Integer Parts Course
Master floor, ceiling, and fractional part functions with rigorous examples, proofs, and sums. Build tools for counting, divisibility, inequalities, and error-free integer arguments in research, contests, and advanced mathematics.

from 4 to 360h flexible workload
certificate valid in your country
What will I learn?
The Integer Parts Course gives you a fast, practical command of floor, ceiling, and fractional part functions. You will master core properties, key inequalities, and efficient manipulations, then apply them to sums, counting arguments, divisibility, and interval problems. Short proofs, worked examples, and quick checks help you avoid common errors and write clear, concise solutions with confidence.
Elevify advantages
Develop skills
- Master floor and ceiling laws: rigorous, fast evaluation in real problems.
- Compute and simplify floor/ceiling sums: grouping, index shifts, double counts.
- Apply integer-part tools to counting, divisibility, and remainder proofs.
- Control errors: avoid off-by-one, sign, and inequality mistakes with checks.
- Use fractional and nearest-integer parts in concise, competition-ready 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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