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SATACS Courses

WELCOME TO THE SOUTH AFRICAN THEORY AND COMPUTATIONAL SCHOOL (SATACS)

SATACS is a decentralised, semi-virtual, national teaching programme in theoretical and computational sciences. Our goal is to provide teaching of the highest quality and at a level similar to that found in elite postgraduate programmes around the world.

A critically important aim is to provide a pathway to this world-leading material for students who are registered at a university, with a particular emphasis on transformation. Crucially, we want to build and promote a South African community of students who will work together, learn together, and support each other through in-person and, especially, virtual platforms.

We intend for the knowledge presented in these courses to broaden and deepen the base of knowledge for students to then use to perform research of the highest quality and have a background that allows engagement with the elite research and researchers of the world. Therefore, courses are pitched at an Honours / Masters level.

Please see the courses for 2025 below. The individual courses will only be run if there is sufficient student interest. Please click to view the courses presented in previous years.

COURSES FOR 2026:

Mathematics courses

Advanced Partial Differential Equations – Dr Vishnu Kakkat (UNISA)

Course dates:
1 January 2026 – 31 May 2026.

Outline:
Topics include:

  • Introduction
  • Transport Equation
  • Laplace’s Equation
  • Heat Equation
  • Wave Equation
  • The Vibrating Drum
  • Hilbert Space Theory
  • Second-Order Hyperbolic Equations
  • Systems of First-Order Hyperbolic Equations
  • Calculus of Variations
  • Existence of Minimizers
  • Regularity
  • Critical Points.

To encourage collaborative learning, the lecturer will set up a dedicated online discussion forum or group where students can share ideas, ask questions, and assist one another with problem sets. Optional group-based homework discussions and problem-solving sessions will also be held online, enabling students to engage with peers, explore alternative approaches, and deepen their understanding of the material.

Skills outcome:
Students will develop a graduate-level understanding of partial differential equations and gain the analytical tools necessary to independently pursue advanced topics in PDEs.

Prerequisites:
Partial Differential Equations 1.

Lecture format:
Weekly 3-hour lecture delivered via Zoom on Wednesdays from 17:00 to 20:00.

Method of evaluation:
Students will pass the course if they achieve a final score of more than 50%.

Lecturer biography:
Dr Vishnu Kakkat is a Postdoctoral Fellow in Mathematical Sciences at the University of South Africa and a NITheCS Junior Associate. He received his PhD in Mathematics from Ariel University, Israel, under the supervision of Prof Gilbert Weinstein, focusing on geometric and analytical aspects of general relativity. Prior to his current role, he served as an Assistant Professor at the University of Calicut, India. His research interests include mathematical relativity, partial differential equations, and gravitational waves.

E:  kakkav @ unisa.ac.za  |  Website

Theoretical Physics courses

Advanced General Relativity – Dr Vishnu Kakkat (UNISA)

Course dates:
1 January 2026 – 31 May 2026

Course outline:

  • Describing curved spacetimes,
  • Field equations of general relativity,
  • Schwarzschild geometry and tests of general relativity,
  • Static and stationary black holes,
  • Gravitational waves and Cosmology.

Skills outcome:
Students will gain a solid understanding of the geometric foundations of general relativity and the ability to derive and analyze Einstein’s field equations. They will be able to study and apply exact solutions such as the Schwarzschild metric to understand physical scenarios involving black holes and the classical tests of general relativity. The course will also equip them with the skills to explore gravitational wave phenomena and cosmological models within the framework of general relativity.

Prerequisites:
None.

Lecture format:
3-hour lectures on Zoom (Mondays, 17h00-20h00 SAST)

Method of evaluation:
A final exam.

Lecturer biography:
Dr Vishnu Kakkat is a Postdoctoral Fellow in Mathematical Sciences at the University of South Africa and a NITheCS Junior Associate. He received his PhD in Mathematics from Ariel University, Israel, under the supervision of Prof Gilbert Weinstein, focusing on geometric and analytical aspects of general relativity. Prior to his current role, he served as an Assistant Professor at the University of Calicut, India. His research interests include mathematical relativity, partial differential equations, and gravitational waves.

E: kakkav@unisa.ac.za  |  Website

Quantum Field Theory II - W. A. Horowitz (UCT)

Course dates:
16 February 2026 – 22 May 2026​

Course outline:

  • Brief introduction to group theory and representations and their importance in quantum state space and constraining potential Lagrangians
  • Non-relativistic quantum rotations and spin
  • Irreducible representations of the Lorentz group SO(3,1)
  • Free 2D Weyl spinor fields
  • Interacting 2D Weyl spinor fields
  • 4D Majorana and Dirac fields
  • Free spin-1 gauge fields. BRST gauge fixing. Non-abelian gauge theory.

Students will be encouraged to work together on the homework sets, as well as during the synchronous recitation and help sessions.

Skills outcome:
Students should have a thorough understanding of quantum field theories for particles up to spin-1.

Prerequisites:
Quantum Field Theory I.

Lecture format:
Asynchronous lecture recordings, distributed lecture notes, synchronous recitation sessions, and synchronous help sessions.

Method of evaluation:
Weekly problem sets and a final project.

Lecturer biography:
Associate Professor W. A. Horowitz received his PhD in Physics from Columbia University in 2008. He held a postdoctoral research position at the Ohio State University from 2008 to 2010 before joining the faculty at the University of Cape Town. Prof Horowitz is an expert in the use of perturbative quantum field theory and AdS/CFT methods in phenomenological high-energy quantum chromodynamics applications.

E: wa.horowitz @ gmail.com  |  Website  |  Publications


COURSES FOR 2025:

Mathematics courses

Logics for Artificial Intelligence - Tommie Meyer (UCT)

Course dates:
Mid-July to end-August 2025.

Course outline:
Students will be introduced to propositional logic and description logics. The course will cover the semantic of these logics, outline reasoning algorithms for these logics, and prove the correctness of the algorithms.

Skills outcome:
An understanding of propositional logic and description logics as reasoning tools.

Prerequisites:
A basic understanding of discrete mathematics.

Lecture format:
The course was originally delivered in person as part of an MSc programme at the University of Cape Town, comprising 18 one-hour lectures. Students will have access to video recordings of these lectures. Assignments are designed to encourage and support collaborative work.

Method of evaluation:
Two assignments (each contributing 25% to the final mark) and an exam (contributing 50%).

Lecturer biography:
Prof Tommie Meyer is a Professor of Computer Science at the University of Cape Town (UCT), Co-Director of the Centre for Artificial Intelligence Research (CAIR), and the holder of the NRF SARChI Chair in Symbolic Artificial Intelligence. Prior to this, he held positions at the CSIR in Pretoria, National ICT Australia (now Data61), the University of New South Wales, the University of Pretoria, and the University of South Africa. He is internationally recognised as an expert in Knowledge Representation and Reasoning and is one of only three South African Computer Scientists to have received an A-rating from the National Research Foundation. He is a member of SAICSIT, AAAI, ACM, the Academy of Science of South Africa (ASSAf), and the African Academy of Sciences (AAS).

E: tmeyer @ cair.org.za  | Website  |  Publications

Data Science courses

Trustworthy Machine Learning - Dr Makhamisa Senekane (UJ)

Course dates:
4 August – 2 November 2025

Outline:
This course will cover the following topics:

  • Introduction to Machine Learning (ML)
  • Introduction to trustworthy Machine Learning
  • Privacy Enhancing Technologies (PETs)
  • Differential Privacy
  • Federated Learning
  • Explainability in Machine Learning
  • Machine Learning robustness
  • Machine Learning fairness
  • Conformal Prediction.

Throughout the course, exercises will be used to foster collaboration among students.

Skills outcome:
At the end of the course, the students are expected to:

  • Appreciate the need to build trustworthy ML models
  • Have a firm understanding and application of PETs such as Differential Privacy and Federated Learning
  • Understand and be able to use the ML explainability frameworks
  • Be well equipped to the ways of building robustness in Machine Learning models
  • Appreciate the value of fairness and the dangers of bias in ML models
  • Understand the use of conformal prediction for uncertainty quantification.

Prerequisites:

  • Linear Algebra
  • Probability Theory
  • Calculus
  • Programming, especially in Python.

Lecture format:
Synchronous virtual weekly lecture sessions (2 hours) and tutorial sessions (2 hours). All sessions will be recorded.

Method of evaluation:
The course will use continuous assessment, where students are expected to submit four assignments. Each assignment will have an overall mark of 25%.

Lecturer biography:
Makhamisa Senekane is a Senior Researcher in the Institute for Intelligent Systems at the University of Johannesburg. Prior to that, he worked as a Lecturer in the Department of Physics and Electronics at the National University of Lesotho, as a Senior Lecturer in the Faculty of Information and Communication Technology at Limkwokwing University of Creative Technology (Lesotho), and as a Lecturer in the Faculty of Computing at Botho University (Maseru Campus). He obtained his PhD in Physics from the University of KwaZulu-Natal, his MSc.Eng in Electrical Engineering from the University of Cape Town, and his B.Eng in Electronics Engineering from the National University of Lesotho. His research interests include data science, data security, data privacy, artificial intelligence (machine learning, computer vision, and natural language processing), and quantum information processing (quantum cryptography, quantum computing, and quantum machine learning).

E:  makhamisa.senekane @ nithecs.ac.za

Parallel Computing with GPUs and Agent-Based Artificial Intelligence - Prof Martin Bucher (SU), Prof Japie Greeff (NWU) & Ms Jacqui Muller

Course dates:
Second semester 2025

Course outline:
This course bridges breakthroughs in high-performance parallel computing and low-code agentic AI. A key challenge in computing is facilitating human-computer interaction and developing software with an interface accessible to non-specialists without programming expertise. Low-code platforms emphasize graphical interfaces. Agentic AI defines autonomous systems making decisions and performing tasks without human oversight. Moore’s law has come to an end as single-processor computational power has reached a plateau, and massive parallelism with GPUs is in the process of becoming ubiquitous.

By the end of the course, students will be able to create and deploy autonomous intelligent applications through low-code apps and visual reports. They will also master programming and tuning for GPUs as well as integrating with more complex systems.

Lectures:
Week 1: Introduction to Parallelism and the Agentic Paradigm
Week 2: Core Concepts in Parallel Computation
Week 3: GPU Programming with CUDA
Week 4: High-Level GPU Acceleration with JAX and THRUST
Week 5: From Raw Data to Model Input
Week 6: AI and ML Model Design
Week 7: Real-Time Inference and API Integration
Week 8: Enter the Agent: Foundations of Agentic AI
Week 9: Automating and Orchestrating Intelligence
Week 10: Low-Code Applications as Agentic Interfaces
Week 11: Data Integration and Analytics
Week 12: Term Project Presentations

Students will interact during the practical/discussion sections.

Skills outcome:
Students will be able to:

  1. Understand the advantages and challenges of parallel computing and GPU acceleration.
  2. Design and implement basic GPU-accelerated programs using CUDA, JAX, THRUST, and NUMBA.
  3. Develop and train simple machine learning models using parallel processing techniques.
  4. Deploy models via API for real-time inference and connect them to front-end solutions.
  5. Understand agentic AI and how to apply it to real-world challenges.
  6. Create low-code applications using Power Platform integrated with intelligent backends.
  7. Visualise model predictions and business insights using Power BI.
  8. Deliver a fully integrated capstone project combining all course components.

Prerequisites:
Basic proficiency in Python or some other programming language..

Lecture format:
Online, with one 90-minute theory session and one 90-minute practical session per week.

Method of evaluation:
Several programming assignments throughout the semester and a final term project.

Lecturers’ biographies:

Prof Martin Bucher
Martin Bucher is a Fractional Professor at Stellenbosch University, affiliated with both the Department of Data Science and Computational Thinking and the Department of Physics. He also serves as Directeur de Recherche at the CNRS in Paris, France. His expertise spans theoretical physics, observational cosmology, and computational physics. He has authored numerous publications and holds an H-index of 74. Prof Bucher is an elected member of the Academy of Science of South Africa and was awarded the 2018 Gruber Prize in Cosmology as part of the ESA Planck Space Mission Team.

E: bucher @ sun.ac.za

Prof Japie Greeff
Prof Japie Greeff (PhD, University of Johannesburg) is currently an Extraordinary Professor in the Department of Computer Science and Information Systems at North-West University, where he previously served as Associate Professor and Deputy Director. He is also the Research Coordinator at Belgium Campus iTversity. In addition to his academic roles, Prof Greeff has extensive industry experience and has participated in start-ups. He is an Associate of NITheCS and a member of the BRICS South African Skills Development, Applied Technology, and Innovation Working Group national committee.

Ms Jacqui Muller 
Jacqui Muller is a UiPath MVP, solution architect, and researcher specialising in intelligent automation, process optimisation, and agentic AI. She is Director of JPanda Solutions and Tegnika Unlimited, and serves as Industry Coordinator at Belgium Campus iTversity. She is also a researcher at North-West University, where she is pursuing a PhD in automation governance. As a BRICS Standardisation Working Group expert, she contributes to global frameworks for responsible technology adoption. Jacqui is recognised for her leadership in community-driven innovation and her advocacy for inclusive, future-ready digital education.

Theoretical Physics courses

Data to Discovery: A Step-by-step Guide to Understand the Physics at the LHC - Prof Deepak Kar (WITS)

Course dates:
Week of 28 July – week of 1 September 2025 (6 weeks) and
Week of 22 September – week of 13 October 2025 (4 weeks).

Course outline:

  1. What does LHC data contain?
  2. How do we simulate Standard Model and new physics events (and the role of simulation)?
  3. How do we look for new physics (or try to find broken pieces of a needle in a haystack)?
  4. How do we present our results?
  5. What have we learned so far, and what is next?

Students will typically collaborate on assignments. Active participation through discussion and brainstorming will be encouraged during the lectures.

Skills outcome:
Students will be able to critically engage with research papers from LHC experiments – an essential skill not only for experimentalists, but also for aspiring theoretical particle physicists and particle astrophysicists.

Prerequisites:
Knowledge of Special Relativity and Quantum Mechanics.

Lecture format:

  • The course consists of 15 lectures, each about 45 minutes long (roughly three lectures per topic). Depending on student availability, some weeks may include double lectures.
  • Lectures will be conducted online via Zoom. If there is sufficient interest from students based in Johannesburg, we may secure a venue and transition to a hybrid format.

Method of evaluation:
In-class quizzes, online assignments, and final presentation on a randomly assigned paper.

Lecturer biography:
Deepak Kar is a particle physicist and is a part of the ATLAS experiment at CERN. He grew up in India, and after finishing his PhD from University of Florida, was a postdoctoral researcher at TU Dresden and at University of Glasgow. He joined University of Witwatersrand in 2015, and was promoted to full professor in 2023. His research interests span measurements sensitive to different aspect of Quantum Chromodynamics (QCD), and searches for new physics in novel final states. He has established himself as a pioneer in designing and performing strongly interacting dark sector searches, a recently popular model of dark matter. He spent 2024 on his sabbatical at the University of Glasgow, funded by Royal Society Wolfson Visiting Fellowship. He wrote a popular textbook on particle physics, based on the honours course he started at Wits.

E: deepak.kar @ cern.ch | Website

Quantum Field Theory I - W. A. Horowitz (UCT)

Course dates:
28 July – 24 October 2025​.

Course outline:

  1. Postulates of QM and SR
  2. Quantizing the free scalar field
  3. Interpreting the results
  4. Connecting to experiments; in and out states; LSZ reduction
  5. Lehman-Kallen representation; Gell-Mann–Low theorem; cross sections
  6. Feynman rules for scalar fields
  7. Introduction to QED, QED Feynman rules, and trace technology for cross sections.

Students will be encouraged to collaborate on the problem sets. They will also work together during synchronous teaching sessions, interacting with both the lecturer and tutor.

Skills outcome:
By the end of the course, students will have developed a solid understanding of:

  • Free scalar quantum field theory
  • Feynman calculus for computing cross sections involving scalar particles

In addition, students will gain proficiency in computing Feynman diagrams and cross sections for processes in quantum electrodynamics (QED).

Prerequisites:
Students should have completed an advanced course in quantum mechanics, as well as a course that has detailed special relativity.

Lecture format:
Asynchronous lecture recordings, distributed notes, synchronous recitation sessions, and synchronous help sessions.

Method of evaluation:
Bi-weekly problem sets and a final exam.

Lecturer biography:
Associate Professor W. A. Horowitz received his PhD in Physics from Columbia University in 2008. He held a postdoctoral research position at the Ohio State University from 2008 to 2010 before joining the faculty at the University of Cape Town. Prof Horowitz is an expert in the use of perturbative quantum field theory and AdS/CFT methods in phenomenological high-energy quantum chromodynamics applications.

E: wa.horowitz @ gmail.com | Website | Publications

HOW TO APPLY

Successful applicants will be informed shortly before a course begins and given further details to participate.

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