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MATH10040

Academic Year 2024/2025

Numbers & Functions (MATH10040)

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
1 (Introductory)
Credits:
5
Module Coordinator:
Professor Gary McGuire
Trimester:
Autumn
Mode of Delivery:
Blended
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

This module is an introduction to the joys and challenges of mathematical reasoning and mathematical problem-solving, organised primarily around the theme of properties of the whole numbers.

It begins with an introduction to some basic notions of mathematics and logic such as sets and functions, proof by contradiction, and different types of proof by induction. This module also introduces injective, surjective and bijective functions, equivalence relations and equivalence classes.

The remainder of the module is devoted to number theory: integers, greatest common divisors, prime numbers, Euclid's algorithm, the Fundamental Theorem of Arithmetic, congruences, Fermat's Little theorem, Euler's theorem, factorizing, and arithmetic modulo a prime. The module concludes with some applications to cryptography such as the RSA encryption system.

The module will introduce students to the writing of correct and complete mathematical arguments and proofs.

About this Module

Learning Outcomes:

On completion of this module students should be able to:
1. use mathematical induction, and investigate basic concepts associated with functions,
2. calculate greatest common divisors, and apply the theorems of Fermat and Euler to deduce properties of integers,
3. understand the concepts of number theory, such as prime numbers, and their relevance to codes,
4. write clear, complete and correct mathematical arguments.

Student Effort Hours:
Student Effort Type Hours
Lectures

24
Tutorial

12
Autonomous Student Learning

76
Online Learning

12
Total

124

Approaches to Teaching and Learning:
A flipped classroom approach will be taken. The lectures and tutorials will aid problem-based learning.

Requirements, Exclusions and Recommendations
Learning Requirements:

at least H4 in Higher Leaving Cert Mathematics (or equivalent)


Module Requisites and Incompatibles
Incompatibles:
ECON10030 - Intro Quantitative Economics, MATH10210 - Found. of Math. for Com.Sc. I, MST10040 - Combi & Number Theory


 

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Exam (In-person): Final exam End of trimester
Duration:
2 hr(s)
 Alternative linear conversion grade scale 40% No
70
 No
Exam (Online): Midterm exam Week 7 Alternative linear conversion grade scale 40% No
10
 No
Quizzes/Short Exercises: online quizzes Week 1, Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10, Week 11, Week 12 Alternative linear conversion grade scale 40% No
10
 No
Participation in Learning Activities: Tutorial worksheets Week 1, Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10, Week 11, Week 12 Alternative linear conversion grade scale 40% No
10
 No

Carry forward of passed components
No
 

Resit In Terminal Exam
Spring 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
Professor Gary McGuire Lecturer / Co-Lecturer
Mr Oisin Campion Tutor

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Thurs 11:00 - 11:50
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Tues 12:00 - 12:50
Autumn Tutorial Offering 1 Week(s) - Autumn: All Weeks Fri 13:00 - 13:50
Autumn Tutorial Offering 2 Week(s) - Autumn: All Weeks Thurs 15:00 - 15:50
Autumn Tutorial Offering 3 Week(s) - Autumn: All Weeks Fri 10:00 - 10:50
Autumn Tutorial Offering 4 Week(s) - Autumn: All Weeks Fri 11:00 - 11:50
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