Module Title:   Fundamental Mathematics

Module Credit:   20

Module Code:   CM-0125L

Academic Year:   2015/6

Teaching Period:   Semester 1

Module Occurrence:   A

Module Level:   FHEQ Level 4

Module Type:   Linked 10+10

Provider:   Computer Science

Related Department/Subject Area:   School of Electrical Engineering & Computer Science

Principal Co-ordinator:   Dr C Lei

Additional Tutor(s):   Prof A Vourdas

Prerequisite(s):   None

Corequisite(s):   None

Aims:
To develop geometric skills and knowledge of basic matrix methods. To present an introduction to the concepts of complex number theory.

Learning Teaching & Assessment Strategy:
The basic theory and illustrative examples are presented and developed in formal lectures. Complementary tailor-made example sheets are provided. These are discussed, and assistance with their solution is provided in tutorials, either on a one-to-one basis or as a staff or student-led group, as appropriate.

Formative assessment assignments encourage the ongoing digestion of the material, with the extent of the cumulative

Lectures:   24.00          Directed Study:   149.50           
Seminars/Tutorials:   24.00          Other:   0.00           
Laboratory/Practical:   0.00          Formal Exams:   2.50          Total:   200.00

On successful completion of this module you will be able to...

show a breadth of knowledge of, and the utility of, algebraic manipulation and calculus, geometry, matrices, sequences, series and complex number theory.

On successful completion of this module you will be able to...

manipulate with and apply the fundamental properties of geometry, matrices, sequences, series and complex number theory.

On successful completion of this module you will be able to...

show a breadth of knowledge of, and the utility of, geometry, matrices, sequences, series and complex number theory.

  Coursework   25%
 
  2 assignments consisting of questions taking approximately 2 hours to answer per assignment
  Examination - closed book 2.50 75%
 
  Examination
  Examination - closed book 3.00 100%
 
  Supplementary examination

Outline Syllabus:
DIFFERENTIATION: first principles; product, quotient and composite rules; curve sketching; second-order derivatives; parametric differentiation, L`Hopital`s rule, Leibniz`s theorem. POWER SERIES: Maclaurin`s and Taylor`s series; polynomial approximation. INTEGRATION: inverse of differentiation; standard forms; substitution; partial fractions; by parts.
GEOMETRY: line, circle, ellipse, parabola; polar forms; parametric forms. VECTORS: preliminaries; vector addition; geometrical applications; components; vector multiplication; triple products; lines and planes. MATRIX METHODS: notation; matrix algebra; transpose; rank; inverse; simultaneous linear equations in matrix form and solution by Gaussian elimination; inversion by Gauss-Jordan reduction; determinants and their manipulation; adjoints and cofactors.
PROOF BY INDUCTION. SEQUENCES AND SERIES: monotonicity of sequences; convergence; recurrence relations; partial sums; positive series; comparison test; ratio test; alternating series; absolute and conditional convergence; re-ordering; power series; radius of convergence. COMPLEX NUMBERS: algebraic rules; modulus; geometrical applications; Argand diagram; polar forms, multiplication, division; De Moivre`s theorem; Euler`s formula; exponential form; multiple angles; roots of complex numbers.

Version No:  4