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Applied & Computational Mathematics

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If you enjoy studying Mathematics for the Leaving Certificate, Applied & Computational Mathematics at UCD will train you in the essential mathematical and computational skills in modelling, analysis and simulation needed to solve problems arising throughout the physical and life sciences, engineering, business and finance sectors. Today’s challenges faced by science and engineering are so complex that they can be analysed and solved only through mathematical and computational modelling. Mathematical models create representations of complex real-world phenomena in a precise, quantitative way. Fundamental insights can then be obtained by analysing these models through a combination of mathematical analysis and computational simulation. Outside the traditional spheres of science and engineering, mathematical modelling and simulation techniques are increasingly used in the social sciences, communication, business and finance sectors.

About This Course

If you enjoy studying Mathematics for the Leaving Certificate, Applied & Computational Mathematics at UCD will train you in the essential mathematical and computational skills in modelling, analysis and simulation needed to solve problems arising throughout the physical and life sciences, engineering, business and finance sectors. Today’s challenges faced by science and engineering are so complex that they can be analysed and solved only through mathematical and computational modelling. Mathematical models create representations of complex real-world phenomena in a precise, quantitative way. Fundamental insights can then be obtained by analysing these models through a combination of mathematical analysis and computational simulation. Outside the traditional spheres of science and engineering, mathematical modelling and simulation techniques are increasingly used in the social sciences, communication, business and finance sectors.

Information on all our courses including pathways, internships and careers information is available in the UCD Science Undergraduate Courses Entry 2025 Brochure (PDF).

Click here to Download Course Pathways document.

Applied & Computational Mathematics is one of the degree subjects available through the Mathematics stream in the common entry Science course.

Students study similar modules for all degree subjects in the Mathematics stream in first year and will study modules for a minimum of two degree subjects in second year. At the end of second year, students choose their degree subject. We do our best to ensure that students go on to study their top degree subject choice but degree subjects can be competitive. As we offer a number of degree subjects in each stream, students have a number of similar degree subjects to choose from as their degree major. If a degree subject is oversubscribed, places are allocated on a competitive basis. For more information on choosing a degree major at the end of Second Year, visit the Mathematics stream page.

This is a sample set of modules that an Applied & Computational Mathematics student could study each year in UCD.

First Year

Scientific Enquiry • Introduction to Applied & Computational Mathematics • Calculus in the Mathematical and Physical Sciences • Applications of Differential Equations • Linear Algebra in the Mathematical and Physical Sciences • Statistical Modelling • Mathematical Analysis • Numbers & Functions • Option Modules • Elective Module 

Second Year

Computational Science • Classical Mechanics • Calculus of Several Variables • Introduction to Probability • Oscillations & Waves • Vector Calculus • + modules for 1 other Subject • Elective Modules

Third Year

Advanced Computational Science • Advanced Mathematical Methods • Complex Analysis • Partial Differential Equations • Mathematical Biology • Metric Spaces • Numerical Methods • Dynamical Systems • Option Modules • Elective modules

Fourth Year

Research Project • Mathematics of Complex Networks • Mathematics of Machine Learning • General Relativity & Black Holes • Mathematical Fluid Dynamics • Option Modules 

Timetables & Assessment
Each student will have their own timetable based on their individual module selection. This is a full-time course and classes may include lectures, practicals and tutorials, depending on the subjects. Students will also be expected to study independently (autonomous student learning). Assessment varies with each module but may comprise continuous assessment of practicals, written exams and online learning activities.

Students may apply to study abroad for a trimester in third year in partner institutions internationally.

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.

 

Students have the opportunity to complete a Professional Placement module worth 5 credits. This module provides students with an opportunity to undertake a placement in industry (6-10 weeks) in the summer following Third Year. Students in recent years have completed internships in Flutter and Met Eireann. Students can also apply to complete research bursaries in UCD Research labs.

Placements are secured on a competitive basis and are subject to change each year.


Assistant Professor James Herterich
UCD School of Mathematics and Statistics
askscience@ucd.ie


Below is a list of all modules offered for this degree in the current academic year. Click on the module to discover what you will learn in the module, how you will learn and assessment feedback profile amongst other information.

Incoming Stage 1 undergraduates can usually select an Elective in the Spring Trimester. Most continuing undergraduate students can select up to two Elective modules (10 Credits) per stage. There is also the possibility to take up to 10 extra Elective credits.

Module Type Module   Trimester Credits
Stage 2 Core Modules
 ACM20030 Computational Science Autumn  5
Stage 2 Core Modules
 ACM20050 Classical Mechanics Autumn  5
Stage 2 Core Modules
 MATH20060 Calculus of Several Variables Autumn  5
Stage 2 Core Modules
 STAT20110 Introduction to Probability Autumn  5
Stage 2 Core Modules
 ACM20060 Oscillations and Waves Spring  5
Stage 2 Core Modules
 ACM20150 Vector Integral & Differential Calculus Spring  5
Stage 2 Options - A) Min 0 of:
For students progressing to a degree in Applied & Computational Mathematics, the modules MATH20300 and STAT20100 must be taken in either Stage 2 or Stage 3
MATH20300 Linear Algebra 2 for the Mathematical Sciences Autumn  5
Stage 2 Options - A) Min 0 of:
For students progressing to a degree in Applied & Computational Mathematics, the modules MATH20300 and STAT20100 must be taken in either Stage 2 or Stage 3
STAT20100 Inferential Statistics Spring  5
Stage 2 Options - B) Min 0 of:
If not previously taken in Stage 1, students enrolled to Stage 2 Applied & Computational Mathematics must take MATH 10320 in Stage 2.
MATH10320 Mathematical Analysis Spring  5
Stage 2 Options - C) Min 0 of:
Additional modules can be taken from the options below. Alternatively, modules can be taken from the BSc programme or, students can select 10 credits from elective modules.
 STAT20230 Modern Regression Analysis Autumn  5
Stage 2 Options - C) Min 0 of:
Additional modules can be taken from the options below. Alternatively, modules can be taken from the BSc programme or, students can select 10 credits from elective modules.
 MATH20310 Groups, Rings and Fields Spring  5
Stage 3 Core Modules
 ACM30130 Advanced Computational Science Autumn  5
Stage 3 Core Modules
 ACM30190 Dynamical Systems Autumn  5
Stage 3 Core Modules
 ACM30220 Partial Differential Equations Autumn  5
Stage 3 Core Modules
 ACM30020 Applied Analysis Spring  5
Stage 3 Core Modules
 ACM30140 Numerical Methods for PDEs Spring  5
Stage 3 Core Modules
 MATH30040 Complex Analysis Spring  5
Stage 3 Options - A) Min 0 of:
If not previously taken in Stage 2, students must take MATH20310, MATH20300, and STAT20100 in Stage 3.
MATH20300 Linear Algebra 2 for the Mathematical Sciences Autumn  5
Stage 3 Options - A) Min 0 of:
If not previously taken in Stage 2, students must take MATH20310, MATH20300, and STAT20100 in Stage 3.
MATH20310 Groups, Rings and Fields Spring  5
Stage 3 Options - A) Min 0 of:
If not previously taken in Stage 2, students must take MATH20310, MATH20300, and STAT20100 in Stage 3.
STAT20100 Inferential Statistics Spring  5
Stage 3 Options - B) Min 0 of:
Students must select a minimum of 20 credits of options in Stage 3. If not previously taken in Stage 2 these options may need to include MATH20310, MATH20300, or STAT20100. Otherwise, all Stage 3 option modules must be taken from the list below.
 MATH30090 Metric Spaces Autumn  5
Stage 3 Options - B) Min 0 of:
Students must select a minimum of 20 credits of options in Stage 3. If not previously taken in Stage 2 these options may need to include MATH20310, MATH20300, or STAT20100. Otherwise, all Stage 3 option modules must be taken from the list below.
 PHYC30020 Classical Mechanics and Relativity Autumn  5
Stage 3 Options - B) Min 0 of:
Students must select a minimum of 20 credits of options in Stage 3. If not previously taken in Stage 2 these options may need to include MATH20310, MATH20300, or STAT20100. Otherwise, all Stage 3 option modules must be taken from the list below.
 STAT20230 Modern Regression Analysis Autumn  5
Stage 3 Options - B) Min 0 of:
Students must select a minimum of 20 credits of options in Stage 3. If not previously taken in Stage 2 these options may need to include MATH20310, MATH20300, or STAT20100. Otherwise, all Stage 3 option modules must be taken from the list below.
 STAT30090 Models - Stochastic Models Autumn  5
Stage 3 Options - B) Min 0 of:
Students must select a minimum of 20 credits of options in Stage 3. If not previously taken in Stage 2 these options may need to include MATH20310, MATH20300, or STAT20100. Otherwise, all Stage 3 option modules must be taken from the list below.
 ACM30090 Mathematical Biology Spring  5
Stage 3 Options - B) Min 0 of:
Students must select a minimum of 20 credits of options in Stage 3. If not previously taken in Stage 2 these options may need to include MATH20310, MATH20300, or STAT20100. Otherwise, all Stage 3 option modules must be taken from the list below.
 ACM30110 Advanced Computational Finance Spring  10
Stage 3 Options - B) Min 0 of:
Students must select a minimum of 20 credits of options in Stage 3. If not previously taken in Stage 2 these options may need to include MATH20310, MATH20300, or STAT20100. Otherwise, all Stage 3 option modules must be taken from the list below.
 ACM30200 Mathematical Fluid Dynamics I Spring  5
Stage 3 Options - B) Min 0 of:
Students must select a minimum of 20 credits of options in Stage 3. If not previously taken in Stage 2 these options may need to include MATH20310, MATH20300, or STAT20100. Otherwise, all Stage 3 option modules must be taken from the list below.
 ACM30210 Foundations of Quantum Theory Spring  5
Stage 3 Options - B) Min 0 of:
Students must select a minimum of 20 credits of options in Stage 3. If not previously taken in Stage 2 these options may need to include MATH20310, MATH20300, or STAT20100. Otherwise, all Stage 3 option modules must be taken from the list below.
 MATH30250 Cryptography: Theory & Practice Spring  5
Stage 4 Core Modules
 ACM40980 Research Project 2 Trimester duration (Aut-Spr)  10
Stage 4 Core Modules
 ACM40690 Applied Complex Variables Autumn  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 ACM40010 Electrodynamics & Gauge Theory Autumn  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 ACM40070 Math Fluid Dynamics II Autumn  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 ACM40750 Gen Relativity & Black Holes Autumn  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 ACM41020 Maths of Machine Learning Autumn  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 MATH30340 Peer-Assisted Tutoring Autumn  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 MATH30360 Measure Theory and Integration Autumn  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 SCI30080 Professional Placement-Science Autumn  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 STAT30010 Time Series Autumn  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 ACM40890 Advanced Fluid Mechanics Spring  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 ACM41010 Math of Sust & Environment Spring  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 ACM41030 Optimization Algorithms Spring  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 ACM41040 GR and Gravitational Waves Spring  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 MATH30250 Cryptography: Theory & Practice Spring  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 MATH30370 Markov Chains Spring  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 MATH40480 Probability Theory Spring  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 MATH40830 Maths of Quantum Computation Spring  5
Stage 4 Options - B) Min 9 of:
Students should select at least 9 modules from the list below. Please note that students who successfully completed SCI30080 will be registered by the School to the module. Additional options may be selected, subject to the approval by the program director of ACM and depending on timetable and availability of places. Students take MATH30340 subject to resourcing and approval of module coordinator.
 STAT40150 Multivariate Analysis Spring  5

After my first Applied & Computational Mathematics class, I knew it was the right choice for me. The chance to study the mechanics and structure of Mathematics and learn how to apply it to not just Physics and Computer Science but to a wide range of other fields was thrilling. That, along with my time spent as a class representative, was so rewarding; getting to organise events, trips and hoodies for my class. As well as this, UCD Science gave me the opportunity to spend a trimester studying abroad in California, broadening my perspective and giving me a more varied education.

PJ Nee, Graduate

After my first Applied & Computational Mathematics class, I knew it was the right choice for me. The chance to study further the mechanics and structure of Mathematics and learn how to apply it to not just Physics and Computer Science but to a wide range of other fields was thrilling. That, along with my time spent as a class representative, was so rewarding; getting to organise events, trips and hoodies for my class. As well as this, UCD Science gave me the opportunity to spend a trimester studying abroad in California, broadening my perspective and giving me a more varied education. My time at UCD left me well prepared for a masters at the University of Cambridge.

PJ Nee, Graduate

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General application route(s) for Irish/UK/EU applicants* for International (non-EU) applicants* to Applied & Computational Mathematics:

ROWCLASS Apply to   Application Type  
showAudience-audienceInt SCU1
Science
Bachelor of Science		 Commencing 2024/2025 September Undergraduate Degree (Non EU)
Non EU Undergraduates		 Apply
showAudience-audienceInt MHS2
Science: Mathematics (includes Applied/Financial/Statistics)
Bachelor of Science		 Commencing 2024/2025 September Undergraduate Degree (Non EU)
Non EU Undergraduates		 Apply
showAudience-audienceEU DN200
Science
Bachelor of Science
Full-Time
Commencing 2024/2025 September
 Application through CAO Apply via CAO
showAudience-audienceEU DN200
Science: Mathematics (includes Applied/Financial/Statistics)
Bachelor of Science
Full-Time
Commencing 2024/2025 September
 Application through CAO Apply via CAO
* you can change options at the top of the page

Additional special entry route(s) to Applied & Computational Mathematics:

These options have additional eligibility requirements to cater for specific applicant cohorts. You should not apply via these routes before consulting the requirements or contacting the responsible UCD office.

ROWCLASS Apply to   Application Type  
showAudience-audienceEU showAudience-audienceInt SCU1
Science
Bachelor of Science		 Commencing 2024/2025 September Access Progression Pathway
Access Progression Pathway
Application to this Non-EU Access Progression Pathway is by invitation only. If you are not currently enrolled on an Access programme at UCD, your application will be marked as invalid.
If you are not a current Access student, but you are a non-EU applicant seeking admission to an undergraduate degree, please submit an application via the "Undergraduate Degree (Non-EU)" course type.		 Apply
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