This module complements the core Real Analysis module by developing the notion of convergence in discrete contexts. Here the underlying functions are sequences of real numbers, and the fundamental concept of a convergent series is explored in depth. Significant emphasis is placed on mathematical proof, and the development of fundamental skills and techniques that underpin much of contemporary mathematics.
Learning Outcomes
By the end of the module students should be able to:
State the definitions of convergence for both sequences and series.
Use definitions and standard techniques, such as proof by induction, to construct proofs of simple statements involving convergent sequences and series.
Determine the convergence of various sequences and series from first principles, and using standard results, such as the algebra of limits and the series convergence tests.
Understand how the theory of convergent series may be applied to the study of functions defined by power series, and compute Taylor series of elementary functions.
Assessment
34047-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions
1.5 hour Written Unseen Examination (80%); In-course Assessment (20%)
