Lectures

• 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

April 03, 2021