Mathematics for Game Developers

Overview

Faculty: Games
Duration: 8 Weeks – Wednesdays 6pm – 9pm
Delivery: Online
Levels: Certificate
Start Date: 3rd August 2022
Course Director: Dr Ronan Mulhaire
Fees: €200
Certification: Pulse College Certificate

COURSE CONTENT

In order to be a successful games developer or programmer, it is important to have some understanding of mathematics; it is necessary to have some knowledge of mathematical concepts, such as algebra, for example.

This programme does not present maths in the abstract, such as you may have encountered them in school. Rather, it is designed to give you the grounding in maths and programming that you will need to succeed as a games developer. Each week, core mathematical principles are introduced by our expert lectures, but are always related back to a specific aspect of programming or game design.

Week 1

Algebra and Programming
Algebra and Programming

(1) Negative Numbers, Absolute Value, Exponents, Square Roots, Decimals, Fractions, Percentages, Order of Operations:
In the first part of the lecture, these main algebraic topics will be presented, along with the specific rules for their manipulations. Examples and exercises will be included.

(2) Variables, Data Types, Arrays:

The second part of the lecture consists of a short introduction to the types of variables used in programming languages.

Week 2

Algebra and Programming
Algebra and Programming

(1) Coordinates, Functions, Polynomials, Rationals, Exponentials, Logarithms:
In the first part of the lecture, students will explore the use of coordinates. A definition of functions of one variable will follow, along with four main examples: the polynomial functions, the rational functions, the exponential function and the logarithmic function. Exercises for each case will be included.

(2) Functions (in programming):
In the second part of the lecture, the concept of functions and subroutines in the case of programming will be discussed.

(3) Introduction to Blender:
The third, and final part of this lecture introduces the free, open-source graphics software, Blender.

Week 3

Geometry and Programming
Geometry and Programming

(1) Lines and Rays, Parallel and Perpendicular Lines, Segments:
In part one, the concepts of lines, rays and linear segments will be introduced before we move on to the definition of parallel and perpendicular lines and explore a number of examples.

(2) Loops and Conditionals:
In the second part of the lecture, the concepts of loops and of conditionals will be discussed. The use of loops and conditionals in programming will be demonstrated by means of examples.

Week 4

Geometry and Trigonometry
Geometry and Trigonometry

(1) Angles, Measuring and Drawing Angles; Types of Angles, Trigonometric Functions, Triangle and Trigonometric Identities, Triangles, Rectangles and Polygons:
In the first part of the lecture, the main trigonometric concepts and rules will be presented, with emphasis placed on the types of angles, their measurement and uses. Following this, the main trigonometric functions (sin, cos, tan, cot) will be introduced and examples will be given. Finally, the main triangle and trigonometric identities will be shown.

(2) Use of Angles for Vision, Perspective and Scaling in Video Games:
In the second part of the lecture the use of angles in the context of video games will be discussed, by reference to specific examples, such as the vision of game characters, the scaling of game landscapes, etc.

(3) Use of Triangles and Polygons to Create Realistic Models for Objects and Characters:
In part three, the use of 2D and 3D polygons in the context of game design will be explained. Students will be introduced to the creation of realistic models for objects and characters by the use of these geometric tools.

Week 5

2D Vectors & Programming
2D Vectors & Programming

(1) Definition of 2D Vectors, Operations with 2D Vectors:
The first part of the lecture will introduce vectors in two dimensions; both Cartesian and polar coordinates. The main definitions and operations for 2D vectors will be presented by means of examples and exercises.

(2) 2D Vectors in Game Design:
In the second part of the lecture, the use of arrays in describing vectors in the context of programming will be discussed. Examples of vectors being used in game design will be presented.

Week 6

3D Vectors
3D Vectors

(1) Definition of 3D Vectors, Operations with 3D vectors:

In part one, the main definitions and operations for 3D vectors will be demonstrated by means of examples and exercises.

(2) Use of Vectors for Motion, Velocity, Force, etc. in Games:
In the second part of the lecture, the physical concepts of velocity, momentum and force will be introduced so as to describe motion in three dimensions. Examples from game design where vectors are used to describe motion will be thoroughly discussed.

Week 7

Matrices & Programming
Matrices & Programming

(1) Definition of matrices, Dimension and Elements, Operations with Matrices:
In the first part of the lecture, matrices will be introduced and their distinct characteristics (dimensions and elements) will be discussed. Following, the basic operations of matrices (summation, subtraction, multiplications) will be presented, along with examples and exercises.

(2) Determinants, Cofactors, Transpose, Inverse, Types of Matrices:

The second part of this lecture will introduce the distinct features and functions of matrices, including determinants, transposes, and inverses. Examples for each will be presented. Furthermore, we will explore examples of different types of matrices.

(3) Matrix Representation in Programing (Simple Calculations):
In the third part of the lecture, the use of arrays in describing matrices in the context of programming will be discussed.

Week 8

Physics and Games
Physics and Games

(1) Motion of Bodies, Rotation of bodies:

In the first part of the lecture, the main physical concepts of motion of bodies will be extended. Students will explore the use vector algebra in understanding how a body moves and rotates.

(2) Fluids and Gases

In the second part of the lecture, the main ideas on the motion of fluids and gases will be explained. Examples of their use in game design will be highlighted.

(3) Use of Scaling Matrices, Translation Matrices, Rotation Matrices, etc. in Games:
In the third part of the lecture, the use of matrices to represent motion in games will be discussed. The main types of scaling matrices (for perspective), translation matrices (for linear motion) and rotation matrices (for turns and twists) will be demonstrated.

DR NIKOLAOS CHATZARAKIS

Dr Chatzarakis holds a PhD in Political Economy from the Aristotle University of Thessaloniki, and is currently working on a second PhD, in Mathematical Cosmology, in Trinity College Dublin. He holds two Masters degrees – in Computational Physics and in Economics – from the Aristotle University of Thessaloniki, and was also awarded a BSc in Physics by that same institution. His work has been published in a number of peer-reviewed journals, including Annals of Physics, Nuclear Physics, Structural Change and Economic Dynamics, and the European Physics Journal. Dr Chatzarakis has presented at a number of international conferences in Greece, Spain, South Korea, Bulgaria and Slovakia, and has tutored in Trinity College Dublin.

WHO IS THIS COURSE FOR?

  • School leavers hoping to study games development or computer science at third level, but who find the maths-intensive curricula of those courses daunting
  • Individuals that are currently employed but are looking to retrain or upskill in programming, but find the maths component of programming to be a formidable barrier to them

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HOW TO APPLY

Admissions

This course is a direct application course. Applications are currently taken through the Application Form below. Upon receiving your application form our Admissions Team will be in contact. No industry experience is required and applicants may be accepted without formal academic qualifications. If you wish to gain further insight into what this course has to offer, please don’t hesitate to contact us.

Start Date:

August 3rd 2022
8 Week Course:
6pm – 9pm on Wednesdays

Interview Process

There is no interview application for this course but we would be delighted to invite you in for a private tour of our campus; to meet our course lecturers and gain further insight into what our course has to offer.

FEES

Irish / EU (Residing in Ireland)

€200*
*Full Payment Required to Confirm Place
**Please note: Fees are non-refundable

International / EU (living outside of Ireland)

€200*
*Full Payment Required to Confirm Place
**Please note: Fees are non-refundable

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