The INEQUALITY quest!

Inequalities are important for olympiads and I.S.I., C.M.I. entrances. Sometimes they appear as standalone problems. However mostly they are clubbed with other problems (geometry, calculus etc). The Cheenta Inequality course is a 7-session-super-course to achieve excellence and efficiency in solving inequalities. The course work consists of 600 problems on inequalities with interdisciplinary treatment in certain special areas. For example while discussing triangular inequality or Euler's inequality we bring geometry in action. Similarly we discuss Lagrange's mean value theorem, idea of limit while discussing sequential inequalities, convexity of function and so on.
The 600 problems are sourced from:

• 70 problems from Little Mathematical Library
• 125 problems from Arthur Engel
• 100 problems from Excursion in Math and Challenges and Thrills of Precollege Math
• 300 problems from Inequalities: An Approach Through Problems By Venkatchala, International Math Olympiads and other national olympiads.

The course is resumed with certain trivial-looking ideas (natural numbers can be counted, ordered, square of real number is always non-negative, positive times positive is always positive). In the first stroke we cover inequalities related to Means, Bernoulli, Cauchy–Bunyakovsky–Schwarz, Holder. We also cover the simple cases of approximating sequential sums.
Then we move over to Jensen (convexity etc.) Rearrangement, Schur, Murihead and some other not-so-trivial-looking inequalities. Triangular inequality and application of calculus in understanding inequalities is discussed in the final phase.
The Kiran Kedlaya Inequality pack and similar courses available freely online were helpful. We tried to incorporate the best part of all of them. A course on inequality must be holistic as well as efficient. We must not loose our focus from problem-solving techniques. At the same-time the course must bear an elegance of the art-form.

15th May 2011 class preview

On 15th May 2011 (Sunday) we focus on inequalities once more. We have already covered Problem Sheet 1 and Problem Sheet 2 on inequalities which covered the Little Mathematical Library booklet on inequalities. Problem Sheet 3 will conclude the LML book and assist a migration to the Arthur Engel- Problem Solving Strategies collection on inequalities.

• Diagnosis Test (covering Problem Sheet 1 and 2 on inequalities)
• Problem Set 3 (on inequalities) with a marathon revision of previous two sheets.
• Regional Mathematics Olympiad 1993 paper discussion
• International Math Olympiad 1959 paper discussion
• Effect Test (covering Problem Sheet 3 with special stress on Holder's inequality)

IMO and RMO related discussion will need prior preparation in the part of the student.In fact that is of the homework of current week. This class is open to all. Students from class 9 to 12 may attend it. Practice Problems for next week includes 100 problems from Arthur Engel inequalities, Inequality chapter from Excursion in Math, Challenges and Thrills of Precollege Math, Mathematical Circles (especially triangular inequalities) and IMO, INMO, RMO level inequality problem collection.

In May will have 3-4 classes (since it is summer vacation in most schools), which are open to all. We want to complete Functional Equation (the book by Venkatchala, and problem collection in Arthur Engel). We enter June to work on Combinatorics and Geometry.

In December the Regional Math Olympiad is due. Summer Vacation is really the prime time for preparation. Look out for more updates in this blog.