Current Phase 1/7
The Mathematical Substrate
Dec 11, 2025 – Mar 15, 2026
Assignments
0/13
Study Time
0h
Total logged hours
Focus
Rigorous Proofs & Geometry
Ability to derive gradients and visualize high-dimensional spaces.

Upcoming Deadlines

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Phase 1 Resources

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  • 📖
    Linear Algebra Done Right
    Sheldon Axler
    primary
  • 📖
    Introduction to Linear Algebra
    Gilbert Strang
    secondary
  • MIT 18.06 Linear Algebra
    Gilbert Strang
    secondary
  • 📖
    Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach
    John H. Hubbard, Barbara Burke Hubbard
    primary
  • 📖
    Calculus on Manifolds
    Michael Spivak
    alternative
  • 📖
    Introduction to Probability
    Joseph Blitzstein, Jessica Hwang
    primary
This Week0.0h
Target2030h
Progress0%
Weekly Progress0.0h / 30h

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About This Curriculum

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The landscape of artificial intelligence has shifted dramatically from the era of isolated academic curiosity to an industrial arms race driven by "frontier labs"—organizations like OpenAI, Google DeepMind, and Anthropic that operate at the cutting edge of capability. For a university student aspiring to join these ranks, the standard "data science" curriculum is no longer sufficient. The modern Research Engineer (RE) at a frontier lab is a hybrid archetype: part mathematician, part systems engineer, and part experimental scientist. They must possess the theoretical intuition to diagnose why a loss curve is diverging and the systems-level expertise to implement a fix across a cluster of thousands of GPUs.

This report outlines a rigorous, exhaustive, and self-directed curriculum designed to bridge the gap between a student with basic software knowledge and a candidate capable of contributing to the development of next-generation foundation models. This is not a path of least resistance; it is a path of maximum depth. The curriculum prioritizes "first-principles" understanding over high-level API usage. While it is possible to train a classifier in three lines of Python, doing so without understanding the underlying calculus, optimization dynamics, and memory hierarchy renders one incapable of pushing the boundary of what is possible. As identified in industry analyses, the most successful research engineers often hold advanced degrees or equivalent self-study depth in computer science, mathematics, and physics.

Phase Overview

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Phase Focus Dates Checkpoint Status
1 The Mathematical Substrate Rigorous Proofs & Geometry Dec 11 – Mar 15 Linear Algebra Done Right (Axler) Current Upcoming
2 CS Fundamentals & Systems Algorithms & Systems Mar 16 – May 30 The Algorithm Design Manual (Skiena) Upcoming
3 Classical ML Theory Statistical Learning Jun 1 – Aug 15 Pattern Recognition & ML (Bishop) Upcoming
4 Deep Learning Architectures (Transformers) Aug 16 – Nov 30 Understanding Deep Learning (Prince) Upcoming
5 Frontier Systems Distributed Training (CUDA) Dec 1 – Feb 28 CMU 10-714 (Needle) Upcoming
6 Frontier Research Topics LLMs, Generative AI Mar 1 – May 15 Stanford CS324 (LLMs) Upcoming
7 Research & Portfolio Reproduction & Innovation May 16 – Jun 30 Reproduction Project Upcoming