We will follow in the footsteps of the pioneering mathematicians of the 19th century and formally define limits of sequences of real numbers. We will then use these definitions to rigorously deduce important properties of sequences, series and so on, which make up the bedrock of Real Analysis.

Topics investigated will include: The Completeness Axiom, Sequences, Series, Absolute and Conditional Convergence of Series,

Power series, Countability of sets, Continuity and properties of continuous functions, the Boundedness Theorem and the Intermediate Value Theorem.

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*Curricular information is subject to change*

Learning Outcomes:

On completion of this module the student should be able to

1. Compute the supremum and Infimum of sets of real numbers,

2. Prove or disprove elementary statements concerning the supremum and Infimum of sets of real numbers,

3. Show that certain sequences converge or diverge and determine their limits when they converge,

4. Use the Monotone Convergence Theorem to establish various properties of sequences and subsequences,

5. Test for convergence a wide range of series,

6. Be able to distinguish between the concepts of absolute and conditional convergence,

7. Determine the radius of convergence and interval of convergence of a power series

8. Be able to distinguish between countable and uncountable sets,

9. Prove or disprove elementary statements concerning continuous functions.

Student Effort Hours:

Student Effort Type | Hours |
---|---|

Lectures | 36 |

Tutorial | 10 |

Autonomous Student Learning | 65 |

Total | 111 |

Approaches to Teaching and Learning:

Lectures, tutorials, problem-based learning

Lectures, tutorials, problem-based learning

Requirements, Exclusions and Recommendations

At least H4 (or equivalent) in Leaving Certificate Mathematics

Module Requisites and Incompatibles

MST20040 -

Students must have completed MATH10350 or MATH10140. It is strongly recommended that students complete MATH10140 Numbers and Functions before taking this module.

Assessment Strategy

Description | Timing | Component Scale | % of Final Grade | ||
---|---|---|---|---|---|

Not yet recorded. |

Carry forward of passed components

No

No

Resit In | Terminal Exam |
---|---|

Autumn | Yes - 2 Hour |

Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Name | Role |
---|---|

Mr Oisin Campion | Tutor |

Saeedeh Mohammadi | Tutor |

Anton Sohn | Tutor |