# Applied & Computational Mathematics Joint Major (APJ1)

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Applied mathematics  is the branch of mathematics focused on developing mathematical methods and applying them to solve real-world problems in science, engineering, industry and technology. Computational mathematics utilises computational techniques and simulations to produce problem-solving techniques and methodologies. This programme is aimed at students who wish to gain a deep understanding of the concepts of modern applied mathematics, and a mastery of the associated mathematical and computational skills. Our students will become autonomous learners capable of formulating and creatively solving relevant problems through techniques in mathematical and computational modeling. Our students will become flexible enough in their thinking and training to apply these techniques to a wide range of fields in the traditional application areas in the Physical Sciences, but also in emerging application areas, such as finance and biology. Our graduates will be in demand by employers and academic research institutes for their ability to use the tools they have learned to explain, describe and predict. We value students who are motivated to find the underlying physical causes for observations and patterns. We aim to provide a teaching and learning environment that develops confidence and independence through a wide variety of interactive formats, both inside and outside the classroom, including lectures, tutorials, on-line course material and computer assisted labs.

1 - Demonstrate an indepth understanding of core mathematics and a solid knowledge of both abstract mathematics and statistics
2 - Demonstrate strong proficiency in mathematical and computational methods, including computer programming.
3 - Apply the tools of mathematical and computational methods, including computer programming to at least one application area which the students will have studied in depth
4 - Model real world problems in a mathematical framework, at the same time demonstrating a real understanding of the limitations of modeling and the restrictions imposed by modeling assumptions
5 - Use the language of logic to reason correctly and make deductions
6 - Approach problems in an analytical, precise and rigorous way
7 - Analyze and interpret data and model predictions, find patterns and draw conclusions
8 - Work independently and as part of a team
9 - Carry out research into a specific topic, including a survey and synthesis of the known literature
10 - Give oral presentations of technical mathematical material at a level appropriate for the audience
11 - Prepare a written report on technical mathematical content in clear and precise language
Students who return failing grades in a trimester amounting to 15 credits, or more, will be identified under the UCD Continuation – Academic Progress policy. Students whose rate of progression and performance over two academic years is deemed unacceptable will be referred to the Governing Board to be reviewed for exclusion from the programme.

Students who fail to progress from the stage of the programme they are registered to for more than two academic years (except where a period of Leave of Absence has been granted for one of those years) will also be contacted under the Continuation – Academic Progress Policy.

As Stages 3 and 4 have the most dynamic components of the programme, and the material studied previously may no longer be relevant, a student who has been away from the programme for a significant period should be required to register again to Stage 3. The upper limit for completion of Stages 3 and 4 should be six years if they choose to do 120 credits with 20 in each year.

Graduates with training in Applied & Computational Mathematics work in fields as diverse as analytics and forecasting, meteorology, energy systems, electronics, biomedical applications and bio-information, finance, pharmaceutical industry, environmental agencies and companies, and computing in business, technology, research, and academia.

Stage 3

Students take 2 core modules. Students must also take 15 credits of options from the option list below.

Stage 4

Students take 1 core module. Students must also take 25 credits from the option list below.

Module ID Module Title Trimester Credits
Stage 3 Core Modules

ACM30220 Partial Differential Equations Autumn 5
ACM30020 Advanced Mathematical Methods Spring 5
Stage 3 Core Modules

Stage 3 Options - A)MIN2OF:
Option Modules

ACM30010 Analytical Mechanics Autumn 5
ACM30130 Advanced Computational Science Autumn 5
ACM30190 Dynamical Systems Autumn 5
STAT30090 Models - Stochastic Models Autumn 5
ACM30090 Mathematical Biology Spring 5
ACM30110 Advanced Computational Finance Spring 10
ACM30200 Mathematical Fluid Dynamics I Spring 5
ACM30210 Foundations of Quantum Theory Spring 5
Stage 3 Options - A)MIN2OF:
Option Modules

Stage 4 Core Modules

ACM40690 Survey of Appl and Comp Math Autumn 5
Stage 4 Core Modules

Stage 4 Options - A)MIN4OF:
Students select at least 25 credits from the list below.

ACM40980 Research Project 2 Trimester duration (Aut-Spr) 10
ACM40010 Electrodynamics & Gauge Theory Autumn 5
ACM40070 Math Fluid Dynamics II Autumn 5
ACM40750 Gen Relativity & Black Holes Autumn 5
ACM41020 Maths of Machine Learning Autumn 5
MATH30360 Measure Theory and Integration Autumn 5
SCI30080 Professional Placement-Science Autumn 5
ACM40900 Weather & Clim Num Modelling Spring 5
ACM41010 Math of Sust & Environment Spring 5
ACM41030 Optimization Algorithms Spring 5
ACM41040 GR and Gravitational Waves Spring 5
MATH30370 Markov Chains Spring 5
MATH40480 Probability Theory Spring 5
Stage 4 Options - A)MIN4OF:
Students select at least 25 credits from the list below.

See the UCD Assessment website for further details

Module Weighting Info
Award GPA
Programme Module Weightings Rule Description Description >= <=
BHSCI001 Stage 4 - 70.00%
Stage 3 - 30.00%
Standard Honours Award First Class Honours

3.68

4.20

3.08

3.67