DCU Transition Year Programme - Mathematics

Mathematical thinking is based on pattern recognition and a strong desire to understand and explore new phenomena arising in our everyday lives. As mathematicians, we often start from a minimal number of assumptions that we accept to be true (so-called "axioms") and then focus on the derivation of further implications from these assumptions. This allows us to address fundamental questions such as "What are numbers actually, and why do they behave as they do?" or "Are there other numbers with surprising properties such as 5 = 0?"

However, we cannot and should not view mathematics as an isolated science independent of real-world applications, but instead, as an indispensable science; one that bridges abstract reasoning with modern applications, laying the foundation that allows us to advance and solve numerous problems that stem from other disciplines. For instance,

• Modern encryption/decryption techniques are deeply rooted in the theory of prime numbers studied in algebra and cryptography.
• Dynamical systems studied in Mathematics provide a powerful framework for epidemiology that allows us to predict the spread of diseases.
• In engineering sciences, Mathematical Analysis is frequently used for shape optimisation of cars, aeroplanes, and spaceships leading to more efficient shapes and hence increased travel distances.
• Probability Theory provides a powerful framework that is commonly used to describe and predict uncertain phenomena (e.g. emergence of mutations in human tissue or future movements of financial assets).
• Statistical methods lay the foundation for modern advances in Artificial Intelligence and big data analysis becoming more and more present in our everyday lives (see e.g. ChatGPT).

It is therefore not surprising that a variety of branches in mathematics are deeply rooted in concrete problems that are emerging, e.g., from Physics, Biology, Chemistry, Computer Science, and Finance. 

Therefore, learning mathematics goes hand-in-hand with developing an intuition for its applications towards complementary disciplines as mentioned above. To demonstrate this view on mathematics, we provide a 1-week workshop consisting of lectures and student projects:

• During lectures (45 - 90 min each day), we will motivate, present and discuss new Mathematical results in an enjoyable and accessible way. 

• Student projects (90 - 135 min each day) will form the heart of this Transition Year programme. During these projects, students will work on suitable research questions exploring mathematical patterns, revealing hidden relations, and obtaining new insights for designated applications. All participants will be guided by our experienced staff and additionally supported by our exceptional current students.  

The combination of lectures and student projects allows participants to receive a unique first-hand experience of University life, get to know our staff at the School of Mathematical Sciences, and have the opportunity to speak with our current students in Mathematics.