Module: Geometry

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Geometry
Module Code	MS302 (ITS) / MTH1049 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Marco Viola
Module Teachers	Louise Nolan, Thorsten Neuschel
NFQ level	8	Credit Rating	7.5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

None

Description

This module focusses on the axiomatic approach to Euclidean geometry, paying particular attention to the role of this topic in the Irish second level mathematics syllabus. Non-Euclidean geometry will also be studied and students will use dynamic geometry software in the module.

Learning Outcomes

1. Describe the roles of defined, undefined and implicitly defined terms, axioms, lemmas, theorems and corollaries in a system of geometry.
2. Present proofs and constructions in Euclidean and non-Euclidean geometry
3. Solve problems in Euclidean geometry and plane trigonometry.
4. Describe applications and manifestations of geometry in the natural and man-made world.
5. Use dynamic software in teaching geometry.

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	24	Two lectures each week
Tutorial	12	One tutorial/problem session each week
Independent Study	139.5	No Description
Laboratory	12	Geogebra sessions in the computer lab.
Total Workload: 187.5

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

Indicative Content and Learning Activities

The terms and axioms of Euclidean geometry

Topics in Euclidean geometry
a. Length, distance, angles and angle measure b. Equivalent characterisations of congruent triangles c. Parallel and perpendicular lines; parallelograms and quadrilaterals d. Ratios and similarity e. Area and Pythagoras’s theorem f. Circles and special triangle points

Constructions in Euclidean geometry

Applications of Euclidean geometry

Non-Euclidean geometries

Using Geogebra

Assessment Breakdown
Continuous Assessment	25%	Examination Weight	75%

Type	Description	% of total	Assessment Date
Course Work Breakdown
In Class Test	n/a	5%	Week 3
In Class Test	n/a	5%	Week 6
In Class Test	n/a	5%	Week 10
Assignment	Series of assignments using the Geogebra software package.	10%	As required

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 1

Indicative Reading List

Department of Education and Skills: 0, Geometry for School Mathematics (Section B, Leaving Certificate Mathematics Syllabus),

Other Resources

None