#appliedmathematics — Public Fediverse posts

Reflections on the 2026 Leaving Certificate Results

Yesterday I attended my last two Examination Boards for the year at Maynooth University. one for graduating MSc students and another for undergraduate repeat students in Engineering (which I attend because I’m teaching a mathematics course they do). That, more or less, is the end of the business (for me) for the 2025/6 academic year. No sooner is that done, however, than preparations for the start of the 2026/7 teaching session begins, as we wait to find out how many new students we will be admitting to our courses in September.

Today’s the day that over 70,000 school students across Ireland received their Leaving Certificate Results. As always there will be joy for some, and disappointment for others. The headline news relating to these results is that the proportion of students receiving the top grades in higher level examinations (i.e. H1) is down significantly from 11.7% last year to 10.1% this year. This fall is because various adjustments that were made during the Covid-19 pandemic are gradually being wound down. After next year they will disappear altogether.

I thought I would have a quick look at the results for subjects relevant to Physics:

(A is higher level and G is ordinary level). Please note that this year’s numbers are provisional and may change as a result of appeals, etc. The full details can be found here.

You can see that the number of students taking these subjects has increased since last year, but in all cases the percentage getting top grades has fallen. Note the very low numbers in the last row, meaning that most students who take Applied Mathematics do the Higher level version. The numbers mean that exactly 2 people got the top grade in 2026 and 2025!

Comparison with earlier years is interesting. Here are the H1 percentages for Mathematics, Physics and Applied Mathematics since 2019:

You can see that although these percentages have declined from their respective peaks they remain well above 2019 pre-pandemic levels.

It is also worth noting that the number of students taking Physics (A) nationally seems to be recovering from a sharp drop in 2022-4, the numbers being: 6583(2019); 7037(2020); 7210(2021); 6487(2022); 6143(2023); 6009 (2024); 6592 (2025); and 6855 (2026).

Anyway, now that the results are out there will be a busy time until next Wednesday (26th August) when the CAO first round offers go out. That is when those students wanting to go to university find out if they made the grades and university departments find out how many new students (if any) they will have to teach in September. Incidentally, colleagues in the UK might be interested to know that, here in Maynooth, departments have no say in admissions decisions: these are all made centrally.

P.S. When I was a little kid we used to call a “Certificate” a “Stiff Ticket”. I just thought you would like to know that.

Frenet–Serret Formula ✍️

It explains how a curve reveals its hidden geometry by tracking the way it bends and twists through space. Imagine tracing the path of a roller coaster, a winding river, or the spiral of a DNA strand. At every point along the path, the curve is constantly changing direction, and the Frenet–Serret formulas provide a precise way to describe that change.

They do this by attaching a moving frame of three special directions to each point on the curve. The first points forward along the path, showing where the curve is heading. The second points inward, toward the direction of bending. The third stands perpendicular to both, capturing how the curve twists out of its plane. Together, they form a local coordinate system that travels with the curve itself.

As you move along the curve, these three directions rotate and evolve. The formulas measure this evolution using two key quantities: curvature and torsion. Curvature tells how sharply the path bends, while torsion tells how strongly it twists into three dimensions. If curvature vanishes, the path becomes straight; if torsion vanishes, the curve lies flat in a plane.

Mathematicians and physicists use the Frenet–Serret formulas to study motion, design smooth paths in engineering, understand particle trajectories, and analyze natural shapes. They transform a simple line into a rich geometric story, revealing exactly how space is being navigated at every step.

#FrenetSerretFormula #DifferentialGeometry #Geometry #Mathematics #Math #PureMathematics #AppliedMathematics #MathematicalPhysics #Physics #STEM #ScienceEducation #MathEducation #Curvature #Torsion #SpaceCurves #VectorCalculus #Calculus #LinearAlgebra #GeometricAnalysis

“My PhD was all about understanding what happens to blood flow in collapsible blood vessels like the giraffe jugular vein. In my postdoc I was investigating how to optimise ventilator settings for patients in ICU and then how to deliver inhaled therapies into the lungs. Since then, my focus has been in trying to understand how diseases like Asthma and other respiratory diseases originate and then progress. This involves incorporating biology and physics into mathematical and computational models, using approaches from different areas of applied maths. More recently I have started to look into the mechanisms that could lead to a rare lung disease called lymphangioleiomyomatosis (LAM) and Long Covid.” - Bindi Brook

➡️ https://hermathsstory.eu/bindi-brook/

#Academia #PhD #Professor #AppliedMathematics #MathematicalBiology #MathematicalMedicine #UnconsciousBias #WomenInMaths #WomenInSTEM #HerMathsStory

“Since my goal was to solve a problem no one had ever solved before, it required a creative and flexible approach, one that emphasized the exploration, experimentation, and steady refinement of ideas. But perhaps the most important lesson I learned was that there is no single “correct” way to be a mathematician.” - Katy Micek

➡️ Find the full story at https://hermathsstory.eu/catherine-micek/

#PhD #WomenInMaths #WomenInSTEM #HerMathsStory #AppliedMathematics #DataScience #MachineLearning

"The realization that mathematical concepts and theory could directly impact and improve real-world problems...fueled my passion for pursuing further research and applications that bridge theory with practice" - Anna Ma

➡️ https://hermathsstory.eu/anna-ma/

#Academia #AppliedMathematics #WomenInMaths #WomenInSTEM #HerMathsStory

“(...) My students have used their knowledge to model the oil spill in the Gulf of Mexico, analyze income inequality in New York City using the Gini coefficient, and determine appropriate drug dosages, among other projects. These projects not only deepen their understanding of mathematical concepts but also highlight how mathematics can be a powerful tool for analyzing and solving real-world problems. By exploring the intersection of social justice and mathematics, students gain a broader perspective on how their skills can contribute to meaningful change in society.” - Mónica D. Morales-Hernández

➡️ https://hermathsstory.eu/monica-d-morales-hernandez/

#Academia #AssistantTeachingProfessor #Educator #AppliedMathematics #ComputationalMathematics #Physics #SocialJustice #Classism #Sexism #Racism #Volunteering #WomenInMaths #WomenInSTEM #LatinaInSTEM #HerMathsStory