Learn scientific computing with known answers

Your starting point

You can use arithmetic, functions, and arrays. Start with idealized examples whose assumptions are written down.

• Basic algebra and graph reading
• A local scripting or browser environment for calculations

Your finish line

You can distinguish model assumptions, numerical error, random variation, and implementation mistakes using small repeatable experiments.

Stack up four small wins

1. STEP 1 OF 4

   Write the mathematical contract

   Choose a quantity, its unit, valid input, and an independently calculated expected output.

   Bro tip: Put the expected answer and its unit in the same note. Check it independently rather than calling the new implementation a second time.

   What you’ll learn

   • Units and valid ranges
   • Absolute and relative tolerance
   • Hand-checkable examples
   You’re ready to move on when

   A sample answer can be checked without using the same implementation twice.

   I can do this step

2. STEP 2 OF 4

   Build a quantity conversion lab

   Implement a small converter with explicitly compatible unit families.

   Bro tip: Start with one known conversion and one incompatible pair. Inspect the underlying number as well as the displayed unit and rounding.

   What you’ll learn

   • Conversion factors
   • Affine temperature conversions
   • Input validation
   You’re ready to move on when

   Known conversions and round trips pass justified tolerances; incompatible quantities are rejected.

   Open project: Quantity conversion lab

   I can do this step

3. STEP 3 OF 4

   Inspect a numerical approximation

   Simulate idealized exponential decay and compare the numerical result with its exact formula.

   Bro tip: Hold the initial value, parameter, and final time fixed while comparing step sizes. Record the error beside each result.

   What you’ll learn

   • Time steps
   • Analytical comparison
   • Convergence experiments
   You’re ready to move on when

   The error is measured over the same interval and the effect of a smaller step is visible.

   Open project: Decay time-step explorer

   I can do this step

4. STEP 4 OF 4

   Separate randomness from correctness

   Estimate a geometric area from sampled points and verify the classifier with a deterministic fixture first.

   Bro tip: Check the point classifier with fixed examples first. Then record the generator, seed, sample count, and configuration for each random run.

   What you’ll learn

   • Seeded generators
   • Monte Carlo estimates
   • Repeatable experiments
   You’re ready to move on when

   The same recorded configuration reproduces a run, while different seeds show variation honestly.

   Open project: Monte Carlo area lab

   I can do this step

Your build lineup

1. Quantity conversion lab

   Convert a small set of compatible units and verify the numerical meaning with known examples.

2. Decay time-step explorer

   Compare a simple numerical approximation with an exact exponential-decay solution.

3. Monte Carlo area lab

   Estimate a quarter-circle area with sampled points while keeping deterministic checks separate from random variation.

Watch it. Then build it.

Start with a worked example, then connect the recording to your own small, checkable build. Videos open on their creator’s or publisher’s website.

Read Vibe Bro’s written lesson briefing ↗

1. Beginner · Video course · About 1 hour

   Python NumPy Tutorial for Beginners

   freeCodeCamp.org · Keith Galli

   Introduces array creation, shapes, data types, indexing, arithmetic, statistics, and reshaping in NumPy.

   For step 1: Write the mathematical contract

   Before watching: Basic Python lists, variables, and functions, plus school algebra. The later linear-algebra and trigonometry sections can wait.

   Watch, then try

   Practice array arithmetic on a handful of known quantity conversions. Keep unit labels explicit and compare results with independently calculated answers before adding more inputs.

   The lesson teaches Python and NumPy; the starter also works in another established calculation stack. Add compatible-unit validation, temperature offsets, and justified comparison tolerances in your lab.

   Watch course ↗ · Practice: Quantity conversion lab

   Publisher’s course details · checked October 28, 2026

2. Next step · Video

   Lecture 6: Monte Carlo Simulation

   MIT OpenCourseWare · John Guttag

   Uses Python probability experiments, including roulette, to introduce Monte Carlo simulation.

   For step 4: Separate randomness from correctness

   Before watching: Introductory Python at MIT 6.0001 level or comparable functions, loops, and collections; basic algebra and probability. Review the course's earlier stochastic-thinking lessons if needed.

   Watch, then try

   Adapt the experiment structure to the area lab. Verify the point-inside-shape classifier with known points, then record the seed and sample count and compare several repeated experiments.

   An optional follow-up after your first numerical exercises. The course uses Python and predates current tooling. The area classifier, seed log, and deterministic fixture are additional practice for our stack-flexible starter.

   Watch video ↗ · Practice: Monte Carlo area lab

Video links selected October 28, 2026. Selection checks cover publisher metadata and topic fit.

The docs behind it

These references explain the underlying concepts and APIs. The prompt templates and project plans are original examples to adapt to your own setup.

• SciPy — Integration, time steps, and error tolerances
• NumPy — Random-number generators and seeds
• Pint — Units, quantities, and dimensionality checks

Documentation links checked October 27, 2026.

Keep the momentum going

• Array broadcastingCoding term
• Array vectorizationCoding term
• Create a reproducible simulation experimentCopyable prompt