Teaching materials · Cycle 3
The Cauchy Bunyakovsky Schwarz Inequality.
Three live sessions developed a central olympiad inequality through its classical form, Engel and Titu forms, reverse techniques, and applications. Teacher presentations closed the cycle in April 2026.
Coach: Prof. Zdravko Cvetkovski (Macedonia). Three live sessions took place on 6 February, 13 February, and 27 March 2026. Teachers closed the cycle on 10 April with presentations about the Cauchy Schwarz inequality.
What the cycle covered
- 6 February 2026. The Cauchy Bunyakovsky Schwarz inequality, Engel and Titu forms, and immediate corollaries.
- 13 February 2026. Reverse technique and unconventional methods.
- 27 March 2026. Applied olympiad inequalities.
- 10 April 2026, cohort teacher presentation. Teachers presented on the Cauchy Schwarz inequality.
The cycle stayed close to problems teachers actually meet in olympiad coaching, working from the classical statement to the forms that do most of the heavy lifting in practice.
Exercise collection
The problems from Cycle III.
The full exercise collection worked across this cycle, kept as a single document so the mathematics can be revisited in its original form.
These are the exercises used in the cycle's sessions. Individual problems are drawn from the olympiad problem literature and compiled for the Academy's teaching. External publications are listed on the Resources page.