 Welcome back to the session on latex. In this session, we will learn two types at mathematics in latex. Tech and latex became very popular because of the ease with which one can write mathematics. In fact, it is the greatest strength of latex. There is no need to include any package if your document has basic mathematical expressions. But for some complex ones, you can include AMS math or math tools for more complex ones. Note that AMS math is included in math tools. So, if you include math tools in your document, you need not include AMS math. One needs to write mathematics between the dollar sign or the slash box bracket signs. Well, let us start with simple mathematics like 2 square plus 2 square is equal to 8, 4th root of 4096 etcetera. While you write a document and when it comes to typesetting mathematics, it would be a good practice to first write the expression on a piece of paper or a book and then write the commands. This way, you shall not only make fewer mistakes, but will also be able to write faster and efficiently. Let us try these out. I have some text already written here and I have included the AMS math package. Now, let us write dollar to indicate that there is some mathematics over here. Let us try our first mathematical expression 2 raise to 2 plus 2 raise to 2 equal to 8 and in another dollar 2 times which is nothing but in 2 to equal to 4. Let us build and run. As you can see, this expression was typeset along with the regular text. So, there are two ways of typesetting mathematics. The first is to display inline that is along with the text which we just did. The next is to display it on a separate line in a larger font size. The syntax is slash box bracket and slash box bracket again. So, now, let us type another expression slash cos square slash theta plus slash sin square slash theta equal to 1. Build and run. There you go. We have this expression on an x line center. Now, let us try another example which has some set theory symbols. For example, the union of two sets A and B is denoted as in dollar A cup B equal to in curly brace. So, we escape it by the slash character and we write x in A or x in B. Let us build and run. The union of two sets A and B is denoted as A union B is equal to x lies in A or x lies in B. Well, it looks good, but not great. Notice that the word or has got attached to the word A and x. This needs to be interpreted as normal text whereas, let us has interpreted it as a mathematical expression. To avoid this, we write the command slash text slash text and in curly brace we write on. Now, build and run. Well, we still need some space here. So, we add slash slash. Let us build and run. There you go. This expression is typed set beautifully. Let us go back to our slides. These go through the first link that lists different latex symbols. These have been organized into different categories like Greek, punctuation, etcetera. Now, assume that there is a mathematical expression wherein there is one symbol which you do not know. It would be very difficult for you to search in a pool of mathematical symbols. The second link allows you to draw the symbol and suggest what you might have meant. Let us have a look at it. Let us draw in this box. So, suppose there is some command like this which I do not know. Well, after I finish drawing, I see that there are some suggestions over here on the right which mentions the latex command and the package name if needed. This really helps you out when you are getting accustomed to latex mathematical commands which you need frequently. So, for example, what I meant here was pi. Well, let us try another one. Well, this could either mean delta or you could mean up delta with a package called up Greek, etcetera, etcetera. Let us go back to our slides. Fractions are typed set using the command slash frac and mentioning the numerator and the denominator in the respective curly braces. You can see a list of different fractions type set using latex and its commands. Let us try some out. A good practice is to write the syntax of a command first and then start filling the numbers. So, let us write slash frac and I press enter which gives me the basic syntax. Now, let us fill up the numbers. In the numerator, I write a and in the denominator, I write b. Well, build and run. We have a fraction called a by b which appears over here. Let us extend the example to make it a bit more complex. Instead of denominator b, we have slash another fraction which is b by c which is then multiplied. So, I write times and I write another fraction with the numerator having another fraction called frac d by e and denominator f. And let us say I want to say it is greater than or equal to sorry g e q 1. Let us build and run. So, we have numerator a by denominator b by c into numerator d by e denominator f which is greater than equal to 1. Let us add some random text before this. We are learning fractions and after the mathematics we write which is good. Let us build and run. So, now, we have a text followed by mathematical expression followed by another text. Let us display the same fraction on a different line. So, basically we copy this, we paste it here and instead of dollar we write slash box bracket and we end the slash box bracket over here. Build and run. There you go. So, this is displayed on another line with a larger font size. Let us add one more fraction slash box bracket and over here we write in curly brace. So, we escape it by the slash character and we write in round brackets slash frac a by b and we come here and we say plus in another round bracket we write slash fraction c by d. So, basically what we are saying is a by b plus c by d. Observe that the numbers are displayed in a larger font size, but the brackets are still very small. To address this issue let us go back to our slides. Well, the syntax for varying the size of the braces is a style and the appropriate brace. The styles are b i g g with a capital B, b i g g with a small b big with capital B and big with small b. As you can see this particular expression is written using this command. Let us modify the example that we just created. So, we write slash b i g g for curly brace for round bracket we write slash b i g g in small. We end it using slash b i g g. We start the round bracket using slash b i g g, end it slash b i g g and here end it with slash capital B i g g. Let us build and run. Well, now it looks perfect. Let us go back to our slides. The summation is represented as slash sum followed by an underscore followed by the minimum value in curly brace followed by the raise to character followed by the maximum value in curly brace. Let us try out these two commands. So, I begin my mathematics mode and I write slash sum underscore which goes from i is equal to a to b and g of i equal to 0. Let us have some text that is for b less than a. Let us build and run. So, we have a summation which goes from i is equal to a to b, g of i is equal to 0 for b is less than a. Let us write one more. In box brackets we write slash sum which goes from i is equal to 1 raise to n where i is equal to a fraction n into n plus 1 and denominator is 2. Let us build and run. There you go. So, this is how we type set summation as well. With the end of this session, we can now type set simple mathematical expressions, fractions, summation and vary the size of the brace. We can also find out a symbol which we do not know. Thank you. Have a nice day.