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MA140-10 Mathematical Analysis 1
Department Warwick Mathematics Institute Level Undergraduate Level 1 Module leader Dmitriy Rumynin Credit value 10 Module duration 10 weeks Assessment Multiple Study location University of Warwick main campus, Coventry
Description
Introductory description
Mathematical Analysis is the heart of modern Mathematics. This module is the first in a series of modules where the subject of Analysis is rigorously developed.
Module aims
The principal aim is to develop Analysis in dimension 1, with much greater precision and rigour than the students had at school. While the high-school Analysis is focusing on problem solving methods, the university-level Analysis is switching the focus to the mathematical concepts and clarity of thought.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
- Inequalities
- Real numbers
- Sequences of numbers
- Limits
- Series
- Continuity
- Uniform continuity
Learning outcomes
By the end of the module, students should be able to:
- develop deep understanding of the real numbers and the symbol `infinity' develop working knowledge of sequences and series, including limits, conditional and absolute convergence
- learn the properties of continuous and absolutely continuous functions
Indicative reading list
M. Hart, Guide to Analysis, Macmillan. M. Spivak, Calculus, Benjamin. R.G Bartle and D.R Sherbert, Introduction to Real Analysis (4th Edition), Wiley (2011) L. Alcock, How to think about Analysis, Oxford University Press (2014) View reading list on Talis Aspire
Subject specific skills
Analysis gives first-year undergraduates a first excursion in to pure mathematics. The students will gain a new perspective and a deeper understanding of familiar mathematics which they have seen in school (e.g. real numbers, functions and differentiation). In Analysis, these concepts are developed with mathematical rigour, which characterises much of university mathematics to follow.
Transferable skills
Students will acquire key reasoning and problem solving skills, empower them to address new problems with confidence.
Study
Study time
Type Required Lectures 20 sessions of 1 hour (20%) Online learning (independent) 9 sessions of 1 hour (9%) Private study 13 hours (13%) Assessment 58 hours (58%) Total 100 hours
