 Hello and welcome to the third of a series of screencasts on LaTeX, the scientific document typesetting system. In this video, we're going to expand on the simple hello world document you made in typeset in the second video to add some mathematics. We're going to learn about how to typeset mathematics inline or alongside text, how to typeset math displayed or set off from text, how to typeset exponents and subscripts, how to use curly braces for larger arguments and exponents and subscripts, and then do a simple case study where we typeset the statement of the Pythagorean theorem. So here's the hello world document we made in the last video. Let's add on a separate line a very simple equation, 3x plus 2 equals 7. We'll actually set this up with some text. I'd like to put the equation alongside my text here, which we call inline math. To change from text entry to inline mathematics entry, we type a dollar sign, then the equation we want, then close the dollar sign. The dollar signs mark the beginning and end of inline math entries. Now typeset it and we see that the math comes up and it is visibly different than the text around it. Another way to enter in math is in displayed mode in which the math will be on its own separate line and centered. Let's set up a new equation. Then we're going to type two dollar signs with no space in between. Then our math, then close the dollar signs. And for effect, let's enter in some more text underneath. When I compile, I see that the new equation has been put on its own line and centered, setting it off from the text around it. Let's suppose we wanted to add squares to all three of the variables above. To add an exponent, just use the up arrow key, which is shift and then six, then compile. And we see that the exponent has been added. That also works in inline mode. For a subscript, for example, if I wanted to add a sub i to the variable in the first equation, use the underscore character, then i, then compile. We can even add both superscripts and subscripts to the same variables. If I were to use a larger exponent, say, to the tenth power and compile, notice that the one is exponentiated but not the zero. So to use exponents or subscripts that involve arguments larger than one digit or character, just encase the argument and curly braces as if it were a latex command, and then compile. Let's end by type setting the Pythagorean theorem, which has a nice mix of text, plane math, and exponents, and displayed math. First, I'll type out the start of the theorem. Notice that I am blending math and text together inline here. Now I'll type out the conclusion of the theorem in displayed mode, since it's important and needs to stand out. Once I'm done, I compile and there's our Pythagorean theorem. That's it for now. In the next video, we'll look at some more mathematical commands for latex such as roots, fractions, and Greek letters. See you there.