What are any of you familiar with technical standards and how they're creating what they're all about?  It's something that you will not have heard of before because we just talked about it We launched it at the end of August of this year And then finally I want to talk a little bit about standards in education and some of the material that's available In case you want to further your education standards all year at the university So as you can imagine technical standards are everywhere that you see Wi-Fi Smart grid USB Ethernet even the electrical socket in the middle. That's a standard From one country to the next. I wish it were all the same, but it's not I've never seen a socket like this That has USB right next to it I don't know where this picture came from but you can see that's the evolution of the electrical socket is that USB will be charging things as well The quote on the top is from Ken Olson who founded digital equipment and those of us in the standards business I think this is rather amusing That the nice thing about standards is there are so many to choose from because normally when you think of the standard You think there should be one but in reality there are countless numbers of standards thousands of standards organizations around the world producing them and of course all industries and Social change and so forth that uses standards to leverage their advancing The quote on the bottom is from me from the book that I wrote and I have to emphasize that the Ten Commandments has no religious connotation whatsoever I Put that in the intro. You know, this is not anything that has to do with God. This is just my experience Going through many many years of working in standards So what I firmly believe is that we in industry and we in academia in the government We should cooperate on standards and then fiercely compete on the products They use those standards and that's the formula that works best So standards actually accelerate innovation once one's a technology or a method or a process Have been proven to be successful then it's appropriate to standardize it But that's not the end of it what happens then our products are built on top of it those products emerge with possibly new Versions of the standard being required and the standard itself will evolve along with the technology and along with the products So at the top you see us B. I recently had the pleasure of interviewing the president of the USB Implementers forum and in the second part of my presentation I'll tell you where you can watch that interview, but they described how USB is moving from Regular just connectivity to now being a charging mechanism and super speed USB Which has phenomenal speeds that and in rates that you can charge things What was most encouraging is the future of USB will be no longer Do we have the separate power cords for different computers and so forth to be able to charge one thing with USB? Exclusively and I can't wait because I'm tired of you're carrying around all the adapters and all the plugs and so forth DDR is another good example DDR has been progressing from DVR to DVR 3, 4 and it will continue as the technology advances And even JPEG moving into MPEG the motion picture Entertainment group that is used for video and audio and all that type of communications those standards continue to evolve The turn on the bottom shows the progression of ethernet so from twisted pairs all the way up to fiber optics and the incredible Advances that that ethernet has brought and so if you imagine what the world would be like without either net it well It's kind of hard to imagine So not only do the products evolve, but so do the standards and then the products and then the standards and so in lockstep That's why standards accelerate the innovation By the way when I'm talking about standards today. I'm talking about technical standards I'm not talking about educational standards or standards of human behavior There are those I wouldn't touch anyway, but these are all technical standards that will help products and services So as you can imagine everywhere you look there are personal health care devices That is either a heart rate monitor. Well that that seems to be monitoring heart rate body temperature A variety of things in that handheld device on the left At the bottom we're representing smart electric meters that will measure how much electricity you use And then if you happen to be generating electricity if you have a wind tower or some type of a solar mechanism You can actually put that electricity back on the grid and be paid for that So these smart electric meters are going to be prominent throughout the world over the next say decade or so Mobile phones where would people be without their mobile phones? like this these days and I was just sharing both We have the new sense of galaxy s3, which is a beautiful machine and You know that these kinds of evolutions are just as rapid as you can imagine I don't know if you've tried the Google talk where you actually can see someone's face and My son and I were playing with that the other day Well, you don't need to because they have a feature in there where you can change your facial expressions You can make your eyes grow big you can make your nose small and it's really hilarious. You have to try it And finally probably one of the most Life-changing and life-altering things that we have in the world right now is the internet and the world like web Every single one of these has standards at the heart of that to make it work and make them function with each other So what's coming in the future? I'm sure you've heard of cloud computing Cloud computing is changing the nature of communication of data storage Being able to handle what they call big data, which is massive amounts of information all around the world that are delivered either privately or publicly on the cloud The smart grid is something that will revolutionize the way that Electrical grids are delivered in in countries So India, I don't know if you heard the story recently where India's power grid had gone down in most of the country There were 600 million people without power if you've ever been to India the power flickers on and off all the time So smart grid will have an awesome effect in a country like India to keep their power stable as well As to be able to move where power requirements and demands happen and Remove power from where there's a surplus and all of this is interestingly enough using information and communications Technology so all kinds of IT things are behind the smart grid Have you heard of the Internet of Things? Anybody heard of the IOT Internet of Things? This one is really going to be cool Basically every object will have its own IP address So things will be able to communicate with each other as if they're computers on the internet And so the story I've been telling in our media is if your refrigerator detects that you've run out of eggs It'll send a message to your car and tell your car to drive over to the store and pick up some eggs and bring them back Some of this already exists today The car that I drive has RFID chips and the tires and so it will send the email when my tire pressure gets low So all of these kinds of things will make it odd to become smarter and become connected with things all around the world And of course they they won't take over humanity Is any number I don't know if anyone here is old enough to remember them old movie called the Forbidden Project It's great old movie. It's really corny if you go see it You can find it on YouTube But there's a Russian computer and American computer and they're talking to each other and then they decide that the computers We're going to take over the world and destroy all mankind It's a really great old sci-fi movie, but of course even things try in the end They probably already can There's always the element of big brother. There's always the fear of privacy in Beijing There's the 1984 story from Elm's Huff Lady And I personally think that for every good thing that we invent there's going to be something bad But yet humanity is always going to persist. I don't think we'll destroy ourselves So I think if the IRS does spy on the refrigerator, you'll figure out a way to put a little piece of duct tape on top of the camera Here's some other future innovations based on standards E-governance will allow more efficient communication between nonprofits governance industry it's a way to control documents and Supply chains things like that will be very very helpful in making the world operate more efficiently eHealth, of course will revolutionize the health care industry around the world. I've been Just a tiny bit working with an organization that wants to create a mobile Platform of medical devices based on standards to take to remote areas of Africa and deliver better health care to areas The Automated cars are fascinating. So in Silicon Valley, you can actually see Google's driverless cars going down the highway all by themselves. They have a Like a satellite radar thing spinning on the top, which is accessing the internet Looking forward to where the traffic patterns are Deciding when to turn left when to merge how fast how close they can go to each other It's absolutely astonishing The cars actually will have people sitting in the front seat So but their hands are not on the steering wheel. They are there to give instructions Please take me to synopsis headquarters or please take me over to You know the Armenian ambassador or something like that and then Google of course with all of its knowledge We'll be able to download the instructions to the car and have the car drive So the idea is that the cars now will be able to travel within a few inches of each other at very high speeds with very few if any traffic accidents whatsoever and It will also allow people in the cars then to be texting and watching video Doing whatever they want in their car without risking lives around them. I hope you get a chance to see these cars They're kind of freaky actually Rosanna it has been my translator in your van this week I don't know that there's a translation of the word freaky into Armenian. So we'll have to we'll have to work on Do you know what freaky would be How about strange or unusual amazing weird Yeah So the last thing that I do want to mention is sustainability Because all of us are very interested in preserving the planet's resources There are standards emerging for the disposal of computers how to Make products that are safer for the environment. So standards will also be at the heart of sustainability Closer to our industry which is electronic design. So semiconductors computer chips We are continuing to develop standards Constantly, what are our newest technologies that's represented in this picture on the right of a right is 3d? I see so this is where you take the semiconductor chips and Skept them on top of each other and that will allow you to have more chips in a smaller space that are more powerful and faster And as you know, we always want smaller faster more powerful using less power and More functions and more features in our in our semiconductor chips So in order to design a 3d. I see many many standards are required to say how do you place the little pieces? How do you connect them? What materials do you use? So that's a really big in area of interest for us these days So on things like verification methodologies So if one one train or one semiconductor chip the size of your thumbnail has 10 billion Transistors 10 billion switches on it. You need to verify every single one of those before you manufacture it And so all of our verification techniques require standard methods of Ensuring that that chip is going to work properly when you manufacture it Constantly we need new standards for modeling these devices as we move from 20 nanometer designs now to 14 nanometer designs We need to be able to model what that device is going to do in addition to how we Manufacture it what layers of material we place how we route the wires together On the multiple layers and all of these modeling characteristics need standards They need standard languages and standard formats to be able to represent them The system level power intent is extremely important So I keep talking about low power design and the need to use less battery power Today's smartphones are increasingly Frustrating because their batteries go dead very very fast and so our industry is working very hard to say at a system level How can I shut down parts of the chip that aren't being operated and while firing up other ones? So when your screen goes dim because you're not using it That's part of these low power design techniques and all of them of course use standards Someone asked me in the last lecture about is it difficult to get people to come together and agree upon a standard? Especially when different companies have different interests and the answer is yes, absolutely purpose of standards is to attempt to drive consensus amongst Many maybe different interests in different companies So in order to develop a standard for low power where we were representing this is what the chip should do in order to preserve its power There were seven or eight different companies that came to the table some of us bitter competitors We all contributed our technology and we argued for several months before we chose the best aspects of each company's Contributions and then that became a formal standard Oftentimes these standards can take years and years to create it depends on the conflicts that might come up It depends on their business aspects It depends on the technical aspects how difficult the material happens to be that low power design Intent standard that I just mentioned took us only five months to complete It was kind of a miracle the reason it was so short is because we had our customers demanding We must have this standard because we can't design these chips unless you create it So I had the pleasure to actually sit in on those committees and watch the chair person at the time sort of orchestrate I know you don't appreciate this and I know that yours is this way, but he actually brought it all together in a phenomenal success Some of the other areas that we're creating interface or pardon me standards would be interfaces to debug the circuits Analog and mixed signal is very important Most of our industry has been digital because digital is very easy to work with but Analog and mixed signal are now the interfaces of all of the chips there That's the part that you know faces with the real world. So you need analog to digital converters and an analog interface So again standards required there and finally design rule checks So as we get smaller and smaller geometries the factories and the manufacturing Facilities they're saying you can't have a wire closer than you know this certain distance Otherwise, you'll have noise and you'll have signal transfer jumping across the wires So all of those rules are written in a standard language There are a lot of ways to create standards. You can have them created by Industry and de facto usage. So everybody just happens to like it. It becomes a standard.  There are actually and this is new to me Honestly, there are many major organizations around the world that use a national body representation model And what that means is a country each country comes together And votes one time so one country one vote on a standard that will be used around the world the most prominent and the most familiar organization that does this is known as ITU the International Telecommunications Union and they are Headquartered in Geneva. They are an assembly of the United Nations So they get together one country one vote and they set industry standards in the telecommunications industry And they've been very effective at doing that for many years and they will continue to do so other organizations that use this national body model are IEC the International Electro Electro technical Commission, which is kind of near our semiconductor industry as well as ISO So I'm sure you're familiar with ISO ISO 9000 and not that whole ISO family of Quality standards and other standards. So that's the model they use However, most interesting to me is what we are now describing as open stand Which is the modern paradigm for creating global standards? And it's also the easy way to think about it is market-driven standards as opposed to country and government-driven standards So that's why I want to talk to you about it Next so These types of market-driven standards have been created for decades. This is not a new concept What's new is putting a name to it Quite recently several organizations that set global standards got together and said, you know We realized that industries and markets have created these phenomenal standards around the world Most noteworthy would be the internet and they have nothing to do with governments or countries And we would like to be able to describe these and have them recognized on par with those that come from ITU IDC and ISO to say that those standards are good And so are the market-driven ones that we've created in the world of the internet and other industries as well so five organizations got together the IEEE and Next year in the following year I have the honor of being the president of the IEEE standards association So I'm really proud of this effort that we're doing the first woman by the way in 100 years of them being an operating A little bit scary, but you know and this is completely irrelevant to my talk today But when I come to our media and I see so many young women studying technical fields It's very encouraging to me because back in the United States. There's still maybe 8 to 10 percent women in Science technology engineering math. So you guys are absolutely awesome. I just love to see you guys are good too I don't want to do that I see so many men you know day after day after day It's really nice to see a lot of my female companion. Okay back to the back to the front So the IEEE the Internet Society W3C which is the worldwide rev consortium the internet advisory board and the internet engineering task force These are the organizations that have actually created and maintained HTTP TCP IP all of these types of things 802 which comes from the IEEE These are what make the internet work These are the things that have created the internet around the world and they are not controlled by government They're not controlled by anybody these organizations oversee them and people come and make them Advanced and make them work So we all like together and said let's put a name to market-driven standards and let's talk about them More broadly so that governments will be able to say Oh, I can procure a product that's based on a market-driven standard in the same way I can procure a product that was developed based on an IEEE or an ISO standard We created out there's a website open-stand.org you can get more information there if you're interested, but we said there are five Principles if you like of what a market-driven standard is all about and the first one is cooperation This is extremely important because it means cooperation between standards organizations So I said there's thousands of standards organizations out there Each one of them has their own process and they've proven that I can create a very effective and useful standard using my methods And you may have done the same but your methods are different So we have to respect each other and say I respect your process And I'm not going to attempt to make you change just because I like my process better And each of these organizations has slightly different ways of producing standards and yet we say Obviously what you've done works and obviously what we've done works as well. So let's not change each other's processes That's respected and cooperating each other the second principle is adherence to the fundamentals of standard development and these are actually ones that are Proved by the World Trade Organization is these are the proper things that you need to do in order to create Effective standards and the first is due process You need rules and regulations and policies and procedures that can seem very cumbersome But these are the things that control the outcome of the standard such that it's technically the best But everybody's voice has been heard that it's been vetted and approved and it can be Very tedious I'll admit it's very tedious for these processes, but they're required in order to ensure the quality of the outcome of the standard The second fundamental is broad consensus No one company can come say to the IEEE and say I want my Technology to be a standard and I don't care what anybody else says that is not one of the principles of open standards So you have to have consensus from not only industry But also academia from government from individuals from any interested parties We all get together and say this is what we agree upon and we make trade-offs and we make You know cooperation and consideration and sometimes compromise well a lot of times compromise So what consensus is different on different organizations? But I truly defines consensus and when they go through their balloting process You have to have seventy five percent approval in order for emotion to pass not fifty fifty one percent So it's a supermajority which helps drive consensus more than just half of the participants agree Transparency is very important. What this means is no secret deals behind closed doors Everything that you do and all of the operations have to be clear and out in the open So that people can scrutinize that you're not doing something that is not fair to the general market in the general society Balance is very important. This says no one company can dominate no one interest can dominate You have to have an equal balance between suppliers and consumers and regulators and so on and so forth I'll tell a story about not balance One of the IEEE working groups years ago One of the companies wanted to dominate the outcome of their vote.  Hi we're here to vote on behalf of this company and There it was a shock throughout the entire standards organization. You can't you cannot do that the company that That that was engaging in that their upper management had no idea was happening and immediately they apologized publicly They said we will never do this again And so because of that the IEEE constantly watches and so do the other organizations Making sure that there is fair balance that nobody's dominating and cheating The final fundamental is openness and what this means is that anybody who's interested is allowed to participate So if you have a material interest in participating in a standard be if you're representing the company you're representing your industry your Personal experience you are allowed to participate in the development of these standards. So people cannot be shut out And that's that's very important one thing I will point out is open doesn't mean free Sometimes people think that open standards mean they're free at no cost, but it's very expensive to produce It takes a lot of resources It takes not only people whose salaries are paid by companies or who are investing their personal funds But it also takes computers and conference calls and facilities and food And so openness means open participation, but standards need to be available at reasonable costs, but they're never free Even the internet standards that you see they're free. They're funded through different funding models Nothing in the world is free unfortunately The third principle is collective empowerment and what this is embodying is the idea that an emerging Economy will be equally as empowered as a mature economy So the emerging economies in smaller countries have as much say as those of big countries that have been established themselves and what this allows is smaller companies emerging economies to participate at the global standards table just like anyone else and it's very It's very motivating. It's very inspiring and something that smaller countries have not experienced before They are used to saying well I guess I need to follow what China says or I guess I need to follow what Europe says or the United States because I'm just small Guy, I don't have a voice but now through collective empowerment these smaller countries will be able to come and say listen You need to understand what my environment is like when you're creating standards for the smart grid I'll give a great example. I was in India a few years ago and Someone was proposing Well, we need to do this and that and the other with all of our IT infrastructure and so on and so forth So we can have an India smart grid on the opposite side of the room There were some Indian gentlemen saying have you been to rural India? You don't understand that 60% of our power is stolen So what you're proposing can never work in rural India where there are no substations where there are no Infrastructure and so this type of arguing back and forth was fascinating to me There's a perfect example of collective empowerment. We the rural Indians have something to say I mean listen to us before you create your massive smart grid standard Number four availability. This is what I alluded to a minute ago and Standards need to be available widely to everyone if you say only this particular segment of society is allowed to use this Standard to their advantage, then you're disadvantaged in other aspects of the world And that is absolutely not part of what the modern paradigm of global standards says So availability you can sell standards at a reasonable cost You can give them away if you have other funding, but you have absolutely have to make an available worldwide The last one is really interesting and important these standards need to be adopted voluntarily as an industry I need to be able to select the standards that will make my products the best I as a consumer want to select products that are based on standards that serve my needs the most I do not want a government dictating to me You will all do it this way because we said so because that could be inferior that could stifle innovation So I'm not saying that governments don't have an extremely important role So if you want to you know Standardized a telephone system. It's very good for the government to step up and say okay everybody do it the same way However with market driven standards You want the market to say you know that technology is much better than this one And I'd like to move there when I feel like it's fast what I can or as slow as I can if it's not quite quite ready So voluntary adoption Anyway, you may see you may hear about this more especially if you get involved in standards or Any technology things you may hear more about this and if you're interested as a website we have endorsements from people from countries I have never heard of so it's true Yeah from a standard person it's pretty exciting the rest of you may say yes Anyway your choice And then That's exactly correct the analogy of the Of the voluntary adoption was Blu-ray versus The format wars we've seen them often so those standards were created Blu-ray HD DVD they were created by their separate organization The end competing absolutely competing and what happened is then because they were voluntary adopted by the consumer market The consumers made the decision I prefer Blu-ray and the other one disappeared So if if Blu-ray and HD DVD had been national body standards It would have been the government's sitting down together and saying okay, which one do we want our citizens to use? And so that's why voluntary adoption is completely different than the national body The society made the decision if you like there was no entity that said Blu-ray has won it simply occurred and Slowly HD that the suppliers of the HD DVD standards said Yeah, the decision I think that you're referring to if I if I remember correctly is where a group of leading suppliers Leading manufacturers got together and said you know what? They said this HD one isn't working for us We all are going to use Blu-ray and then that momentum shifted because those companies that the industry said this is the one We prefer and they said that because they watched their consumers What's interesting to me is when I noticed that blockbuster, you know the blockbuster Company that's almost out of business right now But when blockbuster started carrying Blu-ray on their shelves instead of HD DVD I think that was a big indicator that Blu-ray was going to win But yes, so the companies themselves got together and say, you know, we think this is the right answer But again, no government was involved. It was definitely market for them I Dominance can be very distasteful. It can also be very effective. So I will use Apple computers an example So Apple's products are dominant. They clearly dominate the market and they do so with closed standards, by the way How many people have got Apple products in the last year not me by the way because I stand for open standards Android People we were having a discussion at lunch time That there was fear that Microsoft would dominate the world and they did for a while But now Google is starting to be the dominant player in the world. So I think it's a natural evolution Yeah, the big companies could dominate Everybody's everybody's smiling about synopsis. So Some people think synopsis is dominating the industry and others think we're a small player So that's a matter of opinion But but the thing that's important about open standards like this When you come to for instance the IEEE and we have what we call an entity model for developing Every company gets one vote. So so synopsis vote has equal weight to Microsoft equal weight to Cisco equal way to your startup company that's in your in your house and So that brings more of the consensus that drives the broad the broad consensus in the balance So so it doesn't allow dominance The balance prevents dominance from happening in the standards world in the product world You're right, you know the products can dominate but the standards themselves are created in a more fair way If I may just add as an agenda to that I think that the concept of certain words like anti-monopoly Antitrust that's not necessarily in this domain. That's a legal issue that sort of societies in different countries have different solutions or allowances or tolerance levels to so That's something. I mean that's a separate very maybe related but a separate issue Yes, standards are benefit for the society they do not address Well, actually in a way they do so. So yeah monopolies and antitrust are part of the government to prevent those monopolies from occurring When a company like synopsis goes to acquire another company We have to prove to our federal government that we participate in open standards with our competition And that's part of the fundamental approval process for us to acquire other companies Not the open standards, which is related to fairly Separated between the companies but it after short but China will follow the rush for example to find this issue British with the United States is the political and economic Issues Yeah, I think that's I think that's correct Someone else That was the There was a technical flaw And and yet I think if the market Had wanted and said well, we know there's a technical flaw, but we happen to like that standard better They would fix that technical line take it forward. So there's always a balance between Technology the technical aspect and the business aspect of it the political aspect the delicate balance Oh Oh He's asking about the competition and the collaboration between Sony Hollywood motion picture groups and Philips and I Remember reading the whole story and other life, but that was a few years ago So I'm afraid I to misspeak so I'm not going to go into into details because I might say something that's not true but you're absolutely right the tension was incredible and Because you're because you are competing in such a large market and an important economic market that the deals that are made between the companies and the suppliers and the motion picture people are intense and powerful and very very real and so when Organizations standards organizations say we produced a standard that was fair because we allowed the broad Consensus and we allowed the balance and we allowed the openness then those standards will have more credibility Than ones that were done behind the scenes So and and closed standards can be extremely effective here if you have a technology and it is So awesome and irresistible and you keep it to yourself and you make a lot of money There's really nothing wrong with that, but at some point as an industry leader You'll be expected to potentially open that up Is this true when itunes was first created the format of itunes was proprietary and then they moved to mp3 Yeah, they use the app but now they support mp3 because the industry demanded so Apple built a wonderful environment around itunes proprietary but then market forces of society said, you know enough is enough I want to be able to put my songs on devices I'm glad you guys are finding this interesting Usually when I say I work in standards people go Okay, so let me wrap this up a little bit by saying education for standards is really important and Most of us who work on standards never learned this at the university level. We learned it once we went into industry We learned it the hard way we made mistakes. We did things we wish we had never done We probably weren't as effective as we could have been learning, you know on the job is as we move along So we're recognizing that if we can get material into the curriculum of Universities to show students the importance of standards and how they're created then when you enter the workforce You'll be better prepared to do a better job than we've done and you get the standards out more effectively and more efficiently and less painfully so Knowledge about standards from students percent perspective will help you not only facilitate communication, obviously But once you are performing your professional tasks, you'll know how to do these in the same way There's a standard that's very well-known in our industry called system barrel log. It's for representing circuits So if you learn those standards in universities then when you go into industry you immediately can work with other Design engineers And of course it forms the foundation in the framework of innovation and Product quality and interoperability and interoperability meaning you know things plug together easily These are some of the benefits of being able to put standards into your curriculum Obviously you get skills ahead of time just like when you're using Synopsis tools in your studies now you can be learning the standards and you have that much extra experience once you graduate And I think the bottom one is interesting too. You're going beyond theory So standards are about as practical of an experience as you could possibly have So let me show you a little bit about the IEEE. Come on here as a member of the IEEE Let me back up I'll explain the IEEE a little bit the IEEE is the world's largest professional society They have 420,000 members around the world in in our field electronics, electrical engineering Information technology communications technology microwaves biomedical. They have 38 societies that address all of these technical fields And they provide career development. They provide 30 of the world's literature is published dramatically in our fields So massive publications and technical knowledge base is available And so I encourage you even as students to join I joined as a student a long time ago And the IEEE has helped my career all along very important organization and very inexpensive to join as a student And can really benefit your your entire career your life cycle as an engineer The IEEE has six major areas of focus They publish they have technical activities and research and so forth IEEE USA needs to change a bit That's an artifact of the IEEE being a very old institution But that's where all the career development comes from and also things like life insurance medical insurance benefits can be obtained through IEEE At lower cost perhaps then you would get on your own Member in geographic activities looking regions all around the world. What are your needs from an engineering perspective? How can we get together and learn from each other? By me at the top we have the educational activities One of the fundamental beliefs of the IEEE is to improve the education of engineers all around the world Lot of effort of lot of resources put into education and of course standards the standards association that produces right now I think we have over a thousand active standards the anything from wi-fi to nuclear safety standards to One of my favorite examples is IEEE has a standard for the clothing that power line workers wear when they're dangling out of a helicopter So the IEEE has a massive amount of standards How wide should the lapel be is a standard uh So between the Educational activities and standards association. It was recognized that how can we teach students how can we bring education about standards to the world And the standards education And that's where the resources are provided and it's a really great committee What their approach is is they want to reach the audience at the basic level By providing a variety of things in addition to course material I'll talk about the grants in a minute because that's kind of the most fun because it means money for the students Grants there's an online magazine There is a speakers bureau where industry experts can come and speak at your universities There's a lot of cooperation with other standards developing organizations the most thousands out there that I mentioned And certainly developing products and services for universities as part of this committee This is the website that you can find standards education dot org And this is where you can find the course material All types of information And what's really good to know is that this is available at no cost It's being funded by the national science foundation. And so you can pay all these materials without paying for them Here's a picture of the the website itself Um One of the features is the 802 family of standards, which is ethernet and wi-fi are now available to everyone at no cost They're being funded by industry behind the scenes And so you can actually obtain those standards if you want to study them and build projects around them and use them in your academic activities There are tutorials and case studies available One of them is on system barrel lock that I worked on a long time ago It probably needs to be updated by now, but you can see some of the examples engineering technology Standards in cellular telephony Standards in electrical power systems. So there's all types of Courses and information that you can use there to learn about them So the grants So these grants are given to students who supply a proposal for some type of a project that would use a standard And I try to lose standard and if your proposal is approved, then you will receive 500 us dollars And your faculty mentor receives 300 us dollars. So it's good for the professors as well as the students You have to just describe specifically how you will use 802 or system barrel lock in a project And all of these results are published as student application papers So it can be very nice and a resume. It can be a very good Opportunity to do a special project while you're in school Here's the distribution by region of who has received these grants over the last few years I keep saying that when I come back to our meeting next time I'll expect a bar that shows our meeting away over to the right all the student parents coming from here And the actual Acceptance rate is quite high. So over the last few years of 128 applications that were received 83 of them were approved So that's a very high rate of approval. So The comp it's not that the competition isn't really fierce, but it's that There's a lot of high quality students like yourselves that are applying for these grants. So do apply for a grant if you're interested Here is the online magazine. That's me down below my colleague He's he's very active in the standards of education committee from India And so he's like you know in his heart. We need to educate the engineers to see about the magazine Um, here's an example of one of the most popular workshops and that's um understanding 802 802 is a very complex standard as you can imagine Moving from local area networks to wide area networks to wireless to mobile wireless and this tutorial will help people understand It's a full day of you know, all the details are If any of the instructors are interested in embedding this in there It could be very helpful Right wi-fi so 802 is a big family 802 is ethernet so wired as well as wi-fi, which is 802 11 And then there's 802 15. There's there's a whole variety of them Right, right, yeah all the 802 11 a b c d d. Yeah, that's all part of the atrible family Um, we'll provide these slides and this information here people at the atrible that you can contact and My colleague at the bottom from synopsis actually if you're interested more in atrible standards and education So I encourage you if this seems of interest to you to certainly become a member of the atrible in your local chapter There's a lot of good support for meeting other students and other people in our industry Um, be aware of standards when you start your field of work and think about these things Oh, you know, I'm going to build a product shouldn't conform to certain industry standards Would I like to take my convention Once it becomes stable and turn it into a standard Can you imagine how proud you'd be if you'd say I was the one that invented wi-fi, you know, that'd be pretty cool And you probably could who knows what the next one will be. So, um, you know, please keep standards in mind as you go forward And I'm happy to answer questions or move on to the next topic whatever you guys are like Am I taking too much time? We're okay for time All right


What a beauty, the first ThinkPad ever! Well, that was back in 1992 and now exactly 30 years later, we have the newest ThinkPad Z13 in our laboratory. So what do 30 years of experience look like? There are a lot of cool features in Z13, but one of them makes it one of the best laptops in the world. Watch until the end of the review and you will find out. Durability-wise, ThinkPads have always been tough and we are happy with the rigidity of the Z13 too, especially with such a level of portability, weighing 1.19kg and having a profile of 14mm. The design is radically different with the silver exterior, sharp edges, rounded corners and glossy sides, both on the lid and the base. The lid and base surface by themselves are matte. The keyboard spans edge-to-edge utilizing the full widths of the chassis, plus they have a fair bit of space between them. The key travel is short due to the scene profile, but the feedback is very clicky. In the middle of the unit, just like its great-grandpa, it has a classic red track point. This time its buttons are hidden below the top portion of the touchpad with the haptic motor inside. It also mimics a click across the whole pad. The pad is covered in glass and is quite large for the size of the laptop. The I.O. is very simple, with two USB-4 ports, an auto jack and a SIM card tray. The Full HD Plus IPS resolution is totally enough for a 13.3-inch display. It is great for general use thanks to its wide viewing angles and 424 nits max brightness. It's good even for creator work as the panel offers 95% sRGB coverage and great accuracy with our design and gaming profile. You can find a link to our display profiles in the description below the video. Only 2 per 100 people watching this video are subscribers. If you decide to just start following us, we'll be able to reinvest more in our laboratory, thus making even more helpful videos for you. Thank you, you're awesome! In addition to the qualities of the display, creators will be happy with the Ryzen 7 Pro 6850U, which offers flagship performance from a ULV CPU. Plus, the CPU runs at a much higher wattage than its advertised 15W TDP. On the graphics end, the URDNA 2 Paste Radial 680M has decent performance gains when compared to the latest Intel integrated graphics. Trying to keep the Ryzen 7 in check is only a single heatpipe, one long heatsink and two fans that are punched up together. Here we see that the Z13 isn't suitable for video editing since the cooling can't maintain high clock speed for long periods of 100% load, but it's great for photo editing or other types of work where short bursts of power are needed. The two fans spin really fast, leading to some noise. The warmest point is the 45°C, which is okay. Since this is a small notebook, we have soldered LPDDR5 RAM, which at least runs in quad channel mode and reaches high speeds of 6400 MHz. For storage, there is one M.2 PCI-E X4 slot that fits Gen4 drives. Click the teardown link in the upper right corner in the video if you want to know how to access it. As we promised, we saved the best for last. Imagine that you are flying from New York to Austria and you need to work on the go. Well, we think that this team would be able to work through the whole flight, even if you have accidentally bought ticket to Australia. The 51.5Wh battery pack lasts for 22 hours and 37 minutes of web browsing, or 15 hours and 50 minutes of video playback on a single charge. Z13 is a super stylish air of the legendary ThinkPads and shows how far the technology has come in the last 30 years. Yes, we'd love to have some more ports and better upgradability, but apart from that, the model is one of the best compact devices on the market. With great display, extremely long battery life and simple class durability. If you want to see more tests and details about the device, you can check out our in-depth review. The link is in the video description below. If you think that our reviews are helpful, hit the like button and subscribe to our channel. Thank you!


Welcome to lecture 37 on measure and integration. If you recall, in the previous lecture, we had started looking at the theorem called fundamental theorem of calculus for Lebesgue integrals. We will continue looking at the same in this lecture also and try to complete the arguments today. So, today's topic is going to be looking at fundamental theorem of calculus for Lebesgue integrals. If you recall, we had defined in the previous lecture what is called absolutely continuous functions, which are absolutely continuous and showed that every absolutely continuous function is a function of bounded variation and hence it is a difference of two monotone functions and as a consequence it becomes differentiable almost everywhere. Of course, there exist functions of bounded variation that are not continuous and hence not absolutely continuous. We had looked at such things also and there exist functions of bounded variation that are continuous but not absolutely continuous. In the previous lecture, we had also looked at the notion of indefinite integral of integrable functions. So, we defined what is called f of x as the indefinite integral a to x f t d lambda t, where f is a Lebesgue integrable function and for such functions we proved that these functions are absolutely continuous. So, indefinite integral of Lebesgue integrable functions are examples of absolutely continuous functions and essentially fundamental theorem of calculus says that these are the only ways of getting absolutely continuous functions and once it is absolutely continuous, it also becomes the function of bounded variation and hence becomes differentiable almost everywhere. The main name of fundamental theorem of calculus part one is to identify the derivative of this function.  So, we have already observed that this function is absolutely continuous, the indefinite integral is absolutely continuous and hence differentiable almost everywhere. So, to prove the fundamental theorem of calculus, we have only to identify its derivative. So, for that we need a lemma which essentially says that for a function integrable function, if its function is differentiable, if it says that if an integrable function which is monotonically increasing, then of course, it is differentiable almost everywhere by Lebesgue's theorem and the lemma says that the derivative becomes integrable and the integral of the derivative for this monotone function is less than or equal to f of b minus f of a. So, this is a lemma that we will require. So, we will prove this lemma first. So, to prove this lemma, we first note that being monotonically increasing, this function is a measurable function. The reason for that is every monotonically increasing function is a function which is continuous almost everywhere. That is a theorem normally proved in basic courses in real analysis. So, if a function is monotone, it is continuous almost everywhere and hence measurable. So, that is one way of looking at monotone function and proving it is measurable. Or there is a direct, you can use also the definition and look at the inverse image of an interval that it is also going to be an interval for a monotonically increasing function or a union of two intervals at the most. So, that is another way of looking at the measurable of monotone functions. So, every monotonically increasing function is a measurable function and by Lebesgue's theorem, in fact, it becomes differentiable almost everywhere and the derivative let us note it by f dash of x. Let us define g n of x to be equal to f of x plus 1 over n minus f of x divided by 1 over n whenever x belongs to a b and let us, this is not f of x, let us extend f outside the interval a b to be as f of b. So, for x bigger than b, we will treat f of x as f of b. So, for example, when this is b, b plus 1 over n will be treated as f of b. So, g n is a function which is the increment of f at the point x by an increment in x by 1 by n. So, clearly because the function f is differentiable, this function g n x converges to the derivative of the function f whenever the derivative exists. So, the first claim is that each of this g n is a measurable function and g n x converges to f dash of x for almost all x. That g n is a measurable function that is obvious because f is measurable. So, f of x plus 1 over n, this function is a translate of the measurable function is measurable. So, difference of measurable functions and divided by a constant that is a measurable function. So, g n x is a measurable function converging almost everywhere to the derivative of the function f dash of x. Let us compute apply Fautou's lemma to this. So, by Fautou's lemma, we know that first of all note that g n x also is a non-negative function because f is a monotonically increasing function. So, the numerator f of x plus 1 over n minus f of x divided by 1 over n that is a non-negative function. So, g n is a sequence of non-negative measurable functions converging almost everywhere to f dash of x. So, by Fautou's lemma, first of all f dash is a measurable function because it is a limit of measurable functions and by Fautou's lemma, the integral of f dash of x which is the limit of g n will be less than or equal to limit inferior of g n over a to b. So, Fautou's lemma says that if a sequence of non-negative functions converges to a function, then the integral of the limit inferior is less than or equal to limit inferior of the integrals. So, this is the direct consequence of Fautou's lemma applied to the function g n.  So, this integral splits into two integrals, n times integral a to b f of x plus 1 over n d lambda minus n times integral a to b f of x d lambda x. Let us use the fact that Lebesgue measure is translation invariant. So, this integral a to b f of x plus 1 over n can be written as integral a plus 1 over n to b plus 1 over n of f x d lambda x. So, here we are using the property that the Lebesgue measure is translation invariant. So, the right hand side is limit inferior n going to infinity of n times integral a plus 1 over n to b plus 1 over n f x d lambda x minus the integral a to b. So, now using the fact that the Lebesgue integral is additive over the limits of integration. So, this difference is nothing but, so a to a plus 1 over n and then 1 over b a. So, this integral a plus 1 over a to b can be written as a to a plus 1 over n and the second integral integral being a plus 1 over n to b.  So, here we are using the property that the integral is additive over the limits of integration. Now, we use the fact that f is a monotonically increasing function. So, the first integral is b to b 1 b plus 1 over n, but we have defined f of x to be equal to b whenever x exceeds b plus 1 over n. So, the first integral is nothing but f of b divided by 1 over n, n cancels. So, first integral is just f of b minus. So, limit inferior of minus n integral, but recall the fact that the limit inferior of minus of a sequence is equal to minus of the limit superior. So, this becomes minus limit superior n integral a to a plus 1 over n f x of d x. Now, use the fact that f is a monotone function. So, this integral of f of x from a to a plus 1 over n will be less than or equal to f of a for the whole interval, length of interval is 1 over n. So, this is less than or equal to is a monotonically increasing function. So, we are putting the value f of a. So, it is f of a divided by n into n and that is independent of the limit superior. So, that is just f of b minus f of a. So, here we have used the fact that f is a monotonically increasing function. So, that proves the lemma. Namely, if f is monotonically increasing, then its derivative function is integrable and the integral of the derivative function, so integral of f dash a to b f x d x is less than or equal to f of b minus f of a. So, this lemma we will be using in the proof of the theorem, fundamental theorem of calculus part 1. So, let us prove the theorem, fundamental theorem of calculus part 1. So, we want to prove that the integral a to x f of t d lambda t, this function f of x for x between a and b, we want to show that this is differentiable. Of course, we know already that it is differentiable with derivative f dash of x equal to f of x for of almost everywhere. So, this is what we want to prove. So, as a first step, we are saying that let us assume that the function. So, step 1 is that we may assume f is bigger than or equal to 0. So, the reason for that is f. So, reason for that is because f belongs to l 1 of a b. So, f can be written as the positive part minus the negative part of the function and recall that f plus f minus both are non-negative functions and f plus and f minus both belong to l 1 of a b. So, as a consequence of this, the function f of x can be written as integral a to x f plus t d t minus a to b f minus t d t.   The important thing to note in this is that both f plus and f minus are non-negative integral functions. So, in case we have already proved the theorem for non-negative integral functions, this will imply that f 1 dash of x is equal to f plus of x and f 2 dash of x is equal to f minus of x. Hence, as a consequence of this, we will have that f 1 minus f 2 dash of x is equal to f 1 x minus f 2 dash of x and this ends by the step 1. If it is already true for non-negative integrable functions, this is f plus of x almost everywhere and that is f minus of x almost everywhere and that is equal to f of x almost everywhere. So, that will prove that f dash of x. So, implying f dash of x is equal to f of x almost everywhere x. So, if we can prove the theorem for non-negative integrable functions, then we will be through. So, step 1 says let us assume f is non-negative. Second step says let us assume that the function is a bounded function and let us prove the result when f is a bounded function. So, we will assume for the time being that f is a bounded function and let us assume m is the constant such that f of x is less than or equal to m, bigger than or equal to 0 for every x belonging to AB. In that case, let us define f n of x to be equal to f of x plus 1 over n minus f of x divided by 1 over n whenever x belongs to AB, where as usual f of x plus 1 over n is defined as equal to f of b for x bigger than or equal to b. Then each of f n is a measurable function. In fact, each f n is an absolutely continuous function and hence is also measurable and f n x converges to f dash of x for almost all x belonging to AB, because it is function is differentiable almost everywhere being absolutely continuous. So, the derivative exists almost everywhere and the right hand side is nothing but converging to the derivative of the function f of x. And since we have assumed that f is a bounded measurable function, f is bounded.  So, this difference numerator is nothing but the integral from x to x plus 1 over n f t d lambda t and this is less than or equal to integral absolute value of the integral is less than or equal to integral of the absolute value and hence this absolute value is less than or equal to n times absolute value of m f which is less than m into the length of the interval which is 1 over n. So, that cancels. So, this is less than or equal to m. So, f n is a sequence of measurable functions and each of them is bounded by a constant m and we are over a finite space AB. So, Lebesgue's bounded convergence theorem or also the dominated we can call it as dominated convergence theorem says that for every c belonging to AB if we apply it over the interval a to c then integral over a to c f prime t d lambda t is equal to limit of the functions f and t d lambda t. So, here we are applying bounded convergence theorem or dominated convergence theorem. So, that gives you because f n converges to f dash and all of them are integrable functions. So, integral a to c of f prime t d lambda t is equal to limit n going to infinity a to c f n t d lambda of t. And now, we will write down the values of f n. So, what is f n? f n is equal to n times f of t plus 1 over n minus f of t divided by 1 over n.  So, now we will use the fact that this integral is with respect to lambda which is translation invariant. So, the first integral which is f of t plus 1 over n can be written as integral of f of t d lambda t from a plus 1 over n to c plus 1 over n. So, the first integral is transformed to n times integral a plus 1 over n to c plus 1 over n f of t d lambda t. And of course, the second integral remains as n times a to c f of t d lambda t. So, this is using the fact that the Lebesgue measure is translation invariant. And now once again as we have seen earlier integral Lebesgue integral being additive over the limits of integration. So, this integral from a plus 1 over n to c plus 1 over n minus the integral a to c gives us the integral of f of t from c to 1 plus 1 over n to integral from a to a plus 1 over n of f t d lambda t. And now we use the fact that f is a non-negative monotonically increasing function and this is why is this capital F non-negative monotonically increasing function because the function small f. So, the reason for that is the claim is that this function f of x which was defined as a to x f t d lambda t then f of x is monotonically increasing. And the reason is because f is non-negative. So, that implies that for y bigger than x f of y which is minus f of x will be equal to integral x to y of f t d lambda t which is bigger than or equal to 0. So, that implies that the function f t is monotonically increasing. So, since the function f is of course a non-negative you are integrating a non-negative function and it is monotonically increasing. So, the integral c to c plus 1 over n f t d lambda t will be bigger than or equal to the value at the lower end point that is f of c into the length of the interval 1 over n into n. So, that gives you f of c. So, the first integral is n times c to c plus 1 over n is bigger than or equal to f of c and of course it is less than or equal to the value at the upper end point into the length of the interval. So, that gives you f of c f at c plus 1 over n. So, that is the first integral is between f of c and f of c plus 1 over n and similarly the second integral is between f of a and f of a plus 1 over n. Now, these two inequalities along with the fact that the function capital F is absolutely continuous and hence continuous gives that as n goes to infinity f of a plus 1 over n is going to go to f of a. So, the second integral will go to f of a which is equal to 0 and the first integral will go to f of c because it is sandwiched between f of c and f of c plus 1 over n. So, that implies that the limit n going to infinity of n times the integral c to c plus 1 over n f t d lambda t minus a to a plus 1 over n f t d lambda t is equal to f of c which is equal to nothing but a to c of f t d lambda t. So, what we have shown is that the integral of the derivative of capital F for over the interval a to c is equal to integral over a to c of small f of t d lambda t and this holds for all values of c between a and b and that implies because these two are equal. So, that implies that small f of t must be equal. So, this is a mistake which should be writing at f dash of t capital F dash of t must be equal to small f of t. So, what we are saying is integrals of two functions non-negative functions are equal over all integrals all intervals of the type a to c where c belongs to a to b that means the two functions must be equal almost everywhere. So, f prime of t must be equal to f of t for almost all t.  So, here the two written wrongly it should be capital F dash of t is equal to small f of t. So, that proves the fundamental theorem of calculus for bounded non-negative integrable functions. For the general case when f is general non-negative function one uses what is called the truncation of the function f. So, we will just give you outline. So, namely what one does is look at the function f of x which is f of x if f of x is less than or equal to n and is equal to n if f of x is bigger than n. So, whenever the graph of the function goes beyond n you cut it and put it equal to n. So, f this f of n is called the truncation of the function f beyond n. So, each f n is a non-negative integrable function and this f n converge to the function f for every x belonging to a b.  So, g n is a increasing sequence of functions and it is derivative g n of x non-negative for every x because it is a monotonically increasing function. So, its derivative must be non-negative and it exists because it is absolutely continuous function.   So, if you take it on the other side we get f of x is equal to g n x plus a to x f n t d lambda t and from here because f dash exists for almost everywhere. So, by the earlier case we have got that f n is a non-negative bounded measurable function. So, when we apply the earlier case to this indefinite integral its derivative exists and is equal to small f n. So, that gives us that for almost all x f dash of x is equal to g n dash of x plus f n of x for almost all x belonging to x. So, g n this is non-negative. So, that implies that f dash of x must be bigger than or equal to f of x for every n and for almost all x belonging to x and this is happening for all n. So, in the limit that gives us that f dash of x is bigger than or equal to f of x for all x belonging to a b.  So, that implies that the integral of f dash of x minus small f of x is equal to 0 over the interval a to b. So, this is a non-negative function whose integral is 0 that means this function f dash of x must be equal to f of x for almost all x belonging to a b. So, that completes the proof of fundamental theorem of calculus part 1 namely the indefinite integral of a function from a to b f x. If I take an indefinite integral a to x f t d lambda t for an integrable function then this indefinite integral is absolutely continuous and n derivative exists and not only that the derivative f dash of x is equal to small f of x for almost all x belonging to a to b. So, this is fundamental theorem calculus part 1 which corresponds to the fundamental theorem of calculus part 1 of Riemann integrable functions namely if you take a function f which is continuous on an interval a b then the indefinite integral is differentiable everywhere and the derivative is equal to small f. In this case for Lebesgue integrable functions we get that the indefinite integral is an absolutely continuous function of course and it is differentiable almost everywhere and derivative is equal to the integrand f of x for almost all x. If you recall the fundamental theorem of calculus also had the second part for Riemann integrable functions namely if you integrate the derivative then you get back the values of the function. So, a corresponding result is true for Lebesgue integrable functions also so we would like to prove that. So, the claim is that if f is absolutely continuous so its derivative exists almost everywhere and the claim is that if we integrate the derivative derivative is an integrable function and its integral is nothing but the values of the original function. So, to prove that we need a theorem, we need a lemma which will not prove which says that if g is an absolutely continuous function and its derivative is equal to 0 almost everywhere then g is a constant function. This is if you recall that is also required. So, a similar result is required for functions which are Riemann integrable and in the fundamental theorem of calculus part 2 namely if g is a function whose derivative is equal to 0 everywhere then the function is a constant function. So, this is a parallel of that result for absolutely continuous functions. So, if for a absolutely continuous function the derivative is equal to 0 almost everywhere then the function is a constant function. So, we will assume this result and for a because a proof requires is a slightly technical proof and requires the use of what is called Vitelli's coverage theorem which we have not covered in this part of the lectures. So, those interested can look at the proof and the text book which is referred earlier. So, the result lemma is that if a function is absolutely continuous and its derivative is 0 almost everywhere then the function is a constant function. So, using that we will prove fundamental theorem of calculus part 2 namely which says that if f is absolutely continuous function then of course we know that the derivative exists almost everywhere. The claim is that the derivative is a integrable function and the integral of the derivative from x to y is equal to f y minus f of x for all points x less than y between a and b. So, that will complete the proof of the that will complete the statement and analysis of fundamental theorem of calculus. So, to prove this let us look that the function capital F which is given to be absolutely continuous and every absolutely continuous function is of bounded variation and hence we can write F as a difference of two monotone functions monotonically increasing functions say f 1 and f 2 where both f 1 and f 2 are monotonically increasing functions and of course by fundamental theorem of calculus we know that f 1 dash exists derivative f dash exists by fundamental theorem of calculus and it being a difference of two monotone functions which are also differentiable almost everywhere by Lebesgue's theorem. So, the derivative is equal to f 1 dash x minus f 2 dash x for almost all x.  So, the derivatives are integrable functions. So, that follows from the lemma that we just now proved for the monotonically increasing functions the derivative exists and are integrable. So, as a consequence we get f 1 dash is integrable f 2 dash is integrable and being a difference of two integrable functions the function capital F is dash is also integrable and not only that we also have that f 1 of x is less than or equal to a 2 x f 1 dash of t d lambda t that was also a part of the lemma and similarly f 2 of x is also less than or equal to a 2 x f 2 dash of t d lambda t. So, as a consequence we get f dash is l 1 that we have already observed. So, let us write g of x as equal to a 2 x f dash of t d lambda t. So, what we want to prove is that this g of x is f of x minus f of a which is 0. So, we want to prove g of x is equal to f of x. So, now let us observe that if we define g of x to be equal to this then we that g of x is absolutely continuous its derivative exists and derivative is equal to f dash for almost all x. So, g dash is equal to f dash of x for almost all x and we know that this is a function g of x its derivative is equal to 0 almost everywhere and g of x is absolutely continuous function. So, by the lemma just now we stated that g of x is absolutely continuous function whose derivative is equal to f dash of x. So, that implies that the function g of x must be equal to f of x for almost all x. So, that completes the proof of fundamental theorem of calculus part 2. So, fundamental theorem of calculus has two parts. So, let me once again recall fundamental theorem of calculus. It says that if f is l 1 of a b then that implies that the integral f of t d lambda t a to x x belonging to a to b is. So, if we call this function as capital F of x then f dash of x exists almost everywhere and f dash of x is equal to f of x almost everywhere. So, that is fundamental theorem of calculus part 1 and fundamental theorem of calculus part 2 says that if f a to b is absolutely continuous then this implies that the derivative exists. Of course, because absolutely continuous implies it is differentiable almost everywhere is l 1 of a b and integral of f dash of t d lambda t say a to x is equal to f of x. So, these two put together are called fundamental theorem of calculus for Lebesgue integrals. As a consequence if you recall that for functions, if you recall for Riemann integrable functions fundamental theorem of calculus gives many consequences. Essentially saying that the derivative, integration of the derivative is equal to the function gives consequences like integration by parts, it gives you integration by substitution, it gives you chain rule and so on. Similarly, the Lebesgue integral fundamental theorem of integral calculus for Lebesgue gives all similar results. We illustrate this by giving one result called integration by parts. So, integration by parts states the following namely supposing f and g are two functions which are absolutely continuous functions. Then the claim is that because they are absolutely continuous, so the derivatives exist. So, the claim is that f of b into g of b minus f of a g of a is equal to integral a to b of f dash g d lambda t plus integral a to b f g dash d lambda t. So, basically it is same as for Riemann integral that if f and g are absolutely continuous, then we know that f dash exists. So, it says integral of f dash g d lambda t is nothing but if you take it on the other side, it is same as you look at the integral of f dash which is going to be f of b.  So, that is precisely the integration by parts for Riemann integrable functions. So, a proof of this is obvious from the fundamental theorem of calculus. Let me illustrate that. So, first note that since f and g are both absolutely continuous, so it follows that the product function f g is absolutely continuous that we have already indicated and hence it is differentiable almost everywhere. In Riemann integrable functions, it is just saying that f and g are differentiable, so product is differentiable. Here because they are absolutely continuous, so the product is absolutely continuous and hence is differentiable almost everywhere. Further, by the product rule for differentiation, the derivative of the product function of course is equal to f into g dash is equal to f multiplied by g dash at x plus f dash into g at x for almost all x in the interval a to b. So, this is just wherever the function is differentiable, the derivative of the product is equal to f g dash plus f dash of g and this is true almost everywhere, so this is equal to almost everywhere. Once that is true, now we can apply fundamental theorem of calculus part 2, so we can integrate f g dash, so integrate both sides. So, integral of f g dash will give us f b minus f b into g b minus f of a into g of a because this will give us the integral will give you the value of the function at b minus the value of the function at a, the function being the product function f into g.  So, that is called the integration by parts. Similarly, other results like integration by substitution and so on can be obtained by using chain rule and other things. So, those interested should refer the text book for the same. So, basically what we have tried to prove in the last two lectures is that for corresponding to the theorem, corresponding to the theorem on fundamental theorem of calculus for Riemann integrable functions, there is a theorem for Lebesgue integrable functions and it says that a function capital F from a to b defined on real values is absolutely continuous if and only if it is the integral of its derivative function. That is basically saying that because it is absolutely continuous, the derivative exists and the integral of the derivative is nothing but function can be obtained as the integral of the derivative. So, this is the perfect extension of the fundamental theorem of calculus for Lebesgue integrable functions. So, the notion and in this proving this fundamental theorem of calculus, we need it the notion of absolute continuity of functions. This absolute continuity of functions is related in another way to the properties of measures called absolutely continuous functions, absolutely continuous measures. So, in the coming today and in the next lecture, we will look at what are called absolutely continuous measures. .. So, let us define what is a absolutely continuous measure. So, let X S mu be a given measure space and let F be a non-negative real valued measurable functions on it. Let us define for any measurable set E in the sigma algebra S, nu of E to be integral over E of F d mu. So, the right hand side is a number which depends on E. So, nu of E is the integral of F with respect to the measure mu over the set E. So, this gives us a set function E going to nu of E and if you recall, we had shown that nu is a measure on the measurable space X S and has a very special property namely if this set E over which you are integrating the function F has got mu measure 0, then obviously this implies that nu of that set E is also equal to 0. So, this measure nu which is defined via integration with respect to the measure mu is related, these two measures are related by the property that nu of the set E is equal to 0, whenever the measure mu of the set E is equal to 0. So, if a measure nu is defined via integration, then the null sets of mu are also null sets of E. So, this property is known as absolutely continuous continuity of measures. So, let us write this define two measures mu and nu are set to be absolutely continuous with respect to. So, we say that the measure nu is absolutely continuous with respect to the measure mu, if nu of E is equal to 0 whenever mu of E equal to 0. So, nu is absolutely continuous with respect to mu whenever the null sets of mu are also null sets of mu and this we write as nu with these two arrows less than less than double sign of less signifies that nu is absolutely continuous with respect to mu. So, it is easy to remember mu of E equal to 0 implies nu of E equal to 0. Let us give some examples of absolutely continuous measures. Of course, just now we said that if you take a non-negative function f which is integrable or even just a measurable for non-negative measurable function on the measure space Xs and integrate it with respect to nu, then integral of f over E with respect to mu gives you a measure nu which is absolutely continuous. So, this measure nu is absolutely continuous. Let us look at the counting measure on the Lebesgue measure space that is a real line. So, what is the counting measure? For every set E in R, the counting measure mu of E is defined as the number of elements in the set E. If E is a finite set and it is defined as mu of E equal to infinity, if E is a set which is not finite. So, for finite sets mu of E is the number of elements in E and for an infinite set it is the number we call it as plus infinity. Then we claim that lambda is absolutely continuous with respect to mu where mu is the Lebesgue measure. So, we want to prove the following fact. Let us observe. So, mu is counting measure and lambda is Lebesgue measure. So, claim is that lambda is absolutely continuous with respect to mu. So, to show that let us take a set E which is Lebesgue measurable and mu of E equal to 0. But that means this implies what are the sets for which mu is the counting measure. So, if a measure of a counting measure of a set is equal to 0, that means E must be equal to empty set. So, for counting measure empty set is the only set of measure 0. So, that obviously implies lambda of phi which is same as lambda of E equal to 0. So, that implies obviously that lambda is absolutely continuous with respect to the counting measure and this is happening because for counting measure only null set is the empty set. Let us take X to be equal to the set of all natural numbers and S to be the set of all power set of natural numbers namely all subsets of natural numbers. And let us define two measures mu and mu. Say that mu of empty set is same as mu of empty set is 0 and for every other set which is not empty set let us define mu of E to be equal to sigma of 2 to the power n whenever the natural number n belongs to E and mu of E to be summation of 1 over 2 to the power n for all natural numbers n belonging to E. It is easy to check that these two sets two set functions mu and mu are measures on the measure space X and S. Then if mu of E is equal to 0 let us assume that mu of E is equal to 0. This is possible only when this E is empty set and similarly mu of E is also equal to 0 when E is equal to empty set. So, mu and mu are two measures which have only empty set as the null sets. So, that clearly proves that mu of E is equal to 0 if and only if mu of E is equal to 0. Hence that says mu is absolutely continuous with respect to mu and mu is absolutely continuous with respect to mu. So, these are some of the examples of absolutely continuous measures, but as you would have noticed these are obvious examples of absolutely continuous measures. And the only non-trivial way we got absolutely continuous measures was the first example where mu was defined as integral of a non-negative function with respect to a measure mu. And there is no wonder that we are not able to get any examples, because there is a very strong powerful theorem which says that the only way one can obtain absolutely continuous measures are via integration. Hence that example of that when you integrate you get absolutely continuous measures are the only ways of obtaining absolutely continuous measures. This leads to a theorem called Radon Nicodem theorem which is very powerful and very useful and we will prove it in our next lecture. Thank you.


Welcome everyone. I'm Chris Kaplus. I'm the Director of the SCX MicroMasters Program in Supply Chain Management. I'm here with Jim Rice, who is the Deputy Director of CTL here and runs all of our Executive Education, as well as our Partners Program. And we're here to talk to you about the new offering that we have, specifically only for SCX students, and that's the Boot Camp. And so this is the Boot Camp for Supply Chain Management that, as I said, is only open for those who have completed at least three of the SCX courses. And we thought we'd explain why we're doing this. So the first is, you've all done these online courses, and you've come to realize by now, I'm sure, that some things you can learn online, and some things are best taught face to face. And that's what we want to cover in this Boot Camp, from August 22nd to August 25th. It's a very intensive four days where you get to do a lot of those things you can't just do online. The second thing is that we found that some students, they finished the MicroMasters, but they can't come and quit their job for five months to come get a master's degree. I'm a big believer in coming for that full intensive time period, whether it's 10 months, five months, or two years. But that's not feasible for some people in their current state of their life. So this is another offering. It's another piece of the portfolio for the education. The third is, some of the offerings we offer for Executive Ed aren't quite suited for the SCX students. They're either a little too general, and they don't leverage the kind of learning that you've already taken and that you've acquired. So we've really kind of focused it on those kind of things, and that's why we're offering this. And the final reason is because we can scale. A one week offering is something we're going to do as a pilot, because we're testing it. We haven't done this before. If it works, then I can see replicating this multiple times in terms of frequency, but also location. We have a lot of learners in Latin America who would probably be more willing to come to Bogota for a lesson. In Southeast Asia come to Kuala Lumpur, or in Europe come to Zaragoza or Luxembourg. So we're playing with this. We're going to see how it works the first time through, and it's an experiment like everything else we're doing in this program. And so we don't quite know how it's going to turn out, but you're in here for the journey. And so I asked Jim to talk a little bit about Executive Ed and what he's done in the past and what they couldn't expect. Yeah, thanks Chris. Let me just address one comment you just made. We don't know how it's going to turn out. Well, I think that based on all the Executive Ed we've done in the past, we have a pretty good feeling for how things are going to go. You know, we've done short programs, long programs, custom programs, open enrollment, and most recently, almost all of our programs are what we call blended, meaning that there's an online component to it. One thing that is in common we have across all these is that when we bring people together, in person, there's the chance for that transformative experience. And you'll find that as an online learner, your experience is going to be very different. Your experience is going to be where you're going to share an idea and it's going to get challenged.  So whatever ideas you have come in to say a case discussion, it's going to get challenged. And then real time, you're going to have to say, Oh, wait a second, I have new information. What does that make me think now? Right. So to tie on to that, everything we do online is what's known as asymmetric. You can do it at any time because you're across the world, we can't have everyone online or in the same room at the same time. What Jim's alluding to when we do a case study, like when we did it online, you all commented by yourself, there was very little interaction back and forth.  And that's where the real learning takes place. That's why we're going to stock the this bootcamp with a lot of case studies where there's a lot of discussion debate. There's not always a clear answer. Because that's another problem, strength and a weakness with the online. There's always a correct answer. For cases, it gets a little fuzzy. Yeah, you'll your your ability to think critically is going to be challenged at this. And just as Chris mentioned, it's going to be very intensive. There's lots of interactive activities. In fact, that's one of the big distinctions between online. I mean, this bootcamp and our open enrollment programs, this one is almost all interactive, you know, two cases a day, interactive exercises, and then we have research briefings from faculty members across MIT. So it's going to be really exciting, I think. So it's going to be very intensive for those four days. We're packing it in. And because it's a trial, we reduce the price. So hopefully you can join us. We'll be here along with our colleagues on 20 to 25 August. Now's the time to register if you want to try and join us for this first initial pioneering bootcamp. Hope you're there. Cheers.


Our subject in this particular case study is an enormous basalt pillar bearing the law code of Hammurabi. And I brought in these two views to give you a sense of the massiveness of this particular work. It is a steely or large stone with relief carving on it. And you can get a sense from the people in the Louvre of just how large it is. When I say that the steely of Hammurabi with the law code on it was a basalt pillar, it came from a setting very much like what you see here. This is a photo that I took on our vacation in 2016 in Scotland. And you see my son at that time, I think he was seven. He is standing on some of the basalt on the island of Stafa in Scotland. And behind him are lots and lots of basalt pillars. And you can see that these sort of stepping stones that we are all walking on here are basalt pillars that have broken off. But you can imagine that something like the pillar that was used for the steely of Hammurabi would have been relatively easy to quarry because it would have come in a large pillar-like shape and could be just sort of dragged off and used in that state. Here are some more basalt pillars. I'm showing you two views from a mine near the city of Mayen in Germany. And on the left you see a pillar of basalt just out in the landscape. And you can see a portion where it's begun, it's sort of cracked halfway. On the right we're actually at the entrance to what is now a bat cave. But this was a very important quarry for basalt. And you can see that the quarrymen simply took the individual pillars that had formed and just removed them and used them wholesale. So again I think you can imagine the steely of Hammurabi starting out with a shape very much like this. And by the time that we're talking about the steely of Hammurabi at Babylon we're talking about a new civilization, the Babylonians, who clearly did not have the negative association with basalt that the much earlier Sumerians did. And they, in the case of the law code of Hammurabi, are attracted to probably first the ease in quarrying it and second to the fact that it is a very hard material and like the diorite used for the Gudea figures, something that would be eternal. Now we're back to the steely of Hammurabi. And what this is, is a massive basalt pillar that includes the entire text of the law code of Hammurabi, the ruler of Babylon, that he tells us was given to him by the god Shemash. And what we see here on the front of the steely is Hammurabi on the left bearded with a cap that looks very much like the caps that we saw on Gudea. So it's a sign of his royalty. He's wearing very rich robes. Usually if you see a figure with lots and lots, wearing lots and lots of fabric in art, that means that they are at the very least wealthy enough to own that much fabric. So it's a sign of status. He's a bearded figure and he's shown in a stance and in a pose that indicates that he's speaking with his god. You see he has his hand up to his face. Shemash, on the other hand, is seated and wears much more elaborate clothing with layers and layers and layers of fabric. So even more important, even more wealthy if you will. And look at this. Look at the fact that the heads of the two figures are even. So if Shemash stood up, he would tower well over Hammurabi. Size here is something that matters. Size tells us that Shemash is the most important figure here. He's also seated on a throne and the throne is shown with some characteristics of a mountain. He has sort of stones at his feet and this kind of many layered throne. And oftentimes gods were associated with the mountains because the mountains allowed people to get closer up to the heavens and to the realm of the gods. He has beams of light coming out of his shoulders. He has a long elaborate beard which was a symbol of authority. And you might also notice that he has this really sort of elaborate headdress that kind of looks like a twisty soft serve ice cream cone but in fact those are overlapping bull horns and bulls as you might recall from when we looked at Lapis Lazuli and the bull headed liar. Bulls were symbols of power in the ancient Near East. And so bull horns are often associated with the headdresses of rulers. And what's happening between these two figures is Shemash is handing a staff of authority and also a ring of authority to Hammurabi as the two speak. Although the law code of Hammurabi is not the first law code we know of in ancient history, it is one of the most important and certainly the best preserved. We have fragmentary law codes that also exist. We have indications of others that existed but we have the entire law code of Hammurabi. And I've got a couple of examples of laws here. They tend to be sort of eye for an eye, tooth for a tooth sorts of punishments. So for example, law number two, if anyone bring an accusation against a man and the accused go to the river and leap into the river, if he sink in the river his accuser shall take possession of his house. But if the river proved that the accused is not guilty and he escaped unhurt, then he who had brought the accusation shall be put to death. While he who leaped into the river shall take possession of the house that had belonged to his accuser. So here we have sort of a trial, a trial by water, sink or swim, and a result that would certainly discourage false accusations. Number 57, down below, if a shepherd without the permission of the owner of the field and without the knowledge of the owner of the sheep lets the sheep into a field to graze, then the owner of the field shall harvest his crop and the shepherd who had pastured his flock there without permission of the owner of the field shall pay the owner 20 gur of corn for every 10 gun. And those are probably weights and measures that I don't know exactly what they're for. But this is a good example of what many of the laws are about and it's sort of dealing with everyday business between individuals and reflects the fact that by the time we get to ancient Babylon we have very complex societies with a bunch of different jobs and roles being played by individuals, lots of areas of specialization. And so a law code would be needed to keep peace and order between all of these disparate groups. I think one of the most interesting parts of the law code of Hammurabi is its epilogue. And I gave you some excerpts from that epilogue as a reading assignment to go over prior to this case study. And I want to call out one particular portion of that epilogue and that's the quote you see here on the right. It says, in future time, through all coming generations, let the king who may be in the land observe the words of righteousness which I have written on my monument. Let him not alter the law of the land which I have given, the edicts which I have enacted. My monument, let him not mar. If such a ruler have wisdom and be able to keep his land in order he shall observe the words which I have written in this inscription. The rules, statute and law of the land which I have given, the decisions which I have made, will this inscription show him? Let him rule his subjects accordingly. And you might remember that he also emphasized that he gets the law from Shemash, that he is favored by a whole laundry list of gods including Marduk, the patron god of Babylon. And there's also a bunch of curses that will affect anyone who changes or destroys this law code. And if you think about it, the laws of the ancient Israelites that we learn about in the Bible that were given to Moses, those were given on stone tablets. There's clearly a sense that something as important as law should be recorded on something that cannot easily be destroyed.