•
•
•
•
•
•
1
•
•
2
•
•
3
•
•
4
•
•
5
•
•
6
•
•
7
•
•
8
•
•
9
•
•
10
•
•
11
•
•
12
•
•
13
•
•
14
•
•
15
•
•
16
•
•
•
•
•
•
•
•
•
•
•
•
1
•
•
2
•
•
3
•
•
4
•
•
5
•
•
6
•
•
7
•
•
8
•
•
9
•
•
10
•
•
11
•
•
12
•
•
13
•
•
14
•
•
15
•
•
16
•
•
17
•
•
18
•
•
19
•
•
20
•
•
21
•
•
22
•
•
23
•
•
24
•
•
25
•
•
•
•
•
•
Publications
El-Sheikha, H., and Mahmoud, M.A., Varphi: A Description Language for Turing Machines. Western Canadian Conference on Computing Education (WCCCE ’25) (2025)
Mahmoud, M.A., Degrees of Categoricity of Trees and the Isomorphism Problem. Math. Log. Quart. (2019)
Csima, B.F., Deveau, M., Harrison-Trainor, M., and Mahmoud, M.A., Degrees of Categoricity Above Limit Ordinals. Computability (CIE) (2019)
Ahmed, T.S., and Mahmoud, M.A., On the Multi-modal Logic of Substitutions. Studia. Sci. Math. Hungarica (2019)
Other Writings
This is a work in progress. It offers a rigorous yet accessible foundation of Computability Theory and Computational Complexity.
Rather than merely covering a wide array of topics, this book prioritizes building the mathematically mature understanding of the fundamentals,
which is normally only available in more dense texts, while accessible traditional introductions often sacrifice formal precision; this book
rectifies that imbalance
This is a lecture developed for an introductory Machine Learning course. It provides a formal definition of the k-Nearest Neighbors algorithm,
demonstrates its non-parametric nature, and then explores the deep mathematical challenges that arise when applying distance metrics to
high-dimensional spaces (the curse of dimensionality). Associated Jupyter Notebooks are available at the title link.
This is an formal introduction of Finite Automata (FA), a simple kind of an abstract computer, simpler than the Turing Machine (TM).
If you are familiar with TMs, imagine a TM in which the reading/writing head is only moving to the right.
We think of FAs as a program made of lines of triples, similar to how TMs are lines of quintuples (or quadruples in some formulations).