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New lecture has been uploaded to UNIZOR.COM - Physics4Teens - Waves - Mechanical Oscillations - Problems 1: A. Analyze the free oscillations of a pendulum in a uniform gravitational field. B. Analyze the ball's rolling freely inside a semicircle in the uniform gravitational field.

Mathematics for Teenagers Math is my favorite subject. It was my major in college and it has played extremely important role in my career. It has shaped my thinking, it influenced approaches I took when dealing with complex problems and helped to maintain a healthy balance in life. Educational material in this section is devoted to mathematical topics addressed usually by those high school teachers and advanced students who strive to deepen their understanding of principles and concepts of mathematics. The topics are presented in a relatively rigorous way with plenty of logical justifications and, most importantly, many problems to be solved by students. It is a very strong opinion of many math teachers that the main purpose of studying math is not accumulation of facts (theorems, rules, properties etc.) but rather developing an unfailing logical approach to solving problems of all kinds, starting with mathematical ones and leading to real life challenges. That is why it is extremely important for students to attempt solving as many problems presented here as possible. Some of them will be discussed on this site and solutions will be suggested, some are presented for self-study. But if you want this study to be successful, try to solve as many as you can. This is a main key to develop analytical approach that is extremely important for a successful career in many areas. I'd like to extend my deep appreciation to my math teacher Felix Barenbaum who is not only a wonderful teacher but a great inspiration as well. I know him since my 5th grade in school and we still, though separated by an ocean, maintain close relationship. In addition, I'd like to mention that most of non-trivial problems you will see on this Web site are taken from books "Special Problems in Elementary Mathematics" by P. Modenov published in Moscow in 1960 (in Russian, of course) and a few books of problems published under editing supervision of M.I.Skanavi (also in Russian). Additional references are mentioned under "References" item of the Main Menu of this course.

"Education is what remains after one has forgotten everything he learned in school" - Albert Einstein. "Each success only buys an admission ticket to a more difficult problem" - Henry Kissinger. Point: Problem solving and proving theorems might sometimes be boring and time consuming, but it makes you SMARTER. Students: You are not looking for fun lifting weights in a gym. You spend time and effort there to achieve meaningful results in physical development. Don't look for fun developing your mind. You have to spend time and effort to achieve meaningful results that last the life time. If you do it, these results will amaze you. Product: UNIZOR is a gym for your mind that helps you to develop your intellectual strength, creativity and analytical approach to everything you face in real life. The educational process presented on this Web site is aimed to develop your intellectual abilities which cannot be forgotten. Key: Parents and responsible adults supervising the education are the customers and the main party of interest. They can and should personally or through representatives actively manage the educational process. Parents: IF YOU CARE ABOUT EDUCATION OF YOUR CHILDREN, TAKE CONTROL. THIS SITE GIVES YOU A PROPER TOOL TO ACHIEVE IT - THE CONTENTS, THE PROCESS, THE RESULTS.