The Path of Mathematics

Desmos is an online graphing tool, sometimes I also use it as a calculator. Here are some useful tips for beginner: Desmos uses x as the independent variable. When making a graph, you don't need to type "y=", simply type the right hand side.  For example, You can graph multiple functions at the same time, or hide some of them. Simply click on the circle to the left of the function. If you want to change color, you can find the setting on the top of left panel. By register for an free account, you can save your graphs and use it later. You can also download the graph as a PNG, using "export image" on the right panel. Have fun and mess around!

 

In the previous page I mentioned some common operations. It may seems a lot, but the operations are really connected with each other: They often work in pairs. Think of one operations "do" something to the number, then there will be another operation "undo" the work. For example, subtraction "undo" addition, so if you add 3 then subtract 3, essentially you did nothing. Those pairs are called " inverse operation " of each other. Addition and Subtraction are inverse operations Multiplication and Division are inverse operations Power and Root are inverse operations Exponential and Logarithm are inverse operations... Some operations are more "compact" way of doing the other operations: Multiplication is a compact way of doing addition, say to add 2 five times, you can either do addition: 2+2+2+2+2, or you can simply do 2*5. Now, which operations will you choose when you need to add 2 a hundred times? Power is a compact way of doing multipli...

After knowing the numbers, we want to play around with them, such as add, subtract, multiply, divide, those actions are called "operations".  Some basic operations: Addition Subtraction Multiplication  Division Some more operations: Power     Root       Exponential Logarithm Some advanced operations: Factorial    Integral     (in Calculus) Differentiate   (in Calculus) Power and Root are big families, the "square" and "cube" you are familiar with are really special case of power. (Square is power of 2, and cube is power of 3). Similarly, square root and cube root are special case of root. More stories of operation see the Intro to operation(2)