This programme is aimed at students who wish to gain a deep understanding of the concepts of modern mathematics and statistics, and a mastery of the associated skills and technologies. Our students will become autonomous inquisitive learners capable of formulating and creatively solving relevant problems in the language of mathematics and statistics. Our graduates will be in demand by employers and academic research institutesfor their ability to explain, describe and predict using the tools they have learned. We value students who are motivated to find the underlying mathematical causes and reasons 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, webwork, blackboard and computer assisted labs.

1 - Demonstrate an in-depth understanding of mathematics
2 - Use the language of logic to reason correctly and make deductions
3 - Approach problems in an analytical, precise and rigorous way
4 - Explore and manipulate abstract concepts
5 - Apply mathematical reasoning and techniques to formulate and solve problems
6 - Model real-world problems in a mathematical framework
7 - Confidently analyze and draw information from large quantities of data
8 - Analyze and interpret data, find patterns and draw conclusions
9 - Use the power of modern technology to augment mathematical problem solving
10 - Work independently and as part of a team
11 - Carry out research into a specific topic, including a survey and synthesis of the known literature
12 - Give oral presentations of technical mathematical material at a level appropriate for the audience, whether specialist or nonspecialist
13 - Prepare a written report on technical mathematical content in clear and precise language

Students’ performance will be reviewed at the end of the academic year. Students who fail 50% or more of their registered modules, and who fail to progress to the next stage of their programme, will be identified under the UCD Continuation – Academic progress policy. Students’ performance will continue to be reviewed in subsequent trimesters and students will be invited to meetings with the College of Science office for support and guidance.

Where the rate of progression and performance over two academic years is deemed unacceptable, a case will be submitted to the Governing Board for review. A recommendation for discontinuation may be the outcome of this review.

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.

Each year sees new applications of sophisticated mathematical models and procedures in insurance and actuarial services, data analytics, the stock market, banking and industry. Employers in all of these areas seek mathematics graduates for their critical thinking and problem-solving skills. 

Our recent graduates are working in many diverse areas, including actuarial science, banking and financial services, civil service, coding and cryptography companies, IT industry, meteorology and research. 

Opportunities for further study include MSc and PhD programmes in the mathematical sciences in Ireland and abroad, leading to research positions in universities or industry. 

Students take 6 core modules and 4 option modules from the list given below. Elective modules may be selected from this list to complete Stage 3.
If you are interested in doing an Internship as part of Stage 4, you must indicate your interest now (in Stage 3). See full details www.ucd.ie/science/careers/internships/students/

Students take 7 core modules and 4 option modules from the list given below.

Module ID	Module Title	Trimester	Credits
Stage 3 Core Modules
MATH30030	Advanced Linear Algebra	Autumn	5
MATH30090	Metric Spaces	Autumn	5
MATH30360	Measure Theory and Integration	Autumn	5
MATH30040	Complex Analysis	Spring	5
MATH30120	Topology	Spring	5
MATH30400	Further Groups and Rings	Spring	5
Stage 3 Core Modules
Stage 3 Options - A)MIN4OF: Students take MATH30340 subject to resourcing and approval of module coordinator.
ACM30130	Advanced Computational Science	Autumn	5
ACM30190	Dynamical Systems	Autumn	5
ACM30220	Partial Differential Equations	Autumn	5
MATH30340	Peer-Assisted Tutoring	Autumn	5
MATH40510	Set Theory	Autumn	5
MST30020	History of Mathematics	Autumn	5
STAT20230	Modern Regression Analysis	Autumn	5
STAT30010	Time Series	Autumn	5
ACM30020	Applied Analysis	Spring	5
ACM30090	Mathematical Biology	Spring	5
ACM30140	Numerical Methods for PDEs	Spring	5
MATH30370	Markov Chains	Spring	5
MST30030	Financial Mathematics	Spring	5
STAT20100	Inferential Statistics	Spring	5
Stage 3 Options - A)MIN4OF: Students take MATH30340 subject to resourcing and approval of module coordinator.
Stage 4 Core Modules
MATH40560	Final Year Project	2 Trimester duration (Aut-Spr)	10
MATH40310	Functional Analysis	Autumn	5
MATH40370	Differential Geometry	Autumn	5
MATH40710	Galois Theory	Autumn	5
MATH40480	Probability Theory	Spring	5
MATH40870	Algebraic Geometry	Spring	5
MATH40880	Number Theory	Spring	5
Stage 4 Core Modules
Stage 4 Options - A)MIN4OF: Students who successfully completed SCI30080 will be registered by the School to the module. Students take MATH30340 subject to resourcing and approval of module coordinator.
ACM40690	Applied Complex Variables	Autumn	5
ACM41020	Maths of Machine Learning	Autumn	5
MATH30340	Peer-Assisted Tutoring	Autumn	5
MATH40510	Set Theory	Autumn	5
SCI30080	Professional Placement-Science	Autumn	5
STAT30080	Models - Survival Models	Autumn	5
STAT30090	Models - Stochastic Models	Autumn	5
STAT41020	Survey Sampling	Autumn	5
ACM41030	Optimization Algorithms	Spring	5
MATH30250	Cryptography: Theory & Practice	Spring	5
MATH40830	Maths of Quantum Computation	Spring	5
STAT40150	Multivariate Analysis	Spring	5
Stage 4 Options - A)MIN4OF: Students who successfully completed SCI30080 will be registered by the School to the module. Students take MATH30340 subject to resourcing and approval of module coordinator.

		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
			Second Class Honours, Grade 1	3.08	3.67
			Second Class Honours, Grade 2	2.48	3.07
			Pass	2.00	2.47