Integer Parts Course
This course delivers mastery of floor, ceiling, and fractional part functions through rigorous examples, proofs, and sum techniques. Develop powerful tools for counting problems, divisibility proofs, inequalities, and precise integer arguments in contests, research, and advanced math, ensuring error-free results every time.

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 calculations.
- Simplify floor and ceiling sums using grouping, shifts, and double counting.
- Deploy integer-part methods in counting, divisibility, and remainder proofs.
- Prevent errors like off-by-one, sign flips, and inequality slips via 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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