Module Specifications.
Current Academic Year 2024 - 2025
All Module information is indicative, and this portal is an interim interface pending the full upgrade of Coursebuilder and subsequent integration to the new DCU Student Information System (DCU Key).
As such, this is a point in time view of data which will be refreshed periodically. Some fields/data may not yet be available pending the completion of the full Coursebuilder upgrade and integration project. We will post status updates as they become available. Thank you for your patience and understanding.
Date posted: September 2024
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Repeat examination |
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Description This module introduces students to the principles and practice of mathematical analysis via the study of sequences and series. There will be an emphasis on constructing rigorous mathematical proofs of results from analysis. Students will also learn how to use diagrams and informal ideas to develop their knowledge and skills in this area of mathematics. Students will attend interactive lectures in which the class build some definitions of mathematical constructs, and engage in creating convincing mathematical arguments and proofs to support given statements. | |||||||||||||||||||||||||||||||||||||||||||
Learning Outcomes 1. apply the epsilon-X formulation of statements involving convergence of sequences and series; 2. construct rigorous arguments using the epsilon-X formulation and be able to distinguish between rigorous and informal arguments; 3. construct and analyse their own examples and counterexamples of mathematical objects arising in analysis; 4. use different structured approaches to solve problems in mathematical analysis. | |||||||||||||||||||||||||||||||||||||||||||
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
Sequences Introduction to sequences. Null sequences. Convergent and divergent sequences. Monotone sequences and the Weierstrass-Bolzano theorem. Cauchy's criterion for convergence. Series Introduction to series. Series with non-negative terms. Tests for convergence. Series with positive and negative terms and absolute convergence. Rearranging series. | |||||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources None | |||||||||||||||||||||||||||||||||||||||||||