24th June at Cheenta

We have three events coming up today.

1. The 2013 graduating batch will attend class at 7:30 AM
2. The 2014 graduating batch will attend class at 11 AM
3. Mock interview session for Indian Statistical Institute B.Math aspirants

The first class will begin in an hour. We will focus on two themes:

• Geometry - Stewart's Theorem and an introduction to mass point geometry
  
• Complex Numbers - Elementary inequalities involving complex numbers and further discussion on their geometry

The two problem sheets on geometry and two problem sheets on complex numbers will aid the discussion. We will resume the two-test structure from today. That is to say the class will begin with a d-test (diagnosis test of 15 minutes) and end with an e-test (effect test of 15 minutes).

Rittinkar did the maximum amount of homework last week. He will be awarded with a book. I like his diligence very much. Even Krishnendu has worked hard (he submitted some INMO problem solutions yesterday).

The discussion on geometry will introduce mass-point technique (the lever of Archimedes :)). In the long run I want to link barycenter and complex number application. In fact the discussion on complex numbers is mainly motivated from geometry of Vector Algebra. We have considered some problems on geometry in the last class (and applied complex numbers to solve them). We want to continue the journey.

The second class is equally interesting.

We will again focus on two themes:

• Inequalities
• Differential Calculus

The concept of inequality and calculus are intertwined historically. In fact, quite a few calculus books begin from this perspective. The one I like most however attacks limiting processes through the discussion on sequences (the book is Pre-calculus by Tarasov which happens to be our prize book too).

We have already covered some grounds in inequality, We are freely talking about Arithmetic and geometric means, Cauchy Schwarz, Jensen's inequality etc. In today's class we want to focus on some problem solving (from problem sheet 1 and 2).

The discussion on differentiation, continuity etc. will follow. We will discuss Rolle's Theorem, Lagrange's Mean Value Theorem (with geometric intuition). Presently we are following I.A. Maron's Calculus in One Variable. The Art and Craft of Problem Solving by Paul Zeitz is also a nice book (it has a section on calculus).

The Mock Interview Session will follow the classes.

Subhojit and Shalmali will attend the session. I have also invited Abhra Abir. There will be board-work, problems and interactions. I am looking forward meet them one more time.