 We will continue with figures. So, let us we had skipped a few slides because they were going out of the margins. Let us go back to this. Let us go back to the slide about the figures because the font sizes were made larger it was going out of the page and in beamer in which the slides have been made that was on retake only. There it does not automatically go from this page to next page. So, we will say these environments are in some sense not so easily flexible between each other. So, in the figure environment there is a p for top of the page, b for bottom of the page, p there is a option p for separate page for floats. So, we do not want two floats to come on the same page. H for here wherever the command has appeared in the source in the tech file it will come there it will maintain the same sequence. An exclamation mark for override latex internal parameters the internal parameters are for good position, but you override them. Why? Because you might in your discretion decide that it has to be here a hook or crook in that sense you are overriding latex internal parameters for good positioning. So, one can also give captions to the figure one can give it labels. You can give a label to a figure or a table and you can refer to it. In that sense latex is a markup language. You can do a lot of cross referencing between figures between tables between sections chapters. In fact perhaps if you use pdf latex it also becomes clickable. Let us have a look. Let us look at this figure. We have to latex it two times. So, for example, so right now what you see here you can do a good amount of cross referencing by making another number to come at a specified place. Now, this is this happens to be a reference. So, whatever has come in square brackets that is by convention the reference in a bibliography and perhaps you will like that when you click on this you will go to that reference directly. You might want that the pdf file has internal links not just that it shows number 2 here and the number 2 there is indeed that particular reference, but when you click on this it should go there. These things are also possible using a package called hyperref. If we had done in the very start use package I do not know if it is there on this computer, but let us quickly latex it and see. So, it is not there that is why it is giving an error, but if you use that particular package if you use this package which I have commented out because on this particular computer it is not there. If you use that then you can also click on a particular reference and go to where it is defined to the label. In that sense not just for visibility purposes even you can actually click inside and interlink these in that sense it is a markup language. So, let us go to the next slide. The figures like tables are all floats they will be auto numbered if you put a caption then they will also give a number and the caption will appear there table is for the same purpose. We already saw using tabular we did not put a table begin table end table environment around it. In that sense I think it is it was not a float it would appear wherever we put it, but for bigger tables we also have to allow it to be a float we also might want to give a caption also the caption should come in a list of tables in the first or second third page of a report. So, that is done by specifying begin table end table environment and specifying again T for top B for bottom C for center that is when you can give a caption label etcetera. The table will then have a number let us go back to our present slide and see present document and see that the table does not have a number the tabular environment tabular has made this into a table, but there was no place where we could give the table a name we could not give a table number. So, why do not we specify begin table this begin tabular end tabular we have put inside a begin and end table now it becomes a float you can specify caption here tables caption here you also give a label tab label now it is given a label it is given a table caption here it is given a number to that table as a table caption come above the table only because we put the caption above let us see that is something to be the table environment let us put it below here the same thing can be verified for a figure also now the table caption has come below the best of my understanding I think it is a convention to put the for tables to put the caption above and for figures to put the caption below. So, wherever you put the slash caption that table caption will come there in any case it will get that label that number that label will get that number and you can also cross reference that. So, let us go to the next slide we can get the list of tables list of figures by just this command wherever you put it the table of list of tables will get generated and we put there in the final document. Now, coming to this important topic called type setting math many of the equations many of the questions on chat ICR about this. So, any mathematical symbol mathematical mode is between two dollar signs. So, dollar sign if you use the first dollar sign that comes is the beginning of a math mode the second dollar sign is where it ends in the middle only you are allowed to use various math symbols. You can also use slash round bracket slash round bracket first one open second one close for starting math mode and ending math mode respectively. So, this is one other way to go into math mode, but dollar is easier in my opinion. So, this is what is very useful for having mathematical symbols in line in line what is in line about it in regular text while you are reading it will just continue in that line it will not open it in a in a new line called equation it will continue we will see the difference of these both, but many symbols are available by using AMS math AMS stands for American Mathematical Society they have plenty of symbols plenty of fonts and those all are available as used by using the package AMS math. So, we can see a quick demo about this we can also see matrices B matrix is the default for defining a matrix B matrix will very similar to a tableau environment columns are separated by ampersand and double line the slash for starting the next row instead of the B matrix and other matrices what is the exact difference we will see using an example. So, let us come back to this this is example of math mode alpha x cube. So, all these alpha beta are all just straight forward you can type a slash alpha and you can be sure that it will be alpha equal to 89 yeah if you do this it is also let us compile this and see what happens. So, it has created this alpha x cube beta superscript I said super hat for superscript underscore for subscript alpha beta equal to 89 how much spacing to leave here these are all default in math mode. If you extra spaces here in math mode spacing is extremely different yeah please note as soon as you are between in the math mode you can go into math mode by a variety of ways yeah one of the ways is to put it between two dollar signs they are the same we can see that by just repeating this and replacing the dollar signs by open round bracket and close round bracket preceded with a slash it will turn out to be the same yeah here notice that all these spaces we put did not cause any space here in the math mode spaces are at different ball game yeah always note inside the math mode spaces are always ignored keeping that in mind if you want a space you have to use a different mechanism yeah why because to make mathematical equations readable in plain tech in just tech you have to leave enough spaces and you do not want it actually to affect the equations. So, let us see what is the difference between in line. So, these both are in line if you remove this double slash it will come in line, but you might also want this to be an equation that time you will use square bracket yeah if you enclose it between square brackets then it will become a separate equation notice that this has got repeated two times because I removed the double slash and that is why it is in line yeah, but as soon as you encounter it between square brackets slash that is another way of going to math mode these are all math mode because it is math mode q raise to 3 works raise to 3 works here, here it works here, it works here not just that alpha beta these are all symbols for the math mode only yeah if you do not put if you write a slash alpha and do not put a math mode you will not get alpha you will have an error, but then what is in line about this is continuation of text you can have some text after this also unlike this where this is equation only that this this equation does not have a number how to put a equation how to put a number to this equation that also we will see, but I hope everybody appreciates the difference between in line equation in line math mode and math mode that is completely a line. So, let us instead of this you can also say begin equation this will make it into a these are two separate things I am doing together we have some continuation of text but then when you begin equation then you have suddenly become you have come you have gone to math mode, but not in line math mode yeah it is a separate line not because there is a empty line here you can remove this line if you if you doubt that yeah. So, now let us see what happens this is the example of math mode this continuation of text here that is a significance of in line then we have said begin equation end equation that is why this has come as separate line of course it came as separate line even when you enclose this between square brackets, but that time the number had not come equation numbers has equation numbers come because you use begin equation end equation and by convention equation numbers are put between round brackets even when you refer to them you have to put them between round brackets we let us give again you can give a label to this equation 1 yeah instead of 1 you can also call it 100 and 1100 you do not have to choose the right number and then you can refer to this number suppose equation yeah equation what have we done we have given it a label and we have referred to that label here that number 1 has come we gave the label only now equation was there from before, but the label we gave only now and of course immediately it does not know what number to put there because first time it was compiling it had the number had not it got generated to that label when you let take it a second time then the numbers have come correctly yeah. So, whenever you see question marks that is because some labels have been redefined or were not defined before the first time second time they will indeed come in to the document how do I have multiple equations begin equation as I said you can always disable the numbers by using star of course in that case you should not be putting labels, but you can disable the number by putting a star you already saw one method by which you will have it in equation mode sorry not here if you put a star here then it will disable the numbers there is also a way of disabling the numbers is number 1 has not come here, but then if that label has not got a number still you are referring to it then some question marks are inevitable yeah if you do not want the number you had better not be giving a label the fact that you gave a label means you require that number. So, whenever you are going to refer to that particular label it will give a question mark then you should not be putting a star, but we are more concerned with more number of equations, equation array you can have new more equation another frac phi times slash frac, frac for fraction beta gamma all these are extremely readable for alpha you always will type it as a l p h a alpha yeah equal to 56, 56 subscript it says begin equation some there is some spelling mistake in equation array please ensure that please ensure that when you latex it should always come back to the prompt here it has two equations 1 and 2 yeah equation array and notice that we did not put this in curly bracket that is the only 5 has gone as a subscript 6 has not gone as a subscript this is also created fractions phi by 6 was one fraction beta by gamma was another fraction this question mark is coming because we are still referring to a label which is not there anymore or may be there it was there, but we did not compile twice we can do that now. Now, that equation has come that number the first label referred to this equation if you want this number 2 you have to use separate label now yeah the first one has already come label second equation please give meaningful labels the good practice to do that you can give you can so the second label can also be referred somewhere inside this you can refer to when you have multiple equations inside multiple lines of equation that is when you will use e q n array equation array that time you can refer to different numbers this is where often you might say you want multiple lines of equation, but you want to give a you want to give a number to any one of them not to all or may be there is one line one line of equation to which you do not want a number yeah there might if you do not want for any of them of course you can just do star to the whole thing you can you star here can you star here the numbers is disabled for everything, but if you do not want only for the second one number is generated whether you give a label or not because it slash no number slash no number means that equation will not get a number yeah if you are not giving that equation number better do not even refer to that yeah so now the second one does not have a number, but each line is still an equation I hope this answers the particular question that had come on chat somebody said please show the code for a few seconds after showing the output it will it will be hard for us to do this slides are all available and it is all there inside the slide yeah it would take too much time to and what would you work after the sessions if you wait for so long with the code visible yeah we want to go a little fast about this and the coordinators will appreciate that we finish the entire latex in one and a half hours during the coordinators workshop we are already going extremely slow to go slower is not a good idea idea of latex is when you need it you look up for the net for information on the net let us see how to build a matrix that is important as it says you will use the matrix but matrix is built only in the math mode so you will say a equal to begin the matrix and the matrix yeah whether you leave for readability it is best to put them on separate lines somebody said that they are not getting the correct output for frac you see frac we will do in little more detail for now slash frac frac request two arguments first argument is a numerator second argument is a denominator each argument should be between curly brackets like any arguments to a command in latex let us come back to begin matrix n matrix so here it it is understood the number of rows number of columns is decided automatically by the number of ampersands just six alpha six beta yeah to say that these are separate columns you have to again separate them with ampersands now for new row double line new one might be gamma frac 4 by 5 4 by 5 is two arguments to the command frac first one is 4 second is 5 e pi yeah this is how you build a matrix let us compile this and see also since you started the math mode it was end the math mode using a dollar so this is how this we have defined we forgot to put a ampersand here that is why it has put 4 by 5 times e all inside the same entry the b matrix is what decides that this should be square brackets yeah square brackets is getting decided by this one ampersand was less that is why the last one has been left blank not a good practice to do this let's correct this ampersand will what is what tells that it's the next column now here I put ampersand between 4 by 5 and e and hence e has got shifted to the next column and hence pi is the last one so pi if you read it as pi pi slash pi is a symbol alpha beta gamma notice that constructing a matrix is extremely easy it was never easier one should note of course this is in line yeah it is in line because we use a dollar symbol one can have continuation continuation of text here yeah perhaps some text already here we have put some text before the dollar sign they put some text at the end of the dollar sign right we have to save the file will come as continuation for matrices this is not good but at least you will notice that more space has been left between consecutive lines because this is this coming a little low yeah so if you want it to be instead of dollar you can put other again the same thing applies yeah how did this become a separate line in itself it became a separate line instead of in line because we replace the dollar with this and this why this because we didn't want a equation number if you wanted a equation number you will use begin equation and equation or begin equation array and equation array equation array can also be used when you have any one equation disable the number there you can just put a star yeah that that's easier suddenly if you if you decide that you don't want the numbers star is the easiest rather than replacing begin equation by slash square bracket okay let's go back to the slides so as I said B matrix is what decides that should be a square bracket opening a square bracket closing for the equation itself you might want to make a matrix without these square brackets yeah that time you will just use begin matrix P matrix for round bracket capital B in the B matrix for curly brackets just vertical for determinant for example we just use vertical line to slash yeah I hope this is visible so these are the different begin instead of begin B matrix we can use different things okay so we go to the next slide subscripts and superscripts we have already seen you can have subscript of subscript superscript of superscript you can have a subscript of superscript plenty of this is possible there is no end there is no limit yeah like somebody has noted for enumerate there you can do only four or five but for success superscript there is no end any number is okay the subscript superscript have the obvious meaning when you use it with some commands like some integration whenever you do summation you are always summing from summing from something up to something when you are integrating you are integrating from something up to something that time the lower and upper limits are also specified using this symbols upper limit by superscript lower limit by underscore yeah similarly for integration the slash sum for summation sign slash int for integral that time these symbols have that obvious meaning from where up to where summation from where up to summation till where integral from where up to where yeah display equations are the other type of displaying math you can also display equations ms math has a number of environments yeah there are some small certain differences you already saw this if you don't put the star you get the numbers in equation array you can also have some alignment yeah we saw a place where there was only one entry in each in each equation but one can also have some ampersands inside the equation array that I am that is very useful if you have multiple equations and you want all the equality signs to be aligned yeah often we do some big set of calculations and we say equal to this the next line again equal to the next line that is when you also want some alignment that I am equation array is the right thing to do fractions we already saw fraction is a command that takes two arguments first one is numerator second one is denominator the numerator denominator themselves can be fractions yeah each numerator in case of numerator you just put superscript subscript whatever is required square root we just put square root sign above above something if inside the square root if you want some particular symbol then you can use a option argument called n yeah this is something we can see again here square root of x so it is a good idea to say in math mode not x because this is math mode it should be in dollar sign otherwise there will be an error or if you want the two of course that is default but you might want to say it yeah after square root we know is cube root of x is therefore each we have so many we cannot keep inventing different commands right please read you can also make this visible along with the PDF file please hold on this is our this is what we typed and the output has come here on the screen square root of x notice that because we put in between dollars this x has come like this this is what x would come without math mode yeah so it is always a good idea that if you are using the x in math mode then you should write it between dollar signs whenever you require it that is when it will put this x yeah and not not just this x without the dollar signs without the dollar signs it will give a regular Roman font x is by square root of x whether if it is if it is only one letter under the square root sign then you can choose to not put the square curly brackets yeah this is just like some other we have text TTE I think there also you do not need the square curly brackets if there is only one letter for which you want the square root sign if there are many then you have to put it in curly brackets yeah so notice that these both have the same effect only because we did not use the curly brackets and there was only one letter if you want the number 2 here then you have to give that as an option argument here yeah and finally if you want not to put some other n then you give it as an option argument to square root of x option arguments will come in square brackets so surds so this having a square root of third root fourth root of some complicated thing is also called surd something that we all studied really long ago all Greek letters alpha beta extremely readable capital alpha capital beta just make the a b capital gamma pi for example pi we require for product for product just like summation is sigma capital sigma like that product we need capital pi inside math if you want spaces I said there is a different complication so for little space slash comma slash colon for little space for more space semicolon quad quad then double queue really much more space if you want two equations on the same line inside equation mode negative space was a possible that is very important slash exclamation mark yeah I didn't know in fact that there are this other spelt out these commands also but these are the shortcuts that one uses you can also use slash exclamation mark 3 4 times one after another then it will become more and more negative spaces yeah this this sort of complete math mode the strength of latex is that math mode math mode is extremely easy really complex complex big matrices sub matrices they all can be specified in a very easy way very easy readable way the next topic is bibliography bibliography also works fairly similar to lists only that bibliography now has there are different ways of bibliography I triple is I triple uses two three styles different companies use different ones because of which bibliography is a special list that has different way of calling it also in bibliography sometimes you want to cite you want to cite a particular reference you want to also put the you also want to at that time put the page number where this particular statement occurs in a book yeah so these are things that are extra required in bibliography which are not required for general label refs the bibliography is the environment that provides a clean and simple way to add bibliography to latex documents they then begin the bibliography and the bibliography is allowed to have maximum the width of the label don't have you don't you please don't worry about the maximum width of the label it's relevant for only certain types of certain styles each item in the bibliography similar to an item in a list we already saw begin by term label this label is an optional thing that is not relevant for general list they might have and the name this particular name is what we will refer to in the content in the document bibliography typically comes at the end wherever you write the bibliography will come there but we want to refer to let's say the fifth item in bibliography to be my term whatever label name sorry whatever name we have here that name we will say slash site name yeah site for citation you cite that particular name in the content of in the document yeah that is how you will get the number of this bi-term inside this number if you use a different style file then you can get the first letters of the authors and different ways of doing this let's stick to numbers for the timing again like any typical label ref combination bi-by-term site combination also requires you to compile twice first time the numbers are generated and second time they are all available for citing in the text of the document we can see an example about this before we go to the very important topic about beamer so let's go back to we'll remove unnecessary things here here we have something called site pi lab this is the name we have given nobody will know what item what name you are given to this particular site let us go to where the pile up has been called yeah look in bi-by-term there is one bi-by-term called pi lab it doesn't have any optional argument there is no label this pi lab is what this entire thing will be called this information will be called as pi lab when you cite it in the text then whatever number gets allotted to this particular bi-by-term that number will appear there how did it know that it should put numbers yeah so some bibliography style can be specified if you don't want numbers numbers happens to be the default in article if you don't want this if you want some other way then you can also choose bibliography style by using the command bibliography style let's compile this so I am not doing this slowly because there is enough in this tech file but we are interested in references yeah notice that bi-by-term pi lab has occurred the second year yeah it says there is some particular style of putting these references or name of the author then the title of the title of the taper if it is a journal then the journal name comes in italics then the volume of the journal the issue number the pages some people also put the month and the month explicitly and this is some DOI that may or may not be required to be put yeah if you use bibliography then automatically this reference word has got generated it's put there it might come into the table of content also that depends on whether you're using book or report if it doesn't come you can always put it by using add to contents line command so let us this number two could easily become number three if you add another reference in the middle yeah so that number two should be called very carefully using using site command so let us look where we had called it so I only missed it yeah it happened to be here inside the appendix this number two has come because we gave bi-by-term that particular bi-by-term where we want to cite this as a particular name and we cited the same name yeah what name you choose is not important yeah some other name because this particular item if you use this some other name you can just as long as you call the same one number will be the same yeah just some internal referencing cross referencing so we gave a new name and the first time compiling it has given a question mark here let's compile again now the number two has come yeah why number two come here because it happened to be the second one in the bibliography list this happens to be number three let us see what this three is there is a third one another site for I pie it is good to give some suggestive names some other name extremely bad way of number labeling bad way of choosing names for either bi-by-term or labels yeah one should give very suggestive names and the first name was pile up and that's indeed a good name to give let us see what is this site I pie site I pie name happens to be here here bi-by-term name yeah so this is how one uses bibliography and after this of course there is a end document so that completes bibliography it was extremely important how to cite more than one reference in the same line yeah somebody is asked how to cite multiple ones let us see this so here you can easily type same line I think he means inside the same square bracket same line is of course possible because that would not be a problem anyway some other name inside the same square bracket you can put comma and put these other things it will come in the same sequence here three has come first and then two has come yeah this particular space it has left you do not have to say that somebody has asked how to link citation link I guess the question is hyperlink you link this and automatically it will get connected to the web may be for example DOI is also a permanent link you might want the question perhaps how to link the citation is also very much possible you have to again you have to use hyperref in the PDF file if you want to link one to another within the same PDF file or to the web you have to use hyperref package this is what I typed earlier before but that is not part of this course last important topic we have to cover is to use the beamer how to make presentations using how to make presentations using beamer so hyperref package will also help in when you click a citation if you go to the reference it will also put where all which all pages the citation has been referred to these are all possible okay now let's start this important topic called beamer beamer is a separate package that runs on latex yeah if you have a presentation again to compile it you will use PDF latex use beamer why use beamer now why not I you have written the entire document in latex and now will you shift to open office no why because all your math all your latex code is directly usable in beamer yeah if you if you have written the document if you have written a report in latex already now you have to make a presentation about that report it is best to do it in something that is very well compatible with beamer with with latex and beamer is an example there are others also which are used for making packages beamer is a recent relatively recent phenomena there used to be prosper there is to be tech power there used to be something called slide tech also overlays slide tech various have been there beamer is by far the most flexible the most powerful in my opinion off late it's recommend that you start with one of the beamer templates yeah let's look at speaker introduction template document class it's not report it's not proceedings proc it is not article it's not book it beamer now so it will automatically look for beamer packages yeah so please ensure that you install beamer packages before you try to do PDF latex beamer also doesn't come the default one so beamer the content is divided into slides that is a important difference and material cannot spill from one slide to another in a document you want the material to all be written up and automatically it will go from one page to another will continue from one page to another and that is a for tables and figures you have to do something about it but for beamer all the content is automatically is manually divided into slides beamer will not do this automatically for you second is you have to use some theme theme meaning what for example look at the slides that we are using on the top there is some name of this topic here there's something else here presentation beamer yeah notice below that there is a author name here please look at this mouse this pointer there also some topic the topic the title of this presentation there's something about page numbers here inside this you will notice that these are all actually hyperlinks in the PDF file these are all hyperlinks what is seen here one can go to next page one can rotate the one can zoom from within the PDF file so these possibilities are there because of a particular theme being used in beamer so use theme is used to do about that as the most common is Warsaw there are several themes we will the easiest that we can do is will give you the tech file for our slides yeah you can have a look at that is also been made in beamer only I can also use some color themes important is begin frame title of the frame subtitle if you want two things to come there and finally the end frame whatever comes between these is a content yeah if this particular slide contains something that's like verbatim LST listing then there's something called fragile yeah I recommend that don't worry about fragile wherever it is said you put the fragile just put it it is harmless to put fragile in any case what is this fragile exactly see these are all environments LST listing is an environment verbatim is an environment begin equation end equation all these are different types of environments and there is generally speaking some compatibility problems between these environments and in such a case you have to resolve it and that is when you specify something called fragile yeah so it is best to just call it fragile nothing will go wrong for all basic things you can also you can also put content and make it come little by little rather than all of it come together you can make it come in bits and pieces you can make it come one particular sentence comes in this slide next time you press pause it will you press the space button next slide it will not be there yes all this is possible by using slash pause these are all called overlays so what all is achievable in beamer there is no end to it like the complete capability is not going to be easily easily utilized by us people yeah so I only showed some examples of what was done in beamer in the morning the set of these slides are also are done in beamer only yeah so this completes all the all the content somebody's question on chat is the beamer output does not display numbers for figures tables or references to the best of me knowledge it puts figures numbers but maybe the fragile option is required to be put so in beamer one can very comfortably put equations figures tables it is also true that in a presentation there are less number of tables less number of figures cross referencing is not so relevant here because people will not do this by themselves you are always going to be presenting it to some extent some things are not working is possible but I have not heard of this problem before are there any questions we can take up questions both on chat and using the hand raised button there were also some question while you ask the questions let me answer the questions that were on chat somebody has asked that when you are making a figure sometime we have a figure 1.1 ABC yeah so one can have multiple figures one can have figures kept beside each other that is possible that's a little advanced thing but we are not doing that in the course but I have done this myself it is not difficult another thing is you can have inside a big table you can have one particular entry itself a table array array is also very useful for this begin array end array can help you achieve many of these things do you have a somebody asked do we have a spelling facility of spelling check in content writing somebody has asked can you check the spelling of what content you are writing so this is something the editor provides yeah I use the WIM editor and the WIM editor allows you to show wrong spellings correct the spelling include it into one's own dictionary personal dictionary please note that this making the PDF file has been split into three separate things one is content is put in is going to be put in using a editor plain text editor then there is a PDF later command that takes the tech file and makes a PDF file out of it and then the PDF file will be viewed by using a document viewer yeah the fact that these three things are separate is really a big advantage yeah as I said all this integrated development editors cannot cannot reach that advantage so editor is the one that will provide you the spelling check facility so please show us one slide presentation using beamer so the entire this presentation tech file is what we will make available yeah I think that should be more than enough that's plenty of pages 53 pages to be precise because at the bottom of the slide it says 53 somebody has said if there are multiple references many if there are many references and you want to go to multiple slides then beamer will not do it yeah because unlike dog unlike report article these floats are a problem you have to split it where you think and start it on another one but table table also I said cannot be split across pages long table begin long table is the one to be used for making a table continue from one page to another especially if you have a table that doesn't fit on a full a full page at all so I think I've answered all the questions on chat that have been asked on chat so the question was what is the difference between site and ref so site is to be used only for bibliography that is where the label comes as bibbyterm yeah so they are like a pair the label ref is one pair of one for defining the label rather for referring to it like that bibbyterm and site again form a pair bibbyterm will define the name and site will site the name yeah so in bibliography the bibliography that is first of all a list that is has to be very versatile because different different formats are there some people want the site to come in the sequence in which you cited some other publishing agencies want some first letters of authors to come because of these differences they have provided this bibliography style the bibliography is an environment that is not label ref but it is bib item site yeah so in the context of bibliography bib item and site is what you have to remember and it works very similar to label and ref which you will use for all other counters somebody has asked how do how do you place a block of text next to a picture inside inside inside a presentation you typically want to have a picture have some text beside it also I showed some examples of a presentation where you had blocks of text between beside each other they were like individual pages mini page can help you do this but in beamer you can also use begin columns and you can have left side column right side column you can specify the column where one of the columns and can actually be a picture so more more example about this in beamer in slides is hard for us we can put up some example tech files on moodle so that you can compile them yourself ensure that use package beamer package beamer package has already been installed can compile it yourself and we will give you some very simple templates from the template itself you can guess what's going on yeah if there are no more questions we should stop now