# Blog Archives

## The Five Second Rule: A Simple Everyday Question Leading To Quantum Mechanics and Biology

Sometimes the simplest question can lead down a deep rabbit hole to new worlds. How fast germs contaminate food that falls on the floor is a good example of such a question. When you start to think about it, you realize that you don’t quite now what it means for two objects to touch, and when you start analyzing the microscopic and then the quantum mechanical details, you cross multiple scientific disciplines.

This is the intellectual journey that Michael Stevens goes on in his video that debunks the “five second rule,” a popularly held belief that food that falls on a dirty floor is safe to eat if it is picked up quickly enough. One of the main benefits of this type of video is its ability to connect seemingly unrelated issues and motivate viewers to conduct their own thought experiments. You may think it’s a silly question, but you’re sure to be surprised by at least some aspects of the answer.

## Problem Solving Russian Style

You’ve read about the lack of proper problem solving in schools and you’ve even started thinking about a few recommended nonstandard elementary problems, now what? You could browse the Web looking for puzzles or math olympiad problems, but a much better approach would be to find a source of problems that is structured by topic, ability level, and that has been tested on tens of thousands of students of all backgrounds. Mathematical Circles: Russian Experience is exactly what you need. Most of the topics in this book, including parity, combinatorics, basic number theory, the pigeon hole principle, proof by induction, invariants, and inequalities often appear in math competitions, but the goal of this book is not narrowly focused on competition preparation. In some ways that would be just as bad as “teaching to the test.” The ultimate aim of Mathematical Circles (Russian Experience) is to start with quite simple problems that anyone can solve and then, in bite-size increments, increase the difficulty of the problems until a whole branch of mathematics has been introduced. The selection of the problems, the detailed guide for teachers, and the depth of coverage makes this book stand out among other great problem solving books. It is geared towards middle school and high school teachers who would like to enrich the standard school curriculum, but even regular students who don’t attend math clubs and competitions would benefit. In fact, we would recommend this book as the best form of standardized test preparation. Anyone who can solve at least a few of the problems in each of the sections of the book is, in our experience, ready to tackle the hardest SAT problem. As is typical for Russian math literature there are a few extra fun topics included, such as strategy games, that one rarely encounters in English-language books. If you’re looking for one book that contains a complete problem solving curriculum that has stood the test of time, this is a good place to start.

## Art of Problem Solving Classes

We prefer to review high quality online courses that are free, but for the Art of Problem Solving (AOPS) classes we need to make an exception. The Internet is flooded with free courses taught by first-rate instructors, but with scale comes an often overlooked problem. A popular free online course that has an enrollment in the thousands cannot provide the kind of student-teacher interaction that is vital for learning. Art of Problem Solving math classes are relatively inexpensive, but because of limited enrollment, students can communicate with their instructors in real-time. Unlike massive open online courses, Art of Problem Solving classes are built on fairly basic technology that does not include audio or video, but this does not take away from the learning experience because students receive individual attention and are required to do in-class work that is immediately available for their instructors to review. The other defining aspect of these classes is the quality of the mathematical content. Unlike various other online resources, AOPS focuses on sometimes difficult yet engaging problems (after all, problem solving is in their name) instead of simple textbook exercises. For advanced or motivated students in grades 5-12 who do not have access to local high quality math instruction and for homeschoolers, these classes are worth looking into.