The Path of Mathematics

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From my experience, there are several ways to look for research experience: The approach I use, ask professors directly.  Check department website for research opportunity. Some school have programs helping students to do research. Join those programs if possible. I will use myself as an example to expand a little bit on the first approach. Find something that interest you. You don't have to understand it super well, because the chances are you couldn't. But do some research on this topic is important. Learn professors' field of study and interests. Once you get in the master program, it's time to start looking for research opportunities. You can ask classmates/professors to collect some information.  Talk to the professors you want to work with. The key is to spread the words and let others know you want to do research. Even if some professors don't need a student at the moment, they may refer you to other professors, or remember you next semester when they want so...

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)