Many students I worked with tend to think that many notions they learn in mathematics are just that, notions and have little or no utility in real life situations.
So, I like to give them problems, where they need first to derive their own equation or system of equations and then solve it.
Here is a funny problem that never fails to surprise students: at first they feel lost for it sounds...
If you are like me and share an interest in your family tree, you might have noticed that family trees get larger and larger with every generation. A legitimate question is how big can they really get. The answer is that they can get really big. Here is
a simple example.
Let's compute how many ancestors each of us has had over a period of 1,000 years.
I will assume that every generation...
In answering questions for the quantitative section of the GRE, it is paramount to be able to use smart approaches to avoid brute force calculations and to use as little time as possible that can be spared for other questions. The use of calculators, while
not forbidden, should be limited to the bare essentials, i.e. almost never. Here is an interesting example to explain my point: