What is Expositio?
A public repository for expository academic papers, with an integrated scholarly record.
Expositio is a place to read and cite expository work. Papers are published as stable,
citable records, while remaining connected to later versions, editorial decisions,
and related context.
Some papers are early drafts; others have been peer reviewed or formally published.
Each paper remains readable on its own, while preserving the history behind it.
The result is both a reading room and a record: a place to browse by field, read
papers in stable form, and follow their development over time.
v1
In statistics, signal processing, and machine learning, the information we want from a matrix is carried by its singular values and singular vectors, yet the matrix we observe is almost never the one we want: it has been corrupted by measurement error, finite-sample fluctuation,…
Mathematics / Linear and multilinear algebra; matrix theory
v1
A tropical curve is a graph with specified edge lengths, some of which may be infinite. Various facts and attributes about algebraic curves have analogs for tropical curves. In this article, we focus on divisors and linear series, and prove the Riemann-Roch formula for divisors …
Mathematics / Algebraic geometry
v1
This paper tries to create an intuition behind the proof of the fundamental
theorem–Weierstrass approximation theorem–which will be shown using Bernstein polyno-
mials and its generalization beyond polynomials–the Stone-Weierstrass theorem. The paper
will look at a few applic…
Mathematics / Approximations and expansions
v1
An essay that presents a first-principles approach to eigenvalue dynamics of the wave equation applied in context of timpani tuning.
Mathematics / Functional analysis
Physics / Acoustics
Mathematics / Partial differential equations
v1
This expository paper explains tessellations of the hyperbolic plane from a differential-geometric viewpoint. We review the upper half-plane (H) and Poincaré disk (D) models and the Cayley transform linking them. We prove that orientation-preserving isometries are precisely PSL(…
Mathematics / Differential geometry
v1
In this paper, we begin with the concept of a projection in the familiar vector space R^n, and then extend it to an arbitrary inner product space. This foundational idea enables us to compute a line of best fit, approximate functions using polynomials, and decompose a function i…
Mathematics / Abstract harmonic analysis
Mathematics / Group theory and generalizations
