One of the critical roles of the House of Science, as an overarching innovation space for the added value enrichments to the AIMS academic programme, is to identify gaps in the provisions to AIMS students and work to support and address them with a view to strengthening their academic and mathematical knowledge, skills and aptitudes. Thus, during the August and September 2022 period, the AIMS House of Science offered two courses – Introduction to Subdivision Theory and Applications (Subdivision; Review Course) and Mathematics for Machine Learning (Math4ML; Skills Course) to the current January intake students’ cohort. The courses provided the basis for enhancing the mathematical knowledge and understanding, relevant skills and values of the students. These courses also served to broaden the horizons, scope and dynamic understanding of the post-AIMS career progression of the students in utilising this cutting-edge mathematical knowledge and skills.

The Subdivision Course introduced students to some history, evolution, recent developments, future prospects, and applications of subdivision. Furthermore, the Course provided students with a deep understanding of basic mathematical principles and analysis of underlying subdivision algorithms, thereby allowing them to make an informed choice as to their future specialisation. Attention was also given to the implementation/graphical illustrations of the subdivision theory and algorithms in Python. The field of Subdivision has, over the last few decades, developed into a fast-growing powerful tool in a variety of application areas (e.g., computer graphics, animation movie production, aircraft design, automotive industry, consumer products, 3D computer games design, image processing and numerical solutions of partial differential equations). This is due to its computationally efficient properties compared to other modelling approaches for smooth curves and surfaces. As an area of research, significant areas of subdivision theory have reached a state of maturity. However, there are some key and long-established problems (e.g., higher smoothness of the limit curves and surfaces to provide more useful tools in CAGD, creased edges, etc.) that remain to be solved. Even the new developments raise new challenges that need to be addressed. That said, for students who would like to pursue research in this area, there are plenty of opportunities. For instance, the Machine Learning approach to Subdivision is a new exciting area. 

Math4ML Course was delivered for the first time at AIMS South Africa. The Course provided students with fundamental mathematical concepts behind Machine Learning. It was designed as an introductory course to help students master the Mathematical foundations required for writing programs and algorithms for Artificial Intelligence and Machine Learning. The field of Machine Learning with its three core components (data, model and learning) has dramatically grown in recent years. Similar to their counterparts elsewhere in the world, many AIMS students are becoming more and more interested in this field due to its popularity and career prospects. At AIMS centres Machine Learning/Data Science has been one of the most popular courses and research topics that are offered every year. However, over the years, it became evident that AIMS students are not exposed to the deep Mathematical Foundations of Machine Learning. Mastering the mathematics theory behind Machine Learning and its relevance is crucial for the students as this will set them apart from other graduates or practitioners in the Data Science area. In relation to AIMS students who have a strong interest in Machine Learning and have strong mathematics backgrounds, it is also critical to help them on how they can leverage their mathematical knowledge and make better transitions.

“From my experience teaching the Math4ML course to mathematical sciences graduates and in other AIMS centres, I found that students are jumping into Data Science without learning the necessary mathematics behind it,” said Prof Franck Kalala Mutombo

“Two of the most questions asked during the Apres-Lunch with Scientists webinars by students to the Data Science professionals is what kind of maths and programming language does one need to be a Data Scientist,” said Dr Rejoyce Gavhi-Molefe

Outcomes & Impact: Students’ Testimonials from the Course

Feedback/evaluation forms were distributed on the last day to get insight into the students’ experiences (e.g., the ease or difficulty of content, engagement, assessments, classroom activities, the potential for Course improvement and learning goals) and teaching quality and effectiveness. The students’ feedback was positive. For instance, it pointed to well-explained and structured content that deepened their understanding of Subdivision, and coding skills. For them, the Course also engendered greater interest in research prospects and applications. They described it as very informative, interesting, intensive, interactive and well-organised. They appreciated it for covering both theory and practicals; enhancing peer-to-peer interaction and students’, lecturers’ and tutors’ interaction; and improving one’s confidence and presentation skills and capabilities. Below are some testimonials from the participants, which elucidate the impact of the Course in terms of the following aspects:

Subdivision:

“This Course showed or enlightened me or us on how mathematics can be applied in real-world problems like animation.”

“I benefited a lot from the Course, it was new content but I enjoyed the process and spent more time to be on the right track. I learned a lot, especially the programming part. This module helped me to improve problem-solving skills and programming approaches.”

“I gained a new method of problem-solving, a new skill in terms of creating smooth and convergence curves for a given set of control points. They could help me to also  improve my skills in science communication.” 

“The course should be offered next year to inspire and attract students who might be interested in continuing with research in the subdivision.”

“The benefits of this course were mainly on the practicals where we tested our programming skills by developing a python code following or given an algorithm. The transformation offered by this course was very huge. It exposed us to the field of maths that we did not know.”

Math4ML:

“I got to understand the concepts for my Research Project more and appreciated Algebra and Vector Calculus more.”

“I have learned a lot about how mathematics is applied or how machine learning uses mathematics to solve problems. I now understand that mathematics goes a long way and it is a tool one has to have to solve any problem.”

“The mathematical rigour in this course will really be beneficial in understanding Machine Learning. The knowledge will be very useful even in other courses and future research questions.”

“Math4ML is important for everyone who wants to work in Machine Learning. I suggest that the Course can run for more than two weeks and it would be better if they provide it to the students at the beginning of the program”

“Personally I can say that I have benefited a lot from working and presenting in groups. I can therefore say that my presentation skills have really improved than before.”

The courses were facilitated and co-facilitated by Dr Rejoyce Gavhi-Molefe, the Manager of the House of Science and Prof Franck Kalala Mutombo affiliated with the University of Lubumbashi, DRC, and vice versa. Dr Dinna Ranirina, a postdoctoral researcher at AIMS South Africa was a tutor.