- 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
- Real variable calculus (so far covers introduction to limits and derivatives)
- 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

## Saturday, April 3, 2021

### Lecture Notes

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