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: six 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), 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

Six self-directed weekend courses, run in parallel. Courses 1–4 follow the same weekly rhythm: read concept → prove/exercise → implement it → benchmark it → write a staff-level note. Course 5 is the shared mathematical and theoretical foundation underneath them. Course 6 is a 10-week practical microelectronics and signal-processing course on the bench.

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 — Autonomy ML Systems + Embedded Robotics + Vision + Jetson

Covers the ML systems, GPU compute, and embedded robotics foundations for AV and robotics engineering roles, building on the math from Course 5 and the signal processing from Course 6. Three phases: GPU compute and ML numerical foundations → prediction, planning, and ML efficiency → embedded robotics and Jetson integration.

Target roles: ML Frameworks & Efficiency Engineer · Prediction & Planning ML Engineer · Embedded Software Engineer

→ Syllabus

Course 2 — C++20 + Vulkan Graphics/Physics Engine for Self-Driving Car Simulation

Builds a real-time simulation engine from scratch in C++20 and Vulkan: road networks, traffic controls, vehicle physics, ego vehicle, RGB/depth/semantic camera sensors, perception baselines, and planning test hooks. The synthetic world can be used to test self-driving vision and detection algorithms.

Target skills: Real-time graphics architecture · Physics simulation · Sensor simulation · AV scenario testing · C++20 systems design · Vulkan GPU programming

→ Syllabus

Course 3 — 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 5. 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

Course 4 — Low-Level CS: Bits, CPU, ARM Assembly, Linux Internals, and Performance

Builds low-level CS intuition from first principles: data representation, digital logic, CPU architecture, ARM64 and x86-64 assembly with LLVM IR as the neutral bridge, C/C++ memory layout, Linux processes, virtual memory, filesystems, boot, networking, devices, and performance engineering. Every week follows the Diiv.io pattern: read concept → exercises → implement → benchmark → write a staff-level note.

Target roles: Systems Software Engineer · Embedded Software Engineer · OS/Linux Platform Engineer · Performance Engineer · Robotics/Edge AI Systems Engineer

→ Syllabus

Course 5 — Mathematical & Theoretical Foundations

The mathematical backbone under the other courses: a 20-week theory course 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, classical mechanics, differential geometry, and electrodynamics/optics. 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 6 — 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 SPICE, 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