An Illustration of Applied Stochastic Geometry: Coverage Probability in a Simple ALOHA MANET
This article weaves high level concepts from stochastic geometry into a practical description of wireless network coverage under the Aloha protocol.
The Math Citadel
Recent articles from The Math Citadel.
Latest posts
Markov Decision Process Basics
This article discusses the practical basics of Markov decision processes, with machine repair and a garden fertilization examples.
An Interesting Prisoner's Dilemma
This article will explore a generalization of a problem Traylor found in S. Ross's "Applied Probability Models with Optimization Applications" involving a strange prison and some basic probability reasoning.
Concatenation as an Operation
This article explores the definition of an operation using the familiar notion of concatenation.
Defining an Anomaly
This article details some of the challenges in anomaly detection, particularly in defining an anomaly "globally".
Taking Things for Granted: Elementary Properties of Groups
Many concepts in basic algebra are also taken for granted, such as cancellation of terms, and commutativity. This post will revisit some basic algebra (think solving for x), but with some of those things we took for granted removed.
Group Theory, XOR, and Binary Codes: Introducing Coding Theory
This article gives an introduction to coding theory by looking at the group structure of binary words under the exclusive-or operation.
Interventions, not Anomalies
This article gives a suggestion for dealing with time series anomalies.
Maximum-Likelihood Decoding
This post will now allow us to explore some more interesting topics in coding theory, courtesy of Pinter's A Book of Abstract Algebra. We'll introduce the notion of a code, informations, and parity check equations.
Like Clockwork: Modulo Addition And Finite Groups Of Integers
This article eases a reader into finite groups and modulo arithmetic.
A Partition By Any Other Name
This article looks at cosets of a group and notes how they partition a set, then mentions an application of the result to coding theory.
All the Same Opposites
This article examines the surprising richness in the field of two elements.
Applications of Reflections: Taking a Group to its Abelian Form
This article looks at the definition of the categorical concept of a reflection and gives a clear application with full construction.
Beyond Cookbook Mathematics, Part 1
This article gives a more colloquial introduction to the importance of mathematical definitions and framing practical problems mathematically.
Beyond Cookbook Mathematics, Part 2
This article continues colloquially discussing how to look at and read mathematical proofs.
Building a Ground Floor: Topology Basics, Part 1
This article gives a short introduction to basic topological concepts, with concrete examples.
Cauchy Sequences: The Importance of Getting Close
This article gives a short exposition of a Cauchy sequence of real numbers.
Energy Levels of Molecules are Bounded Below
This guest submission is from Nikita Lisitsa, a professional software developer and mathematician.
Equivalence v. Isomorphisms in Category Theory
This article discusses the difference between equivalence and isomorphisms among categories, with concrete examples.
Using Theoretical Chemistry to Engineer Better Packet Flow
This article reviews a technical report on the application of chemical kinetics to packet flow management in computer networks. Much more detail is given.
The Convenience of Isomorphisms
This article gives a simple introduction to the utility of isomorphisms, using an example on Z_4 and a group of complex numbers.
Mailbox Answers: Calculating New Parity After an Overwrite
This article is inspired by an e-mail question regarding parity for a data stripe on a storage system. It provides motivation for an elegant mod 2-based proposition and proof.
On the Optimal Storage of Bulk Cargoes
This article gives an extremely practical application of basic (though nontrivial) calculus involving the optimization of storing bulk cargoes on ships.
Networking Mathematics: Random Early Detection and TCP Synchronization
This article discusses some computer networking basics and reviews an interesting algorithm for buffering and queue management.
Paper Review: Active Queue Management with Non-Linear Packet Dropping Function
This article reviews a network engineering paper and points out some issues.
Reduce the Problem: Permutations and Modulo Arithmetic
This article explores the elegant connections between permutations and modulo arithmetic.
Should I Accept This Shipment?
This article gives a manufacturing application of the hypergeometric distribution in shipment sampling and acceptance.
Sequences and Tendency: Topology Basics Part 2
This article helps the reader to understand what convergence means when we strip the idea of "distance" away.
The Cartesian Product of Two Graphs
An exploration of what "multiplication" can mean for two graphs.
The Red-Headed Step-Distributions
This article discusses the notion of singular continuous distributions, and a lone constructive example.
Regression and Time Series
This article discusses the similarities and differences between ordinary linear regression and time series models.
Topologies v. sigma-algebras
This article discusses the similarities and differences between topologies and σ−algebras, aiming to clear up the two definitions with explicit examples.
Using Boolean Algebra to Find all Maximal Independent Sets in a Graph
This article details some frustration in finding maximal independent sets of a graph.
Using Dirac Delta Formalism to Calculate Shear Force and Bending Moment
This article gives a very interesting application of the Dirac delta function to a common mechanics problem.
Welcome to GF(4)
This article discusses the Galois field on 4 elements, with an emphasis on solving linear equations with altered definitions of addition and multiplication.
Poisson Processes and Data Loss
This article discusses the Poisson process as it may (or may not) apply to data loss in enterprise storage systems.
The Hathlor Classification System
This article explains our novel technical book classification system that we employ in our library.
Simulating Soundscapes Using Convolutions
This article gives a fantastic application of convolutions as applied to music and signal processing. Audio is included.