Integer Parts Course
Master floor, ceiling, and fractional parts through examples, proofs, and sums. Develop skills for counting, divisibility, inequalities, and precise integer arguments in contests, research, and advanced maths, ensuring error-free solutions.

flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
Gain quick practical mastery over floor, ceiling, and fractional part functions. Learn 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 solutions.
Elevify advantages
Develop skills
- Master floor and ceiling rules for fast, accurate real-world calculations.
- Simplify floor and ceiling sums using grouping, shifts, and double counting.
- Use integer parts for proofs in counting, divisibility, and remainders.
- Prevent errors like off-by-one, sign flips, and inequality slips with checks.
- Apply fractional and nearest-integer parts in sharp competition 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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