Nihal Uppugunduri's WebsiteWe attempt to generalize the notion of “normal subgroup,” used in studying kernels and homomorphisms, to a “normal subset” that does not have the requirement of being a subgroup, and we see whether it is possible for a normal subset to exist that is not a normal subgroup.
In this post, we discuss some questions concerning the philosophical foundations of ZFC.
My philosophical post on the circularity of mathematics implies that formal logic must rest ultimately on an informal foundation. In this post, I discuss what that means for our definition of mathematical rigor, which will be an important reference for future philosophical discussions.
We list some facts concerning bijections and isomorphisms between algebras for my learning (“algebra” in the universal algebra sense here, not the specific vector space based algebraic structure.)
Intuitively, a plane is a flat surface that extends infinitely in all directions. How can we interpret this definition in a formal way, and in particular use that discussion to derive the standard equation of a plane?
In this post, we investigate further the sine angle addition functional equation that I introduced in a previous post, Trigonometric Identities as Functional Equations. (See the work done there before reading this post.) Specifically, the question is to find all functions 
A typical definition of model theory is “universal algebra plus relations.” However, the term “model” in natural language can typically be used quite generally, especially if we consider how people typically understand its meaning for designing and developing any kind of system. Thus, we could guess just based off terminology that in mathematics, a “model” could be defined, as generally as possible, basically as an “example” (set plus interpretation function) that satisfies any given set of axioms. Is this equivalent to the traditional formulation of model theory? In other words, does the traditional formulation of model theory capture the most general kinds of axioms that an “implementation” could satisfy?
In this post, we continue the exploration started in Topology as an Algebraic Structure.
Can we express the axioms of topology equivalently as the axioms of an algebraic structure?
We know that model theory is at least a non-strict generalization of universal algebra. Indeed, we can consider model theory to be “universal algebra, but with relations instead of operations.” We can actually replicate the main definitions of model theory with an exact replacement of “operation” by “relation” in the universal algebra definitions, which yields more generality since every 
