← Science SchoolAdministration

E-TRADE TOGETHER GLOBAL ACADEMY

Computational Experimentation

DEEP REBUILD · COMPONENT-LEVEL FORMAT PARITY · PYTHON RUNTIME NOT VERIFIED

3 modules · 7 canonical classes · 2 laboratories · 3 module assessments · project · final

Administrator review mode

No payment, enrollment or prerequisite restriction. Review content is available only to authorized administrators.

UI/UX authority: current Mathematical Foundations implementation. Rendered-content verification requires format parity.

MODULE 1

Computational experiment design

Purpose: Define reproducible questions, baselines, parameters, controls and comparison cases.

Learning outcomes: Define a reproducible question; distinguish variables, parameters and controls; establish a baseline; and design controlled comparisons.

Dependencies: Courses 6.1 and 7.1; scientific Python foundations; numerical-method vocabulary.

Classes owned: 7.2.1 · 7.2.2

Related laboratories: Reproducible Parameter Sweep

Next-module connection: Numerical evidence, data quality and validation.

7.2.1 · v1 · 100 minutes

Reproducibility

Why it matters

A computational claim is useful only when another learner can reconstruct the same model, inputs, method and evidence.

Learning objectives

  • Create a complete experiment manifest with units, method and expected evidence.
  • Distinguish repeatability, reproducibility and independent validation.

Prerequisites

Courses 6.1 and 7.1; prior canonical classes where applicable.

Concept and explanation

A reproducibility record binds a question to a model version, code, parameters, units, numerical method, seed when random, expected outputs, tests and limitations. Re-running the same code is repeatability; reproducing from the record tests whether the work is independently reconstructable.

Key terms

manifest; provenance; repeatability; reproducibility; seed; environment; version; audit trail

Domain-specific notation and representation

Record QUESTION → MODEL v1 → INPUTS/UNITS → METHOD → EXPECTED EVIDENCE → TESTS → LIMITS. Runtime and package versions remain unclaimed because PYTHON_RUNTIME is NOT_VERIFIED.

Worked computational experiments

Worked experiment 1

Question: Can a cooling calculation be reconstructed from a manifest?

Expectation / hypothesis: With fixed parameters and time points, the expected temperatures are identical.

Model: Newton cooling: T(t)=20+60 exp(-0.1t).

Inputs and parameters: t=[0,10,20] s; ambient 20 °C; initial 80 °C; k=0.1 s⁻¹.

Baseline: Model v1 with k=0.1 and unchanged units.

Experiment design: Compute only declared times and compare with hand evaluation at t=0.

Code / algorithm:

from math import exp
times=[0,10,20]
result=[20+60*exp(-0.1*t) for t in times]
print([round(x,2) for x in result])

Expected output — not executed:

Expected/precomputed: [80.0, 42.07, 28.12]

Results: Temperature decreases toward 20 °C; the manifest preserves every input.

Verification and validation: Verify t=0 gives 80 exactly; validate only against suitable cooling data for an intended use.

Sensitivity and uncertainty: Changing k changes cooling rate; measurement/model uncertainty is not removed.

Interpretation: The record supports reconstruction, not physical validation.

Limitations: Constant ambient temperature and lumped body assumption.

Reproducibility: model=v1; code hash pending; units SI; method=closed form; runtime NOT_VERIFIED.

Worked experiment 2

Question: Does a fixed seed make a stochastic estimate repeatable?

Expectation / hypothesis: The same seed and sample count produce the same expected sequence in one specified generator.

Model: Estimate a Bernoulli proportion from 8 declared draws.

Inputs and parameters: seed=17; n=8; threshold=0.5.

Baseline: Seed 17 and n=8 are fixed.

Experiment design: Record generator, seed, sample count and statistic before inspecting results.

Code / algorithm:

import random
r=random.Random(17)
x=[r.random()<0.5 for _ in range(8)]
print(x, sum(x)/8)

Expected output — not executed:

Expected/precomputed for Python's documented generator: [False, False, False, True, False, False, False, True] 0.25

Results: Two successes yield 0.25.

Verification and validation: Verify arithmetic 2/8; validation requires a justified probability model and adequate sample.

Sensitivity and uncertainty: A different seed changes sampling variability, not numerical error.

Interpretation: A seed aids repetition but does not make n=8 sufficient.

Limitations: Generator details and small sample constrain transfer.

Reproducibility: seed=17; n=8; statistic=mean; expected result labeled; runtime NOT_VERIFIED.

Common mistake / invalid experiment

Failure: reporting results without the parameter file, units, seed or model version prevents reconstruction and hides changes between runs.

Flawed evidence

run_model()  # parameters and version not recorded

Correction and recheck

config={'model':'v1','k_per_s':0.1,'times_s':[0,10,20]}
assert config['times_s'][0] == 0

Guided practice

Guided activity 1

Complete the question, expected evidence, inputs, parameters, controls, baseline and metric table.

Guided activity 2

Select verification evidence, independent validation evidence, sensitivity checks and uncertainty statements.

A/B/C/D practice

A — Foundation

Audit a manifest for missing units.

B — Application

Write a reproducibility record for a deterministic case.

C — Reasoning and error detection

Repair an unrecorded-seed experiment.

D — Challenge / transfer

Explain why reproducible is not automatically valid.

Validation and reproducibility

CODE → PREDICT → TRACE → EXPECTED OUTPUT → DEBUG → TEST → VALIDATE. Successful execution is not claimed and would not by itself validate the model.

Knowledge check and summary

  1. Identify question, output, inputs, parameters and controls.
  2. Compare baseline and controlled case with a declared metric.
  3. Separate verification from validation evidence.
  4. State sensitivity, uncertainty, limitations and reproducibility.

Mastery criterion: 4/4 checks plus two worked experiments, two guided activities, four A/B/C/D responses and one corrected failure with fresh reassessment.

Related laboratory

Next class: Parameter sweeps

Sources and references

  • Academy-original bilingual instructional material.
  • National Academies — Reproducibility and Replicability in Science.
  • NIST/SEMATECH e-Handbook of Statistical Methods.
  • Official Python, NumPy, SciPy and Matplotlib documentation where referenced.

Science & Mathematics Tutor

Context: Course 7.2 · Module 1 · Class 7.2.1. Ask for help with the active experiment, code trace, error diagnosis, validation or related lab. The Tutor follows the selected language and does not fabricate execution.

Academic review

Review dimensions

VERIFIED · MOBILE QA = ENVIRONMENT_BLOCKED

Mathematical Foundations format parity

MATHEMATICAL_FOUNDATIONS_FORMAT_PARITY = PASS

The current Mathematical Foundations implementation is the UI/UX authority. Canonical identities govern academic structure, and approved academic content governs instruction.

Standard
ACADEMY_STANDARD_LESSON_EXPERIENCE_V1
Class version
v1
Format review
2026-09-19

Version and review history

  • 7.2.1 · v1 · 2026-09-19 — Canonical identity and approved academic content preserved.
  • DEEP FORMAT REBUILD · 2026-09-20 — Module, class, laboratory, practice, assessment, Tutor and review presentation rebuilt to the Mathematical Foundations experience.
  • MOBILE QA — ENVIRONMENT_BLOCKED