Integer Parts Course
Gain mastery over floor, ceiling, and fractional part functions through rigorous examples, proofs, and summation techniques. Develop essential tools for counting problems, divisibility tests, inequalities, and reliable integer-based arguments in research, mathematical competitions, and advanced studies. This course equips you with the precision needed for complex problem-solving across various mathematical contexts.

4 to 360 hours flexible workload
valid certificate in your country
What will I learn?
This course delivers rapid, practical expertise in floor, ceiling, and fractional part functions. Learners will grasp fundamental properties, essential inequalities, and adept handling techniques, applying them to sums, counting problems, divisibility, and interval analysis. Featuring concise proofs, detailed examples, and verification exercises, it ensures avoidance of frequent pitfalls while fostering confident, succinct solution writing.
Elevify advantages
Develop skills
- Master floor and ceiling principles for swift, precise evaluations in practical scenarios.
- Calculate and streamline floor and ceiling sums using grouping, index adjustments, and double counting.
- Employ integer-part methods in proofs for counting, divisibility, and remainders.
- Prevent errors such as off-by-one, sign issues, and inequality pitfalls through verification techniques.
- Leverage fractional and nearest-integer parts for succinct, competition-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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