School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2020/21 Last Updated: 11 July 2020

MAT-20029 - Analysis II

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This module builds upon the material on real analysis covered in Exploring Algebra and Analysis. The module will study infinite series, limits of functions, continuity and differentiation from a rigorous point of view. The results covered enable calculus to be placed on a secure theoretical footing. An understanding of the core techniques in analysis is advantageous when studying certain level 6 modules.

The aim of this module is to provide students with further core knowledge of real analysis, which builds upon the material covered in Exploring Algebra and Analysis. In particular, the module is concerned with infinite series, limits of functions, continuity and differentiation.

state clearly the key definitions and theorems of real analysis related to infinite series, limits of functions, continuity and differentiation: 2

prove and apply the key theorems of real analysis related to infinite series, limits of functions, continuity and differentiation: 2

use the concepts and theory covered in the module to develop mathematical and logical arguments: 1,2

use the concepts and theory covered in the module to make judgements and to evaluate different approaches to solving problems: 1,2

prove and apply the key theorems of real analysis related to infinite series, limits of functions, continuity and differentiation: 2

use the concepts and theory covered in the module to develop mathematical and logical arguments: 1,2

use the concepts and theory covered in the module to make judgements and to evaluate different approaches to solving problems: 1,2

48 hours of scheduled classes, including lectures and tutorials

30 hours portfolio preparation

70 hours independent study

2 hours unseen examination

30 hours portfolio preparation

70 hours independent study

2 hours unseen examination

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Portfolio of work created over the semester

A portfolio of work created over the semester through 10 short exercises (equally weighted). The exercises, ¿when combined, form a portfolio of work that develops students' ability to use module concepts, theory and solve mathematical problems. Over the semester, students can expect to spend a total of 30 hours creating their portfolio.

2-hour unseen examination

The examination paper will consist of no less than five and not more than eight questions, all of which are compulsory.