Diiv.io

I’m currently a staff software engineer at Apple in the Apple Services Engineering org, working on distributed systems and mobile device management. Find me on LinkedIn, X / Twitter, and GitHub.

This site documents my ongoing weekend projects: four self-directed courses, and worked proof sets from the mathematics textbooks that underpin them.

Book Proofs & Solutions

I work through selected proofs and exercises by hand on paper first. Once I’m satisfied with the solution, I typeset it in LaTeX/KaTeX using Claude — Claude handles only the typesetting so I can stay focused on the mathematics. Solutions are organized by book and chapter in Books.

  • Math — Axler (Linear Algebra Done Right, Measure, Integration & Real Analysis), Ross (Elementary Analysis), Munkres (Analysis on Manifolds), Strichartz (A Guide to Distribution Theory and Fourier Transforms), Mendelson (Introduction to Topology), Bak & Newman (Complex Analysis), Trefethen & Bau (Numerical Linear Algebra), Bertsekas & Tsitsiklis (Introduction to Probability), Boyd & Vandenberghe (Convex Optimization), Pressley (Elementary Differential Geometry), Pinter (A Book of Abstract Algebra)
  • Physics — Morin (Introduction to Classical Mechanics), Griffiths (Introduction to Electrodynamics), Hecht (Optics)
  • CS — Dasgupta, Papadimitriou & Vazirani (Algorithms), Sipser (Introduction to the Theory of Computation)
  • Computer Vision — Szeliski (Computer Vision: Algorithms and Applications)
  • Robotics / AI — Thrun, Burgard & Fox (Probabilistic Robotics), Goodfellow, Bengio & Courville (Deep Learning)
  • NLP — Jurafsky & Martin (Speech and Language Processing)
  • EE — Oppenheim, Willsky & Nawab (Signals and Systems), Oppenheim & Schafer (Discrete-Time Signal Processing), Cover & Thomas (Elements of Information Theory)

Courses

Four self-directed weekend courses, run in parallel. Course 1 is the shared mathematical and theoretical foundation; Course 2 is a practical bench-based microelectronics and signal-processing course. Courses 3–4 are applied build courses, and all follow the same weekly rhythm: read concept → prove/exercise → implement it → benchmark it → write a staff-level note.

A note on AI use: The weekly lecture notes are drafted with AI assistance so each week has a consistent structure. The substance is hand-done: every math proof and exercise solution is worked by hand on paper first and then converted to LaTeX/KaTeX/MathJax using AI for typesetting only, and all code is written by me — because the whole goal is to learn.

→ All Courses

Course 1 — Mathematical & Theoretical Foundations

The mathematical backbone under the other courses: a 15-week core theory course (plus five optional weeks) working through the highest-value sections of the core textbooks, ordered by dependency. Linear algebra and numerical computing, real analysis and topology, probability, convex optimization, information theory, complex analysis, signals and transforms, algorithms and computation theory, and differential geometry. Pure study notes — definitions, key theorems, and intuition — with the proofs worked by hand.

Target skills: Mathematical maturity · Numerical reasoning · Probabilistic and information-theoretic thinking · Optimization theory · Signals and systems · Theoretical CS foundations

→ Syllabus

Course 2 — Microelectronic Circuits & Signal Processing: Theory to Bench

A 10-week bench-based course that builds from Maxwell’s equations and the lumped-circuit model up through resistive networks, energy-storage elements, transients, AC and phasors, analog filters, semiconductor devices and op-amps, and then into signal processing: LTI systems, Fourier, sampling, and digital filters. Every circuit is predicted by hand, simulated in software, and measured on real instruments — a Fluke multimeter, an LCR meter, and a 100 MHz oscilloscope — with the Jetson Orin Nano as the data-acquisition and DSP target. Capstone: capture a real analog signal, filter it digitally, and reconcile the digital filter against its analog twin.

Primary resources: Ulaby & Maharbiz Circuit Analysis and Design · Scherz & Monk Practical Electronics for Inventors · Platt Make: Electronics · Griffiths Introduction to Electrodynamics · Oppenheim Signals and Systems and Discrete-Time Signal Processing

Target skills: Analog & mixed-signal circuit design · Bench instrumentation · Filter design · Semiconductor device intuition · Continuous and discrete-time signal processing · Embedded data acquisition

→ Syllabus

Course 3 — Computer Graphics, Vision & Autonomous Robotics

Builds a graphics→vision→robotics stack from scratch: a real-time C++/Vulkan renderer that also generates synthetic RGB/depth/semantic data with ground truth, a CPU-and-GPU computer-vision pipeline (filtering, features, stereo, optical flow, and a learned CNN detector), and a Jetson Orin Nano “vision-car” that runs GPU perception, visual SLAM, and an exploration policy on a minimal real-time embedded runtime to map a region autonomously. Builds on the math from Course 1 and the signal processing from Course 2.

Target roles: Graphics / Engine Programmer · Computer Vision Engineer · Robotics / Perception Software Engineer · Embedded / Edge-AI Software Engineer

→ Syllabus

Course 4 — NLP + Deep Learning + LLM

Covers classical NLP through modern LLMs: tokenization, n-gram language models, embeddings, RNNs and LSTMs, sequence labeling, parsing, attention, transformers built from scratch, large language models, masked language models, instruction tuning, alignment, retrieval-augmented generation, information extraction, and agentic systems — building on the probability, optimization, and information theory from Course 1. Portfolio project: a citation-grounded RAG assistant over technical documents with BM25 + dense retrieval, reranking, and evaluation metrics.

Primary resources: Stanford CS224N · MIT 6.S191 · Jurafsky & Martin Speech and Language Processing

Target skills: NLP engineering · LLM application engineering · RAG and search engineering · Speech/NLP multimodal systems · Information extraction · LLM evaluation and benchmarking

→ Syllabus