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MATH10320

Academic Year 2024/2025

Mathematical Analysis (MATH10320)

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
1 (Introductory)
Credits:
5
Module Coordinator:
Dr Harriet Walsh
Trimester:
Spring
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

Mathematical Analysis is a large and important branch of modern mathematics with a long history. The core notion is that of a limit, which gives the "long-term" behaviour of some process, or computes what happens as one variable gets closer and closer to a given value. The limit notion is behind many other fundamental concepts, such as continuity, derivatives, integrals, and so on. Historically, such ideas were discussed and used since at least the 17th century (for example, in connection with mathematical physics or statistics). However, they were not precisely understood; the working definitions of the day typically involved somewhat vague ideas of "infinitely small" or "infinitely large" quantities, and these can lead to confusion.

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.

About this Module

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
Autonomous Student Learning

65

Lectures

36

Tutorial

10

Total

111


Approaches to Teaching and Learning:
Lectures, tutorials, problem-based learning

Requirements, Exclusions and Recommendations
Learning Recommendations:

At least H4 (or equivalent) in Leaving Certificate Mathematics


Module Requisites and Incompatibles
Incompatibles:
MST20040 - Analysis

Additional Information:
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 Must Pass Component % of Final Grade In Module Component Repeat Offered
Assignment(Including Essay): Homework Week 2, Week 4, Week 5, Week 6, Week 7, Week 8, Week 10, Week 11, Week 12 Standard conversion grade scale 40% No
15
No
Assignment(Including Essay): WeBWorK Week 4, Week 5, Week 7, Week 8, Week 10, Week 11, Week 12 Standard conversion grade scale 40% No
15
No
Exam (In-person): Final exam End of trimester
Duration:
2 hr(s)
Standard conversion grade scale 40% No
70
No

Carry forward of passed components
No
 

Resit In Terminal Exam
Autumn Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Name Role
Saeedeh Mohammadi Tutor
Mr Daire O'Donovan Tutor
Anton Sohn Tutor

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Thurs 11:00 - 11:50
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Tues 12:00 - 12:50
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Wed 16:00 - 16:50
Spring Tutorial Offering 1 Week(s) - 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Mon 13:00 - 13:50
Spring Tutorial Offering 2 Week(s) - 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Mon 14:00 - 14:50
Spring Tutorial Offering 3 Week(s) - 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Thurs 12:00 - 12:50