Mathematics and Statistics Consulting

Mathematical Modeling

Mathematical modeling is about creating an abstract framework for real-world scenarios and express the related real-world problems into mathematical problems.

The purpose of mathematical modeling is to use powerful mathematical techniques to tackle real-world problems.

Here are some examples of mathematical modeling:

Differential equations have been used to model the Earth’s climate, atpmosphere, and oceans to make predictions.
Stochastic calculus, probability theory, and partial differential equations are used in derivatives pricing and risk/portfolio management.
Probabilistic graph theory, game theory, and abstract algebra are used to solve problems in cybersecurity.
Geometry and vector calculus are used in construction.
Optimization theory and probability theory are used in supply chain management.
Linear algebra and multivariable calculus are used to represent and solve problems about machine learning models.
Topological manifolds and homology are used to analyze datasets.
Stochastic differential equations are used to model biological phenomena.
Probability theory and combinatorics are used in the design of games.

Statistical Modeling

Statistical modeling is about creating an abstract framework to study datasets. These datasets can be from real-world scenarios or abstract objects.

The main purpose of the study is to discover relationship between variables and to make predictions.

Here are some examples of the statistical modeling:

Multiple regression modeling can be used to understand which variables are likely to predict phishing attacks in cybersecurity.
Regression modeling is used to predict property prices and market trends in real estate.
Markov chain models have been used to predict possible deviations in a construction project schedule and the future progress of a project.
Ridge regression has been used to predict weather patterns.
Nonlinear time-series models are used to analyze and predict financial data.
Diagnostic models are used to assess and improve the performance of retail operations.

Mathematical Research

Mathematical research is about asking questions about abstract systems to better understand them. Some of these investigations may result in new abstract systems.

The more abstract systems there are and the more results are discovered
about these systems, the more likely these systems and their results can be used to tackle real-world problems.

I have experience in several areas of mathematics at the research and graduate levels, some of which are:

category theory
graph theory
hypergraph theory
combinatorics
elliptic curves
type theory
real analysis
complex analysis
probability theory
mathematical logic
set theory
abstract algebra
topology
algebraic topology
linear algebra
differential equations

Projects

Predictive Algorithm Design and Development for Lottery Games

The goal of this project was to design and develop an algorithm that can predict the outcomes of lottery games and to backtest the algorithm. The client was satisfied with the performance of the algorithm.

Racing Simulation System Design for an NFT Game

The goal of this project was to create a mathematical model of an NFT game and implement the model in C++.

Power BI Dashboard from MySQL Data

The goal was to create a Power BI dashboard from data of houses listed for sale in California, US. The real estate data was uploaded from a MySQL table.