College tracks

Grade 9 — start one project

You are on one track. The project lasts four years. This year you start it and keep a log. The log is the start of the file you will send. Do not open a second project.

Every week, do four things inside that project:

1. Compute a quantity with units, state the uncertainty, and say what decision it supports.
2. Write one claim, two reasons, and one real objection. About one page.
3. Read one short original — a figure and its caption, a statute section, a schematic, or a specimen — and write what it says, separate from a summary.
4. Add to the log.

Finish these rungs on the First Principles ladder. Each one has a gate. The rung is done only when the gate is done.

1. Instructions a machine could follow
2. Loops and branches
3. Variables and state
4. Function as a black box
5. Balancing equations
6. The coordinate plane
7. Python: syntax and types
8. Python: files and automation

School courses beside the project: algebra and geometry, and a first lab science, usually biology.

Mechanical engineering

Build an object that must hold a known load. Before the test, write the load and the failure point you expect. After the test, write the measured failure point and the difference. Justify the equation line by line: every step names the operation applied to both sides.

Done when a second person can rebuild the test from the log and get a failure point in the same region.

This week. Span a gap with a strip of cardboard or a thin wood slat. Write the mass you think will break it, in grams, before you load it. Add coins or sand until it fails. Record the mass that broke it and the difference from your prediction. Write the weight as mass times 9.8, and name the operation on both sides of each line.

Log for this week. Date. Length of the gap. Material. Predicted failure mass (g), written before loading. Measured failure mass (g). Difference. Weight = mass × 9.8, with each line naming the operation on both sides. Who will rebuild the test.

Grade 11 — let someone break it

Same project. Someone outside your household tries to break the result. Their paragraph stays in the log. That person is the one who can write the letter.

Before you register for grade 12, write three lines from the course list your desired college publishes: courses you will have finished, courses still missing, and the term you will take each missing one. Add a missing course around the project. Do not drop this track’s mathematics, lab line, or memo to make room for an elective.

Every week, inside that project:

1. Use a rate, an accumulation, or a comparison, with units and the uncertainty, on the project's claim.

2. Write a timed page a stranger could grade. Answer the other side in the text.

3. Cite one paper, case, dataset, or specification. A textbook restatement does not carry the claim.

4. Put the outside reader's paragraph in the log before you answer it.

5. Limits

6. The derivative

7. Rules of differentiation

8. The chain rule

9. Integration and the fundamental theorem

10. Series and convergence

School courses beside the project: precalculus finished and calculus started, and physics.

Mechanical engineering

The prediction uses a rate, a stress, a torque, or a flow from physics or from the derivative. Design the test to attack that formula’s assumption. Hand the report to someone who was not in the room for the build.

Done when the writeup names the assumption the test attacked and the measurement that decided it, and the outside reader can say whether the test actually attacked that assumption.

This week. Write one assumption in a sentence: the beam fails when the bending in the middle reaches a load you calculate, not when it slips at a support. Set the next test to attack that sentence, for example by shortening the overlap at the support. Record which failure happened. Give the page to someone who was not there for the build.

Log for this week. Date. Assumption sentence. How the test attacks it. Which failure happened. Outside reader’s name. Their verdict on whether the test attacked the assumption.

Grade 12 — an artifact a stranger can grade

Same project. The artifact is what a stranger can grade. One reviewer has watched the work long enough to describe it.

Every week, until that artifact is the one you send:

1. Use the mathematics your first college course will assume, on this project, with units.
2. Keep the claim in a piece a reviewer can check against the sources.
3. Let a primary source carry the claim. A summary does not.
4. Write in the log what would change the conclusion.

Finish these rungs:

28. Vectors
29. Matrices as transformations
30. Systems, determinants, rank
31. Basis and change of basis

School courses beside the project: calculus underway or complete. By the end of this year the lab sequence is biology, chemistry, and physics.

Mechanical engineering

Write the design report: requirement, model, build, measurement, failure, revision. If the forces or the supports are a system, vectors and linear systems are part of the model.

Done when someone who does not know you can say whether the model predicted the measurement, and can find the revision that followed the failure.

This week. Open the report with four labeled lines: the requirement, the failure mass your model predicts, the failure mass you measured, and the one revision you made after the failure. Stop there. A stranger should be able to tell whether the model matched the measurement.

Log for this week. Date. Requirement. Predicted failure mass. Measured failure mass. One revision. Stranger’s judgment: model matched measurement?

What you send

The application is this project. By the time you apply, the file has these parts:

1. The grade 12 artifact for your track.
2. The log, showing the same question across four years and what changed.
3. A letter from the person outside your household who tried to break the work.
4. The course record this lesson names: calculus and the lab sequence where your track requires them. Also take the courses your desired college publishes as required. If one of those crowds out the project, add it around the project. Do not drop the lab line or the mathematics line to make room for an elective.
5. The undergraduate admission test that college requires, on the calendar that college publishes. If your track has a mathematics line, take the test after that mathematics is underway. This is not the medical-school, law-school, or doctoral test, and it is not a substitute for the project.
6. An essay that states the claim, the best objection, and what the project changed. It is not a list of activities.

What you enroll in

The first year of college keeps the next gate open. Add a course only when it serves that gate.

Once a week, in the hardest course you are in, take one problem the exam could ask. Close the notes. Write the diagram, the equation, or the rule before you look up the solution. Record whether you finished it and where the solution disagreed. That page is the log. A course you only follow in lecture is not done.

Mechanical engineering. Calculus through the multivariable course if grade 12 did not finish it, calculus-based physics, and statics. Linear algebra and differential equations as soon as the calculus sequence allows. Read every statics problem the way you read the design report: diagram, equation, number, measurement.

Through the degree, to the gate

The first year is the start. The gate opens only if the later courses are the same kind of work.

Mechanical engineering. After statics: dynamics, mechanics of materials, and thermodynamics. Then fluid mechanics, heat transfer, and machine design or controls. Differential equations and linear algebra sit under those courses. The senior design or research report uses the same shape as the grade 12 report: requirement, model, measurement, failure, revision. Graduate mechanical engineering expects that report plus calculus, differential equations, and calculus-based physics already finished.