a stabiliser subgroup;

8. Understand the concept of a group homomorphism and be able to show (in simple cases) that two groups are isomorphic;

9. Understand the principles of binary coding and how to construct error-detecting and error-correcting binary codes.

- Dynamic Modelling (MATH122)
**Level**1**Credit level**15**Semester**Second Semester**Exam:Coursework weighting**80:20**Aims**1. to provide the basic methods for modelling mathematically topics in subjects like biology, engineering, physical sciences and social sciences;

2. to discuss the advantages of using mathematics in modelling;

3. to demonstrate some simple models involving differential equations and difference equations;

4. to provide a foundation for an understanding of mechanics.**Learning Outcomes**After completing the module students should be able to:

. solve simple differential equations;

· understand some methods of mathematical modelling and, in particular, the need to attach meaning to mathematical results;

· develop some differential equations for population growth, and interpret the results;

· understand Newton''s laws of Mechanics;

· do simple problems in projectiles and orbits, some involving polar co-ordinates.

- Introduction To Statistics (MATH162)
**Level**1**Credit level**15**Semester**Second Semester**Exam:Coursework weighting**80:20**Aims**To introduce topics in Statistics and to describe and discuss basic statistical methods.

To describe the scope of the application of these methods.

**Learning Outcomes**After completing this module students should be able

- to describe statistical data;

- to use the Binomial, Poisson, Exponential and Normal distributions;

- to perform simple goodness-of-fit tests;

- to use the package Minitab to present data, and to make statistical analysis.

In the second and subsequent years of study, there is a wide range of modules. For the programme that you choose there may be no compulsory modules (although you may have to choose a few from a subset such as Pure Mathematics). If you make a different choice, you will find that one or more modules have to be taken. Each year you will choose the equivalent of eight modules. Please note that we regularly review our teaching so the choice of modules may change.

- Ordinary differential equations
- Group projects
- Iteration and Fourier series
- Complex functions
- Linear algebra and geometry
- Commutative algebra
- Geometry of curves
- Introduction to the methods of applied mathematics
- Vector calculus with applications in fluid mechanics
- Mathematical models: Microeconomics and Population Dynamics
- Classical mechanics
- Numerical analysis, solution of linear equations
- Introduction to methods of operational research
- Introduction to financial mathematics
- Statistical theory and methods 1
- Statistical theory and methods 2
- Operational research: probabilistic models

- Ordinary Differential Equations (MATH201)
**Level**2**Credit level**15**Semester**First Semester**Exam:Coursework weighting**90:10**Aims**To familiarize students with basic ideas and fundamental techniques to solve ordinary differential equations.

To illustrate the breadth of applications of ODEs and fundamental importance of related concepts.

**Learning Outcomes**After completing the module students should be:

- familiar with elementary techniques for the solution of ODE''s, and the idea of reducing a complex ODE to a simpler one;

- familiar with basic properties of ODE, including main features of initial value problems and boundary value problems, such as existence and uniqueness of solutions;

- well versed in the solution of linear ODE systems (homogeneous and non-homogeneous) with constant coefficients matrix;

- aware of a range of applications of ODE.

- Group Project Module (MATH206)
**Level**2**Credit level**15**Semester**Second Semester**Exam:Coursework weighting**0:100**Aims**· To give students experience of working effectively in small groups.

· To train students to write about mathematics.

· To give students practice in delivering presentations.

· To develop students’ ability to study independently.

· To prepare students for later individual project work.

· To enhance students’ appreciation of the connections between different areas of mathematics.

· To encourage students to discuss mathematics with each other.

**Learning Outcomes**After completing the project the student should be able to:

· Work effectively in groups, and delegate common tasks.

· Write substantial mathematical documents in an accessible form.

· Give coherent verbal presentations of more advanced mathematical topics.

· Appreciate how mathematical techniques can be applied in a variety of different contexts.

- Complex Functions (MATH243)
**Level**2**Credit level**15**Semester**First Semester**Exam:Coursework weighting**80:20**Aims**To introduce the student to a surprising, very beautiful theory having intimate connections with other areas of mathematics and physical sciences, for instance ordinary and partial differential equations and potential theory.

**Learning Outcomes**After completing this module students should:

- appreciate the central role of complex numbers in mathematics;

- be familiar with all the classical holomorphic functions;

- be able to compute Taylor and Laurent series of such functions;

- understand the content and relevance of the various Cauchy formulae and theorems;

- be familiar with the reduction of real definite integrals to contour integrals;

- be competent at computing contour...