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.

Computer science

Write a specification in sentences, then a program that meets it. A classmate chooses an input you did not use. The log includes a script that reads a real file from the project, reports something you did not already know, and runs on a second file without an edit.

Cryptography is not a separate track. If that is your aim, stay on this project: the specification still comes first, and by grade 12 a classmate tries to break a piece you designed (a toy cipher, a password check, a signature, or an access rule) on your own system in a closed setting — not on a live network.

Done when the classmate’s input is in the log with the result the specification promised and the result the program produced.

This week. Specification, in sentences: the program reads a text file of one number per line, prints how many numbers it read, their sum, and the mean, and refuses a file that contains a word. Write that before you write the program. A classmate supplies a second file you have not opened. The log records what the specification promised and what the program printed.

Log for this week. Date. Specification sentences, written before any code. Your file’s count, sum, and mean. Classmate’s file name. What the specification promised for that file. What the program printed. Where they disagree.

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

Also finish:

25. Recursion
26. Trees and heaps
27. Sorting and searching under constraint

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

Computer science

State an invariant or write a proof for one piece of the program, on a claim you have not been shown worked. Separate the base case and the inductive step, and use the assumption. If the project is a recursive structure, a tree, or a search with a budget, that structure has to meet a time or space limit you wrote down first.

Done when a test that would violate the invariant is in the project, and the proof or the code changed because of it.

This week. Write one invariant for the file program: after each line, the running total equals the sum of the numbers read so far. State the base case, the empty file, separately. Add a test that would make the invariant false if the code is wrong. If the test fails, change the proof or the code, and point to that change.

Log for this week. Date. Invariant. Empty-file base case. Test that would falsify it. Result. Proof or code change, with the line pointed out.

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

If grade 10 did not already finish them, finish Proof technique and Counting. For a cipher, a password check, a signature, or an access rule, also finish:

38. Continuous distributions and PDFs
39. Expectation, variance, covariance
40. Bayes' theorem

Those three do not replace the linear-algebra rungs above. The break attempt below is where you use them.

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

Computer science

Keep the specification. A classmate tries to break one piece you designed: a toy cipher, a password check, a signature on a message, or an access rule. The target is your system, in a closed setting. Write the adversary’s goal and whether the break worked. Finish the linear-algebra gates even if the break attempt is the center of the project.

Done when the writeup states the goal, the result, and the change you made if the break succeeded.

This week. Give a classmate one hour and a closed copy of a password check or a toy cipher you wrote. Tell them the goal in one sentence: produce an accepted password they were not given, or read a message without the key. Write whether they did it. If they did, change one thing and say what. The target is your program, not a live system.

Log for this week. Date. Adversary goal in one sentence. Did they succeed. Change made if they did. Confirmation the target was your program only.

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.

Computer science. Data structures and discrete mathematics in the first year. Computer organization when the department offers it. Linear algebra stays in the plan. Cryptography comes after proofs and probability are comfortable. It does not replace data structures.

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.

Computer science. After data structures and discrete mathematics: algorithms, computer organization, and probability. Then a systems course and a theory or second algorithms course. The specification and the tests stay the way you are graded. Cryptography is a later course, after proofs and probability, and it adds an adversary to the specification. It does not replace algorithms or systems. Graduate computer science expects those courses. A cryptography direction expects you can state what an adversary is allowed to do and whether the scheme survived it.