Construction Track: Mathematics & Automated Discovery

Course Catalog & Credential Pathway — Dwg. No. PF-002E

Mathematics & Automated Discovery

Ed. 2026–27grades 9–12 + post-secondary

A field branch of the Construction Track, for students aimed at formal mathematics and machine-assisted discovery — search and verification pointed at open problems instead of open-ended chat.

Field branch of Dwg. No. PF-002, The Construction Track — same core sequence through Phase II, concentrated here into formal proof & automated search from Phase II onward. See also Dwg. No. PF-001, The Verification Track.

Working premise: DeepMind's AlphaEvolve has found new, more efficient algorithms for open problems in matrix multiplication and combinatorics, and systems built on formal proof assistants have started closing in on long-standing open conjectures — work now tracked systematically against lists like the Erdős problems. The interesting part isn't the search algorithm, which is generic; it's the formal verifier that checks a candidate proof is actually correct instead of just plausible-looking.

Five core strands, plus the domain strand this branch concentrates in

MATH
Mathematical Foundations
Linear algebra, calculus, probability, optimization — the language every architecture is written in.
ENG
Software & Systems Engineering
Data structures, distributed computing, performance at scale.
ML
Machine Learning & Deep Learning
Architectures, training dynamics, why a model behaves the way it does.
RES
Research Practice
Reading a paper closely enough to rebuild what's inside it.
BLD
Build & Ship
Open-source contribution, deployment, production ML that survives contact with real load.
PRF
Formal Proof & Automated Discovery
This branch's concentration — deliberately its own strand code, distinct from the core MATH strand.
Phase I

Foundations

Grades 9–10

No frameworks yet, and no formal logic yet either. Two years of straight math and programming fundamentals, identical to the core Construction Track.

CodeDescriptionStrandLoad
MATH 101

Precalculus, Accelerated

Compressed to clear room for calculus by grade 11 — the standard on-ramp for anyone headed toward a quantitative degree.

MATH
1.0 credit
CS 100

Programming I — Python

Variables, control flow, functions, data structures. Fluency, not tricks.

ENG
1.0 credit
MATH 110

Discrete Mathematics & Logic

Sets, proofs, graphs, combinatorics — the math CS theory actually runs on, usually skipped until it's overdue.

MATH
0.5 credit
ENG 105

Technical Writing for Research

Writing a clear methods section and an honest results section — the two paragraphs every paper lives or dies on.

RES
0.5 credit
Phase II

Applied Practice

Grades 11–12

The math and CS sequences converge into an actual first model, same as the core track. The formal-proof layer begins concurrently — by the end of Phase II a student can both train a small model and write a fully formalized proof in a real theorem prover.

CodeDescriptionStrandLoad
MATH 201

Calculus I & II

Through multivariable and the gradient — backpropagation is the chain rule with bookkeeping, and it should read that way.

MATH 101

MATH
1.5 credit
MATH 210

Linear Algebra

Vector spaces, eigendecomposition, matrix calculus. Every tensor operation is this course wearing a framework's syntax.

MATH 101

MATH
1.0 credit
STAT 220

Probability & Statistics for ML

Distributions, estimation, Bayes — framed toward loss functions and uncertainty, not toward the social-science stats track.

MATH
1.0 credit
CS 210

Data Structures & Algorithms

Complexity analysis and the standard structures, drilled to fluency — still the baseline technical-interview bar at every AI lab.

CS 100

ENG
1.0 credit
ML 230

Intro to Machine Learning

Regression through a first neural net, built from array operations before any framework is allowed to hide the mechanics.

MATH 210, STAT 220

ML
1.0 credit
RES 240

Research Seminar — Reading Group

Weekly seminal-paper reads (perceptron through transformers), presented and defended aloud, not just summarized.

RES
0.5 credit
MATH 225

Formal Logic & Proof Structure

Propositional and predicate logic, proof strategy, and the discipline of a fully formal argument — what separates a proof from a convincing sketch of one.

MATH 210

PRF
1.0 credit
PRF 235

Interactive Theorem Proving

Lean and Coq in practice — formalizing existing proofs, then extending them, in the same proof assistants now used to verify machine-generated results.

MATH 225, CS 210

PRF
1.0 credit
Phase III

Apprenticeship

Post-HS, Yrs 1–4

Here the domain degree takes over from the general CS/applied-math track. A pure mathematics-plus-CS program replaces DEG 300 — the depth of mathematical training, not the tooling, is what makes a formalized-proof result trustworthy.

CodeDescriptionStrandLoad
DEG 300

Pure Mathematics Degree

Formal core in a pure mathematics-plus-CS program — the mathematical depth that makes a search-and-verify result trustworthy, not just plausible.

PRF
variable
PRF 340

Search & Evolutionary Program Synthesis

Evolutionary and LLM-guided search over formal search spaces — the AlphaEvolve pattern — applied to an open problem in algorithms, combinatorics, or number theory the student picks and pursues.

PRF 235, ML 230

PRF
1.5 credit
ML 310

Deep Learning for Search & Discovery

Large-scale search, program synthesis, and the LLM-guided-evolution methods behind systems like AlphaEvolve, taught directly against an open mathematical problem rather than as a generic survey.

ML 230

ML
2.0 credit
ENG 320

Systems for ML

Distributed training, GPU/accelerator programming, and the infrastructure a large-scale automated-search run needs to explore a search space at any real breadth.

CS 210

ENG
1.5 credit
RES 350

Supervised Research Practicum

Placement inside a formal-methods or mathematical-discovery research group, with a mentor of record. Graded on a reproduction that actually reproduces, or a contribution that gets merged.

RES 240, ML 310

RES / BLD
2 semesters
BLD 360

Capstone — Build & Ship

One model or tool — a formalized proof of an open lemma, a search-and-verify pipeline against a real conjecture list — taken from idea to a deployed, load-bearing artifact with real users.

ENG 320, RES 350

BLD
1.0 credit
Note: RES 350 and BLD 360 keep the same credit weight and sequencing as the core Construction Track — only the placement changes, into a formal-methods or mathematical-discovery research group specifically.
Phase IV

Continuing Education

No end date: the ML baseline moves every conference cycle, and the open-problem baseline — the Erdős problems and their kin — moves on its own slower schedule that a purely computational graduate can lose track of.

Read weekly Reproduce monthly Ship ongoing Publish on result
Weekly
Paper trackingFollow arXiv's math.CO and cs.LO feeds plus the DeepMind and formal-methods lab blogs — one narrow feed read closely.
Monthly
Reproduction sprintReimplement one result from a tracked paper — a search-and-verify pipeline, a formalized lemma. The one that won't reproduce is usually more instructive.
Ongoing
Ship something load-bearingKeep at least one deployed artifact — a proof-checking tool, a search benchmark — with real users.
On result
Publish or contributeA workshop paper, a blog writeup, or a merged PR against an open-source theorem-proving or search-and-discovery tool.
Drawing
PF‑002E
Pair
PF‑002 Construction
Edition
2026–27
Strands
MATH ENG ML RES BLD PRF