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, divisibility, inequalities, and precise integer arguments in contests, research, and advanced math, avoiding common pitfalls.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
Gain rapid practical mastery of floor, ceiling, and fractional part functions. Master essential properties, inequalities, and manipulations, applying them to sums, counting, divisibility, and intervals. Brief proofs, examples, and checks ensure error-free, confident solutions.
Elevify advantages
Develop skills
- Master floor and ceiling principles for swift, accurate real-world evaluations.
- Simplify floor and ceiling sums using grouping, shifts, and double counting.
- Employ integer parts in proofs for counting, divisibility, and remainders.
- Prevent errors like off-by-one, sign flips, and inequality slips via verification.
- Leverage fractional and nearest-integer parts for compact, contest-level proofs.
Suggested summary
Before starting, you can change the chapters and the 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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