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ACME Module Descriptor
Module Code : MAT101
Module Title : Applied Mathematics 1
Level
School
Division
Tutor
External
Examiner(s)
Prerequisites
Corequisites
Replaced
07
School of Arts, Media and Games
Division of Computing and
Mathematics
Karen Meyer
SCQF 20
S1
Year
2016/7
Brief Description
This module covers the basic concepts of applied mathematics relevant to the Computer Games Technology programme.
Aims
The aim of this module is to provide the student with: the basic ideas and techniques in applied mathematics relevant to Computer Games Technology.
Learning Outcomes
By the end of this module the student should be able to :
1. Use standard functions and approximations to solve problems involving rates of change by calculus methods.
2. Solve problems in plane geometry involving lines, circles, the conic sections and complex numbers (Argand diagram).
3. Apply matrix transformations and vector methods for use in 2− and 3−dimensional space.
4. Apply the equations of kinematics and Newtonian concepts involving momentum, impulse and energy to formulate and solve the resulting models.
Indicative Content
1. Approximation
Basic function definitions, composition, inverse; polynomial, rational, exponential, logarithmic and trigonometric functions. Graphs of functions.
Appreciation of need to approximate functions in some applications and for careful evaluation on computers − errors. 2. Calculus
Rates of change, derivatives of standard functions. Rules for derivatives of sums, products, quotients and composite functions. Higher derivatives and
applications. Indefinite and definite integrals − integration methods. Application to areas, mean values, etc. 3. Geometry
Plane coordinate geometry of lines, circles and conic sections. Operations with complex numbers, conjugates, the Argand diagram, trigonometric and
exponential polar forms. Vectors in 2 and 3 dimensions, scalar and vector products − use in projection and 3D geometry. 4. Matrices and Transformations
Basic matrix operations, determinants, inverses. Solving linear equations by matrix inverse. Matrix transformations of the plane − translations, scalings,
rotations and reflections. Homogeneous coordinates. 5. Kinematics in a straight line
Newton's laws of motion. Momentum and impulse, collision of bodies (1−dimensional, elastic and inelastic). Kinetic and potential energy, elastic strings.
Work and Power. Coplanar forces. Friction.
Statement on Teaching, Learning and Assessment
The module will be delivered by a mixture of lectures and tutorials. There will be a formative test during structured feedback week. The learning
outcomes will be assessed by an end of semester exam.
Teaching and Learning Work Loads : Total
Lecture
Tutorial/Seminar
Supervised Practical Activity
Unsupervised Practical
Activity
Assessment
Independent
: 200
: 36
: 24
: 0
: 0
: 60
: 80
Assessment Type
Description
Scheduled examination
End of Semester
Examination – 2 hours
Final
Grade
Weighting
(%)
Assessment Week Number
Issue
Submission
Return
Assoc
Learning
Outcomes
100
EP
EP
EP
1,2,3,4
Supportive Reading
James J. 2008 Modern Engineering Mathematics (4Th Ed.) Pearson, Prentice Hall
Jefferson B. Beadsworth T. 2000 Introducing Mechanics Oup: Oxford, Uk
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Lengyal E. Mathematics For 3D Game Programming And Computer Graphics (3Rd Ed.) Course Technology/Centage Learning
Teachability Issues for this module are:
Symbolic
Key Transferable Skills for this module are:
Problem Solving
Copyright ­ Abertay University ­ 19­May­2016
ACME Module Descriptor
Module Code : MAT102
Module Title : Mathematics for Application Development 1
Level
07
School
School of Arts, Media and Games
SCQF 20
Division
Division of Computing and
Mathematics
Tutor
Craig Stark
S1
Year
2016/7
External
Examiner(s)
Prerequisites
LV5
Corequisites
Replaced
Brief Description
This module is specifically for Computer Games Application Development students. It consists of the elementary algebraic and geometric topics needed
in the study of computer games application development.
Aims
The aim of this module is to provide the student with: the necessary basic algebraic and geometric skills to enhance their understanding of concepts
used in computer graphics programming.
Learning Outcomes
By the end of this module the student should be able to :
1. Solve algebraic problems using trigonometric, exponential and logarithmic functions.
2. Solve two­dimensional geometric problems involving straight lines and circles.
3. Use matrix and vector algebra proficiently.
4. Use matrix transformations for standard geometric operations in 2­D computer graphics.
5. Use the basic kinematics equations to solve problems in dynamics.
Indicative Content
1. Revision:
Transposition of formulae, indices. 2. Functions:
Standard trigonometric, exponential and logarithmic functions and their graphs (sketches only). 3. Coordinate Geometry:
2­D lines – gradient, equation, length, perpendicular lines, intersections. Circles – centre and radius, equation, tangent and normal. 4. Vectors:
2 and 3­D, modulus, unit vector, component form, scalar (dot) and vector (cross) products. 5. Matrices:
Dimension, addition/subtraction, transpose, multiplication, determinant, inverse (up to 3 x 3). 6. Header 6
Solve linear equations by matrix methods – inverse, Gaussian elimination and Cramer’s rule. 7. Matrix Transformations:
2­D transformation matrices – scaling, rotation, reflection and translation using homogeneous coordinates. Composite transformations by matrix
multiplication. 8. Kinematics:
Use of standard kinematics equations (straight line, constant acceleration) and relation to velocity/time and displacement/time graphical methods.
Motion in two dimensions – projectiles from a horizontal plane – range, time of flight, greatest height etc.
Statement on Teaching, Learning and Assessment
Learning will be achieved through lectures and tutorial sessions, with hand­out material being given to students in class and posted on Blackboard.
Interactive discussion with staff will be encouraged during classes and tutorial sessions will focus on students’ active enquiry into topics covered in the
lectures. Each week there will be two one hour lectures followed by two one hour tutorial sessions. In week 6 there will be a formative, multiple­choice,
online test, which will act as a diagnostic of student progress, and will link with structured feedback week (week 7). Students will be encouraged to
engage with learning technologies that support their subject development, via web references and using specialist mathematics packages (e.g. Derive
and Calmat).
Teaching and Learning Work Loads : Total
Lecture
Tutorial/Seminar
: 200
: 18
: 0
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Supervised Practical Activity : 18
Unsupervised Practical
Activity
Assessment
Independent
: 0
: 80
: 84
Assessment Type
Description
Scheduled examination
Students will sit a 2 hours
closed book examination
during exam week.
Final
Grade
Weighting
(%)
Assessment Week Number
Issue
Submission
Return
Assoc
Learning
Outcomes
100
EP
EP
EP
1,2,3,4,5
Supportive Reading
A Croft R Davidson 2006 Valuepack: Foundation Maths With Mathematical Dictionary Pearson.
J Vince 2001 Essential Mathematics For Computer Graphics Fast Springer­Verlag London Ltd.
Teachability Issues for this module are:
Symbolic
Key Transferable Skills for this module are:
Problem Solving
Copyright ­ Abertay University ­ 19­May­2016
ACME Module Descriptor
Module Code : MAT201
Module Title : Applied Mathematics 2
Level
08
School
School of Arts, Media and Games
Division
Division of Computing and
Mathematics
Tutor
External
Examiner(s)
SCQF 20
S1
Year
2016/7
Karen Meyer
Prerequisites
Corequisites
Replaced
Brief Description
This module expands on the concepts of Applied Mathematics 1, on applied mathematics relevant to the Computer Games Technology programme.
Aims
The aim of this module is to provide the student with: an appreciation of the advanced ideas and techniques in applied mathematics relevant to
Computer Games Technology.
Learning Outcomes
By the end of this module the student should be able to :
1. Use calculus methods to describe/approximate surfaces and to solve optimisation problems.
2. Use the ideas of homogeneous coordinate matrix transformations and quaternions for 3D rotations in computer graphics applications.
3. Use the rays and beams in the modelling of reflection, refraction and collision detection with regular shapes.
4. Solve problems in 1D involving variable acceleration and resistance.
5. Solve problems in 2D, including vector resolution for resultant and relative motion; circular and simple harmonic motion; and elastic collisions.
Indicative Content
1. Calculus
MacLaurin and Taylor series. First and second order partial differentiation. Series of two variables. Extrema of two variable functions. 2. Matrix and Quaternion Transformations
3D matrix transformations: translation, scaling, rotation and reflection. Parallel and perspective projections. Quaternions and their application to
rotations about an axis. 3. Vector Curves and Surfaces
Vector geometry of curves and surfaces in space. Tangent planes and normals. Bilinear surface patches. 4. Ray Tracing
Intersection of rays with spheres, boxes and quadrics. Intersections(cone and sphere) in beam tracing. Tracing reflected and refracted rays of light in 3D
using vectors. Snell's law of refraction. 5. Dynamics
Variable velocity and acceleration. Resultant and relative velocity. Straight−line dynamics with variable forces (e.g. dependent on speed). Horizontal and
vertical−circle motion, SHM. Oblique impact of objects in 2D.
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Statement on Teaching, Learning and Assessment
The module will be delivered by a mixture of lectures and tutorials. There will be a formative test during structured feedback week. The learning
outcomes will be assessed by an end of semester exam.
Teaching and Learning Work Loads : Total
Lecture
Tutorial/Seminar
Supervised Practical Activity
Unsupervised Practical
Activity
Assessment
Independent
: 200
: 36
: 24
: 0
: 0
: 60
: 80
Assessment Type
Description
Scheduled examination
End of Semester
Examination – 2 hours
Final
Grade
Weighting
(%)
Assessment Week Number
Issue
Submission
Return
Assoc
Learning
Outcomes
100
EP
EP
EP
1,2,3,4,5
Supportive Reading
James J. 2008 Modern Engineering Mathematics (4Th Ed.) Pearson, Prentice Hall
Jefferson B. Beadsworth T. 2001 Further Mechanics Oup: Oxford, Uk
Lengyal E. Mathematics For 3D Game Programming And Computer Graphics (3Rd Ed.) Course Technology/Centage Learning
Teachability Issues for this module are:
Symbolic
Key Transferable Skills for this module are:
Problem Solving
Copyright ­ Abertay University ­ 19­May­2016
ACME Module Descriptor
Module Code : MAT202
Module Title : Mathematics for Application Development 2
Level
School
Division
Tutor
External
Examiner(s)
Prerequisites
Corequisites
Replaced
08
School of Arts, Media and Games
Division of Computing and
Mathematics
Craig Stark
SCQF 20
S1
Year
2016/7
Brief Description
This module builds on Mathematics for Application Development 1 to give CGAD students the mathematical building blocks required for 3­D graphics
programming.
Aims
The aim of this module is to provide the student with: the necessary mathematical tools for programming 3­D object characterisations in computer
graphics.
Learning Outcomes
By the end of this module the student should be able to :
1. Formulate and use transformation matrices (2­D & 3­D) for standard transformations and projections.
2. Determine equations for lines and planes in 3­D, using them to compute distances, projections and intersections.
3. Perform collision detection calculations of rays with boxes and spheres.
4. Apply Newtonian concepts involving momentum, impulse and energy to formulate and solve resulting models.
5. Use vector resolution methods for force systems, relative motion and centres of gravity.
Indicative Content
1. Viewing Transformations:
2­D viewing transformation matrices, scaling factors, aspect ratios, windows, normalised device screen, viewports. 2. Lines and Planes:
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Vector (using parameters) and Cartesian equations of 3­D lines and planes. Distances from points to lines and planes. Projection of line onto a plane,
intersection of lines and planes. 3. Matrix Transformations:
3­D matrix transformations of scaling, rotation, reflection and translation (homogeneous coordinates). Composite transformation by matrix multiplication.
4. Projection Matrices:
Standard orthogonal and perspective matrix transformations. 5. Ray Tracing:
Collision detection methods of rays with boxes and spheres. 6. Header 6
Newton’s laws of motion. Momentum and impulse, collision of bodies (1­dimensional, elastic and inelastic). Kinetic and potential energy, elastic strings.
Work and Power. 7. Centre of Gravity:
Centre of gravity of composite body. Use of principle of moments to solve centre of gravity problems. Continuous lamina centres of gravity.
Statement on Teaching, Learning and Assessment
Learning will be achieved through lectures and tutorial sessions, with hand­out material being given to students in class and posted on Blackboard.
Interactive discussion with staff will be encouraged during classes and tutorial sessions will focus on students’ active enquiry into topics covered in the
lectures. Each week there will be two one hour lectures followed by two one hour tutorial sessions. In week 6 there will be a formative, multiple­choice,
online test, which will act as a diagnostic of student progress, and will link with structured feedback week (week 7). Students will be encouraged to
engage with learning technologies that support their subject development, via web references and using specialist mathematics packages (e.g. Derive
and Calmat).
Teaching and Learning Work Loads : Total
Lecture
Tutorial/Seminar
Supervised Practical Activity
Unsupervised Practical
Activity
Assessment
Independent
: 200
: 18
: 0
: 18
: 0
: 80
: 84
Assessment Type
Description
Scheduled examination
Students will sit a 2 hours
closed book examination
during exam week.
Final
Grade
Weighting
(%)
Assessment Week Number
Issue
Submission
Return
Assoc
Learning
Outcomes
100
EP
EP
EP
1,2,3,4,5
Supportive Reading
J Vince 2001 Essential Mathematics For Computer Graphics Fast Springer­Verlag London Ltd.
Teachability Issues for this module are:
Symbolic
Key Transferable Skills for this module are:
Problem Solving
Copyright ­ Abertay University ­ 19­May­2016
ACME Module Descriptor
Module Code : MAT301
Module Title : Module Title: Mathematics and Artificial Intelligence
Level
School
Division
Tutor
External
Examiner(s)
Prerequisites
Corequisites
Replaced
09
School of Arts, Media and Games
Division of Computing and
Mathematics
David J King
SCQF 20
S2
Year
2016/7
Brief Description
This module builds on the ideas of MAT201 to comprise a more advanced study of mathematical methods and models relevant to Computer Games
Technology, and introduces some of the many Artificial Intelligence (AI) techniques which are currently, or could in the near future, be used to enhance
the development of applications in video games, or other entertainment related products. These AI techniques can enhance the immersive properties of
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a game by enabling ‘realistic’ and ‘believable’ game play and character actions, or used to reduce development time by automatically creating content,
etc.
Aims
The aim of this module is to provide the student with: an appreciation of the advanced mathematical methods required in the study of Computer Games
Technology and introduce the underlying techniques used in video games to create the illusion of ‘intelligence’ as well as some real AI techniques which
are, or could be, used to enhance the development of these Game AI methods.
Learning Outcomes
By the end of this module the student should be able to :
1. Model and solve more advanced problems in rigid body and 2­dimensional particle dynamics.
2. Use analytical and numerical methods to solve equations.
3. Develop a critical understanding of AI techniques and technologies.
4. Evaluate the use of AI technologies and techniques in computer games.
Indicative Content
1. Numerical Methods:
Numerical methods for integration (trapezium and Simpson’s rules) and the solution of equations by simple iteration and the Newton­Raphson method.
Numerical solution of DE’s, e.g. Euler, predictor/corrector methods (Euler/trapezium/Simpson), Verlet, Runge­Kutta. 2. Motion of a Rigid Body:
Centroids and moments of inertia of simple bodies, parallel and perpendicular axis theorems. Rotation of a rigid body about an axis, energy, angular
momentum. Rolling and sliding motion. 3. Differential Equations:
Analytical solution of 2nd order, linear, ordinary differential equations. 4. An Introduction to AI for Games:
The importance of good game AI. The differences between Game AI and so called ‘real’ Academic AI and their relative advantages and disadvantages. 5. ‘Traditional’ Game AI:
Pathfinding, including A* and its derivatives, Flocking and Steering, Rule Based Systems, Finite State Machines. 6. Header 6
Fuzzy Logic and Fuzzy State Machines, Genetic Algorithms, Artificial Neural Networks. 7. The use of AI in Games: The use of AI in Games:
Combining AI techniques to produce A­life and Intelligent Agents. The future of AI in games. Combining AI techniques to produce A­life and Intelligent
Agents. The future of AI in games.
Statement on Teaching, Learning and Assessment
Contact time is split approximately 50/50 between lectures and tutorials plus time for supervised practical activity. The learning outcomes will be
assessed by a coursework and an examination. The assessment will cover LO 4, whereas the exam will cover LOs 1 to 3. The tutorial sessions will
allow the students time for active enquiry into the topics covered in the lectures. The supervised practical activity will give students a chance to
investigate various Game AI techniques. Materials are available electronically via Blackboard, which is updated weekly with copies of the lectures,
tutorial activities and also includes information on the assessments.
Teaching and Learning Work Loads : Total
Lecture
Tutorial/Seminar
Supervised Practical Activity
Unsupervised Practical
Activity
Assessment
Independent
: 200
: 24
: 24
: 12
: 0
: 80
: 60
Assessment Type
Description
Coursework
Scheduled examination
Develop and critically
evaluate an AI technique,
and write a report
2 hour closed book
examination
Final
Grade
Weighting
(%)
Assessment Week Number
Issue
Submission
Return
Assoc
Learning
Outcomes
40
19
31
33
4
60
EP
EP
EP
1,2,3
Supportive Reading
James G. 2008 Modern Engineering Mathematics (4Th. Ed.) Pearson, Prentice Hall.
Jefferson B. Beadsworth T. 2001 Further Mechanics Oup: Oxford, Uk.
Champandard A. 2004 Ai Game Development – Synthetic Creatures With Learning And Reactive Behaviours New Riders Publishing.
Teachability Issues for this module are:
Symbolic
Key Transferable Skills for this module are:
Problem Solving
Copyright ­ Abertay University ­ 19­May­2016
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ACME Module Descriptor
Module Code : MAT401
Module Title : Applied Mathematics 4
Level
10
School
School of Arts, Media and Games
SCQF 20
Division
Division of Computing and
Mathematics
Tutor
Craig Stark
S2
Year
2016/7
External
Examiner(s)
Prerequisites
Corequisites
Replaced
Brief Description
This module introduces advanced concepts of applied mathematics relevant to the Computer Games Technology programme.
Aims
The aim of this module is to provide the student with: an appreciation of the advanced ideas and techniques in applied mathematics relevant to
Computer Games Technology.
Learning Outcomes
By the end of this module the student should be able to :
1. Evaluate and solve problems involving Bézier curves and splines.
2. Evaluate and solve problems involving rigid body systems.
3. Apply and critically evaluate advanced mathematical techniques in games development.
Indicative Content
1. Geometric Techniques
Approximation of curves and surfaces in space – Bézier curves, generalized Bézier curves, de Casteljau algorithm, Splines, Catmull­Rom splines, B­
splines, Surface patches. 2. Rigid Body Systems
Eigenvalues and eigenvectors; Diagonalization; Repeated and volume integrals; Inertia tensor; Euler's equation of rotation; general motion of a rigid
body. 3. Games Programming
Games programming applied to realisation of the mathematical topics.
Statement on Teaching, Learning and Assessment
The module will be delivered by a mixture of lectures and tutorials. The learning outcomes will be assessed by a piece of coursework and an end of
semester exam.
Teaching and Learning Work Loads : Total
Lecture
Tutorial/Seminar
Supervised Practical Activity
Unsupervised Practical
Activity
Assessment
Independent
: 200
: 18
: 18
: 0
: 0
: 80
: 84
Assessment Type
Description
Coursework
Coursework
End of Semester
Examination – 2 hours
Scheduled examination
Final
Grade
Weighting
(%)
30
Assessment Week Number
70
Issue
Submission
Return
Assoc
Learning
Outcomes
19
33
35
1,2,3
EP
EP
EP
1,2
Supportive Reading
Nguyen H. 2008 Gpu Gems 3 Addison Wesley
Morin D. 2008 Introduction To Classical Mechanics Cambridge University Press
Xiang Z. Lastock R. 2000 Computer Graphics McGraw Hill
Teachability Issues for this module are:
Symbolic
Key Transferable Skills for this module are:
Problem Solving
Copyright ­ Abertay University ­ 19­May­2016
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ACME Module Descriptor
Module Code : MAT501
Module Title : Applied Mathematics and Artificial Intelligence
Level
11
School
School of Arts, Media and Games
SCQF 20
Division
Division of Computing and
Mathematics
Tutor
David J King
S1
Year
2016/7
External
Examiner(s)
Prerequisites
Corequisites
Replaced
Brief Description
This module covers the basic mathematics necessary for graphics and introduces students to Artificial Intelligence, specifically in Computer Games.
Aims
The aim of this module is to provide the student with: the mathematical techniques involved in creating realistic computer graphics, and a critical
understanding of the basic features and techniques used to implement AI, in a computer game or entertainment product.
Learning Outcomes
By the end of this module the student should be able to :
1. Apply 2 and 3­dimensional vector/matrix/quaternion­transformation techniques to typical computer graphics problems in the area of computer games.
2. Demonstrate the application of the principles of ray tracing and collision detection in 3D computer games.
3. Develop a critical understanding of AI techniques and technologies.
4. Evaluate the use of AI technologies and techniques in computer games.
Indicative Content
1. Revision of Vectors and Matrices
Revision of Vectors and Matrices 2. 3D Geometry:
Lines, planes, angles and intersections. Parametric curves, normal and tangent planes to Cartesian and parametric surfaces. 3. Matrix Transformations:
Homogeneous coordinates, 2D and 3D transformation, projection. 4. Quarternions:
Their algebra and representation of 3D rotations.. 5. Ray Tracing and Collision Detection:
Intersection of rays and various 3D objects, modelling reflection and refraction using vectors. Bounding volumes, detecting collisions between various
3D objects. 6. An introduction to AI for Games:
The importance of good Game AI. The difference between Game AI and so called ‘real’ or Academic AI and their relative advantages and
disadvantages. 7. ‘Traditional’ Game AI:
Pathfinding, including A* and its derivatives, Flocking and Steering, Rule Based Systems, Finite State Machines. 8. Academic AI Techniques:
Fuzzy Logic and Fuzzy State Machines, Genetic Algorithms, Artificial Neural Networks. 9. The use of AI in games:
Combining AI techniques to produce A­life and Intelligent Agents. The future of AI in games.
Teaching and Learning Work Loads : Total
Lecture
Tutorial/Seminar
Supervised Practical Activity
Unsupervised Practical
Activity
Assessment
Independent
:
: 24
: 24
: 12
: 0
: 80
: 60
Assessment Type
Description
Coursework
Scheduled examination
Report
2hr closed book
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Final
Grade
Weighting
(%)
40
60
Assessment Week Number
Issue
Submission
Return
Assoc
Learning
Outcomes
1
EP
13
EP
15
EP
4
1,2,3
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Supportive Reading
Lengyel E. 2012 Mathematics For 3D Game Programming And Computer Graphics, 3Rd Edition Cengage Learning.
March D. 2005 Applied Geometry For Computer Graphics And Cad, 2Nd Edition Springer.
Vince J. 2011 Mathematics For Computer Graphics, 3Rd Edition Springer.
Teachability Issues for this module are:
Visual,Symbolic,Computer­Based,Collaboration
Key Transferable Skills for this module are:
Communication,Problem Solving,Research,ICT Skills,Self Evaluation,Planning
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