Math & Geometry

Mental model

Interviews use math sparingly: gcd/lcm, modular arithmetic, primes, combinatorics, and basic geometry (cross product, line intersection). Recognize the shape of the problem — the formula is a quick lookup away.

How to study Math & Geometry

Begin by restating the mental model in your own words, then connect it to a concrete system you have built or operated. Name the mechanism, the constraint it addresses, and the trade-off it introduces. Use Computational geometry (Wikipedia) to check details, but close the source before writing your explanation. Retrieval is the learning step; rereading is only preparation.

Next, compare Math & Geometry with the neighboring concepts in its roadmap. Ask what changes in correctness, latency, resource use, operability, and failure recovery. Complete GCD and modulo arithmetic and preserve the command, input, output, and one failed attempt as evidence. Finish by explaining the idea without jargon to someone who has not studied the track.

Proof of understanding

• Explain the mechanism from first principles and identify the state it reads or changes.
• Give one situation where the concept is the right choice and one where it is not.
• Predict a realistic failure mode before running the drill, then compare the prediction with evidence.
• Connect the result to a roadmap or build artifact instead of treating the concept as isolated trivia.

Learn from primary sources

• Computational geometry (Wikipedia) (doc)

Practice and explain it back

Review prompts

• What does the sign of the 2D cross product tell you, and which problems does that single test solve?

Build evidence

Use a roadmap capstone to turn this concept into working evidence.

Learning paths

• DSA Practice