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A loop, a condition, and a running total: how to translate a plain-English problem into code that runs, checks out, and earns trust.
Turning Problems into Code
A loop, a condition, and a running total: how to translate a plain-English problem into code that runs, checks out, and earns trust.
Divisibility and Primes
The remainder test, factors, what makes a number prime, and two fast tools: trial division up to the square root and the Sieve of Eratosthenes.
Remainders and Modular Arithmetic
The leftover from a division, generalized: how the remainder powers clock arithmetic, even and odd tests, greatest common divisors, and the wrap-around math behind hashing and ciphers.
Counting Without Counting
The multiplication principle, factorials, permutations, and combinations: how a path-counting problem with billions of cases collapses into one number.
Recursion and Memoization
A function that calls itself, and the cache that stops it from redoing the same work a million times.
Bases and Big Numbers
Place value, binary and hex, and why Python holds 2^1000 and 100! exactly while floating point quietly drops digits.