Mathematicians have always been fascinated by numbers. One of the most famous problems is Fermat’s Last Theorem that, if n≥3, the equation xn+yn=zn has no solutions with x, y, z all nonzero integers. An older problem is to show that one cannot construct a line of length 3√2 with ruler and compass, starting with just a unit length.
Often the solution to a problem will lie outside the confines within which the problem has been posed, and theories must be constructed in order to prove a claim. This is true here, and you will see the second problem solved in your course; the first is far too deep and was famously solved by Andrew Wiles.
These are questions in pure mathematics. In applied mathematics we use mathematical concepts to explain phenomena that occur in the real world. For example, you can learn how a leopard gets its spots, examine the intricacies of quantum theory and relativity, or study the mathematics of stock markets.