Module 01: Mathematics for Systems
Why Math for Backend Engineers?
Backend performance analysis requires math. Not advanced math — but specific applied math that most engineers never learned formally:
- Big-O analysis tells you whether your algorithm will work at 100 rows or 100 million rows
- Probability explains cache hit rates, failure probabilities, and expected values
- Statistics is how you interpret benchmark results without being fooled
- Queueing theory is the formal model behind connection pool sizing and load balancing
- Numerical stability matters when you compute money, time deltas, or coordinates
Contents
| File | What you learn |
|---|---|
01-big-o-analysis.md | Time and space complexity with real backend examples |
02-probability-for-engineers.md | Expected values, distributions, birthday problem |
03-statistics-for-performance.md | p50/p99/p999, histograms, outlier analysis |
04-queueing-theory.md | M/M/1 queue, Little's Law, Erlang C formula |
05-numerical-stability.md | Floating point, integer overflow, decimal arithmetic |
Key Insight
Every performance equation in later modules traces back to this module.
N+1 query cost = O(N) queries × RTT ← Big-O + networking
Pool wait time = L / λ = W ← Little's Law (queueing)
Cache hit rate = Zipf distribution ← Probability
p99 vs p50 gap = heavy-tailed distribution ← Statisticsin this section