CS131 15 CATS (7.5 ECTS) Term 2

Availability

Core - CS and CSBS.

Academic Aims

• To provide students with sufficient mathematical knowledge to enable them to understand the foundations of their subject for both study purposes and later career development
• To bridge the gap in style and content between A-level and university mathematics and to introduce students to the language and methods of professional mathematics.

Learning Outcomes

By the end of the module the students should be able to:

• Carry out formal and informal mathematical proofs.
• Use effectively techniques for the analysis and transformation of vector spaces and the solution of sets of linear equations.
• Perform operations of the differential and integral calculus with confidence and precision
• Understand the basics of probabilistic analysis and be able to apply the methods in practical examples.
  

Content

• Linear Algebra: Vectors, linear independence, subspaces, basis, dimension.
• Matrix Algebra: Linear equations, inverses, linear transformations, eigenvalues/vectors.
• Sequences and Series: Limit and convergence properties of sequences and series.
• Calculus: Limits, continuity, differentiable functions, differentiation of inverse functions, integration, logarithms, exponentials, Taylor’s theorem.
• Abstract Algebra: Introduction to some abstract structures such as groups, rings, fields and vector spaces.
  

Books

• Jeffrey A, Mathematics for Engineers and Scientists (6th ed), Chapman and Hall, 2005.
• Stephenson G, Mathematical Methods for Science Students (2nd ed), Longman Scientific and Technical, 1973.
  

Assessment

Three-hour examination (80%) and problem sheets (20%)

Teaching

30 lectures and 8 seminars