Welcome back to the lectures on the principles of quantum mechanics from the department of chemistry IIT Madras. This is part of the course that I have been offering to our master students. The course contains some mathematical preliminaries which we are currently looking at and today and possibly the next one or two lectures we will look at an important area of mathematics that has been employed in quantum mechanics very thoroughly in the beginning namely differential equations. The Schrodinger equation was proposed initially as a second order differential equation in coordinates and a first order differential equation in time. Differential equations have been well known the theory of functions and solutions of mathematical equations have been studied for more than 200 years earlier and therefore there is a rich history you will not look into any of that and nor are we going to look at even formal aspects of the differential equations that people look at in quantum mechanics namely this term Louisville theory etcetera. I mean it will be nice to do those things but in this course approaching this from the point of view of the chemistry students who want to learn the principles of quantum mechanics to apply them to molecular systems. We shall look at the differential equations that the students have seen in their physical chemistry courses and then give some general rule of thumb rules of thumb or whatever you call it as directives to solving the simple as basically directional aids to solving the differential equations ok. So, I shall start with this with a few simple differential equations and their solutions I am going to state them and if you are not familiar we I expect that you would have studied them earlier and probably not do not remember it now. So, please go back and look at some of these things from the earlier textbooks but solutions of these equations are important. So, this lecture will contain some descriptions of the following four equations d y of x where y is a function of x is equal to a constant times that function ok. Now in all respects it is also a nice starting point because if you remember d by dx as an operator acting on a function giving you the function back multiplied by a constant that immediately this is an eigenvalue equation ok that is a relation of this to what we talked about so far. Anyway I will see these things later on. The next one is d by dx of y of x plus a constant times y of x is equal to another function d of x. So, the first one is the second one third equation that we will look at is d y of x by dx plus p of x instead of a constant now it is a function of x which multiplies y of x is equal to a different function d prime of x or there is the danger of g prime being a derivative. So, let us call it a h of x some other some other function and the last equation that we shall see is d y by dx is equal to f of x y homogeneous and first order that is all we will see. Some of these things you would have seen in the course on thermodynamics or will be seeing them in the course on thermodynamics when you look at the partial derivatives and the Maxwell's equations. In fact, if I have time I shall just end my lecture with a brief introduction to one of the four Maxwell's equations that we can write down very quickly using these types of methods and it is important for you to remember some of the results while being able to understand the others for you to derive them when you need them ok. So, the first part of this lecture will deal with simple first order differential equations d ok. It is easy when you write d y by dx is equal to a constant times y of x that the answer has to be an exponential because that is the only one which when you take the derivative gives itself with the constant. So, immediately you should see that y of x is a constant times exponential of a x this constant is defined for some arbitrary value of x that is the function of y at a particular value of x is the one that determines the c usually at x is equal to 0 the exponential goes to 1 therefore, y of 0 is equal to c is a an initial condition it is a general solution for that equation. And there are a number of such equations particularly first order chemical kinetics first order rate law in chemical kinetics has a as a negative constant d of the concentration of a substance as a function of time by d t. So, this is the rate of change of the concentration of a of t and when you put in a minus it is a rate of decrease of the concentration of a of t as a function of time because a reacts with some other species or with itself this the first order law is it is given by the fact that it is k times the constant a therefore, you can see that minus k is equal to this a and y is a of t and x is t here. So, the solution for this is obviously a of t is equal to a of 0 which is c here and it is e to the minus k of t ok. So, this is for the kinetics of the reactions a giving products and the rate of change of a being proportional to linearly to the concentration a of t. Nuclear reactions you have seen the decay of particles of the nuclei and with the decay constant lambda often written as lambda. So, you can see that d x the concentration of the radioactive a nucleus d t as lambda times x of t and you see that this also has the solution that x of t is equal to x of 0 times e to the minus lambda t ok. Now, the exponential law is very specific law often found in nature that you would have seen the half life or what is called the rate of change in the concentration to become one half of the initial concentration then one fourth and one eighth and so on. So, if you think of that then x naught of t becoming x naught by 2 at t is equal to t the exponential law implies that x naught by 2 will become x naught by 4 at t is equal to 2 t that is if you put the time let us be careful. So, what we have is x naught of t goes over to x naught by 2 at t plus e and this goes over to x naught by 4 at t plus 2 of t 2 times t and so on. So, it becomes x naught by 2 raised to n at t plus n t ok. There is nothing special about 2 about 2 suppose you have x naught goes over to x naught of 3 t x naught of t divided by 3 at t plus t and x naught t of 3 at that instant of time goes over to x naught t one third of that value at t plus 2 t this is x naught by 9 and so x naught by 9 goes over to x naught by 27 same fraction equal fractions decay in equal amounts of time is the phrase with which you are familiar with the exponential law that is what this is. The fraction need not have to be half the fraction can be any value, but it is a same fraction that disappears at any given interval of time and that homogeneity ensures that it is a first order rate law. So, in fact, the best way to construct to the rate law is to look at that fraction constantly. So, if you say at 1 0 at half at time t at one fourth at time 2 t and one eighth at time 3 t and so on and if you start from here and if you connect to that that is the exponential law ok. Again there is nothing special about the 1 by 2 1 by 3 etcetera any if it is 1 by 3 the curve will be steeper if it is 1 by n it is even steeper, but it is still exponential ok. So, this is the first law and a similar equation that you see in the growth of nuclear magnetization when you put a substance in the NMR cube and then you want to study the nuclear magnetic resonance spectroscopy the growth of the nuclear magnetization in a magnetic field d m z the z component of the magnetic field as a function of time which is 0 when the substance is outside there is no magnetic moment, but the moment you put it in the magnetic field the magnetization grows to a certain value and if that value is m naught the differential equation that this satisfies is by t ok m z ah m naught minus m z of t at a relaxation time constant t is called the relaxation time and in this case of course, it is called the spin lattice relaxation time, but that is not what is important the law that governs the growth of magnetization in a magnetic field is subject to a time constant t and the growth is an exponential growth to a saturation it does not grow forever it is grows to be a saturation value and the saturation value is m naught which is 0 initially at t is equal to 0, but it is in principle m naught only at t is equal to infinity, but you know you can hardly discern the difference between the m naught and m z of t for very long times. So, this is the exponential growth with saturation of course, the solution of this equation is ah an exponential minus t by t now simple equations ah the other chemical kinetics equation which are linear you can think about a plus b giving products and you know that the differential equation for second order is the minus d a by d t is equal to minus d v by d t and if it is proportional to the concentrations of a and b then it is called the second order equation, but it is linear in a linear in b, but this equation is by linear and the solution can be obtained by a simple first simple differentiation process involving separation of variables ok. Also you know that minus d a by d t d t is equal to k of a of t square of course, this does not come into the linear equation that we started with. So, we look at that later ok these are one set of differential equations. The next that we can look at is the first order d with constant coefficients that is typically d y by d x plus a y of x this is the constant coefficient is equal to some g of x. The solution is immediate in the sense that you write the left hand side as a simple function whose derivative gives you that and is equal to g of x then you can immediately integrate the both sides and write the function is equal to integral of g of x ok. But what is this function from looking at this form what you have is d by d x plus a acting on y gives you some other function p of x ok. So, in order to get this as the differential of a function all that we need to do is to multiply the left hand side by multiply both sides by exponential a x where this a is the same as this a same a. So, if you do that then you have e to the a x d by d x of y plus a e to the a x y of x y of x is equal to e to the a x g of x. Now, you can see immediately that this is nothing but d by d x of the product of two functions namely e to the a x y of x. So, this is the function that we talked about this is the d by d x of the function that we have here if you remember is equal to it is not g of x as you see it it is e to the a x d of x ok. Then you can write the integral as essentially integral of e to the a x y of x d x is equal to d by d x sorry integral d by d x of this. If you integrate this you get e to the a x y of x and on this side you have e to the a x prime g of x prime d x prime integrated to the upper limit x and if you do not know the lower limit you can write this as a constant. So, the solution is therefore, y of x is given by e to the minus a x inside the integral x e to the a x prime g of x prime d x prime plus c ok e to the minus x. So, this is a simple general solution for a linearfirst order differential equation with constant coefficients. I have some examples in the some problems in the lecture notes that you will find on the website http colon double slash nptl dot iitm dot ac dot in and these this lecture notes on this contains some of those problems and all I would do is request you to solve the following equations namely d by d x of y of y minus 2 y is equal to 2 x e to the 2 x y of 0 is equal to 1. Then I have another example d y by d x plus y is equal to 5 sin 3 x with no initial conditions these are two examples. Just to tell you that to give you a hint this is nothing, but d by d x times e to the minus 2 x y of x is equal to 2 x. The solution of this is when you integrate both sides you have e to the minus 2 x y of x is equal to the integral of 2 x prime d x prime to x plus a constant and then you can see immediately that y of x is equal to e to the 2 x you bring it to the side times x square plus e to the 2 x times s e ok. So, this is the solution that you have to and this you can verify that it gives you when you say d y by d x minus 2 y it should give you the result namely the original equation 2 x e to the 2 x ok. So, this is easy to verify. So, let me stop here and then start with the next set of first order differential equations. So, the next is general first order linear differential equations. So, the equation has the general form d y by d x plus p of x of y of x is equal to g of x ok. So, to do this exactly we do what we did before namely we want to write this d by d x of a function is equal to a g of x times some function some other quantity function 2 this is function 1 you call it function 1 ok. But, since p of x is itself a function of x we cannot use the e to the a formula, but we have to remember the following identity among the differentials the differential of an exponential or not even that let us just look at this. The differential of an integral which depends on x only as a limit and a function inside g of t d t if you do that the result is g of x. This is only if the limit alone depends on x and the function inside does not depend on x and also only the upper limit depends on upper or lower upper limit depends on x ok. Now therefore, if we have an integral in the exponential with the x p of t d t and if we differentiate this we will get the differential of the exponential will anyway give the exponential back. So, you will get p of t d t ok times the differential of what is there in the exponent and the exponent will give you p of x. So, we have to remember this in order to solve this equation d by dx of d by dx of y plus p of x y is equal to g of x. So, what we do is multiply both sides with the integral with the exponential of integral x to p of t d t you multiply that d by dx y plus p of x y is equal to exponential integral of x p of t d t g of x ok. Now, you know that this whole quantity is d by dx of exponential integral x p of t d t times y of x.  So, the differential of this will give you this particular quantity and the differential of y will give you this quantity and therefore, that is equal to exponential of integral x p of t d t g of x. Now it is easy you integrate both sides with respect to x and the answer that you will get is e to the integral x p of t d t y of x is equal to integral with respect to the limit with the upper limit x e to change all the x's to x prime some other dummy variable x prime p of t d t g of x prime d x prime. So, that all quantities inside do not have any x dependence the x is defined by the limit of the integration upper limit plus a constant when youintegrate this equation you get an arbitrary constant. Therefore, now the solution is y of x as you take this to the other side you have e to the minus integral of x p of t d t multiplying this whole quantity namely integral of x e to the integral x prime p of t d t g of x prime d x prime plus c this is the general solution to linear first order equation general solution integral of x e to the integral of x prime yes g x prime d x prime that is correct ok. So, this is the solution slightly more complicated, but these are allstill simple enough anyway and as examples I would want you to check with one or two ofsimple applications namely do these problems like d y by d x plus 1 by x of y is equal to 3 cos 4 x and the condition is that x has all values greater than 0 that is it is defined only for those. Another example is d y by d x minuslet us see or sorry plus y cos x is equal to 1 by 2 sin 2 x ok. This is easy to solve because you know that 1 by x is the p function remember integral of 1 by x d x to x x prime d x prime to x is log x plus c ok. So, if we have to do we will not worry about the c here. So, if we have to worry about e to the integral of x p of t d t then what we have is e to the integral x 1 by x prime d x prime we have e to the integral sorry e to log x, but of course, exponential and log or inverse of each other. So, it is equal to x. So, you can see immediately that x times d y by d x plus 1 by x y which is given as d sorry yeah d of x y. So, this is equal to d by d y by d x plus y that is that this equation is this one 3 cos 4 x. So, you have it is 3 cos 4 x. So, the solution is of course, x y is equal to integral x 3 cos 4 x prime d x prime plus c and therefore, y of x is equal to 1 by x times integral x 3 cos 4 x prime d x prime plus c ok. So, this is the solution. So, if you do the differential of this you will see that this equation is satisfied namely d y by d x plus 1 by x of y if you do that if you calculate the left the left hand side with the differential and then multiply y with 1 by x you will see that the sum gives you 3 cos 4 x. So, that is a verification. So, this is another form of first order differential equation that we have to remember ok. Then the next one that I will talk about in the next part is the separable equation, but we will stop now and we will continue that in the next part of today's lecture separable first order. So, this section we look at both the separable first order d and homogeneous first order shall do very quickly look at what is relevant to us a lot more can be studied, butlet us look at the simple equation d y by d x is equal to f of x y which can be written as n m of x y plus n of x y d y by d x is equal to 0 ok. So, what f of x y is nothing, but the ratio m by n with the negative sign that is how it is this is minus m x comma y by n x comma y that is what we have written ok. So, specific form now if m of x y is only a function of x and m of x only and n of x y is only a function of y only. Then it is easy to separate this equation because it is m x plus n y d y by d x is equal to 0 and you can immediately solve this as m of x d x is equal to minus n of y d y and. So, you can integrate this into m of x d x prime x is equal to y minus n of y prime d y prime plus of course, a constant that you add as the constant of integration. This is an easier way of solving such equations and a typical example of that is for example, for as d y by d x is equal to x square by 1 minus y square. You can see immediately that this x square is like the m of x and 1 minus y square is like the n of y and. So, the solution for this is immediate namely d y times 1 minus y square minus x square d x is equal to 0 and therefore, when you integrate this and you integrate this you get y minus y cube by 3 minus x cube by 3 is equal to 0 or the equation is x cube minus 3 y plus y cube sorry is equal to a constant the integration constant x cube minus 3 y minus plus y cube is equal to a constant ok. Easy to separate the equations if they have a special form that is called a separable form. Another example that I can give you is the solution of this which I will not do, but I will give you this for you to figure out x square by a square times 3 y square solve. It is easy to solve by this separable first order equation and whenever you have an equation like this d y by d x is equal to a x plus b by c y plus d it is a separable equation ok. We will see them when we come across the second order differential equations in the particle in a 2 dimensional box particle in a 3 dimensional box in the hydrogen atom. In fact, the whole body of the model problems in quantum mechanics uses this separability of the wave functions into products of functions of lesser number of variables. Here we have x and y in real world we may have x y z or we may have polar coordinates like r theta and phi and various things. Therefore, separable equations both first order and second order are extremely important to remember and some manipulatory skills are needed for you to appreciate the method of solution for some of the differential equations in quantum mechanics ok. Now, homogeneous equation first order d there again of the form d y by d x is equal to f of x comma y except that the function x f will not depend on either x or y, but the ratio x by y or y by x as the only clearly dependent quantity ok.  An example is for is this one d y by d x is equal to y square plus 2 x y by x square. Now, it is clear that if you divide the whole thing by x square on the right hand side you have y square by x square plus 2 y by x you see immediately that this is what the function depends on it is y by x whole square. So, it is not dependent on y or x, but the ratio y by x. Therefore, y by x can be treated as a variable and then the differentiation can be transferred to the differentiation of that variable and then once you solve that you can come back to the regular equation because these are forms which will be eventually reduced to what are called the linear first order differential equations the general form constant coefficients or this arbitrary functions that we saw in the first part of this lecture. So, the idea is to reduce somewhat more complicated equation, but specific forms this is homogeneous simply because of this ratio that y by x square y by x etcetera that happen. There is a general way of defining that namely a function f of x y is homogeneous in degree or if if x is replaced by a x a y then this function will be exactly the same as a raise to r times f of x y ok. Such functions are known as functions of homogeneous nature and with the specific degree r ok. If r is 1 it is simply that you have a x or a y and if it is x by y of course, a will cancel out and you can see that it simplifies ok. So, this is the definition of a homogeneous function that we often use in in physical in situations in physical chemistry and an example here and example here is for example for dy by dx is equal to x raise to n plus y raise to n by x raise to n minus y raise to n ok. Now, you can see that if we divide the whole thing by either x or y the numerator and the denominator you will get the ratio y by x or x by y. So, if we divide this by x raise to n you have 1 plus y by x raise to n by 1 minus y by x raise to n. So, the general equation that you write dy by dx is equal to f of x y homogeneous is essentially a function of f y by x ok. Now, how do we solve that? It is very simple. Let u be y by x then y of x is equal to x u of x this is a function of x therefore, dy by dx is equal to x du by dx plus u of x and the this is a function of u ok because we have replaced y by x by u. So, this is the quantity that goes in here ok. Then it is easily separable because you can write this x du by dx is equal to f of u minus u or du by f of u minus u is equal to dx by x ok. So, now, you can integrate both sides this with respect to u and this with respect to x with with appropriate limits as given by the problem and then solve for u x solve for u and once you know the answer u, you know that y of x is nothing but x times u of x ok and you get this once you get this. This is called the homogeneous equation and these are easily separable. Now, as a last example let me just give you the differential equation from thermodynamics and let us look at what are known asexact equations and equations that can be made exact can be made exact with an integrating factor. So, let us solve the equation that we started with namely m x y plus n x y d y by dx is equal to 0. Then suppose there is a psi for this such that m of x y such that m of x y is equal to dou psi by dou x and n of x y is equal to dou psi by dou y. Then you can see that the same equation can be written as dou psi by dou x plus dou psi by dou y which is n times dy by dx is equal to 0 or dou psi by dou x dx plus dou psi by dou y dy is equal to 0 and you recognize that this is nothing but the perfect differential d of psi x comma y in two variables. Therefore, the fact that a psi exists such that it satisfies these two relations these m is this and n is the derivative with respect to y and then you can write this as a perfect differential and so if this is 0 then you have the solution psi of x y is a constant. Is the solution also please remember we wrote dou m by sorry we wrote the following dou psi by dou x is equal to m dou psi by dou y is equal to n. Therefore, dou m by dou y partial derivative will be dou by dou y of dou psi by dou x which is dou square psi by dou y dou x and likewise dou psi by dou y is equal to n gives dou n by dou x is equal to dou by dou x of n which is dou psi by dou y and that is dou square psi by dou x dou y. The function is continuous then both these quantities are the same dou square psi by dou x dou y and dou square psi by dou y dou x both of these are the same and therefore, we have in addition a relation namely dou m by dou y is equal to dou n by dou x ok. So, these are all under the assumption that the m and n which are there in the differential equation can be written as partial derivatives with respect to one of the variables only. If we do that then we have a perfect differential and we can solve that and the m and n will also satisfy the additional property that their derivatives with respect to the other variable or equal ok. Now, if they are not what will happen if the condition d psi by d x is equal to 0 that is a perfect when it is called the perfect differential. However, if this is not satisfied that is dou m by dou y is not equal to dou n by dou x ok. Then we have a problem namely m d x plus n d y is equal to 0 is not exact it cannot be written as a derivative of a function with respect to x d x a derivative of a function with respect to y d y is equal to 0. Therefore, the same function if it cannot be written that way if m and n cannot be written that way then it is not exact often what you can do is you can multiply this by another function mu such that mu m and mu n satisfy these conditions that the d by d x of mu m the d by d x of mu m is the new function and the d by d y of the mu n is the new function their sum with with the d x and d y is equal to 0 and then the multiplication by mu to make this an exact quantity an exact differential the factor mu is known as integrating factor integrating factor. Let us see a little bit of this in the thermodynamics as an example and then we will go back to the second order and other differential equations in one lecture before we move on to the formal solution of the Schrodinger equations and model problems. So, let us take the 4 examples that 4 equations that you are familiar with in thermodynamics for the internal energy d u which is T d u which is T d s minus e d v infinitesimally small but what is it called infinitesimally small and reversible processes this is nothing but the delta q and this is the delta w the heat content and the heat change and the work done on the system the two together gives you the total derivative d u, but this itself is not a derivative they mean this is not an exact differential, but d u s.  Now, it is important to put the constancy of the other variable here of course, keep this volume constant and here we keep the entropy constant therefore, you can see that dou squared u by dou v dou s will be dou of T dou v and that is at constant s dou square u for this part by dou s dou v will be minus dou of p dou s at constant v, but u is analytic or it is continuous mathematics tells us that derivative of u with respect to v and s the second derivative it should not matter which order we do the second derivative. If these two are equal then essentially what we have is the relation between the derivatives namely dou T dou v of s is equal to minus dou p of dou s at constant v this is one of the celebrated Maxwell's equations with the statement that d u is a perfect differential. So, you can see that T is expressed as a derivative with respect to one variable and p is expressed as a derivative with respect to another variable and it leads to one Maxwell equation and it is immediate that when you write the other three such quantities namely for enthalpy d h is equal to T d s plus v d p or h as a function of s a functional of s and p you want to write that and d a the Helmholtz free energy as minus p d v minus s d t that is a is a function of v and t and lastly the Gibbs free energy as d g is equal to v d p minus s d t that is g is a function of g p of t you can see that all of these are perfect differentials and therefore, it is possible to take the derivative of t with respect to p and the derivative of v with respect to s and make use of and equate them. Likewise for the derivative of p with respect to t and the derivative of s with respect to v can be equal to the derivative of v with respect to t and the derivative of s with respect to p can be made equal leading to the other three Maxwell's equations and these are all based on the fact that we have an exact differential and therefore, it is possible to express these differentials which are functions of two variables in the form of the celebrated Maxwell's equation. So, a lot of these things are taught in other courses the idea of bringing those things here is a to recall them and see that these are employed in physical chemistry and we will see similar things in the dealings of quantum mechanics at some point or the other perhaps not all of them, but these are related ideas and the use of differential equations in quantum mechanics has been of course, very very I mean it goes back to more than 80 years right from the Deyser-Schrodinger equation a lot of these differential equations have been solved. So, it is important to go back and refresh a bit of this mathematics the lecture notes on the website gives you more problems and assignments for you to solve and some of the solutions to these are also given on in the website. So, I would invite you to go visit the website look at those problems and solutions and if you find something strange or you find something interesting feel free to write to me on the by email or by your comments on the website. We will continue with the differential equations in the next lecture.


Hello everyone welcome to options with Doug streaming live daily. I'm bookmap discord and the bookmap YouTube channel at 130 p.m. Eastern Time Before I get started I need to go through the disclosures general disclosure all book map limited materials information and presentations are for educational purposes only and should not be considered specific investment advice nor recommendations risk disclosure trading futures equities and options involves substantial risk of loss and is not suitable for all investors Past performance is not necessarily indicative of future results Here's my contact information The best way to get in touch with me is through discord on discord. My name is Doug P Also in bookmap discord. There's an options stash Doug chat channel That is a great place to post questions comments and content related to the Topics of my presentation as well as the topics of the channel that I'll go over in just a moment And I'm also on x formerly known as Twitter and my name there is at Doug plus and I would encourage everyone to consider joining bookmap discord if you have not already It's free and open to everyone Whether you subscribe to book map or not There's a lot of great content here. Also the stream in discord is at 1080p versus 720p max for YouTube so higher resolution stream in bookmap discord The focus of my presentation and the focus of the options stash Doug chat channel in Discord is options order flow The impact of options markets on stocks and futures and the influence of market maker hedging flow on price action And note that I focus on options because I think they're forward-looking. They're about Expectations where traders expect price to trade in the future I have a two-step process for trading and the first is Positional analysis so I look at how traders and market makers are positioned in the options market and How those positions change from day to day to develop a thesis regarding the expected trading range and Volatility for the day as well as a directional bias. So if the levels are shifting the key gamma levels open weighted gamma weight Open gamma weighted open interest if these levels are shifting higher for example That indicates to me that traders are looking for higher prices and they're positioning themselves and the options market For higher prices. So that's part of positional analysis And the second step in my process is execution And I look at real-time order flow in bookmap In real-time market maker hedging flow and spot gamma hero to confirm my thesis and for setups for entries and exits And when I talk about setups today, I will be talking about setups in an underlying asset That can be taken any number of ways for example the s&p 500 Setups can be taken with the s futures spy shares spy options spx options or even es futures Questions and comments are welcome and I will be watching both the option stash dug chat channel and discord as well as the Chat and youtube for your questions and comments So please feel free feel free to post and I'll do my best to answer your questions And hello, tony. Welcome glad you're here. Great to see you Here's my agenda for today What I want to cover today first of all news news items economic data events and earnings Then I'll go through my positional analysis Then I'll review some setups from this morning And then I'll take a look at the live market and when I get to the live market If anyone has any stocks they want me to take a look at please let me know and I'll be glad to do that All right, so let's get started with news items So first of all today ppi data came out And here's ppi data mostly Higher than forecast and also higher than previous Year over year month of or month core ppi month of or month year over year again mostly Greater than expected and greater than forecast All right tomorrow cpi comes out should be a higher impact report And could potentially cause quite a bit of market movement And that depends on how market makers are positioned Part of that depends on how market makers are positioned on the gamma curve tomorrow Whether that gamma notional remains negative or becomes more negative Than Than today so we'll take a look at that And just a couple of minutes. All right, so that's tomorrow cpi And then friday consumer sentiment at 10 a.m And most important for today after ppi the f1c minutes come out at 2 p.m So I'll stop wherever I am and we'll take a look at the market as the f1c minutes come out I'm not sure what that will add There were a lot of fed speakers out Yesterday with pretty dovish comments So we'll anyway, we'll stop where I'll stop wherever I am and we'll take a look at the live market to see if there's any impact All right, so that's data for today as well as the rest of the week All right now, let's get started with my positional analysis I'm going to start with the sp500 This is the es futures and book map And before I take a closer look at this chart, I'm going to take a look at a larger time frame I'm going to go to the spx. This is a 30 day one hour chart Showing price and key levels. So let's focus on price first this is the friday september 15th options expiration call dominated expiration and that's when the downtrend began and then this Recent rally began Really on friday Last friday with the jobs report. So price was turning a little bit higher and then rocketed higher On last friday as the jobs report was released And that rally Appears to Have hit a roadblock here at the around the upper weekly expected move Uh for this week All right, so those are the that's the price action Key options expiration and events Marking the turning points in the market All right, let's take a look at some of these levels now. First of all the dash purple lines Are showing the lower and upper weekly expected move That changes every week. That's a one standard deviation move So the options market expects The price to trade Within this range spx of trade within this range 68 percent of the time And that's just based on the options market that information should be available in any trading platform that has an options chain Right next the dash blue lines We're showing the upper and lower daily expected move And note that spx is trading within that range today So trading down below the upper daily and weekly expected move and above the lower daily and weekly expected moves All right, the dash red lines Are spot gamma levels. These are Proprietary spot gamma levels available to spot gamma subscribers. I'm going to point out the key daily levels So first of all 4200 is the put wall That's a strike with the largest net negative gamma that can be expected to act as support The next level up Is the volatility trigger At 4340 That is spot gamma's proprietary gamma flip level Below that level market makers position on the gamma curve is negative In a negative gamma environment market makers have to trade with price to hedge their delta exposure And that tends to enhance or increase volatility On the other hand above that level Market makers position on the gamma curve is positive In a positive gamma environment market makers have to trade against price to hedge their delta exposure And that tends to subdue or decrease volatility And note that is not exact so market makers position on the gamma curve at the beginning of the day According to the gamma notional was still slightly negative But so far really I would interpret gamma notional for spx as really somewhat neutral today The spot gamma gamma index was just above zero And that is actually what Brent at spot gamma looks at All right, so the next level up Is 4400 And that is the call wall the strike with the largest net positive gamma And that's also the absolute gamma strike. That's the strike with the largest absolute positive and negative gamma So that's a very important level Where most of the gamma weighted open interest is concentrated at least for today And note that absolute gamma strike did move higher from yesterday From 4300 yesterday to 4400 today Also, the volatility trigger moved slightly higher from 4325 to 4340 So the shift higher in the absolute gamma strike Was slightly bullish Interpreted I interpreted that as bullish All right, so those are the key levels Let's take a look at a one-day chart for spx so we can just focus on the levels that are in play for today So i'm showing actually two days worth of data here So this is yesterday spx did trade above the Upper weekly expected move Then moved sharply lower. I think there was news that came in came in around 1 p.m. Eastern time And then today that Upper weekly expected move act as re acted as resistance Right at the open And now spx is trending lower All right, let's take a look now at book map So in book map I have my own cloud notes And i'm showing spx levels So here's this 43 76 resistance level that was not shown on the spx chart This is something that is noted in the spot gamma am founders note and I add that To my cloud notes just above that is the Upper weekly expected move Shown with the dash purple lines again. That's for es Then I also have spy levels on this chart Here's the spy 435 volatility trigger And note now price is trading below that level And also down below the 43 50 level that is spx 43 50 So note there is a difference in price between es and spx And it changes a little bit every day. It tends toward zero Toward the end of the Toward the contract Roll over today. It's 32 So spx 43 50 is at es 43 82 All right, so the levels in play the main levels so support I would say yet to be determined But the resistance clearly At the upper weekly expected move For es just like spx In this 43 76 level just below that So clear resistance in the morning We'll take a look at setups in a few minutes and we'll see what options traders were doing as well as other players Shown here in book map So we'll get to that when we take a look at setups So those are the levels in play for today again key levels upper weekly expected move acting as resistance Shifts and levels I talked about shifts and levels higher for spx for the volatility trigger and absolute gamma strike And for spy the volatility trigger also shifted higher From 430 yesterday to 435 today And that's this level right here 435 All right, let's take a look at nasdaq now So here are the nq futures in book map And i'm going to take a look first of all at a qqq chart So I can isolate isolate the qqq levels So here's qqq. I'm showing a little bit of the Price action before the market showing all the concentration around of Price action and volume we'll see in just a minute around the 370 level 370 is the absolute gamma strike for qqq And note the Volatility trigger for qqq is at 369 And now price is trading below that level And 370 again is the absolute gamma strike I'm going to squeeze this in just a little bit to see this Combo level we'll see this on the ndx chart right here In just a moment. So this combo level combines qqq and ndx gamma weighted open interest And shows it in terms of qqq price here We'll see on the ndx chart that level is shown in terms of ndx price again. That's combining qqq and ndx gamma weighted open interest All right, let's take a look at ndx Always like to take a look at this just for completeness. So here's that combo level And just above that Is the call wall. Oops Not sure what I did there All right, let's try this again So here's this Combo level that I just mentioned on the qqq chart and just above that Uh Actually the combo level is above the call wall at 15,250 that is the that's a very important level for ndx That is the call wall and the absolute gamma strike That can be expected to act as As resistance as it did All right, let's go to book map now So here's a book map And again, I have my own cloud notes here There are the ndx levels. There's the 15,250 absolute gamma strike and call wall Acting as resistance And support for today yet to be determined So that um, again, just like the spx that resistance level very clear Uh level that you would expect to act as resistance did For both the smp 500 and nasdaq for the smp 500 upper weekly expected move and for Uh nasdaq it was the ndx Call wall acting as resistance This morning and again support so far yet to be determined All right, so those are the levels in play for uh smp 500 and nasdaq There were some shifts in levels for ndx volatility trigger shifted slightly lower And for qqq the volatility trigger shifted higher From 365 to 369 and the call wall shifted slightly higher from 372 to 373 All right, let me check for questions All right moro van. I hope i'm pronouncing that correctly Uh says hello. Hello moro van. Can you explain levels for gold market? I wish I could but there are no levels for gold Spot gamma does not provide levels for the gold market Um, just the uh, just the equity indexes and stocks all right, um Nice i'm ed I hope i'm, uh, sorry if i'm mispronouncing that. Hello from divi Hello from uh, north carolina for me first time here Do you have any start of video series to understand this type of charting to get started? Um, well for book map, there's a great Um, a very substantial great learning center. Just go to the book map Uh website and look for the learning center. There's a series of start of videos So just go to the book map website great information there. Uh, that should help you get started redis redis Redis, sorry Sorry if i'm mispronouncing ask me if I can take a look at bitcoin and sorry. No, I do not Uh, do not track look at or trade bitcoin um You can see what i'm Trading and what i'm going to talk about Right up here on my book map chart ES futures nasdaq futures and mainly the stocks that i'm going to look at are the large cap main large cap tech stocks the magnificent seven So this is what I trade what I look at and what what many other traders look at again ES and nasdaq futures All right, so sorry about that. Sorry. I can't provide any more information for gold or A bitcoin although when I do when I get to the Live market I can see if gld is included in In the list of stocks that support hero, all right, so uh If I forget maybe you could remind me and we'll take a look and see if gld is in there All right, let's take a look and see how market makers were positioned on the gamma curve at the beginning of the day I'd like to look at this every day. This will give me a sense of How market makers will react Uh, but potentially react to changes in price and applied volatility And also a sense of the Volatility for the day um In a very negative gamma environment, I expect Market makers to be trading with price and that tends to enhance volatility And then a less negative or even positive Gamma notional environment smaller trading ranges and Less volatility for the day So this is how market makers are positioned on the gamma curve at the beginning of the day And i'm going to look at gamma notional for spx spy And qqq. I generally don't look at gamma notional for ndx. It's not significant compared to the others note All these numbers are negative still Market makers gamma notional still negative at the beginning of the day, but less negative than yesterday All right, so again still negative, but uh less negative than yesterday What this indicates that more of the traders are long puts market makers are short puts And as price decreases they have to sell futures to hedge their delt exposure And as price increases they can buy back their short futures. That is a negative gamma environment Let's take a look at the vana model, which will take give us a graphical illustration of that i'm going to start with spx What this chart is showing is delta notional market makers delta notional On the vertical axis and how that changes changes with price On the horizontal axis there are two curves on this chart the light gray curve Shows how market makers delta notional Changes with changes in price only And the purple curve adds Implied volatility to the equation that's showing how market makers Delta notional changes with changes in price and implied volatility And that change in delta notional with the change in applied volatility is the Vana effect vana is a second order greek All right, let's take a look at some prices and spx has been falling all day Let's just take a look at Let's go back to the spx chart So the high day was at the upper weekly expected move Right around 43 76 So let's locate that on this chart So here's 43 76 Summer between these two lines So this is near the bottom of the curve indicating there was not much put vana fuel Left in the tank and i've talked about this every day how this put vana fuel has been diminishing Pretty much burned up since the start of the rally last friday So what this indicates that as price increases There's very little put vana fuel to fuel the move higher market makers Really don't have that many short futures to To buy back on the other hand If price decreases from here And implied volatility increases Market makers will need to sell futures to hedge their delta exposure. So this works both ways So this is what is going on today All right, let's take a look at current price spx right around 43 50 So that's right around here. So This arrow is a little bit exaggerated, but market makers again And this portion of the gamma curve Have to sell futures to hedge their delta exposure as price decreases and implied volatility increases All right, so that's the vana model for spx All right, let me check for questions And tony asked do you look at any smaller large cap stocks? 10 billion market cap Do you look at short floats or just options? So first of all, uh, I showed you again the stocks that I look take a look at apple amd amazon google meta microsoft nvidia tesla As well as the smb 500 futures. Although if you have any specific stocks, you want me to take a look at When I get to the live market, I will try and I'll take a look at those All right, so the second part of your question. I just look at Look at options So the stocks that I consider Or trade most often short float is not a consideration So a lot of people do look at that that's uh, just because I doesn't I I don't look at that doesn't mean it's not valid but You know, that's just something that I don't look at my timers pretty limited and I have understand how the stocks that I look at trade so that is You know, again, that's what I that's what I do all right russia kish Asked how to understand at which market condition which greek Should be traded and why? And also why spot gamma is important to trade um Well, I would say just watch my watch my videos So I'll show you why spot gamma is important to trade and as far as greeks go I I look at delta theta Primarily as the the primary greeks second secondary. I look at vanna and charm Ancient the architect asked you set limit orders when trading futures Uh, or you jump in at the opportunity. I definitely I use bracket orders when I trade futures So I have a a stop limit as well as a take Take profit Order so I use brackets with stop limits and take profit orders always when trading futures And more and more i'm just trading options rather than than futures Which I I really don't you know, you don't need a stop stop limit Stop order with with options Um, I use either buying options or buying spreads So those are all defined risk Or I I sell sometimes sell Spreads or iron condors also defined risk All right, let's take a look at the vanna model for spy real quick And then qqq and then we'll um Then we'll take a look at some setups to get to the market All right, so right now spy is trading at 434 So still pretty close to the uh the lower end of this vanna model here but indicating as price Continues to drop for example Market makers will need to sell futures to hedge their delta exposure So we saw that at the beginning of the day market makers position on the gamma curve was negative still negative And that's why we're looking at this portion of the vanna model this portion of the curve That is skewed upward to the left Let's take a look at qqq qqq trading around 369 So right around here Toward the lower end of the vanna model as well All right, let's take a look at some setups now and again the takeaway from this is that um Still looking for higher volatility, but less so than the Last few days as gamma notional has become less and less negative And market makers As far as a move higher The vanna fuel that was in the tank starting Last friday that helped fuel the sharp rally higher has pretty much been burned up At least according to the vanna models today All right, let's take a look now At some setups and i'm going to take a look at what options traders have been doing today This is the hero signal hedging impact real-time options This is available to spot gamma subscribers Hero stands for hedging impact real-time options So everything that we've looked for looked at so far has been static Information that I use in my planning based on gamma weighted open interest primarily Open interest is updated once daily sometime during the night And spot gamma provides Applies their proprietary algorithms to this data to derive the information that I just talked about that I use in my planning So now we're going to take a look at real-time information Uh in book map and spot gamma hero So this chart is showing price for spx with a white line and the hero signal For a combined signal for spx spy Xsp and es futures So this is showing options trades and market maker hedging activity Again for this combined signal All these major components of the sp500 And note this purple line is trending lower for the day Notional value is negative That's a minus 1.96 billion. So traders net are taking negative delta positions All right, let's Zoom in on this chart and we'll take a look at the setup from this morning So right here, this is the cash open at 9 30 am eastern time and note traders We're taking negative delta positions That flow shifted more negative Right around 9 50 note this alert this flow alert that came in If you weren't watching this was this was a good signal To get your attention All right, let's go take a look at the book map Focus on the morning So we know from the open that traders were taking negative delta positions from the open That we know before the open these two levels here upper weekly expected move and the spx 43 76 level acted as resistance 43 76 noted as resistance in the spot gamma am founders note that was out Uh, I think by 6 a.m. This morning Then at the open again, we saw that traders were taking negative delta positions At the open S&P 500 was back up at this resistance level larger traders Were selling this with iceberg orders iceberg orders they used to hide their size So they were selling this move higher this icon Below here show is showing iceberg orders. That's the on chart indicator It is obscured by the This green dot which is showing a buy stop order. We can see in the sub chart here This falling light blue line indicates Traders are selling with iceberg orders So we know that options traders are fading this move higher Then is With this third check of these levels Aggressive sellers start to come in You can see the shift To magenta volume dots the volume dots are showing market buy minus sell With a green dot shows more buyers than sellers And a magenta dot shows more sellers than buyers So aggressive sellers start to come in With this third test of the level Just around 9 50. That's about the time that alert came in And then Sell stop orders Help to feel the move lower And also cumulative volume delta shown by the dark blue line there Starts to shift lower as well so very clear indication in Book map as well as spot gamma hero Of a short setup Just darken up the heat map a little bit All right, so there's the short setup In the sb 500 Let's zoom back out And there was a slight move up As options traders took took positive delta positions, but that didn't last long Yes, reverse lower below vwap as Option that as traders negative Aggressive sellers came in shown by the magenta volume dots there So that reversal below vwap, which is shown with this Light blue line here. All right, so there's the setup in the sb 500 Nice gradual uptrend a downtrend And pretty nice deep pull backs for short entries All right, let's take a look at nasdaq Pretty similar pattern in nasdaq. Let's see what options traders were doing So i'm going to take a look at a combined signal For indy x and qqq I'm going to zoom in a bit so we can take a look at the morning And this was a very nice divergent short So note there was a sharp move higher at the open And options traders were fading that from the beginning And then price responded lower just a few minutes later As options traders were taking negative delta positions In nasdaq And price reversed at that 250 level so this chart is shown in terms of indy x price There's the 15,250 call wall Options traders were fading this move higher and then nasdaq reverses at the 250 level Let's go take a look at book map Focus on the morning here So here's the initial setup Just right after the cash open aggressive buyers Move price right up to the call wall level Price moves below the qqq 371 level As options traders were taking negative delta positions and then aggressive sellers come in So you can see the very clear shift From green volume dots on the way up To magenta volume dots on the way down That's shown with the cumulative volume delta here Also cell stop orders fuel that move lower So very clear divergent short set up Here was another opportunity Again a pretty clear shift in order flow. It took a while for that to play out Let's go back to hero Zoom out for the entire day. So up until about Say about 1145 This hedging flow was definitely Definitely bearish Then it shifted again around 1145 To bullish Still net negative for the day. That's number is negative negative notional value And price is not really responding To the options trades anymore at least Maybe starting to now, but so far Price has been trending lower Even though the options traders have been taking positive delta positions Let's go back to book map. Let's see who is in control So i'm looking at the sub chart here cumulative volume delta Right here right around here shifted from Positive for the day shown with the dark blue line To negative for the day shown by the dark the magenta line also Cell stop orders still helping to fuel the move lower And large traders net have been buying this move lower But this number is pretty small 125 positive for iceberg orders All right past 2910 Your comments are not appreciated Please move on All right, so that's nasdaq Let's take a look at some stocks now I'm going to go back to hero Start with apple So apple this this morning Short set up Then long set up Note this floor alert came in Pretty timely for a reversal lower All right, let's go take a look at apple And book map So just following the options market today Long short long Not a lot of movement in apple Let's go to amd Nice downtrend and amd here Let's take a look at hero amd So again a very strong correlation between options trades Hedging activity Let's see what traders are doing So they've been selling calls That shown by the Falling orange line Also the negative notional value They have been buying puts that activity seems to have Slowed down somewhat around 120 but still The blue line showing falling blue line showing Traders are buying puts notional value negative Sorry about this. This is not anything that I did. It's a Problem with hero All right, so options traders definitely in charge today for amd. Let's go back to book map And pretty deep pullbacks For short entries as traders take negative delta positions Again selling calls buying puts Note the shifts in order flow here at these turning points A lot of magenta volume dots there aggressive sellers come in All right, the next is google All right, let's take a look at hero. See what options traders were doing So amd good short And google was a good long in the morning Note the very timely flow alert here Drawing your attention to a potential long traders are taking positive delta positions Price breaches the 140 call wall key gamma strike in this case Right around just after 11 options traders take their foot off the gas And price moves lower This is a pretty typical pattern of a a bullish day when this hedging flow shifts from positive to negative or neutral Let's say at this point if you wanted to Either take profits Or sell a call spread or buy a put spread Just indicating that all price has to do is stay below that level That's a very good setup Again, this works mostly, you know, of course on a bullish day where there's bullish trade mostly takes place in the morning Up until 11 30 or 12 And then you can play this reversal Again, a very easy way is just to sell a call spread or buy a put spread And all price has to do is Stay below that level All right, so that's google Long and short The next is meta Meta has definitely been in play this week Note 3 30 is the call wall That was a price target if price continued higher All right, and another timely flow alert for a potential long As options traders were taking positive delta positions And note from this chart as options traders take their foot off the gas Start taking negative delta positions price moves lower Again, a very easy setup here is to buy a put spread or sell a call spread Let's go take a look at book map All right, google reverses right at 141 trend break Move lower as options traders take their foot off the gas Let's go to meta And I completely forgot about the FOMC minutes I'm sorry about that And that Really did not seem to have much of an impact It looks like now the S&P 500 has broken This downtrend and now starting to make higher lows But that started before the FOMC minutes At 2 p.m. And note that large Large traders were Starting to buy with iceberg orders before starting about 1230 That's shown by the falling rising light blue line You can also see the iceberg orders here in the sub chart He indicates executed They continue to buy So for example this icon indicates 1040 contracts were executed All right, then his price starts to move higher aggressive buyers coming in Showing by the green volume dots Rising CVD and then also now buy stop orders Showing by the rising yellow line as well as the This icon here with the small green dot fueling the move higher up to vwap And now the 435 volatility trigger All right, what kind of tack ask has hero reacted to FOMC? Let's take a look Let's go back to hero Take a look at the S&P 500 And yes But note the move started higher Really just between 130 and 145 Right around here And note this flow alert that just came in For the S&P 500 And those floor alerts sometime can indicate a turning point Reversion to the mean let's take a look here So here's the S&P 500 hero flow Let's just see what Traders have been doing in more detail today So the orange line is showing calls And the Blue line is showing puts So the call line was Really slightly negative until about noon 12 12 30 started rise traders started buying calls Sorry about that It's nothing I did Let's go back try again All right, then traders Have also been buying puts all day So this is pretty typical for the S&P 500 traders are Buying calls and buying puts And now they have started selling puts So spot gamma indicates that When the lines are moving in the same direction, this can be a pretty powerful indicator So right around 150 Before the minutes were released Traders started buying calls more aggressively They stopped buying puts And now started selling puts But again this started before the Release of the minutes And we saw on book map aggressive buyers coming in And also large traders were buying With iceberg orders as price moved down And that started before the Release of the minutes as well Let's take let's go back to total signal So there's that flow alert again Indicating can indicate a potential reversal Let's just see what zero DTE traders are doing. Sorry about that Scroll back out zero DTE shown with the the green line and that is uh Higher notional value much higher than the purple line So traders in the options that expire today are a little bit more Bullish than the options traders with a total signal Which is pretty much flat for the day Let's just go to the 30 minute look back period focus more on the Last 30 minutes a day. So this is before I was looking at the entire day Of data and now this is just looking at the 30 last 30 minutes like a 30 minute 30 period moving average all right, so this options trading Now looking at this a little bit closer Time period Fine or rolling uh smaller rolling window period looks like it is leveled off just a little bit Also the flow alert again came in Let's go back to the Let's go take a look at book map So it looks like now that SMB 500 found resistance at this cluster of levels here the SPX zero gamma level just below that the spy Volatility trigger level as well as VWAP and aggressive sellers came in buy stop orders And aggressive buyers fueling the move higher shown by the green volume dots And then aggressive sellers start to come in as options traders were taking negative delta positions And you're welcome got it kind of tack Yeah, I think hero is Is pretty unbelievable too. It's a great great indicator it's um What I really like to see with book map and hero is all the different players Smaller traders with stop orders larger traders with iceberg orders options traders and those various instruments that I talk about and determining who's in control and options traders Often have a very large influence on price when traders Buy and sell calls and puts and spx spy ES and xsp options traders Hedge those trades options market makers hedge those trades with es futures So that's why watching watching hero options trading and hedging activity is so important Let's take a quick look at nasdaq and then uh, then I'll have to wrap it up for the day my time is up Pretty similar reaction to nasdaq Move higher up to the qqq 370 level Price reversed and now maybe trying to move higher again We can just see what options traders are doing go back to the sp500 so far hero Continues to trend higher. Let's take a look at nasdaq and hero also continues to trend higher All right, sorry, I got to the uh, fomc a little bit late. I just got kind of wrapped up in questions and also Looking at setups. Anyway, I want to thank everyone for watching Thank you very much for your questions and comments And remember cpi today data tomorrow at 8 30 a.m. Could be a market mover So we'll talk about that tomorrow So again, thank you very much. Thanks for watching. Thanks for your questions comments and I will see you tomorrow. Bye


Hi everybody it's Sam at Mixed Up Craft, thank you for watching my tutorial today I'm going to be showing you how to make this what's known as a triple cube box card. So I actually saw this come up on one of the Facebook craft groups and when I looked in the comments because people were asking how to make it they said that they just looked up, they said the name and they went onto YouTube. So I had a little look and there's a few people that have made them but the one that I saw and that was from the oldest one I guess was by Iced Images and that's what she's called it there. So I didn't actually look at any of the tutorials because I'm able to just work out exactly what it is because this centerpiece is my floating pop box or the pop boxes that I've done and it's just two extra pieces on the front so it's really really straightforward to do but it really does pack a punch. I think it's just got such a great profile and the whole thing folds flat and this will fit into a six by six envelope and I've made sure that I've got this from a piece of 12 by 12 cardstock but you can easily adapt this once you see how straightforward it is it's very easy to change. On the back you've got lots of room to stamp and write your message, I've got this floaty sentiment here that I've added which I've done the same way as I've done on my pop boxes in the past so yeah it's really straightforward very fun bright and colorful so let me show you how to make it. Okay so the colors I've used for the sentiments for today's I've used the ocean blue quick dry and then this is the fuchsia quick dry and that's the harmony my spectrum noir and then I have used for the sentiments I've used the birthday wishes here which is the woodware big birthday words which I've used so many times I love it. For the oval dies I've used the card making magic A5 oval dies and for the papers I've used my 8 by 8 paper pad and it's the party paper pad and I just pulled out all different. I actually used a lot of my scraps for this one because the pieces you need are actually quite small so we're talked through all the mats and layers in a moment it's pretty quick to do as well so you can see here how this was a piece of 12 by 12 okay and then this is actually I had to scrap in this color but this could be white you know it doesn't have to be the same color as what you've got there but you basically want to score so you want to cut it down so you have one piece that's 6 by 12 okay and you're going to score along the 12 inch side at 2 and 7 eighths of an inch alright 2 and 7 eighths of an inch 5 and 3 quarters 8 and 5 eighths of an inch and 11 and a half okay then you want to cut these two pieces here which are so it would be you know you'd have another 6 by 12 piece cut off from this but you just want to shrink this down a little bit because of the way that I've scored this to have that half inch tab you end up having your squares as being 2 and 7 eighths of an inch squared because that's what this first panel was because we scored there at 2 and 7 eighths so you need this to be 2 and 7 eighths of an inch by 12 so you just want to just take a little bit off of those two there and then again along the 12 inch side you're scoring exactly the same again so it's 2 and 7 eighths of an inch 5 and 3 quarters 8 and 5 eighths and 11 and a half and do that twice okay and then this little piece here is just to help your sentiment pop so this is a little piece here which is 3 by half an inch and along the 3 inch side you just want to score at half an inch 1 inch 2 inches and 2 and a half okay and then for the mats and layers where I've got my scoreboard out so a lot of this is optional I've got it here so I've got ones for inside here now you may choose to just keep it plain it's a little bit of a tie-lip tube but I've got these here so I've got two pieces of the holographic card for the mat layer which is 2 and 5 eighths of an inch by 5 and 3 quarters and then my pattern paper so the layer on top is 2 and 3 eighths of an inch by 5 and a half you want two pieces if you want to do inside if you want to do the white piece for you to be able to stamp and write your message on the back you'll want to in white of that original size that larger size that I just gave you there and I've already got my two pieces prepared then these two here are more of a rectangle than they are a square and that's just for the top two here and these ones are 2 and 5 eighths of an inch by 2 and 7 eighths of an inch and then the pattern paper is 2 and 3 eighths of an inch by 2 and 5 eighths of an inch okay then all of these are just standard squares now I've got 8 in total I've got 4 with this print and then 4 with the stripes but you'll want 8 mat layers that are 2 and 5 eighths of an inch squared all of these measurements will be in my blog and then the pattern paper is 2 and 3 eighths of an inch squared okay so just decide what it is you want to use there and then that's my sentiment there which I've done in that blue with the orange matching card again I just had some in my scrap but you could do that with the holographic card and it would look really nice okay so first of all you want your larger piece well you're going to do it on all of them actually you just want to fold and burnish the score lines okay and then we'll do these two strips first of all so it's just like you were putting a box together you just want to add glue or double-sided tape such you just on your tab fold that over and then fold that one and while that one's drying I'm just going to do the same with the second piece okay so you'll have two pieces like this and then we're going to do the same with this piece now you might want to stick these pieces in before you put this together if you want it you know it might be a bit easier because what's going to happen is this one we're going to stick together and I'm going to have it on the side so that the join will be here so you won't see it in there and you won't have that join on the front either it's going to be on the side with the top with this piece over this piece okay so these are going to stick inside here so if I open it up there's that half-inch tab we just burnished up this way you want to stick these two inside here so I'm going to do that now okay and now you can pop glue on the tab and then just fold that piece right over and when we open it up you've got your pattern there inside and you've got that tab there which you're not going to notice now on my pop boxes I'll link that tutorial if I haven't already but before I stuck it together I cut an aperture there so you had something can floating in the inside with some acetate it looks really cool so now with these pieces here you want again to have the tab piece so you can see where mine is here that's going to be at the bottom facing me so we're going to stick that piece onto there so again that's where my tab is you can see there we go it's just folded and stuck there that's the bottom front alright so I'm going to pop my glue on the back here and then if you want to keep it up this way and then stick it like so that way you know you got it flush with the bottom or you can lay it down make sure it's flush with the bottom you don't need to worry about the tux when it folds it's slightly shorter because of the measurements so you know you're not going to have anything overhanging there just make sure that you get it nicely lined up so they stick either side of the score line there and then again with that one just make sure I've got that tab facing me again if you're using the collow glue this will really become a very strong card you just want to make sure they're nice and flush with each other you fold it up you can you know wiggle it around just make sure they're both sitting nicely like so so while that's all flat I'm flipping it over and I'm going to stick down my white pieces you might want to do another pattern paper on one side but again you've got lots of room here if you want to have a few other people sign it you maybe print you might want to print off something to go on one side of it it's entirely up to you and then I'll flip it back over and you can see now how it all comes together it's really cool it will naturally you know sit like that so now you want to get those two kind of rectangle sizes and those are going to stick here like so and then all of the other squares will cover the two on the front here and then the two on the inside so you can see there if you want to cover here as well you can if you want to cover underneath there you can you just need to cut some more but I'm now going to go and get all of these stuck down okay so they're all stuck down and then I can just fold it up that way and just push down on everything okay now while that's drying you've got this piece here where we've scored so you want to you want to burnish so that you've got the two outer score lines of valley folds like so and then the inner score lines and mountain folds so it should all fold in like that that's how you want it to look okay then you're going to keep them together like this so that you want the ends here you're going to put glue on there if you want to use you know just a little bit of red tape or something you can do I'm just putting a very small amount and you're going to stick this so that it's in the middle of this score line here and it's right across the score line there so I'm just gonna lay that down about there if I bring it up now can you see those two sides are stuck across this score line here and it means this piece now is free for you to stick whatever you want on but it will always face you when you open up the card so then I'm just going to pop again make sure that is stuck down but I'm going to pop another little bit of glue just on the top there and then with my sentiment I'm going to just sit that down and just make sure it's in the center of this part here okay so now you can see that just wobbles about but it will always say nice and centered in the card so all folds up flat you've got all the space on the back there to write your message and when they take it out of the envelope you know it's pretty self-explanatory what they do and how it looks and yeah I think it displays really really well so there's the other one love the colors love these papers and I think the sentiments really work well as well so yeah I hope you've enjoyed it I'll link everything below as always and I'll be back again very soon with another tutorial thanks for watching bye


We have looked at linguistic theory and its components and we have established how study of a structure plays a significant role in answering several theoretical questions in linguistics. We looked at very briefly how we learn a language, the role of knowledge of language and what it consists of and universal grammar, how that makes a difference, how that plays a role in similarities and differences of languages. Then we looked at components of sentences. We also looked at types of verbs, types of objects, how verbs and objects are related to one another and then if we draw a super structure then subjects are outside the predicate and then we have looked at both subjects and predicate as a component of the sentence. Now we are going to look at X bar theory in linguistics structure, how X bar theory captures sentential structure and how a phrase is built around and what is the role of a phrase in a sentence. How X bar theory helps us understand differences and similarities between several components that we have looked at. This is very easy and interesting. I want your total attention for this thing. So, please take a look at that. There are several categories in language. We are going to be talking about four of them and some of them are nouns, verbs, adjectives and prepositions or post positions. We come to this structure and rules underlying this structure in a minute. In order to connect with what we discussed yesterday, I want to take you through one more aspect of it which is called, we looked at verbs and we looked at nouns. Now we are going to look at how and what they carry with themselves. So, we are going to be talking about features on these elements, nouns and verbs. Certain features like tense, aspect, modality and formal distinctions, verbs carry such features. I am going to elaborate on these things in a minute, but let me first make sure, if we have heard these words at least, tense, modality, yes, no, no. What are the tenses that you have heard? Present, past, future. I am glad there are only three of them. Then we talk about aspects. Have you heard these names before? Perfect, imperfect, continuous, yes. Please give me very quickly an example of a present and sentence. Somebody from you. Simple present and sentence. Simple present and sentence. Sun rises in the east. Sun rises in the east. Very nice. Sir, next. Past tense. Any simple sentence? He went there. He went there. So, went shows past tense, if I can assume that. Future tense? I will go there. I will go there. Very nice. I am assuming that we understand why these sentences are present, past and future. We need to focus on more complicated stuff. If we talk about aspects and then say perfect aspect or imperfect aspect, you think you can give me some examples of perfect aspect and imperfect aspect? Any idea? I will need to talk about that. Then how about infinitive and non-infinitive things? I will talk about that. See, any word, something like this. This marker 2 is an infinitive marker. So, to go, to read, to sleep, to eat, all the verbs come with this infinitive marker. It is not language specific thing. It is not only about English. It happens in all the languages. Anybody in Hindi example? How do we say the same thing in Hindi? Padna. So, the na at the end of it is infinitive marker. Na in the word padna is exactly like 2 in the word to read. And the important thing about this is, it works like a wrapper. It is wrapped in a, like verbs are wrapped in this infinitive marker. And the moment we want to use it, we have to remove it and then use the verb in a sentence. So, when we say I want to read a book, we do not say I want to read a book. There are some cases where we use infinitival verbs in sentences, but most of the time when we use them and when verbs have to carry their features, that is when these features of the verb gets activated in a sentence, then we have to remove these infinitive markers. Is this making sense to you when we say verbs have to activate their features? For example, see a verb always carries these features. If a verb has to activate its feature, let us say past tense, it cannot activate that feature without removing this marker. We cannot say to went. We have, in order to say I went there, we have to remove this infinitive marker and then verb transforms into a past tense, transforms into something which looks like a past tense marker. Is this making sense to you? So, these are the features of verbs. I will talk about modality and modality some other time to you. Let me talk about the features and nouns and the reason why I call it features and nouns and verbs is because these features of nouns get into agreement with the verbs. So, features like number, we have heard these words singular number, plural number, features like person, first person, second person, third person. I am not asking you to give me examples of these things at this moment, but I just want to make sure that you have heard these words, first person, second person, third person and then gender like masculine and feminine. These are simple things which are all in coded in nouns. Therefore, these are called nominal features. How about case? Have you heard this word case? Nominative case, accusative case. So, we will talk about them as well. Remember how, what we were talking about sentences yesterday? In a sentence, a noun becomes a subject or an object depending upon its position. Remember that? Those positions are relevant to cases. So, a noun gets either infinitive case or accusative case or genitive case or something else depending upon its occurrence in a sentence. However, the assumption is all nouns carry all features. Depending upon the position of occurrence of a noun in a sentence, a particular case gets activated. So, if we are saying John likes pizza, John being in the subject position activates its nominative case. Therefore, we say subjects always have nominative case. Pizza being in an object position activates its accusative case. If we change these nominals with their different positions, then they will have different cases. Understand this point? The reason why we are talking about this is because it is very significant for us to understand that in a particular position, when a particular noun activates its case, it is not that those verbs, those nouns receive those cases there. They already have their cases and they get activated. There is a big debate in linguistic theory about this particular aspect, whether verbs assign cases to nouns like subjects and objects where that is whether nouns receive cases from the verbs or they carry all the cases and then verbs help them activate their features. This is a big debate in linguistic theory. I will try to make it as simple as I can. The important point is to look at and to know about these features as a nominal features. Are you with me so far? Let us look at one more point before the structure and see how they work, how they are at play. Now I am going to talk about agreement in order to show you these features. Can everybody read this sentence? You can. Raju movie dek raha tha. It is a Hindi sentence. Raju movie dek raha tha. Now I want you to pay attention to the glasses in the second line. Also, at this point I want you to look at it. This is how examples are written in a linguistics paper or a book. This is the convention of writing an example of examples from languages other than English. If we are quoting examples from any language, this is how we write the example. We write the sentence with the help of phonetic transcription as accurately as we can. There are standardized ways of doing this thing and then we give word by word meaning of it which is called gloss. Then we elaborate relevant features of that particular constituent and then finally we give its English meaning. The advantage of this thing is people working with these things do not need to know a particular language. When we put things this way we know we only need to know what we are talking about. For example, if you know Hindi it is good. You do not have to know this thing. What you have to see is Raju is the first noun in this sentence. Movie dek raha tha. Dek raha tha is verb and movie is its object. The order of this is predictable because we know Hindi is a verb final language. We see dek raha tha the whole verbal component verb part at the end of this sentence. Movie is the object in this sentence. It is near the verb. See that in a sequence of occurrence it is close to the verb. We see some of the features activated on these components. Raju it has got masculine gender, nominative case and it is third person singular. It is aspect making sense. Masculine noun should not be difficult. Singular number should not be difficult. It is third person and because it is in a subject position it is nominative case. Movie as a Hindi word it has feminine gender and accusative case. Now look at the verb dek raha tha. Dek raha tha the verb dek na means to see or to watch. Now look at this part of the verb raha tha. This is the part which shows aspectual marker. In this particular case it is progressive aspect or continuous aspect and the last component tha is a tense marker in the sentence. That is tense marker on the verb. Now what is the verb also carries masculine gender and singular form. If you look at these three components of this Hindi sentence is it possible for you to figure out which noun in this sentence agrees with the verb and when we say agrees with the verb we mean the features of the noun agrees with the features on verb. Raju why not movie? It is feminine but the verb tha is masculine so it is not in. Very nice. So it is very simple idea and this is why I am spending couple of minutes on this and want you to understand that when we talk about all these words singular noun, plural, masculine, feminine, nominative, accusative these names may sound like we are listening to these things for the first time but the idea that they depict and the way they work is pretty simple. Agreement simply means its features are going to be matched on verbs and subjects. That is a nominal position nominal element in that position. The fact that this nominal position nominal element in the subject position is masculine and it has it is singular and the verb shows masculine and singular, verb shows masculine and singular features then we know that this noun Raju agrees with the verb. I want you to know at this point that you are going to see this agreement only at the last element, last part of the verb. This whole thing is verbal component. It is also called verbal complex and Hindi, Telugu, Tamil, Malayalam most of the South Asian languages, almost all South Asian languages show the features of agreements at the last element. This is why they are called peripherial features. They will show it on the last element. Now one more point about this aspect Ratha. This indicates continuous aspect marker. What do we mean by continuous? So look at this. When we say tense, tense is different from aspect. Tense only talks about time and whether present, past or future that is about time but the manner in which something is done and also sentences give us more information about a particular accent than the time alone. So this particular aspect talks about the continuity of this action at that point in time which means whenever we are talking about in that present moment the whole act of watching was in progress, was in continuity. That is what that, that aspect of meaning becomes clearer through this word, this element therefore this is called aspect. What was he watching? What was Raju watching? Movie. That it should be difficult for us to figure out that this is the object and what type of a verb is this? Why? Because it answers the question what? It answers the question what? What was watching what? Watching movie. It answers the question what therefore it is a transitive verb. Are you with me now? Do we understand agreement and do we understand how the components and the types of verbs that we discussed yesterday work in a sentence? What are the features on noun that is the subject Raju that takes part in agreement of the noun Raju that is in the subject position in this sentence is playing a role in the agreement. You see there are so many things masculine noun, nominative case, third person, singular mark, singular number. So, which one of these are playing a role in the agreement on the verb? It is not about Hindi or English. Singular number and masculine gender. So, this sentence agrees with the verb in this sentence the subject Raju agrees with the verb in terms of singular number and masculine gender. The features that take place in agreement. Let us go back to the old slide the last one look at the nominal features on the look at the nominal features. There may be a lot of them, but not all the features are always taking part in agreement only some of them will be taking part in agreement. That is not all the features are always active in the sentence. So, going back to the same slide again in the English sentence if you look at the meaning of this Hindi one Raju was watching a movie. If I ask you about this English sentence what are the features that are active in agreement? Do we understand this question? In English sentence Raju was watching a movie. What are the features that are active in the agreement between verb and the subject? Only singular. Raju has masculine masculine gender that is it still has masculine gender, but is that masculine gender playing any role in the agreement in English sentence? No. This is just to show you that in Hindi there are more features that are playing role in agreement. In English one less. Now let us make this sentence Raju was watching a movie. Let us make this verb plural. If we say Raju and Mahesh what do we have to do? Watch watching a movie is that a good sentence? Raju and Mahesh were watching a movie. Is this a good sentence? This is an ungrammatical sentence. Why is this ungrammatical sentence? One person at a time please. Was carrying the singular features, but the subjects are plural. Raju and Mahesh So this element which is subject of the sentence is carrying now plural number and the verb is still depicting singular number. This shows that there is a mismatch in the agreement. In other words the subject does not agree with the verb. Therefore the sentence crashes and therefore it is called ungrammatical. We are talking about a very simple very simple thing, but every time in a discussion like this when someone says the sentence is ungrammatical I want you to know what it means for a sentence to be ungrammatical. At the same time I want you to know that what does it mean when we say the agreement between the subject and the verb is good. So this sentence becomes grammatical when we have a verb showing plural agreement mark. Then the sentence becomes grammatical. Good? Yeah, go ahead. Instead of Raju, I mean take Sita or something. It is feminine, singular. So it is similar to more. It is feminine and singular. So in the last tense, in the last, so it should be T, right? Right. It is also feminine and singular. So both nouns are similar in the carrying a similar. So which noun is in agreement? Which of them? You understand this question? Very significant question. It is asking, in this case we know that the subject has a masculine gender and therefore it is okay for us to figure out about the agreement feature on the verb. What about sentences where subject and object are both feminine and the verb shows feminine agreement marker? In those cases, how do we know which noun agrees with the verb? Do you understand this question? That is his question. The answer is very simple. First of all, therefore I gave you this kind of a sentence to show you clearly that only one noun, only one noun, only one noun, let us say Raju agrees with the verb, that is all right. Raju agrees with the, only one noun Raju agrees with the verb which is masculine and therefore it shows masculine features on the verb. When they are both feminine, the computation in human mind knows about this thing. Which noun is in agreement with the features on the verb? It may not be obvious in the sentence. Suppose if I put both the feminine nouns here, then it is difficult for me to convince you but still our mind knows which noun is in agreement with the verb. To bring that thing out, we do this combination. Under no circumstances, both the nouns will be in agreement with the verb. Only one noun has to agree with the verb and there are cases. We are going to come to those cases, that is those examples to show you that in some cases nouns in the subject position, nouns that may look like in subject positions, subject positions do not agree with the verb and there are additional constraints on that. I will show you that as well but this is a wonderful question and even in the cases where both the nouns are feminine, only the noun in the subject position will agree with the verb. Now we go back to categories of elements in a sentence and we will talk about four of them, that is a noun, a verb, adjective and prepositions. Have we had about these names? These words, nouns, verbs, nouns and verbs we have discussed. Please give me an example of an adjective. Somebody say anything. Example of an adjective. Beautiful. Beautiful. More. Strong, tall. Strong, tall, dark. All those are adjectives. How about preposition? In on, at, right, these are the elements that are prepositions. In a language like English, these elements occur in the, they occur before a noun, therefore they are called prepositions. In languages like Hindi, Tamil, Telugu, Malayalam, these elements occur after a noun. That is they follow a noun, therefore they are called postpositions. So we will be using these two terms prepositions and postpositions interchangeably referring to the same element. The only difference is in a language like English, because they occur before a noun they are called prepositions. In a language like Hindi, because they occur after a noun, therefore they are called postpositions. Another significant aspect from this distinction of preposition and postposition that comes out naturally is prepositions and postpositions always follow only nouns or always precede only nouns and that is also helpful in defining a noun. If we have a question, how do we identify an element in a sentence as noun? You put a prepositions or postpositions after that or before that depending upon the language and then you can see that is a noun or not. Take example, if I say on the table, because it is a good sequence table is a noun, because of the presence of on. Table cannot be anything else because we cannot say on beautiful in a strong. Can we say these sequences? We cannot. So, prepositions and postpositions define nouns in a structural way. We will talk about that. We are going to be also looking at relationship between elements and nodes. I will talk to you about nodes. So, that much we will be able to discuss today. So, let me let me talk about them. I am also going to introduce you to what we mean. Give me an example of a noun. We have talked about a lot of them, nouns and verbs. Give me an example of a noun. Anybody? A good looking noun. By good looking noun, I do not mean anything else. I am only saying which qualifies to be a noun in a nice way. Horse? I take that. I take horse. Can we put an article before that? Can we say the horse? Yes. What is this noun? What is this noun? Horse by itself was a noun. What do we call this sequence noun? The horse. Have you have you thought about this thing? Is it more than a noun now? It has something else. Therefore, it is more than a noun. Now, this will be called a noun phrase. In a phrase, we have something more than what the phrase has in its center, which means if we are talking about a noun phrase, in the center of the noun phrase, we are going to find a noun. Then it may have little bit more elements around them. I am trying to talk to you about the difference between a noun and a noun phrase. This may sound very trivial, but it is a very critical distinction in the formation of a sentence. So, horse is a noun.  So, the way syntax captures this distinction is the following. Let me tell you now, structure of a noun phrase. This is how it is going to look like.  It is a very simple idea. Now, let us see how it works. This is called a tree, a linguistic tree, which captures one particular phrase called noun phrase. Linguistic trees are usually binary. The reason why I am saying usually binary because in older versions of syntactic explanations, we used to have multiple branching trees. Over number of years with lot of research that has gone into it, the trees are only binary. This node tells us that we are talking about a noun phrase. So, everything that comes under this node is part of noun phrase. This is a place for an expression. This is called a specifier. This place is called a specifier which talks about which creates a space for other elements in the sentence, in this phrase that is noun phrase. This phrase is headed by an element which is called noun. So, in the head position of this phrase, we are going to have noun. Then, this element is called complement which creates another space for something to come in as an essential part of this phrase. I will tell you about specifier and complement more in a moment. For the time being, let us look at its branchage, its binary. Everything under this is a noun phrase. Everything under this is part of this phrase and the two sides are called branchage. Two branches in this tree and two branches indicate relationship between two components as equal. The way we refer to it is, see the element noun and if there is a complement related to that, that element both are sisters to each other. That is both are equal. Now, in a specifier, in this phrase, do not have sister relationships. One is higher than the other. Therefore, this relationship becomes hierarchical. For the easiness of this description, we call this node as the mother node. So, this is mother. Then, everything else to this mother, everything else of this phrase is related to this node and then these two have sister relationships among each other. These two also will have the same relationship, but the relationship between this and this, that is these two nodes is hierarchical. Therefore, it has been designed this way because we want to capture the hierarchical relationship between these elements. Are you with me so far? I will show you the relevance of why we capture such relationships and why we need to capture such relationships as well, but right now I want you to pay attention to the tree alone, how this is drawn. If we are talking about a noun phrase, the head of the noun phrase is a noun. The head of a verb phrase will be a verb. Head of a propositional phrase will be a proposition. You understand this thing?  Therefore, this whole thing is called x bar. So, what we do is we call x p, spec x bar and the head here and the compound. That is the reason why this whole idea and whole theory is called x bar theory. They are please please keep only couple of points in the mind. The trees are linguistic structure, structural trees are binary and one of the objective is to capture hierarchical relationship among the elements within that phrase. So, we will stop here at this point and then we will elaborate on what else we do with this x bar theory and how we capture structural relationship between the elements next time we meet.