Mathematical Sciences with a European Language BSc (Hons)

Module details Programme Year One

You will study (a- c) and the equivalent of two modules in the appropriate language, as well as three modules from (d-f), ((g) or (i)) and ((h) or (j)).

Compulsory modules

• 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.

Compulsory modules

• Placement Abroad (MATH270) Level 2 Credit level 120 Semester Whole Session Exam:Coursework weighting 0:100 Aims

  To follow a course of study at a European university in the chosen target language; to broaden the perspective on mathematics by taking courses which complement the studies in Liverpool; to get used to communicating about mathematics in the target language; to be exposed to and engage with the culture of the host country and the approach to teaching mathematics at the host university. Students are required to document their experiences in a log book, which is compulsory but does not carry a separate mark. During the year abroad students carry out a year abroad essay project supervised by SOCLAS.

  Learning Outcomes

  To learn new mathematical subjects according to the choice of courses agreed with the programme director, to improve the ability to communicate in the target language, in particular about mathematics, to deepen the understanding of the culture of the host country; to be able to appreciate the differences in the approaches taken towards education and mathematics in the host country and at home. The ability to engage with the language and culture of the host country is documented through the year abroad essay supervised by SOCLAS.

The modules listed above are illustrative and subject to change. Please refer to the department site for further information