- Calculus (notes in progress in Real Variable Calculus)
- NITheCS Mini-School on Elementary Introduction to Category Theory, a series of lectures for the October Mini-School at the South African Mini-School in Theoretical and Computational Sciences, given jointly with Amartya Goswami
- Abstract Algebra for the Future Mathematician, a book in progress jointly with Amartya Goswami
- The Caravan this is an introductory book in progress on foundations of abstract mathematics.
- My inaugural lecture publication and the lecture.
- See the mathematics playlist of my youtube channel for my video lectures.
- Cardinal Arithmetic (Cantor’s theory of cardinality for Grothendieck-type universes)
- Morphisms of finite spaces (introduction to the basic ideas of category theory via topology and combinatorics)
- Posets and connections (introduction to Galois connections)
- Homomorphisms of monoids (includes products, sums and quotients of monoids)
- Universal algebra (Birkhoff’s variety theorem and some Mal’tsev conditions)
- Abstract logic (work in progress)
- Categories (extremely basic introduction to categories)
- Universal properties (a prelude)
- Regular categories (basics)
- An abelian exploration of diagram lemmas (notes for the lectures delivered under the Erasmus+ program in 2018 at the University of Lovain-la-Neuve)
- Calculus of exact sequences (notes for the lectures delivered under the Erasmus+ program in 2017 at the University of Lovain-la-Neuve)
- Written lecture # 100 on Laplace transform
- Written lecture # 101 on Laplace transform (second part)
- Written lecture # 102 on basic constructions with sets
- #103 on real vector spaces
- #104 on equivalence relations
- #105 types of continuous functions
- #106 constructions with topologies
- #108 open interval topology
- #109 linear maps and the eigenvalue problem
- #110 homeomorphisms
- Incidence relation (a small fragment of Euclid-Hilbert axiomatic geometry)
- Universes of Sets (a first course on axiomatic set theory based on the work of Zermelo)
- Relations (includes functions as defined by Dedekind, equivalence relations and partial orders)
- Natural Arithmetic (axiomatic development of the natural number system within set theory, following Dedekind and Peano)
- #111 the concept of unit fraction
Marine Life (opus 206)
This piece is a celebration of the diversity and the beauty of the inner world of a human soul, symbolized in the video by the marine life: the part of nature that resides within the depths of the seas. The symbolism is revealed towards the end of the video, in the scene with a dressed woman in water. The scene opens with her submerged in water with only her head above the surface of water. She then submerges the head under water too and soon her head rises again above the surface of water, having an invigorated smile on her face.
The music for this piece, Opus 206, was composed in 2016.
Alina (opus 99)
A woman in her early 20's improvising some dance moves in front of a camera with the balloons in the background and informal outfit signifying celebration of freedom of expression.
Alina is a TikToker, with more than 90K subscribers. I am grateful to her for creating the video clips in this music video, which was later matched with Opus 99, an improvisation of mine from 2015. The rhythmic structure of Opus 99 shifts away from the "classical" style common to my work.