Applied Mathematics | Data Science | Machine Learning Systems

I am an applied mathematician and data scientist with a PhD in Mathematics from Rutgers University and an MS in Data Science from Fordham University and 10+ years of experience designing quantitative models, building machine learning systems, and working with distributed computing frameworks. My work connects mathematical theory with practical implementation — particularly in probabilistic modeling, machine learning, and scalable computational systems. I have published research in mathematical physics and machine learning, and I am actively seeking industry roles in applied mathematics, data science, and ML research.

Example output from fractal visualization tool (C/GTK project below)

• Ph.D., Mathematics — Rutgers University (2011)
• M.S., Data Science — Fordham University (2025)
• M.S., Mathematics — University of North Carolina – Wilmington (2005)
• B.S., Physics — University of North Carolina – Chapel Hill (1999)
• Associate Professor of Mathematics, Wilkes University (2015–Present)
• Postdoctoral Researcher — Universität zu Köln (2012–2014)

I build things from first principles to understand core mechanics, bridge mathematical theory and practical implementation, and evaluate tradeoffs through experimentation. I am particularly interested in problems that require both rigorous mathematical thinking and careful engineering judgment.

• Young, B. and Zhao, Y., "Change Point Detection via Hierarchical Dirichlet Process Hidden Markov Models with Topological Emissions," MS Thesis, Fordham University (2025). Submitted for publication.
• Young, B., "Landau Damping in Relativistic Plasmas," J. Math. Physics 57, 021502 (2016).
• Young, B., "On Linear Landau Damping for Relativistic Plasmas via Gevrey Regularity," J. Diff. Eqns. (2015), doi:10.1016/j.jde.2015.04.021.
• Young, B., "Existence of Spherical Initial Data with Unit Mass, Zero Energy, and Virial less than −1/2 for the Relativistic Vlasov–Poisson Equation with Attractive Coupling," J. Math. Phys. 52, 093707 (2011).
• Young, B., "Optimal L^β-Control for the Global Cauchy Problem of the Relativistic Vlasov–Poisson System," Transport Theory and Statistical Physics 40, 331–359 (2011).

Programming: Python, Julia, Go, C, Mathematica
Machine Learning: Bayesian modeling, HMMs, clustering, topological data analysis, neural networks, RAG systems
Data Science: NumPy, pandas, scikit-learn, PyTorch, SQL
Data & Distributed Systems: Hadoop, Spark, MapReduce
Tools: Git, Linux, LaTeX

Bayesian nonparametric model for unsupervised change point detection in time-series data, combining Hierarchical Dirichlet Process Hidden Markov Models with topological data analysis.

• Hierarchical Dirichlet Process prior for automatic state inference — no need to specify number of states
• Vectorized persistence diagrams as emission features, capturing topological structure of windowed time-series data
• Full Gibbs sampling inference pipeline implemented from scratch in Julia
• Validated on synthetic datasets, human motion capture data (MSRC-12), and NASA Solar Dynamics Observatory imagery
• Outperforms generic change point detection methods across all experimental settings

👉 https://github.com/byoung77/hdp-hmm-te

Graph-based approximate nearest neighbor index inspired by HNSW, built for clarity, experimentation, and tunable performance.

• Cosine and Euclidean similarity with tunable search accuracy vs. performance tradeoffs
• Batch construction and dynamic incremental insertion
• Graph connectivity maintained via MST-based reconnection
• Empirical evaluation of recall, inflation, and timing across varying dataset sizes and parameters

👉 https://github.com/byoung77/Approximate-Nearest-Neighbors-Project

Build Times vs. Dataset Size for ANN System

Configurable feedforward neural network implemented from first principles.

• Implemented generic feedforward architecture with user-defined layers
• Coded backpropagation and gradient updates manually
• Designed modular training loop with support for classification and regression
• Trained model exposed as a reusable callable class

👉 https://github.com/byoung77/Neural-Net-Implementation

Neural Net Training Loss for Two Moons Dataset

Go-based distributed systems simulation of Chain Replication with Asynchronous Queries (CRAQ), emphasizing message-passing concurrency, observability, and interactive exploration.

• Message-passing architecture using goroutines and channels
• Chain replication with versioning, commit propagation, and dirty-state tracking
• Deferred-read mechanism using per-key waitlists as a pragmatic alternative to tail forwarding, reducing protocol complexity while preserving consistency guarantees
• Interactive REPL with real-time monitoring via per-node log files

👉 https://github.com/byoung77/Simulated-CRAQ-Server

CRAQ Simulation Architecture

End-to-end retrieval-augmented generation system for question answering over unstructured text, built on Wikipedia data.

• FAISS vector database for semantic similarity search
• Cross-encoder reranking for improved document relevance
• Citation-aware LLM responses for verifiable outputs
• Interactive desktop GUI built with Tkinter

👉 https://github.com/byoung77/Doctor-Who-Oracle

Dr. Who Oracle Interface

An interactive Python implementation of the classic Lights Out puzzle, extended with multiple algebraic state spaces and nontrivial topological grids.

• Variable grid sizes from 2×2 to 15×15
• Multiple state spaces over Z_p for p ∈ {2, 3, 5, 7}
• Nontrivial board topologies: cylinder, Möbius strip, torus, Klein bottle, projective plane
• Built-in solver using linear algebra over finite fields
• Guaranteed solvability via construction from valid press vectors

👉 https://github.com/byoung77/lights-out

Built a Python/MySQL/LaTeX system to replace fragmented committee records stored across multiple documents, enabling searchable history and automated generation of professional PDF reports.

• Designed and built a relational database system to replace fragmented committee records stored across disconnected Google Docs, enabling centralized search and retrieval for the first time
• Developed Tkinter GUI supporting record creation, editing, deletion, date-range queries, and student-specific lookup
• Automated generation of professional PDF reports using LaTeX, including statistical summaries of approval rates, repeat cases, and outcome breakdowns
• Database design was subsequently adopted into a larger institutional student management system at Wilkes University

👉 https://github.com/byoung77/committee-appeals-db

Interactive fractal visualization tool built in C using GTK, for exploring complex dynamical systems in real time.

• Mandelbrot and Julia sets with real-time zoom and navigation
• User-defined complex function exploration
• Iterative numerical algorithms for orbit computation and escape-time analysis
• Optimized for performance in C, enabling high-resolution real-time rendering

👉 https://github.com/byoung77/GUI-Fractal-Project

Complete undergraduate textbook covering calculus, differential equations, linear algebra, dynamical systems, probability, and stochastic processes. Developed for classroom use at Wilkes University and refined across multiple course offerings.

• Covers a full two-semester sequence integrating calculus, linear algebra, ODEs, and probability with a unified modeling perspective
• Emphasizes connections between mathematical theory and real-world systems throughout
• Includes worked examples, problem sets with selected solutions, and supporting appendices
• Written entirely in LaTeX; full PDF available in repository

👉 https://github.com/byoung77/Mathematical-Modeling-Notes

• Email: bojy77@gmail.com
• LinkedIn: https://www.linkedin.com/in/brent-young-6057b0b5/
• GitHub: https://github.com/byoung77

All projects are released under the MIT License unless otherwise noted.