MATH10040 Numbers & Functions

Academic Year 2020/2021

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 proof by contradiction and mathematical induction.

The greater part 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 theorem, Euler's theorem, and arithmetic modulo a prime and applications. The module concludes with some topics from elementary coding theory / cryptography such as the RSA encryption system.

This module also introduces the language of sets and functions, including injective surjective and bijective maps and the related notions of left-, right- and 2-sided inverses. Equivalence relations, equivalence classes.

Show/hide contentOpenClose All

Curricular information is subject to change

Learning Outcomes:

On completion of this module students should be able to:
1. use mathematical induction, solve inequalities, and understand 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

30
Small Group

6
Tutorial

12
Autonomous Student Learning

72
Total

120
Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and 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 Open Book Exam Component Scale Must Pass Component % of Final Grade
Continuous Assessment: Weekly quiz Varies over the Trimester n/a Alternative linear conversion grade scale 40% No

100

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