Good morning. Let me introduce myself first. My name is Vikram M. Gadre and I am a professor in the department of electrical engineering at IIT Bombay. I am going to deliver a series of lectures on the subject of wavelets and multirate digital signal processing. In this first lecture or more appropriately exposition, I would like to bring before you the reason why we should be studying this subject or rather the reasons, the inspirations that have driven researchers and scientists to understand the concepts of wavelets and multirate digital signal processing, the broad themes that we are going to address in this course and finally, a broad outline or a structure of this course. So, before I begin a formal statement of structure, it would be appropriate to put before you the thrill or the fascination of wavelets that I have or the inspiration that leads me to look deeper at this subject, which I would also like to convey to you in a few words and inspire you to study this subject in depth. Typically, this subject follows a basic exposition to signals, system theory, perhaps digital signal processing or discrete time signal processing and other basic courses in communication and signal processing. So, I would pick this course at an advanced level in signal processing. I do not intend to convey from this that the concepts are difficult to understand. As you will see in some of the subsequent lectures, the concepts are actually very easy, very simple, perhaps even simpler than some of the concepts that we learn in a basic course. In a basic course, the whole subject is new to us. When we study signals and systems, the whole idea of abstraction is new. Abstraction of a signal, abstraction of a system, abstraction of a transform, abstraction of a domain. So, we assume that we have crossed that step. We have overcome that obstacle. We have agreed that abstraction is a good thing. In that sense, this course is simple. We are moving one level higher, where we are moving a little closer to reality. In a basic course on signals and systems or in a basic course on discrete time signal processing, we tend to be idealistic. We tend to want to oversimplify. In this course, we will refrain from doing that, at least in total. What do I mean by this? In a basic course on signals and systems, we assume that signals last forever. For example, when we talk about the Fourier transform, we think of basis functions or functions on which the transform is based, which start from time t equal to minus infinity and go up to t equal to plus infinity, t denotes time. In this course, we shall recognize that this is a silly thing to do. No signal in the world, at least no signal that we can deal with realistically is going to last forever. It is going to have its lifetime. It is going to begin somewhere, end somewhere. After all, the analyzer, the person who analyzes is also going to begin somewhere and end somewhere. So, the first thing we understand is we must deal with finite domains. We understand the finite domain as far as the natural domain goes very well. What I mean by the natural domain is, suppose for example, we are talking about an audio signal. The natural domain is time. So, an audio signal begins somewhere in time, ends somewhere in time. We do not listen to a piece of music forever, but for that limited period of time in which we wish to listen to a piece of music, we would like to understand better the content of the music to which we listen. We also wish to be able to develop the ability in a signal processing setup to enhance what we want out of the music and to suppress what we do not. We also wish to be able to characterize a system which does so and all the while recognizing that we are not going to deal with the signal forever. We are going to deal with it over a limited range of the natural domain. So, here as I said in an audio signal, the natural domain is time. Let us take another example of a natural domain. Suppose I wish to deal with a picture. I wish to take a picture in which I have a face and naturally many facial features, the eyebrows, the forehead, the nose, the lips and other features that are associated with a typical face. When I wish to isolate a certain feature, I would imply being able to localize in the spatial domain. Now, this is an example of a two variable domain unlike the other example of audio where it was a one variable domain, only time. Here I have two spatial variables. Localization is the common thing. Let me spend a couple of minutes in explaining that a little better. Suppose I take a piece of audio. Let us assume that in that piece of audio a number of notes are sung. If I take recourse to the Indian processing system of description, you could have a raga in which there are several different notes, the components of the raga. Suppose I wish to build a signal processing system that takes the rendition of this raga and identifies the notes that compose it, the different frequencies so to speak that come together and play to form that piece of audio. What do I need to do in such a circumstance from a signal processing perspective or from the point of view of analyzing signals? One thing is obvious. I need to segment in time so I need to be able to say that in this part of the time axis, I had this note prominently played perhaps only that note was played. In a different part of the time axis, a different note was played. Now, when I say different parts of the time axis, they are not only separated but also might be different in length. So, one note could be longer, another note could be shorter. It is not just a question of which notes have been played but also for how long. Now, what exactly do we mean when we talk about notes? If we take a signal processing perspective, I mean after an introduction to the fundamentals of signals and systems or even for that matter a basic course on discrete time signal processing, all of us are comfortable with the idea of a frequency domain. So, we accept that we can think of continuous signals or discrete sequences as having embedded inside them. A collection of sine waves, if it is a continuous signal that we are talking about, we have continuous sine waves. If it is a discrete sequence that we are talking about, we have sampled sine waves and the whole philosophy of the Fourier transform is most reasonable signals that we deal with can be thought of as comprised of or composed of a collection of sine waves. In fact, in principle if the signal is not periodic, then we are talking about an infinity of sine waves with frequencies ranging all the way from 0 to infinity. If it is a periodic signal that we are talking about, then we have a discrete set of sine waves possibly infinite, possibly finite which we call the Fourier series representation. Anyway, what I am trying to emphasize here is that there is a different domain to which we go when we wish to analyze a signal better. So, in the language of signal processing, if I were to take that raga, that rendition of the audio piece, the elementary audio segment as understood in Indian music and if I were to query what notes are being played I am equivalently asking what is the frequency domain content of this audio piece. If I visualize a frequency axis, what points on that frequency, what points on that frequency axis are occupied, what are the locations where the transform is predominant, is prominent. Now, this is where the whole story starts and perhaps is the most fundamental inspiration for this course and wavelets and multirate digital signal processing. I will first talk about where wavelets come from. Well, Fourier transforms deal with waves, sine waves to be more precise. We recognize the merits of sine waves. Sine waves have many nice properties. For one, they occur naturally in many different circumstances. For example, an electrical engineer recognizes the sine wave as naturally emerging from an electricity generation system when there is electromagnetic induction. If there is a perfectly circular rotating device in a magnetic field and if all is perfect in the generating system, we would be generating a perfect sine wave from the brushes. So, sine wave is a good idealization to work with for an electrical engineer, but that is not the only point. Sine waves are the in some sense the most analytic, the smoothest possible periodic functions. They also have the power of being able to express many other waveforms. That means, they form a good basis from which many other waveforms can be generated. They have many other nice mathematical properties. If I take two sine waves with the same frequency, possibly different amplitudes and phases, I would get back a sine wave of the same frequency of course, with a third amplitude and phase. If I differentiate a sine wave, I get back a sine wave of the same frequency and naturally, if I make a combination of these operations namely differentiation or even integration for that matter and linear combinations and if I restrict myself to sine waves of a particular frequency, I remain within the domain of sine waves of that particular frequency. This is something beautiful about sine waves. It is not easy to find wave forms which obey this and as I said before, sine waves form a good basis. So, they form good building blocks for being able to express a wide variety of signals. For all these reasons, the sine wave has been very popular in a first course on signal systems, discrete time signal processing and what have you, communication. But as I said, right in the beginning of this lecture, one of the reasons why we are not so happy with sine waves is that they need to last forever, begin from minus infinity and go all the way to plus infinity. Otherwise, if you truncate a sine wave, if it is one sided for example and if you look at what happens to an electrical system when you apply a one sided sine wave, by a one sided sine wave, I mean a sine wave which starts from some point, it is 0 up to then and starts from some point and continues afterwards the sine wave, the response is very different from what would be the response for a sine wave that started at minus infinity in general. There would be transients. Which are not periodic and then all these beautiful properties of sine waves and their responses go away. So, if I really wish to be able to apply the basic principles of signal systems and discrete time processing that I have learnt in a basic course, I need something unrealistic. I need a sine wave that lasts forever. How can I be more realistic in my demands? By accepting that I cannot deal with waves, but it is more appropriate to deal with wavelets that is why the word wavelet comes from, small waves, waves that do not last forever, functions that are not predominant forever, they are significant in a certain range of time, perhaps only exist in a certain range of time and insignificant outside. So, they have a certain support over which one might want to use them, one might want to consider them to exist and so on. A much more realistic assumption and that really is what we call a wavelet, not a wave, but a wavelet. For example, you could if you wish think of truncating a sine wave to a rectangular region. That means suppose we take a sine wave to last from 0 to 1 millisecond as an example. It could be an example of a wavelet, later we will see this is not a very good example, but yes in principle a wavelet, a wave that does not last forever, a simplistic explanation of what wavelets means. But that is not the whole story, our whole objective was to talk about the other domain too. So, going back to the example of the audio signal, if I thought of the audio signal as comprising of many sine waves to come together to form an audio piece, then I wish to be able to do something simultaneously in two domains and that is the key idea here. So, for example, to put it in plain language I should be able to say well there was this two second audio clip out of which there were five notes being played. Each note was played for different intervals of time, may be the first note was played for 0.4 seconds, the second note was played for 0.7 seconds, the third note only for 0.2 seconds and so on. So, I need to be able to segment in time, but when I am talking about being able to identify notes, I am also talking about being able to segment in frequency and low and behold that is where the conflict arises. A very basic principle in nature says, if I wish to be able to segment in time and frequency simultaneously, I am going to run into trouble. Nature does not allow it beyond the point and that is something very fundamental. It pops up in many different manifestations in different subjects. In modern physics they call it uncertainty, the uncertainty of position and momentum. In signal processing we call it uncertainty, the uncertainty of the time and the frequency domain. So, to put it simply though not very accurately, the shorter you play a note, the more difficult it is to identify it, not very far from intuition. If you play a note for a long time and listen to it for a long time, you are likely to be able to identify it better. Common sense tells us that, but what common sense does not tell us is that you can never quite go down to identifying one particular frequency precisely. So, if I wish to be able to come down to a point on the time axis, then I need to spread all over the frequency axis and if I wish to be able to come down to a point on the frequency axis, I need to spread all over the time axis. That is of course, the strong version of this restriction, but there is a weaker and a little more subtle version and that is as follows. Even if I am not quite interested in coming down to a point on the time axis, I am content with being in a certain region. As I said in the first 0.4 seconds out of the 2 second clip, I was playing note number 1, that means some frequency number 1. I would be able to say this at least to a certain degree of accuracy, that is what I am trying to point out here. What the principle of uncertainty tells us is that this can be done to a certain degree of accuracy, you can identify that note to a certain degree of accuracy. Well, what uncertainty also tells us in a more subtle form is that if I even choose to relax to a certain region of time. So, I say well in this region of time tell me the region of frequencies which were predominant, even then there is a restriction on the simultaneous length or measure of the time and frequency regions. And of course, they have a tussle with one another. The smaller I make that time region, the larger that frequency region becomes. That means the more I want to focus in time, the less I am able to do so in frequency. This is indeed something that arouses a lot of thought. It may seem something far from our interest at first glance, but when we look at it carefully, we realize it is something very fundamental to what we often desire and that is what I am now going to explain to you with a couple of more examples. We live in an age where we use mobile telephones. In fact, more fundamentally digital communication. What are we asking for in digital communication when we look at it from a signal or system perspective or transform domain perspective or time and frequency perspective? Going right down to brass tags, what we are asking for in digital communication is I should be able to transmit a sequence of bits, binary values 0 or 1 and how do I transmit that sequence of binary values? I choose may be 1 of 2 possible wave forms in the simplest scheme so corresponding to 0, I have 1 wave form corresponding to the bit 1, I have a different wave form. To make life simple, the 2 wave forms have the same time interval. So, for example, we talk about I mean all of us here about computer networks and they talk about the speed of the network. So, they say well this network can operate at a speed of 1 mega bit per second. What does that mean? It means in 1 second I can transmit 10 raise the power of 6 bits. So, you have 1 millisecond to allow each bit to be transmitted. Give it a thought, here we are talking about time. What are we saying about frequency? Now, let us go to the mobile communication context. I have so many different mobile operators. Obviously, each operator will want its own privacy. So, what is being communicated on the network of operator 1 should not interfere with what is being communicated on the network of operator 2. Now, where is this separation going to occur? Not in time. After all, there are many different people simultaneously using mobiles bought from both of the operators. So, the separation cannot be in time. We may argue the separation can be in space. So, in one region you may have mobiles from one operator and another region in space I mean mobiles from the other operator. So far so good. But that is also not always true. It is very common to see mobiles purchased from different operators operating in the same room. So, there is no separation in time, no separation in space. So, where is the separation then? The separation has to be in a domain which is not so easy to see, but once we have done a course on signals and systems reasonably easy to understand and that domain is frequency. So, we say well operator 1 has this bandwidth allocated to him, operator 2 has the other bandwidth allocated to him. When we say this bandwidth may be a certain region of the frequency axis of size let us say 2 megahertz. When we say this region of 2 megahertz is allocated to operator 1 and another region of 2 megahertz is allocated to operator 2. Are we not talking about segmentation in a different domain? In fact, there we are talking about simultaneous segmentation. We have a segmentation in time because you want to transmit different bits in different time segments and you want to have a separation in frequency because what is transmitted by operator 1 should not interfere with what is transmitted by operator 2. So, here is a very common though not so obvious example of simultaneous desire for localization in time and frequency. Other than the audio example which is of course a little more obvious, a little easier to understand, this example is equally common at least in the scenario today, but perhaps not so easy to understand, but a little reflection makes it very clear to us. There is a desire to localize in two domains simultaneously. Let us go to a biomedical example. Very often when one analyzes an electrocardiographic waveform, what one wishes to identify are features in the ECG signal. Now, I do not intend to go into the medical details, but there are different segments in a typical ECG signal. They are often indexed by letters PQ and so on. Without needing to focus on specific details of an ECG signal, let us try and understand the connection to time and frequency localization. When we talk about an ECG signal, all features are not of the same length in time. Some features are kind of shorter, some features are longer. In fact, to go away from an ECG signal, biomedical engineers often talk about what are called evoked potentials. So, we provide a stimulus to a biomedical system or to a biophysical system and we evoke a response and the waveform corresponding to that response is called the evoked potential. It can be studied as an electrical signal. Now, the evoked potential again typically has quicker parts in the response and slower parts in the response. Naturally, we expect the slower parts of the response would be predominantly located if you think of the frequency domain in the lower ranges of frequency and the quicker parts of the evoked potential waveform would be located in the higher ranges of frequency. Now, here is again an example of time frequency conflict. Suppose, I wish to be able to isolate the quicker parts. Is it alright simply to isolate the higher frequency content in a certain signal and which comes from an evoked potential and suppress the low frequency part? Well, you see if we try and suppress the low frequency part, then we have already suppressed the slower parts of the response and if we try and suppress the higher frequencies in a bid to emphasize the slower parts of the response, we have suppressed the quicker parts of the response. So, if we think conventionally in terms of the frequency domain, may be high pass filtering or low pass filtering, nothing works for us. If we do high pass filtering, then we have effectively suppressed the slower parts of the response. If we do low pass filtering, we have suppressed the quicker parts of the response. So, we need a different paradigm or a different perspective on filtering. We need to identify in different parts of the time axis which regions of the frequency axis are predominant and therefore, in a certain sense identify different parts of the frequency axis to be emphasized in different time ranges. This is another perspective again on the time frequency conflict and all this is going to lead us in the direction of building up this course on wavelengths. We shall of course understand some of these concepts a little better as we progress in the lectures. But for the time being, I have given you these three examples with the intent of bringing before you, perhaps not completely, but at least in a way to inspire your imagination, the whole idea of time frequency conflict or more generally the conflict between two domains, domains of analysis and representation of a signal and of course, then going further even of a system. In a first course, we understand the domains very well. We understand as a time domain. We understand as a frequency domain. We do well because we keep them apart. It makes life easier. But what we are trying to bring out through these three examples the audio example, the digital communication example and the biomedical waveform example whether it is electrocardiographic waveforms or the evoke potential waveform. What we are trying to bring out is that one normally needs to consider the two domains together time and frequency. And when we try and do so, there is a certain very fundamental conflict that we have to deal with. That conflict called uncertainty appears as I said in different manifestations in different subjects. And we are going to look at that principle the uncertainty principle as it applies to signal processing in great depth at a certain stage in this course. But before that, we are going to consider one particular tool for analyzing signals, analyzing situations with the recognition that we need to be local and not global. So, we are going to build up the whole idea of wavelets by starting from what is called the Haar multi resolution analysis. Haar incidentally is the name of a mathematician. Call him a mathematician, call him a scientist what you will. But one of the beautiful things that this gentleman proposed was what is called a dual of the idea of Fourier analysis. What do we do in Fourier analysis? We allow even discontinuous waveforms, we allow non smooth waveforms and we convert them into a sum or a linear combination of extremely smooth functions namely the sine waves. Haar said can we do exactly the dual can be in principle take smooth functions and convert them into a linear combination of effectively jagged or discontinuous functions. Why on earth would one like to do something like that? Again let us reflect for a minute. A few years before this might have seemed silly to do, but today it is not. What are you doing when you are doing digital communication?  How does one record digital audio? One firstly samples. So, one takes values of the audio signal at different points in time, one digitizes them and one then records those digital values as a stream of bits. All of these are highly discontinuous operations. You are forcibly introducing discontinuity in time and on top of that you are introducing discontinuity in amplitude by quantization. So, wanting to represent the beautiful smooth audio in terms of very discontinuous bit streams is very very beneficial to digital communication. And in fact, none of us complain when we have a good digital audio recording. Sometimes we even say that a digital audio recording is better than an analog recording as we had in the past. So, going from smooth to non-smooth has its place in modern communication and signal processing. And when HIR proposed that one should look at the whole philosophy and the whole principle of being able to go from smooth to non-smooth perhaps he was looking into the future when this would be absolutely essential. What we are going to do in the very first few lectures immediately following this is to look at one whole angle of wavelets and multirate digital signal processing based on the principles that HIR propounded. So, we are going to look at what is called the HIR multi-resolution analysis. And in fact, if we understand the HIR multi-resolution analysis in depth, we actually land up understanding many principles of wavelets many of the essentials of multirate processing specifically what is called two band processing very well. So, we shall draw upon the HIR multi-resolution analysis to understand some of the basic concepts that underlie this course and of course, build upon them further later on. From the HIR we shall progress to slightly better multi-resolution analysis, better in what sense we will understand. And there are many different families of such better multi-resolution analysis one of them being what is called the Dobash family. Dobash is again the name of a mathematician scientist who proposed that family of multi-resolution analysis. As I said at a certain point in the course immediately following this we shall then look at the uncertainty principle fundamentally and in terms of its implications. From there we shall move to the continuous wavelet transform. So, in the HIR multi-resolution analysis we have a certain discretization in the variables associated with the wavelet transform. Later on we shall go to what is called the continuous wavelet transform where the variables the independent variables that are associated with the wavelet transform all become continuous. Following that we shall look at some of the generalizations of the ideas that we build up earlier in this course and towards the last phase of the course we shall look in depth at some of the important applications to which wavelets and multirate digital signal processing provide great advantages. Now I would like to spend a little while in this lecture on building up in parallel some of the developments that took place to introduce the subject of multirate digital signal processing. What is multirate? What rate are we talking about here and why do we need to talk about multirate? Why is it connected with wavelets let us go back to the audio example or maybe let us first go to the biomedical example. In the biomedical example we said we would have quicker parts in the response and slower parts in the response. The slower parts of the response are likely to last for a longer region in time. The quicker parts of the response are likely to last for a smaller regions in time. So, here other than the concept of being able to localize on a certain region of time and of course correspondingly on frequency there is also the distinction between what kind of localization is required for higher frequencies and lower frequencies. If we spend a little bit of thought and time in understanding these two kinds of components we will realize that most of the time when we are talking about slower parts of the response or lower frequencies we are talking about compromising on what is called time resolution. So, I bring in the idea of resolution here. Resolution means the ability to resolve the ability to be able to identify specific components. So, for example, frequency resolution relates to being able to identify specific frequency components and going further and being a little more pinpointed when I am talking about frequency resolution what I am saying in effect is suppose I have two sine waves whose frequencies start coming closer and closer together. Over what region of time do I need to observe them so that I can actually identify the two frequencies separately? How can I resolve the two frequencies? How much can I narrow down on the frequency axis? Now, what we are talking about is not so much how much we can narrow down, but how much we need to? When we talk about higher frequency content or things that vary quickly it is often though not always the case that we are willing there to compromise on frequency resolution, but we want time resolution. So, things that take place quickly and our transient short lived demand time resolution and things that occupy the lower frequency ranges which last for a long time demand frequency resolution. So, very often it is true that when one goes down on the frequency axis one demands more frequency resolution the ability to resolve frequencies more accurately as opposed to time resolution. The ability to resolve which time segment it occurs and when one goes to higher frequencies one normally demands more time resolution and lesser frequency resolution. One is asking for how closely one can identify two segments or two parts of the waveform which vary quickly that means one is trying to narrow down on the time axis and in doing so then one must compromise on the frequency axis. So, this is what brings us to the idea of multirate processing. You see it means that when I talk about bands of higher frequencies I must use smaller sampling rates in a discrete time processing system when I am talking about lower frequency ranges I must use larger time sampling points or sampling intervals why must I do so to be most efficient in the processing operation when I am talking about lower frequencies. So, in an evoked potential waveform if I am trying to look at the slower components I should not unnecessarily sample too frequently it only increases my data burden and does not offer me anything special. On the other hand when I am analyzing the quicker components it is inadequate to use a low sampling rate. I would be doing injustice to the components for those of us who might be exposed to the concepts of sampling and aliasing. If I am not faithful in my sampling rate of the quicker components I would introduce aliases I would introduce spurious effects which I do not want. So, all in all we recognize that it is not a good idea to be using the same sampling rate for all frequency components. So, unlike a basic course on discrete time signal processing where we assume all sequences are at the same sampling rate here we need to deal with sequences that are effectively at different sampling rates in the same system. That means we also need to deal with systems that operate with different sampling rates and that is why we talk about multirate discrete time signal processing. Now at a conceptual level we understand very well why there is a close relationship between multirate discrete time signal processing, the idea of uncertainty, the requirement of resolution and if we go further then when we do multirate discrete time signal processing we also bring in a new concept of filter banks versus filters. As I said if we go back to the biomedical example there is the effect or there is the desire to separate components. So, when I wish to separate components naturally I wish to have many different operators all at once. So, I need a system of filters which not only have certain individual characteristics, but which also have collective characteristics. So, I need to be able to analyze and then synthesize and all this with localization included. This is what we mean by a filter bank. So, a bank of filters as opposed to a single filter in discrete time signal processing refers to a set of filters which either have a common input or a common point of output or summation output. This concept of a bank of filters and in fact, two banks of filters an analysis filter bank and a synthesis filter bank taken together is very central to multirate discrete time signal processing. We shall be looking at that concept in great depth. So, we shall be building up the idea of a two band filter bank in reasonably great depth in this course. The concept of a two band filter bank is of great importance in being able to construct wavelets. In fact, we shall see even from the R multi resolution analysis example that there is an intimate relationship between the wavelet or the R wavelet and the two band R filter bank. So, much so that if I construct a properly designed two band filter bank I also construct a multi resolution analysis that goes with it so to speak. All this is very exciting and what we intend to do in the lectures that follow from here is to take these concepts one by one. So, in the next few lectures we intend to talk about the R multi resolution analysis to build up certain basic ideas from it. In the lectures that follow as I said before we intend to talk about the uncertainty principle and its implications. Following that we move from the discrete to the continuous wavelet transform and then generalize both the continuous and discrete wavelet transforms to a broader class of transforms. Finally, in the course we would talk about what is called the wave packet transform and some variants of the wavelet transform and variants of filter banks and to end we shall look at several different applications of wavelets taken from different fields. With that then we come to the end of this first introductory lecture on the subject of wavelets and multiracial digital signal processing and proceed there with in the next lecture to talk about the R multi resolution analysis. Thank you.


Okay. Recording is done. Good morning everyone. Welcome to BC214, our course on developing the human spirit. Let's take a moment just to pray together and get started so the others will also sorry, join the class soon. Could somebody lead us in prayer please and then we will start. Father we thank you for this morning Lord we humble ourselves before your presence. We pray O God as we learn from your word it would speak to us and help us to know more about developing our spirits in you O God. We pray that you would speak to our hearts and establish us in your kingdom. We give you all the glory, honor and praise in Jesus name we pray. Amen. Amen. Thank you. Thank you once again. Good morning everybody. Welcome. I know we had a break last week. Sorry I couldn't take my class last week. So let's quickly review what we did the week before in a very first lecture and then we will take things forward from there. I'm going to just share the lecture one notes so that we can all see it and follow along. So we started in section one we started talking about just trying to understand some things that we see revealed to us in scripture about the human spirit. Now we began by saying that we are tripart beings spirit soul and body. First Thessalonians chapter 5 verse 23 the scriptures tell us you know that we are spirit soul and body. So we understand the body is the outer man the outer part of us the soul is our mind our intellect our ability to reason and so on and our spirit is the eternal part of us. It's the part of us that can contact the spiritual realm that can contact God and we must understand that the human spirit is the real person.   Then we started looking at other scriptures we looked at Hebrews 4 verse 12 where we saw that the spirit and the soul are distinct because the word of God pierces penetrates to the dividing asunder of spirit and soul. So the spirit and soul must not be confused. They are very closely intertwined but they are also very distinct the different parts of us so spirit and soul. And then we saw that it is the word of God that helps us understand the difference what is from the soul what is from the spirit because the word of God is a discerner of the thoughts and indents of the heart. So the word of God will tell us clearly help us understand clearly what is coming from the heart what is from the soul which is our emotions and our mind and so on so forth. Then we spent quite some time on first chapter 3 verse 4 where you know the in verse 3 4 of course the context is about the outward adorning and the dressing and all that but in that context Peter says that referring to the heart the spirit he says the hidden person of the heart you know so the real person is the hidden person it's the heart the heart the spirit is a real person and and and then he talks about the beauty of the hidden person which is in the sight of God of great price you know and he talks about characteristics a quiet and a gentle spirit. So these are things to keep in mind that the human spirit the heart has its own character or characteristics in first Peter 3 he is specifically talking about a quiet and a gentle spirit so those are the characteristics that he's mentioning there and like that there can be so many other characteristics of love and joy and peace and these are things that come from the spirit and he says in the sight of God it's of great value you know so God looks at our spirit he sees the character of our spirit and he said that's that's very that's what is very precious to God and that's what he's after you know he's after that because the body you know will crawl and die but the spirit is going to live and that's eternal so the beauty of the outward man is fading but the beauty of the inner man is eternal it's going to last forever and so we emphasize that from first Peter chapter 3 and verse 4. So these are some of the notes that we discovered now some things in relation to the spirit and soul in the New Testament we will find the phrase inner man quite often and when especially in the writings of the apostle Paul he uses this quite a lot and when he refers to the inner man or the inward man it's it's talking about the inner person made up of spirit and soul together you know that means there is a part of our soul that because it overlaps and intertwines with the spirit so closely you know he's talking about this inner person so when we say inner person we are referring to the spirit and soul together or inner man inward man who you are on the inside spirit and soul together so we use that or the New Testament uses inner man like that now what happens at death and this is these are the side notes just to keep us to give us a little understanding it's not as a side note what happens during death at death the body is separated from the inner man which is the spirit and soul so the body which is our flesh and blood and bones that goes into the ground it decays it disintegrates becomes dust but the inner person which is the spirit and the soul will continue either in heaven or in hell so that means this inner person that continues is conscious you know so that's why for example when we see when we read about in Luke 16 we read about this rich man and Lazarus Lazarus was a neighbor I'm supposed to this rich man went into hell and he was in torment and he cried out he said you know can he just dip the tip of his finger in water and come and touch my tongue you know so that so that means he is very conscious he's feeling these things and which you know that this consciousness so this being aware of things is part of our soul and and and so he remembers those things and he even says you know Lord you know I'm sorry he says you know can somebody go and warn my brothers you know see that means he has recollection of those things so there is that consciousness that we that seems to be there even after death you know so that's the inner person spirit and soul now let's pick up from there and share a few more things about the spirit in John chapter four which is 21 to 24 and this is a familiar passage for us what we want to emphasize from John 4 21 to 24 is that our primary engagement with God is in the spirit our primary interactions with him is spirit to spirit so John chapter 4 verses 21 to 24 let's could somebody read that for us John chapter 4 21 to 24 please John chapter 4 verse 21 to 24 Jesus declared believe me women a time is coming when you will worship the father neither on this mountain nor in Jerusalem you Samaritans worship what you do not know we worship what we do know for salvation is from the Jews yet a time is coming and has now come when the true worshipers will worship the father in spirit and truth for they are the kind of worshipper the father seeks God is spirit and his worshipers must worship in spirit and in truth thank you so we are familiar with these scriptures what I want to point out is you know this woman Samaritan woman is trying to discuss with Jesus about the location you know which place like or which mountain must I go to you know to worship God and Jesus responses is focusing on this whole spiritual dynamic that means God is spirit so it's not about which mountain you're going to go it's not about the place from there but it is our spirit that is going to worship God you know that's why he's saying look basically if you want to paraphrase it you can worship God from wherever because it is your spirit that's going to worship God God is spirit and you worship him in spirit and in truth I mean there's a spiritual thing and it is being done in truth or in sincerity you know that you're really sincere about it that's what God is looking for you worship him in spirit and worship him in truth so our primary engagement with God is spiritual now this does not mean that God won't touch our soul and our body of course he's God over our whole being so he can touch our soul he can touch our emotions we can feel we can feel joy we can feel you know all those thing emotions and we sometimes physically also God will touch us all that is there but our primary interaction is spirit to spirit God is spirit and as we interact with him we worship him in spirit and truth another scripture that we want to look at is Philippians 3 and verse 3 it's it's it's similar to what we just read but it's also good to look at it Philippians 3 3 but Paul himself states the same thing somebody could read that for us Philippians chapter 3 and verse 3 please Philippians chapter 3 verse 3 for we are the certain sish who worship God in the spirit rejoice in Christ Jesus and have no confidence in the flesh Amen thank you so similar to what we just read in John 4 Paul is saying we worship God in the spirit same thing right we worship God we engage with God spiritually to spirit to spirit we worship God in the spirit and we are not putting any confidence in the flesh that means in our engagement with God it is not based on what I'm doing in the flesh you know it is my spirit that is going to engage with God and therefore in my spirit you know God is also going to interact with me God is going to engage with me what is interesting is not only does Paul present this in our worship of God he also says that in our service to God it is out of our spirit so it is interesting let's go to Romans chapter 1 verse 9 Romans 1 9 and somebody could read that for us we just quickly look at that for God is my witness whom I serve with my spirit in the gospel of his Son Amen so Paul is saying we serve God I serve with my spirit Romans chapter 1 and verse 9 so our serving God that means our ministry is also coming out of our spirit and so you know last time in the class we just said you know of course when we're doing ministry we look we think about the natural you know what what kind of clothes we're going to wear and how we are going to you know appear in front of people okay fine that has its place we of course have to you know look clean and decent and all of those things but the work of the ministry is actually going to take place out of our spirit right so Paul says I serve God in my spirit or with my spirit no so Christian ministry then comes out of our spirit it is not the strength of our intellect it is not the strength of our physical body although of course we have to use our body and we are using our mind of course that's part of how we engage with the world but it is really out of our spirit that we serve God right so in our worship to God and in our service to God it is coming from our spirit from our spirit and that's why the spirit the human spirit is so important and that's what we're going to talk about as we move along how do we develop our human spirit in our worship of God and in our service to God so that we can do this better right we can worship him better we can serve him well because it is a work of the spirit so we covered till this last class now some additional thoughts concerning the spirit the human spirit what we seem to understand from the scriptures and you know there are only a few verses on this so I don't want to make it like a big doctrine or something but I just want to say what we can see in the scriptures is that the human spirit has a starting point a beginning like just as we are born physically there is a time there is a moment in time when God creates us and when God creates us he creates a spirit soul and body so there's a moment in time so example if somebody asks me my date of birth okay I've said now about 11th this year I was born okay that means that was my physical birth that is the time physically I came into this world but some time which approximately nine months before that some moment in time God created me as a person spirit soul and body somewhere and it happened in my mother's womb okay that's where we all begin right so while the physical process started and we don't know exactly when we don't know exactly how but Almighty God is the one who creates the human spirit so he created the human spirit see man cannot create the human spirit God created so some moment in time God created and what we can see in scripture is that just as there is a physical growth of the body the the organs the human spirit can also grow in it and we feel it from the human spirit has faculties just like the physical body has faculties and we will identify those faculties and these faculties can be developed in the human spirit so if you look at Hebrews 12 let us read those two verses please and Hebrews chapter 12 and we will look at verse nine and we'll also look at verse 23 somebody could read these two scriptures for us Hebrews nine uh Hebrews 12 nine and 23 Hebrews nine Hebrews 12 nine furthermore we have had fathers of our flesh which corrected us and we gave them reverence shall we not much rather be in subjection unto the father of spirits and live verse 23 to the general assembly and church of the first ball which are written in heaven and to God the judge of all and to the spirits of just men made perfect okay thank you now the reason we picked out these two verses is because both these verses are talking of something saying telling us something about the spirit in verse nine Hebrews 12 nine the writer of Hebrews is calling God as the father of spirits so he is the father the one who creates or gives life gives birth to every human spirit so you're the father of spirits every all of us every human being every human spirit started there because God created he's a father but very interestingly then in verse 23 he's saying he's talking again about the spirits but he's saying the spirits of just men made perfect so of course he's talking about people who have come to know God who are been born again and they're part of the church and so he's talking about believers here so he's talking about the spirits of just men or just people people who have been justified made perfect made mature no so that word perfect is being brought to maturity so he's saying it's our believers you think the spirits of these people just people that have been made mature or grown up you know so interestingly and we will of course see other passages that the human spirit is has been made or it is it has gone through this growing process by which it has come to a place of maturity spirits of just men made perfect brought to maturity so our human spirit has a beginning God is the father creator and we are seeing the human spirit is also being made mature being made perfect it's growing you know and there will be other scriptures that we can see now as part of this what is interesting the Bible seems to indicate and you know it's generally referred to as a stage of innocence a stage of innocence now why is this important and why are we making mention of it is because we cannot you know we cannot say this so I don't want to argue I don't want to fight about this I'm just you know sharing this as okay this is something that seems to be there in scripture but you know we don't we can't say everything for sure but it seems like that the human spirit when it is born it is born innocent it is not born so that's a stage of innocence and then after that there is a place where God holds the person responsible for sin now we know and we will look at all these we know that you know from the time out of sin there is sin in this world and by default there is a propensity to go and sin but it seems like there is a time period when God by default holds the person innocent and after the leaders now you're responsible now how can we say that let us look at all these scriptures together let's go to Romans chapter seven so I don't want to present this as you know okay this is the only way it is no I'm presenting it more as here are a few scriptures and again there are not many here are a couple of scriptures that seem to indicate it so just keep it in mind maybe it will help us understand things but even if we don't know this fully well it's okay we understand it in heaven but let's look at this in Romans chapter seven verses seven to ten somebody read this please Romans seven seven to ten Romans chapter seven verses seven to ten what shall we say then is the law sin God forbid no I had not known sin but by the law for I had not known lust except the law had said thou shall not covet but sin taking occasion by the commandment brought me in brought in me all manner of evil desire for without the law sin was dead for I was alive without the law once but when the commandment came sin revived and I died and the commandment which was ordained to life I found to be unto death thank you okay so Paul of course in Romans when he's talking about his life under the law and how he struggled with sin where the law told him you know okay this is the right thing to do and he wanted to do it but he didn't have the power to do it so that's Romans chapter seven but while he's describing that he says in verse nine Romans seven nine he says I was alive once without the law but when the commandment came sin came alive or sin revived sin came alive and I died so this is one scripture and like I said you know we don't have too many scriptures on this but this is one scripture where people when I say people have Bible scholars those interpret scripture Bible teachers think that this seems to indicate a stage of innocence so while we we know that you know in Psalm 51 verse 5, Psalm says in sin my mother conceived me so I was it's like he's saying I was born like as I was born in sin and Romans 5 12 says you know sin passed upon every person so while we do understand that the fall is upon every person the human race and by default we are born in under sin yet it seems to indicate Romans 7 9 that there is a stage of innocence where Paul says I was alive without the law what does he mean I was alive without the law so you think about Paul he was born a Jew that means he was born under the law he was born a Jew they already had the law but he still says I was alive without the law meaning without the knowledge of the law so the law was there it was given to all the Jewish people but till he didn't understand the law he says I was alive but when the commandment came verse 9 that means when I understood the commandment then I died that means now I was held responsible for my choices and my actions and of course I did the wrong thing so sin brings death so I died so it seemed like there's the stage of innocence and again I don't want to present this like as a ultimate doctrine I'm just saying it seems like that you know there's a stage of innocence when the person is not very aware of you know the law the commandment and so until then okay yeah you're born under sin but God doesn't hold you responsible but once you understand the law then God holds you responsible right so pigs and a wife of what relevance would this be because some people ask okay when a baby dies does the baby go to heaven or does the baby go to hell then we'd say you know yes it is true that we are all born under sin because Adam sinned and we're all born under sin but can the baby be held responsible when it has no knowledge you know it hasn't uh people say the age of accountability hasn't come to that place where it understood the law can God you know send that child to hell and so that's where we begin from verse 9 we say okay there seems to be this stage where God doesn't hold even though the human is default born under sin it doesn't hold that spirit responsible until the understanding comes of the commandment so you know so based on that we say maybe you know until that age of innocence in that stage of innocence or until that age of accountability the baby who dies will go straight to heaven and so that's that's kind of how we say it but again you know I don't want to because there's not too much in the scriptures we can't uh you know say this with clarity but there seems to be and I just wanted to share that right but what we do know is I'm going to the next point is that because of sin the human spirit starts off in that place of sin and because by one man sin came into this world death passed upon everybody death passed on the human race so we are born that you know we start off like that so we see this and let's go to divisions too so let us understand the condition of the human spirit uh understand all right this is the way we all start off spiritually being born into this world Ephesians chapter two versus we can read I guess we could read this one and two Ephesians two one and two somebody could read that Ephesians chapter two verse one and two as for you you were dead in your transgressions and sins in which you used to live when you followed the way of this world and of the ruler of the kingdom of the the spirit who is now at work in those who are disobedient so paul is telling us you know god made us alive but what was our our our condition before god made us alive we were dead in sins and we also walked according to the prince of the power of the yeah that's referring to satan the spirit that works in those who are disobedient so before we were born again before god made us alive spiritually we were dead now that doesn't mean our spirit was didn't exist our spirit existed but our spirit did not have life from god and instead he says in verse two the spirit of disobedience was or rebellion was working in our spirit yeah so that's what that was our spiritual condition or the condition of our human spirit before we were born again you know we were we did we were dead and satan was actually working in us we go to chapter four Ephesians 4 paul explains that further and we can just look at verse 18 Ephesians 4 18 someone could read that Ephesians 4 18 having their understanding darkened being alienated from the life of god because of the ignorance that is in them because of the blindness of their heart thank you so again here he's talking about the condition of the unsaved person so Ephesians 2 1 2 and 3 and Ephesians 4 17 18 he's talking about the condition of the human spirit before being saved before being born again here he's saying in verse 18 our understanding was darkened we couldn't understand spiritual things we were cut off from the life of god so we didn't have the life of god so that's what it means but that is spiritual death it means we don't have the life of god in our spirit so it says they were cut off from the life of god and their hearts was blinded their ignorant heart was blind so this is the condition of our spirit or for every human person before born again they be our spirit swollen body but our spirit is dead is blinded doesn't have spiritual understanding dead means it doesn't mean it's not that is there but doesn't have the life of god doesn't have god's life instead the devil is working he's the spirit of disobedience that rebellion is working through our spirit moving us to do all the evil things our hearts are hardened and blinded we can't understand spiritual things it's like we like so the bible says we are in darkness there's darkness over our human spirit but that is where this born again experience comes right so when we are born again and i'll just quickly summarize it because we we know that when we are born again what happens to our human spirit god gives his life the life of god comes into our spirit the very life and the nature of god comes in and the spirit of disobedience that was at work is banished no longer you cannot work in this person's spirit anymore because this spirit is now surrendered to Jesus Christ so the holy spirit comes to dwell in our spirit so before that there was a spirit of rebellion working in our human spirit now god the holy spirit has come to dwell in our humans that's what bible says yet the temple of the holy spirit christ dwells in your hearts and we are born again god gives us his own life and nature now spirit and our eyes are opened we begin to understand spiritual things we have come into the light we're no longer in darkness so this has happened to our human spirit when we got born again so that's why we've become new creation in our spirit you know god is it's it's it's dramatically changed now from where we were he says you were dead spirit of disobedience was working you did not have the life of god your spiritual understanding was darkened your heart was hardened now we've come to Jesus the holy spirit is in us christ is dwelling in us we have the love of god our heart is opened god our eyes are open we understand spiritual things we're in the light so we're born again but what i want to emphasize now is this human spirit this born again human spirit can grow and spiritually can grow and some of the scriptures that we are familiar with first beat two and verse two he does grow of as newborn babies desire the pure milk of the word that you may grow thereby so he's he's he's talking about the human spirit obviously he's not talking about the physical body because he's writing to grown people so to the grown people he's saying like newborn babies you desire the milk of the word so obviously he's not talking about our natural physical growth he's talking about a spiritual growth and he's saying desire the milk of the word so you can grow by it so that growth has to do with the growth of the born again human spirit you can grow there or in second Peter 3 and verse 18 he says grow in grace and in the knowledge of our lord Jesus Christ grow in the grace and in the knowledge no again spiritual growth growth of the human born again human spirit the human spirit the born again human spirit can grow that means it can mature it can increase in grace talking about character and virtue it also grow in knowledge meaning the understanding the learning the revelation spiritually we can increase we can grow so as we've mentioned and there are several other scriptures here we can see where we can increase in revelation Ephesians 1 18 Colossians 3 10 talked about increasing in revelation we can know the will of God that means the human spirit begins to understand will of God this is what God is pleased this is what God wants for me so the human spirit begins to understand that the human spirit can also become strong you know we can grow in strength Ephesians 3 16 so just given these we will talk in depth about the faculties or developing the faculties of the human spirit but I just mentioned this here saying that look we are born again but it's born again each be developed each it's a knowledge to grow in grace and needs to go in strength in other areas of development okay so let me just pause here and see if there are any questions is everybody with me so far any questions here right it's your question John um it says uh this be applicable to what meant each challenge so yeah so you know uh that's also a question we can ask right uh you know what about those who are born you know mentally challenged they don't have the ability to understand things you know uh so we don't have clear chance to go back to what we understand when something but because you don't understand the content uh they may be alive to God he says I have a live most likely again I'm saying most likely looking in words sure um that's the way God would probably you know deal with that not holding them for their sins against them you know and that's all that's that's how we would think that God would deal with them how would live with God to decide on this yeah any question so far what we've covered right so what we've said we've tried to see to make see the journey how the spirit was before being born again and now that you're born again uh we've got the life of God but that doesn't mean this this spirit is in its full full state right we see in scripture that that born again human spirit has to be developed it has to grow and that is the objective of this course how to develop the born again human spirit that means the spirit that has come to life in Christ how to develop that because the Bible tells us to grow in grace to grow in the knowledge to grow in strength to grow in knowing the will of God so how do we grow the human spirit to you know to become all this and eventually the Bible has called us God calls us to grow to the fullness of Christ to be like Christ so how do we make this journey that's the part of this what we're going to cover in this course okay so I think I will pause here today there's a little note about the soul and what will happen when somebody dies I'll I'll just quickly review this or mention about this in the next class and then we will kind of dive into you know okay what are the faculties we will identify what are the faculties of the human spirit as we see in scripture and how do we develop each of those faculties of course everything based on the scriptures based on what the Bible teaches right so we're not not talking anything outside of the Bible everything from the scriptures but I hope this journey is clear we are born again we are new creation in Christ but the spirit has to develop it has to be made mature it has to grow and that's what we want to understand how to grow it according to the scriptures so let's stop here for today and any questions please feel free to ask all right let's pray together and then we will ramp up our class anybody wants to pray please pray Sada we want to thank you for the life of our pastor for the life of our student for the life of our max college we want to thank you for bringing us together we want to thank you for giving us the opportunity to listen to your word I want actors to continue to breath our pastor so that we impact the greater knowledge in us who also ask that you make us receptive make give us a receptive heart and a receptive mind so that we can intake all what they are impacting on us and we continue to go on out and become the salt and the light for this community that we serve we want to thank you for everything we want to thank you and want to continue to bless your name let your name be blessed let your name be glorified from everlasting to everlasting this and every other masses will ask in the name of our Lord and Savior Jesus amen thank you amen amen thank you thank you everyone and uh we'll see you again soon god bless bye now thank you


Hello and welcome to the session. In this session we will discuss the following question and the question says, let O is equal to the set containing the elements 1, 2, 3, 4, 5, 6, be the universal set and A is equal to the set containing the elements 1, 2, 4, illustrate this information on a Venn diagram. Let's start the solution now. We are given that O which is equal to the set containing the elements 1, 2, 3, 4, 5, 6 is the universal set and A which is equal to the set containing the elements 1, 2, 4. We have to draw a Venn diagram for these two sets. So the first step is draw a rectangle which represents the universal set O. So we have drawn this rectangle and it represents the universal set O. Now the second step is draw a circle inside the rectangle which represents the set A. So we have drawn this circle inside the rectangle and this circle represents the set A. The third step is write down the elements of set A inside the circle. The elements of the set A are 1, 2 and 4. So we write down these elements inside the circle. The fourth step is write down the remaining elements of the set O which are not in A outside the circle but inside the rectangle. We can see that the remaining elements of the set O which are not in set A that is elements other than the elements 1, 2 and 4 are 3, 5 and 6. So we write down these remaining elements in this portion outside the circle but inside this rectangle. So this is the Venn diagram for this question where set O which is the universal set is represented by this rectangle and set A is represented by this circle. Elements of set A are written inside this circle and the elements of set O are written inside this rectangle including the elements of set A. With this we end our session. Hope you enjoyed the session.


capacitors, blooms, 104s, 100m5s. I know this isn't very good for you to see this, but yeah it's still not going to be, because I'm still going to put my hand in there. I'm going to pick up something else on this thing, not just that awful noise.  I don't suppose that's where the money's going. Yeah, so why that really displays on? I mean, is that trying to tell us it's cheap? I thought it was supposed to be AM and FM. I mean, that chip's supposed to be AM and FM. You can't twiddle it, it's not doing anything. And it doesn't, like I say, this one goes down, no matter what you do, this up down left, right, plus it, no matter what you do, that goes down on the count. And this one goes up, no matter what you do, up down, left, right, push down, it goes up, and then this one goes down. But there's no way to switch it from AM to FM. And I don't know how I thought that this would be passable. Oh, there's a station there, nearly. I suddenly left a comment in the comments about building a transmitter. And I've already built a little one. But it doesn't work very well, so I was going to try and rebuild it again, not try actually rebuild it again, and have this pick it up, but it's going to be good. This isn't going to do it. That's the best we're getting, I think. I'll get in trouble for that. No, when I don't want to do it, I don't want to have the arm there. I told you ricken off somebody's track. I'm not, I just can't get them off the radio. There we go. Not really my cup of tea, but so you can pick up some stations if you have a different antenna. And we've done something too bad like that. But retuning is just hard to hear anything underneath that. There's no right auto track. Okay, guys, so I've decided that there's no real point. Can't continue with this. You can see in the instructions, even instructions, destructions, we've got a voltage working voltage range. This thing only goes up to five volts, five and a half volts. So the LM386 is going to be running at pretty much the lowest area. It can as it starts at four volts. We got a DC pedestal power supply positive and negative. Do not connect the opposite. I don't know what I mean by that FM range, 87 megahertz, 108 megahertz, good. Frequency modulation step, press step 01 megahertz, 100 kilohertz. Long press frequency modulation key can be added or subtracted continuously. Okay.  Introduce the power saving function after each power on or pressing the FM key. Didn't know there was an FM key. The display frequency of the digital tube is five seconds. And after five seconds, the tube, the digital tube display will automatically shut down. There are two reasons for this design. One is power saving. The other is noise interference when the digital tube display is turned off. So from my understanding, which I would say there's interference when the tube display is turned off. But as we can see, there's interference when the digital tube display is on. When the digital tube display is turned off, the sound is more beautiful. The speaker is set is the speaker for the set meal is two watt eight. So two watt eight, eight euros. And the sound quality is quite good. All right, that's it. I'm not going to go into, there's just no point. So there you go. This is what you get. It's a complete fail as far as I'm concerned. And buy it your own, your own peril. I'll catch you in the next one. Cheers, guys. Bye.


With step one now being pass-fail, pretty much makes step two CK the new step one and that's super important for you to do well on to get into your dream residency. Today, I'm gonna be sharing with you the exact strategy I used to get a 257 on step two CK and the steps you can take to crush the exam as well. Let's get into it. Hey friends, welcome back to the channel. Today, we're gonna do a full breakdown of how to do well on step two CK and we're gonna be covering a lot. So if you're interested, feel free to check out the timestamps down below and go to the part of the video or the episode that is most pertinent to you. But as an overview, a few of the things that we'll be talking about include how much time you need to study, what is considered to be a good score for a competitive residency, as well as what your study strategy should look like when you're on the rotations, as well as when you have dedicated time just to study for step two CK. The very end we'll talk briefly about some of the resources you can use to help you do well but doing it with less stress. And as a teaser, towards the end of the episode, I'm gonna give you one tip that really helped me boost my score on a weekly basis when I was studying for step two CK, as well as one resource that I didn't have access to but I really wish I did because what I made the entire scheduling process so much easier, so make sure you stay tuned. First, let's go ahead and break down how long you need to study. Now, those will vary from school to school as well as your particular situation. So for example, I was able to fit one of my one month vacations during my fourth year during my summer and I was able to study for step two CK during that time. But some students may not have that luxury of having that full month off and so if you're in that situation, I usually would recommend adding anywhere from two to four months into your study schedule and ask yourself how long it will take you to get through your question bank source. Question banks typically for step two CK is going to be your world. So come up with how many questions you have to go through and ask yourself how long would it take me to go through your world about one and a half times? Usually the first pass to do all the questions and then at least another half pass where you're going through all the questions that you've missed or guessed correctly on so that way you're getting a nice review and repetition in. Also keep in mind that compare to step one where most students will delay using your world until it's time to really get into the studying. A lot of students will use your world in addition to the rotations to help them prepare for the rotation itself as well as the shelf exam. So you likely won't have as many questions that you think remaining and so sometimes that four to eight week block of dedicated prep in addition to a busy rotation may be perfect for you. And next let's talk about a question I know all of you guys have which is what is actually considered to be a good score? What should be my goal to go for? Particularly now that step one is pass fail. Now instead of just making up numbers I am big and going into the data so I already done the research for you but if you're interested in actually going through this document just go ahead and Google it charting outcomes NBME match and you'll find the most recent version which as the making of this video is in 2020. So essentially what this will tell you is the data of everyone who has surveyed and actually responded. So that is a caveat to remember of what their scores were what their step one scores were which will matter for you guys because now it's pass fail but also how many research experiences they had to they match or not. And so if we go to the part of the document that we actually care about which is the average step two score then we'll realize that at least in 2020 and keep in mind step one score still existed the average score for people that are matching was 247. Now this comes with a big caveat that this is dependent on the students who are responding to the survey. So if somebody who didn't do so well on step two CK or didn't do well in the residency match they may not have responded to the survey. And so this may actually over inflate what the scores may have been but we have a pretty good amount of data here. We have 16,000 students who matched and about 1500 students who didn't.  Now what will happen over the next few years now that step one has passed fail I typically will probably expect that the score will stay more or less the same until students and schools start to focus more on step two CK study much earlier on. And so you may find that your school starts to give you question resources like you world maybe in your second year for you to start doing question blocks and other resources. And then you may start to see the score start creeping up into the two fifties. In addition to seeing the average score I think more importantly is for you to be able to see the score based off of the specialties you're interested in. So if we go to this document right here and I'm just gonna go ahead and zoom in then this basically breaks down the average step two score and the range for students who matched as well as didn't match. And so if I find the specialty I'm in which I'm an internal medicine physician then I'll be able to see that people that match got between a 230 and a 250. Now I got a 257 so again that basically tells you that there are people who did much better than me who probably just didn't respond and thus is not reported within this document. And then you can essentially find what you wanna do. So if you wanna be a neurosurgeon you can say cool like I'm clearly gonna need a much higher average step two CK score compared to my peers who may be going for family medicine or pediatrics. So if you guys are interested you guys can check out the charting outcomes data I'll actually link it down below in the description so you guys don't have to actually waste time Googling it. Just keep in mind they updated every two to three years so this data will likely change. It's particularly now that step one is past fail. Just expect that score to stay on the high side if not be a little bit on the higher side closer to the low 250s. So usually my answer to a student who's asking like what score should I aim for typically I'll say aim for the 250 because if you get higher than a 250 you can essentially go into any residency without worrying that your step two CK is a check mark that's not quite there. In my personal experience when I saw that score of a 257 I definitely had a big sigh of relief saying that okay my step two CK is not gonna cost me having a spot in a residency program that I'm really interested in. Then I could focus on really building up the rest of my residency CV and doing well in med school. Now let's go ahead and get in part of the episode that I'm most excited about which is the study strategy. First let's talk about what your study strategy should look like on the rotations. Now every rotation will fit on a spectrum of how relaxed it is and how much it allows you to do step two CK setting. So my personal experience certain rotations like psychiatry and neurology definitely gave me a lot more study time compared to rotations like internal medicine or surgery where the hours were long and I just had to always be in the hospital. And here on the channel as well as our website we have tons of videos and blog posts breaking down each individual rotation and what resources and the best tips to help you do well on each of those. And so if you guys are interested I will link down below a link to our website as well as our clinical rotations playlist that we have here on YouTube. But the main thing to remember is once you understand if a rotation is busy then ask yourself okay like how much time and what resource can I really commit to. The main thing in terms of strategy that you should really be focused on for your rotations is having a schedule that you'll be doing for questions, particularly to that rotation. So if I'm on internal medicine I may say every day I'm gonna go for at least five questions on a minimum. The goal is to do 10 to 15. And the way you would come up with those numbers for each rotation is you would look at the you world questions particularly to that subject. So if I was on psych and I noticed they had 400 questions and I had four weeks that means I had to roughly get through 100 questions each week. And then you'll have to ask yourself how many days you'll be able to commit to doing questions. So maybe you have seven days but three of them may be busy for your psych rotations. So you only have four days. That means you have to do roughly about 20 to 25 questions to get to that hundred average by the time the four weeks is done. And once you have your questions scheduled set in stone and again at the very end of the episode I'll talk about a resource that can speed this process up. Then the next thing is ask yourself like what resource can I fit in addition to help me do well for step two CK. Usually I'll have some kind of text that helps me follow along with the rotation as well as my questions. My main focus is questions every day and then do some reading versus all the way around which is most students do which is they focus too much on my reading and then they'll do like four or five questions here and there, it's not very consistent. So a very heavy focus on making sure you do your questions and then use your reading in the same light saying I have four weeks to get through this many chapters. How many do I have to get through on a weekly basis, on a daily basis and then break that down. That will be your schedule for your rotations without making it over too complicated essentially just two resources, one text, one questions with the heaviness on the questions. And my last tip for the rotations to prep effectively for step two CK is going to be essentially creating a list of the questions that you're missing. Now you can do this using whatever technique you want. I actually used a physical notebook when I was in my rotations because I just like actually liked writing things down. But as I got into more and more rotations and things got a little bit busier I started using more digital options. Initially started using Excel but you can use things like Notion or Anki and other flashcard systems. Again, there's tons of videos and episodes that we've made here on the channel on how to study well. I'll link down below an episode that I did on all the study strategies that really helped me get a 3.9 GPA in med school. And most of that GPA actually came from my rotations. So if you guys are interested I would link that down below. But whatever technique you use continue to collect every time you miss a question saying the last thing I want to do is miss it now and also miss it on my shelf exam and particularly on Step2CK. So when you miss something collect it in a way and then come back to it periodically. It may be saying on the weekends I'm gonna review the list of everything that I missed and make sure that I at least have refreshed on the topic and then maybe before my shelf exam and then we'll talk about how you can use it for Step2CK later in the episode. Now let's go ahead and talk about how your strategy would change during your dedicated. Now if you're imagining that you had four weeks because we'll use that as an example the first two weeks really the only goal is get through all the questions you have left or as many that are possible. And so for example as I'm making this episode your world has about 4,000 questions for Step2CK which is crazy but ideally you've been doing questions with your rotations and so you may come into your dedicated finding that you only have 2,000 or 2,500 left to do. And so if we use that example of four weeks you may say okay I have two weeks or less 14 days I may spend two of those 14 doing practice tests so that gives me 12 days to go through these questions. And so you would use the same concept that we did for rotations you would divide the total questions by the days you actually have to study and then come up with a number and ask yourself how realistic it is. For example if you had 2,000 questions put 12 days to review that's about 200 questions a day and you may find that doing four blocks or doing five blocks of your world is just not feasible. And thus you may decide okay let's go ahead and try to finish all these in three weeks and then you'll figure out okay that's 100 and roughly 120 questions and that's three blocks much easier to say yes to. So that main focus during that dedicated during that first two, two and a half to three weeks should be getting through the rest of the questions in your world that you haven't gone through yet. And so usually that would mean that your day will be anywhere from 80 to 120 questions for some students especially if you have a lot more of your world to cover mean that you have to do 160 questions but usually two to three blocks of 40 questions is a sweet spot. Now to finish off practice questions you wanna make sure they're gonna spend all this time doing these questions that you actually learned from your mistakes. So just like we were doing before during rotations use that said study method and collect all of the mistakes that you're making any questions that you got wrong or a question where you guessed correctly but you actually didn't understand what the concept was. Add that to your list, add that to your flashcards and then usually this is what I would do in my personal setting is every morning I would go to that system for 15 to 30 minutes and saying let's just make sure that you don't make the same mistake again Laksh. And ideally now I start to see my score go higher and higher. And for some students the schedule of doing three blocks plus review plus reviewing the mistakes that they've done from prior days may just be all that they have time for but if you do have more time in your schedule or if you have a longer dedicated prep usually I'd recommend finding just one resource that you really enjoy and committing to it ideally in the middle of the day where your energy tends to be lower. So that's a great time to transition into some of the best resources for step two CK and I intend to make a much more elaborative episode on this. So if you guys are interested make sure you add the comment section down below on YouTube. But let us first talk about practice questions I would just stick with you world wouldn't really focus too much on anything else except using the practice MBA me's on a weekly basis to get a practice questions set essentially done. You can also use the examples and the self assessments that you world gives you that's anywhere from five to six exams you have available to you. You by no means have to do all of them my usual schedule was to do one on a Saturday take the rest of Saturday off review the test on a Sunday morning and take the rest of Sunday off and then use Monday and Friday to pretty much be very question heavy. Now in terms of resources that are focused much more on content to help you build that understanding of step two related topics I'll recommend all of those in our future episodes and make sure you guys subscribe but the main one that I enjoyed recommending has to be online method and my personal experience using OME or online method was that I really enjoyed the videos from Dr. Williams particularly during my rotations so nicely fit into my step two CK prep and full disclosure because I wanted to spend more time doing questions actually didn't dive into the videos very much during my step two CK prep instead because I had already seen most of those videos during my rotations I use the nice online meta notes that come with each corresponding video and went through those as a nice review and refresher and if there was ever a point or a topic that I was still struggling on then I would dive into the video to get a better understanding and if you guys are interested in learning more about online meta I've done a full review particularly right after I took step two CK on how I used it so I'll link down below that blog post as well as that video and if you guys want to check it out I'll also be linked down below it is an affiliate link so if you guys are interested we do get a commission but by no means you have to feel pressured to use that link you can just type in online meta and Google and go to third link now the next resource that I just incidentally came across when I was studying for step two CK happened to be step two CK secrets now this is a very small book full of a list of questions that are a fair game for step two CK and the way I use step two CK secrets is I added it towards my last week week and a half again my first two weeks were spent finishing all my year old questions and then I transitioned to just doing all the questions that I had marked because I got it wrong or I guessed correctly I had a step two CK secrets as an additional question source because then I was really just using as a confidence booster it's just a list of questions with the corresponding answer immediately afterwards that doesn't really teach you anything it just gives you the answer there and I could say that if I knew the answer to everything in that book I'd feel pretty confident going into the test and by no means should be your first or your go-to resource but it's a nice confidence booster you can add to the very end so in case you're interested there are plenty of used options that just work perfectly fine I'll link down below some links to Amazon you guys can check out if you're interested now the next resource is something that we've already naturally fit into the rest of the episode that is your personalized list of missed questions and weak topics now we've already talked about how to fit this into your rotations by doing it on a weekly basis as well as how to do this with your UL questions by doing it at the start of your day but it's nice to have a list of questions again on Excel or Notion or flashcards and essentially being able to demarcate where you've been able to cover a topic so for example, I've had a big hundred list of questions that I just missed I could quickly put those topics down on the list and anything that had covered and felt that I had gotten confidently on I would put like a green highlight on them or Notion I may bold it or on my Excel sheet I may go ahead and change it to a different color any topic on my list that I tried to review but I was like, ah, you kind of still suck at this I may color coded as orange or red and saying, okay, this is a good indication that on a weekly basis maybe on a Saturday come back to your list and find the next orange topic and then go watch a video on it so again, my resource of choice was online meta so if I found that I was struggling with OBGYN topics because I always struggled with those for stuff to use CK and particularly I would go to those relevant videos and then if I felt that I had mastered it I would then change my color from orange to green but I found this to be a very nice way of one collecting my mistakes from U-World and putting it in one place but also visually being able to see as I'm going through my reviews the second time of saying, okay everything is now is green your test is tomorrow you got this and your confidence stays up and simply using that trick of going through this list of questions on a daily and a weekly basis and then color coding it based off my confidence level I really found that my score started improving because I was no longer missing those questions that were related in U-World the second time and I saw, okay, I went from 40% on my U-World percentages now 60, 70, 80's and ultimately getting that 257 on step 2 CK now I promised at the start of the episode I'd share a nice tool that'll help you improve and quickly speed up the scheduling process for step 2 CK let's go ahead and dive into cramfighter now if you guys are not familiar with cramfighter it's essentially a nice automated study schedule for essentially any test you want to do and I think the best way to show you how it works is to just go ahead and dive in so you can essentially create a new study plan and we're going to say we're going to study for a standardized exam I'm going to graduate next year that's my med school that I went to and I can say I'm going to study for step 2 CK in this example and I'll essentially ask you like how far is your test? So maybe you are three rotations away or maybe you're six months away we'll say we're three months away now I'm going to start studying tomorrow and I want to finish again I usually want to say a week before the exam so that way if anything goes wrong I still have a buffer time so we'll put that and then boom now once you decide on your schedule you can actually decide on the resources you intend to use so you can actually go in here and type in things like U-World and I may go ahead and click this and then I'll say because I'm three months away every day I'm going to actually try to just do 10 questions that's going to be my total number of daily questions I'm going to do and then add that in and then in addition I'm going to go ahead and add an online med ed as my other main resource and then that's what we'll stop because we'll cover the clinicals now through online med ed I can essentially click through every topic that I haven't covered and so if I've covered anything in the neurology system but I'm using blueprints and cramfighter now I can take those off the list but for this example we'll just say we haven't touched online med ed at all and so I'll just apply all of it so this is going to give me an average amount of time per day and I can also say oh actually like listening to most of my videos at 2x so then I actually adjust everything now once it quickly creates my schedule and I'll be able to see on each and every day what videos I need to go through and then how many U-World questions I have to do and if for any reason if I'm falling behind I can move any topic to the next day or essentially say I've already done it and check it off in cramfighter comes with a bunch of other resources for example I can choose the days that I want to click off so I'm going to go out of the country or out of the city for vacation I can add those days if I want to add a catch up day every few weeks I can put that into my routine and if I know that Sundays are going to be a busy day I can say make sure I do a light workload and then Mondays if I have more time open I can add more work there so lots of little flexibilities and things and again if you guys are interested in learning more about the features that cramfighter offers I've done a full blog post review on them and I'll link it down below but if you guys are interested in checking out cramfighter I'll add their link down below in the description as well now we've covered a lot of how to do well on step 2CK but if you guys are interested on how I use something called the sandwich technique using online meta to get that 257 then make sure you check out this episode which I'll link down below in the description but as always my friends hopefully I was a little helped you guys on your journey thanks for being a part of mine I'll see you guys in the next one, peace.


Yeah, I'm talking about tipi toes. You ever seen? Oh, it's fun to drive Is there any unequal rise fall the chest Hey see to the left leg So We did an obstacle course yesterday. We did land nav We did a pistol shoot and for qual whole bunch of mortar tasks really been getting after it And they've been keeping our days loaded to see who's the best, you know And I think even more than that. It's for us to just get together as a community of mortars And just see you know what other units know and just to challenge each other And ultimately just see who the best is out there and we go back to your units You able to pass on like hey what they did well and you know what we can improve on what keeps me motivated It's definitely the guys just being able to serve them and provide them with the leadership Throughout the competition, you know is really what inspires me watching them, you know work hard every day And just really just busting their hind ends out here getting after it and inspires me and keeps me going And you know, I hope that they feed off my energy too. Oh Team feels accomplished. I hope they go back to the two seven with pride and how they represented third ID And just you know knowing that we really got after it gave it our best shot And I hope that they take a lot more pride in being a mortar you know, we did before we got here but seeing the competitors and You know how hard this competition was I hope they take pride in it And I know I will and we're just ready to continue to get after it and finish out this competition strong