# MATH10040 Numbers & Functions

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.

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Curricular information is subject to change

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

30

Tutorial

12

Autonomous Student Learning

72

Total

114

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 Open Book Exam Component Scale Must Pass Component % of Final Grade

Not yet recorded.

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour