Abstract Theory.
Real-World Impact.

Math applied to software, biomechanics, and financial models.

Discrete Structures & High-Dimensional Topology

COMPUTER SCIENCE & ML

Linear algebra, graph theory, and calculus sit under every serious learning system. Weight spaces, spectral methods, and optimization landscapes decide whether a model converges or collapses. The same toolkit shapes algorithm design, complexity bounds, and the cryptographic primitives that keep data safe. Applied math here means building systems that scale, generalize, and remain stable when inputs drift in the wild.

O(N log N) Graph Analysis
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Spatial Kinematics & Finite Elements

ORTHOPEDIC BIOMECHANICS

Bodies move through space under force, constraint, and tissue compliance. Rotation matrices and quaternions track joint orientation without gimbal lock while PDEs and finite element models estimate stress on implants and bone. Gait simulation and custom fitting pipelines turn that geometry into devices people can wear and surgeons can trust. Math is the bridge between clinical intent and mechanical reality.

Quaternion Kinematic Solvers
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Stochastic Calculus & Risk Engineering

STOCHASTIC FINANCE

Prices are paths through noise, not straight lines. Stochastic differential equations and Brownian motion give a language for drift, volatility, and path dependence. Monte Carlo engines sample that uncertainty into prices, risk metrics, and stress scenarios that teams can act on. The aim is disciplined exposure management when the future is a distribution rather than a single forecast.

Ito Calculus Drift Diffusion
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Cryptographic Algebra & Threat Modeling

CYBERSECURITY MATH

Security is number theory under operational load. Modular arithmetic, elliptic curves, and hard discrete log problems power key exchange, signatures, and zero trust designs. Threat modeling ties those primitives to real attack surfaces, so protocols stay sound when they leave the whiteboard. Strong algebra and careful implementation are what keep identity, money, and private data intact.

Elliptic Curve Cryptography
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Applied
Mathematics

The core of every tech stack.

Neural nets, joint kinematics, cryptography, and markets all share one substrate. Applied math is what turns equations into systems that ship and hold under real constraints.

Neural Net Optimization

Training modern models is an optimization problem first and a software problem second. Loss surfaces are shaped by linear algebra, multivariable calculus, and gradient methods that step through high dimensional parameter space. Backpropagation, weight updates, and regularization are all applications of those tools. When the math is solid, networks converge faster, generalize better, and stay stable under distribution shift. That is the foundation behind computer vision pipelines, language models, and the medical AI systems that need reliable predictions, not just clever architectures.

Deep learningComputer visionNLPMedical AI
eq

L = -(1/N) Σ [yi log(pi) + (1-yi) log(1-pi)]

Spatial Kinematics

Every joint, implant, and robotic limb is a kinematic chain. Rotation matrices and quaternions keep orientation free of gimbal lock while differential equations describe how forces and torques evolve over time. Finite element thinking connects geometry to stress, and gait models link theory to real patient motion. In practice that means better prosthetic fit, safer surgical planning, and simulators that behave like living tissue rather than rigid cartoons. Spatial math is what turns biomechanics into software you can trust in clinic and in the lab.

ProstheticsGait analysisRoboticsSurgical nav
eq

R_θ = [cosθ -sinθ; sinθ cosθ]

Elliptic Trust

Public key security is number theory made operational. Elliptic curves, modular arithmetic, and hard discrete log problems let two parties agree on secrets without sharing them in the clear. The same algebra underwrites TLS certificates, hardware wallets, and zero trust network design. Weak math means broken keys; careful curve choice and implementation discipline mean systems that resist known attacks at practical sizes. Cryptography is where abstract algebra becomes infrastructure that protects money, identity, and private data every day.

TLS / ECCWalletsZero trustProtocols
eq

y^2 ≡ x^3 + ax + b (mod p)

Stochastic Calculus

Markets are noisy, path dependent, and never fully observed. Stochastic differential equations and Brownian motion give a language for that uncertainty. Drift and volatility become parameters you can estimate, stress, and simulate. Monte Carlo engines turn those models into prices, risk metrics, and scenario books that decision makers can act on. The goal is not perfect prediction. It is principled exposure management when the future is a distribution, not a single number, and every trade has to survive that reality.

PricingRiskMonte CarloScenario analysis
eq

dSt = μSt dt + σSt dWt

Good systems are built on calculus, linear algebra, and probability, not code alone.

Technologist

Computational Orthopedics & Math

Orthopedic technology backed by math, computer vision, and machine learning. Focused on models and tools that are useful in real clinical work.

Computational Biomechanics

Modeling complex joint stresses, kinematics, and tissue loads using finite element analysis (FEA) and differential equations to optimize orthopedic implant longevity and performance.

Generative Custom Fitting

Developing algorithmic pipelines that process raw 3D scans and automatically generate optimized, lightweight, 3D-printable custom orthotic and prosthetic structures.

Predictive Gait Intelligence

Training deep neural networks on clinical gait data and wearable sensor streams to predict kinetic anomalies and calibrate active bionics in real-time.

Surgical Spatial AI

Designing real-time computer vision and geometric registration algorithms to assist orthopaedic surgeons with high-precision implant positioning and navigation.

Let's Formulate Solutions

From optimization algorithms and musculoskeletal kinematics software to financial risk models, I help turn mathematical theory into systems that work in the real world.

  • MedTech startups: product-market fit and technical architecture
  • Research labs: signal processing and biomechanical control
  • Clinical translation: engineering for patient care