5 papers · 1 filter
Classifying Groups of Certain Orders
Shihan Kanungo
We will first discuss the question of which integers have exactly one group of order , namely the cyclic group . We will see that these are the integ…
Sobolev Spaces and Their Applications to Partial Differential Equations
Shihan Kanungo
This report provides an introduction to Sobolev spaces, a foundational concept in modern analysis and the theory of partial differential equations (PDEs). These spaces are useful t…
Elliptic Functions and Eisenstein Series
Shihan Kanungo
In this expository paper, we provide an introduction to elliptic functions and Eisenstein series from a classical analytic perspective while highlighting their broader mathematical…
The Grothendieck Group and K-Theory
Shihan Kanungo
In this expository paper, we develop the basic ideas underlying Grothendieck groups and to illustrate their appearance across algebra, topology, representation theory, and homologi…
Space-Filling Curves
Shihan Kanungo
We examine space-filling curves, which are surjective continuous maps from to some higher-dimensional space, usually the unit square . In particular, we define Pea…