A collection of investigations or proofs of interesting mathematical problems or concepts.
Might be easier to view the PDFs from the drive.
Drive: https://drive.google.com/drive/folders/13n47UQXlnNTJlDKoch5AXa9Lmt4QmKT4?usp=sharing
File Descriptions.
A particular sequence of continuous functions
Does there exist a sequence of continuous functions on [0, 1] such that it diverges everywhere but the corresponding integrals go to zero.
On counting special basis of R^3
Counting the number of basis sets of R^3 whose vectors are made only of 0s and 1s.
Open cover around rationals
Finding enumerations {q_n} of the rational numbers such that the family of sets {q_n - 1/n, q_n + 1/n} covers or doesn't cover the whole real line.
p-subgroup of unitringular matrices
A detailed description showing any finite p-group can be embedded in a group of unitriangular matrices over the finite field F_p.