Integer Parts Course
This course delivers rigorous command of floor, ceiling, and fractional parts via examples, proofs, and sums. Develop vital tools for counting, divisibility, inequalities, and precise integer arguments in contests, research, and advanced math, ensuring error-free solutions.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
Gain quick, practical mastery of floor, ceiling, and fractional part functions. Master essential properties, inequalities, and manipulations, applying them to sums, counting, divisibility, and intervals. Use short proofs, examples, and checks to dodge errors and craft confident, clear solutions.
Elevify advantages
Develop skills
- Master floor and ceiling rules for swift, accurate real-world evaluations.
- Simplify floor and ceiling sums using grouping, shifts, and double counting.
- Deploy integer parts in proofs for counting, divisibility, and remainders.
- Prevent off-by-one, sign, and inequality errors through targeted checks.
- Leverage fractional and nearest-integer parts for sharp, contest-level proofs.
Suggested summary
Before starting, you can change the chapters and workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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