Registry
Module Specifications
Archived Version 2021 - 2022
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Description This module introduces students to the formal and rigorous approach to mathematics which underpins mathematical analysis.The students will develop the skills necessary to make the transition from a formulaic understanding of mathematics to constructing their own formal mathematical arguments, and to promote advanced mathematical thinking through the use of guided inquiry and example generation. Students will participate in the following learning activities: Lectures: There will be a weekly lecture introducing material. Group discussions and problem solving: students will spend the equivalent of two lectures a week on guided group discussions in order to derive results or tests for solving problems, generating examples or counterexamples, and so on. Presentations: students will present their approach to solving particular problems to the class for analysis and critique. Portfolio: students will make regular contributions to a portfolio of written assignments examining more general aspects of the module. Reading: students are expected to fully use the lecture notes and textbooks listed below. | |||||||||||||||||||||||||||||||||||||
Learning Outcomes 1. interpret the formal mathematical definitions and statements which arise in analysis. 2. classify and describe the main components of the definitions or statements, and the motivation behind them. 3. give examples or counterexamples of important phenomena which are studied in mathematical analysis. 4. critique and explain the logical steps which are required to apply definitions or theorems to the phenomena which occur in mathematical analysis. 5. critique and explain the main logical arguments which occur in the proofs of a selection of theorems. 6. calculate important quantities which arise in mathematical analysis e.g. bounds of sets or sequences, convergence of sequences or series. | |||||||||||||||||||||||||||||||||||||
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml |
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Indicative Content and
Learning Activities Numbers and setsThe real numbers. Archimedean property of the reals. Least upper bounds and greatest lower bounds.Sequences and seriesMonotone and bounded sequences. Alternating series. Tests for convergence of series. Power series. Move Up | |||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources None | |||||||||||||||||||||||||||||||||||||
Programme or List of Programmes | |||||||||||||||||||||||||||||||||||||
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