Good morning, all of you and welcome to this inaugural function. I have pleasure to invite to the dais for the morning function, Professor Sukhatme, Professor Devan Khakkar, our director and Professor Amitabh Sanyal, the head of the computer science and engineering department. Could you please come over sir, so that I can formally welcome you. Thank you for coming. Thank you, Devan. I would also like to invite the lead faculty for this program, Professor Karmalkar of IIT Madras who has come all the way from Chennai to join us, Professor Karmalkar. Thank you, Professor. Let me very briefly introduce the dignitaries to you. I will begin with the person whom we have requested to preside over today's function, Professor Sukhatme. Many of you would know him as a well-known researcher, but more than a researcher, he has been a great educationist. He has been with IIT Bombay for more years than I care to remember. After retirement, he was appointed as chairman of the Atomic Energy Regulatory Board, but he continues to engage with us. It is very rare not to see him at least three or four times in a week to come to his office. He still writes and he writes research papers. He was also of course the director of the institute and I had the privilege of serving under him as the first dean of resources. The number of changes that he made in the academic program and the focus that he tried to get for the research activities has been remarkable and has been sustained since then. Thank you very much, Professor Sukhatme, for joining us. Next to him is Professor Devan Khakkar, our director of IIT Bombay. Of course, before becoming the director, he was dean of faculty here. He has been a professor of chemical engineering, a very renowned researcher and a dedicated educationist. He is continuing to make changes appropriately in the academic and research framework of the institute, providing more flexibility. He particularly encourages interdisciplinary activities and under his leadership in a short time, the institute has seen major activities reaching to fruition such as flexibility in our undergraduate program, inclusion of research agenda into newer areas such as energy and nanotechnology. Thank you very much, Professor Khakkar, for joining us today. Next to him is Professor Amitabh Sanyal, a hardcore educationist and researcher as you can see from his face, a simpleton but deeply passionate about research and education. He leads us in the department of computer science and engineering and in fact, I jokingly say that he has the privilege of leading the largest group of rowdy computer science professors, about 40 of them. Under his leadership, the department has almost twice the faculty strength as any other computer science department in the country. He probably leads the leading researchers in computer science in the department. Thank you very much, Professor Sanyal, for joining us. We also have with us Professor Karmalkar. As I said, he is the lead faculty member who has come all the way from IIT Madras. A few years ago, we had invited him to talk to our research scholars and he gave a series of lectures titled Introduction to Research. All of us liked them so much. Our research scholars were extremely motivated and much better prepared after that series. We released those lectures in open source but when we decided to do this course on introduction to research methodologies, we thought that we must start with introduction to research and we thought of a person no other than Dr. Karmalkar. Thank you very much Dr. Karmalkar for coming and sharing your thoughts with our people here. I would like to very briefly tell you about the trained thousand teachers programs. Many of you have participated in this. Many years ago in the institute when we started the distance education program, the idea was that we should be able to reach to many people who would otherwise desire to attend programs in IIT Bombay but cannot travel to IIT Bombay, cannot stay away from their places. We morphed this initial program which was meant for students, professionals and teachers into structured workshops for teachers. Under this program, teachers assemble at remote centers which have been pre-designated. At each remote center, we have a workshop coordinator who is an expert in the subject that is going to be discussed. We first collect all the remote center coordinators to IIT Bombay and have a detailed oriental discussion which often lasts one week. Then the workshop coordinators go back, set up their labs, set up the tutorials, set up the experiments as required by the lead faculty here. When the main workshop starts, about thousand teachers assemble at 30-35 remote centers. The two way lectures are transmitted through AVU which is a product developed by a sister or a partner institution Amruta University through which we are talking to each other today. It permits interactive lectures and the afternoon tutorials and labs are conducted in the local remote centers under the supervision of workshop coordinators. We have found that this model works best in the sense that the top experts can be heard and listened to and can be interacted with to understand their ideas about the particular subject. But we still retain in this model the cohesive group work in a classroom such as the common tutorials, common discussion sessions and common lab sessions at a place. We have conducted ten such workshops in the past, empowering more than eleven thousand teachers. Three months ago when there was a review in MHRD, the then secretary of higher education MHRD, Svibhapuri Das and Mr. Sinha suggested that why do not you scale it up further. We told them that we had a plan for a mega workshop for ten thousand teachers in December but we are advised to advance that to June and that is why we decided to conduct this program here. Currently, this is merely a scaled model instead of thirty to thirty-five remote centers. We plan to have two hundred remote centers sadly due to the positive of time amongst large number of applications that we received, we could confirm only hundred and sixty eight remote centers from which we are conducting this program. There was an enrollment of about twelve thousand teachers and PG students. We could not cater to them. We enrolled nine thousand but I understand that some teachers did not get the choice of the center that they had asked for and therefore they may not be able to attain. It is our endeavor to increase these number of centers first by another two hundred before December and then to a total of five hundred remote centers. In fact, it is our ambition that every town where there is an engineering college there should be a remote center because the true benefit of using ICT in this manner is that people do not have to leave their place of residence and they can attain the workshop from wherever they stay reducing cost, time and effort which is otherwise vested in this process. We believe that this mega workshop having more than nine thousand enrolled teaching participants is first of its kind globally. We are very happy to do this experiment thanks to the support from the one sixty eight remote centers and thanks to the participation of all the large number of teachers and some post graduate students who have come to attend this course. I will be speaking more to you about this workshop as also about the subsequent programs that we have in mind. We in fact look forward to greater collaboration not only with the remote center faculty but also with the other faculty members from more than two thousand colleges who have assembled here in future years to come. With that backdrop I will now like to request my director Prasadevan Khakkar to share his thoughts with you. Prasadevan Khakkar. Very warm virtual welcome to IIT Bombay to all of you. I must say that I am very glad to be part of this historic occasion when IIT Bombay connects with eight thousand teachers and a thousand students all over the country. Over the last fifty four years IIT Bombay has built up strong capabilities in education and research. It has also built up a strong international reputation for excellence in these spheres of activities. Today IIT Bombay has about eight thousand students of which more than half are post graduate students. We have two thousand PhD students on the roles today more than five hundred faculty members and more than three thousand m tech students. So in many ways research has become a very important focus and of course our educational programs continue to be strong through workshops such as this one. The aim is to freely share best practices of the institute with teachers across the country. Our hope is that this type of exchange will accelerate the development of quality education throughout the country and also we hope that such kind of information transfer will benefit generation after generation of student in time to come. Sharing of knowledge with other colleges is in fact a part of the mission of the IITs stated in the IIT Act. IIT Bombay has always participated in this kind of workshop teacher training and so forth over the years. We have had our quality improvement program for PhD and master students. We have had summer courses for teachers over the last fifty years but what is now very unique is the availability of this national knowledge network. This is really an incredible resource which can have a huge multiplier effect. The thought of having eight thousand people in one place is almost mind boggling. I cannot imagine that all eight thousand or nine thousand of you could have come to this campus the kind of logistics involved, the kind of expense involved, your time involved would have been too great to make this feasible. As a result in the past all courses have been about thirty to fifty students and this is a very slow way of diffusing knowledge. In this new mode where we can instantaneously connect over the network has a great multiplier effect and we hope that many more such workshops and courses can be done so that there is a close interchange between all, between colleges amongst themselves and between IIT Bombay and all the colleges. Being a teacher all my life I think teaching is certainly the best job that one can have. In this kind of a job you are always together with young people to help them prepare themselves and to inspire them to face the world. College teachers have an extra dimension which makes the job even more interesting and that extra dimension is research. Research generation of new knowledge, scholarship, reading about new developments taking place enables us to renew ourselves, to renew our knowledge to keep abreast of the latest developments in the field and most importantly it actually helps us to build a spirit of inquiry in our own selves and in our students and this is becoming more and more important in today's student and in today's professional. I think this course on research methodology is thus most timely we have some really outstanding people Prof. Sukhatne, Prof. Karmakar, Prof. Narona, Prof. Sahanamurthy, many others who will essentially talk about how one should do research what are some of the ways of may be presenting the work and so forth. So, what is the nitty-gritty that is involved and I think this will have a big impact because in the time to come the importance of research is going to only increase. With these few words I would like to wish you a very successful and enjoyable workshop. I know that it is going to be very intensive knowing Prof. Fatak. So, you will have to work hard, but I am sure that you will enjoy it. Before I actually step off the podium I would like to read out a message from the Chairman Board of Governors of IIT Bombay, Dr. Anil Kakodkar who is himself a renowned nuclear scientist. He unfortunately could not be here, we had invited him, but he could not be here because he is out of town and he requested that his message be read out to all of you. So, this is what he writes, I wish to congratulate you and the entire team involved in this major initiative of IIT Bombay aimed at reaching a large body of faculty and students at different locations in the country. This approach that enables a much wider access to an institution like IIT Bombay and its faculty using the power of ICT while retaining the strengths of face to face learning teaching is indeed the way to achieve the twin objective of quality improvement and scale up to meet education and training needs of our nation at all levels. As you are aware I am keenly watching your efforts in taking Akash forward, affordable low cost tablets that can effectively access education and knowledge resources besides being an effective learning tool by itself can make a huge positive impact on education and training particularly in rural and remote parts of the country. I do hope that the pilot experiment on school education using low cost wireless broadband last mile connectivity, low cost tablets and OERs in Marathi that we talked about would be in place soon. Technology enabled new paradigm in education and development that is learner centric, enabler of lifelong learning and development oriented participation in an A-3 connected society all inclusive and guided by wise council is something that all of us in institutions like IIT should work for with best wishes for the success of your efforts and warm regards. Thank you very much Professor Kakkar for those encouraging words and I would also like to express my thanks to Dr. Kakkar. Dr. Kakkar has been keenly supporting all the initiatives that Professor Kakkar and our leadership team has been taking and as you could hear from his message he himself although he is a nuclear scientist and a great administrator but he himself is a great educationist at heart. You might have heard a brief comment in his message about Akash and many of you may be wondering as to what Akash tablets have to do with this particular workshop. This is something which is known to 168 workshop coordinators but is not known to the other teachers that ever since three months ago we were transferred this project of Akash tablet. We have perceived a plan to work jointly with college teachers such as you and working with you using the Akash tablet in its future deployment is one of our objectives. I believe that honorable minister might have something to say about the Akash tablet as well when he addresses all of you on the inauguration of this workshop. It is very convenient, very important moment to ensure that all those 10,000 teachers who are elected here are very important moment in the event. If you really want to have dreams when the leadership is in their dreams then they have realized that something that we need to be very proud of and I have to congratulate all of you for having made this, made us, made us our dreams. As you know that we all started the National Convention on Education in YGT. This was a program of the government to be here and our leadership was responsible to use YGT which is very important. And as you all know education is fundamental to empowerment. Not just about children but about the community because we empower our children. Ultimately when they grow up they will be citizens who will be committed to the goals of our nation and in that process create a future of Asia that we want to embrace as one of the leading powers of the world. And this cannot be done without empowering our children's way of education. And in the planning world essentially YGT is a very, very useful tool to empower our children and I am absolutely delighted that they want to ensure that I am always talking about the teacher training program or teaching about a thousand teachers at one given point in time. A thousand teachers at every given point in time and I am given to understand that already about ten workshops have been held by IIT Bombay and about twelve thousand teachers have been actually trained. Now why is this important for us? It is important for us because there is a raging debate in our country that the quality of students ultimately depend on the quality of teachers. And unless we empower our teachers then naturally our children will not be empowered because it is the quality teaching that ultimately brings about a quality student. And I have always believed both as a politician and as an academic perhaps you don't know that I started my career as a teacher in Delhi. I know how important it is to provide that inspiration for the student community which can only be provided by leaders in the teaching community. We are in the midst of a crisis, a crisis in which the community believes and we believe that there are not enough teachers in the system, not just not enough teachers but not enough quality teachers in the system. And therefore these kind of programs provide the quality teachers that we need. And what has been done today is something truly historic because instead of conducting these workshops, training a thousand teachers at the time you have taken this enormous step and leap forward by training 10,000 teachers in one go which is really what we are launching today. This is something that perhaps has never been done in the world and thanks to the program by Amrita that they have devised through which this has been made to happen. And this of course, this technology that Amrita has provided allows the student community and the teachers to be interactive. So it's really like sitting in one classroom, 10,000 teachers learning from each other and I don't think that this kind of experiment has been done anywhere in the world. So in that sense, it's not only a leap forward but it's an Indian solution to deal with the challenges that we confront and I don't think that we can really look to the global community to provide solutions for us. We have to look inwards. We have to look at ourselves. We have to look at our problems. We have to address those problems and we have to find solutions for those problems. So this is a very uniquely Indian solution for the problem of bringing quality into the teaching system by empowering our teaching community. So I once again congratulate Amrita. I congratulate IIT Bombay for having taken this forward. The other issue which of course again is a symbol of Indian technology is the Akash. Today we are going to symbolically hand over the Akash to students and I have to particularly thank Professor Pathak for taking this forward. The Akash as you know was launched sometimes way back in October 2011 and unfortunately there was some delay in actually taking this project forward for reasons that I don't want to go into now. But three months ago Professor Pathak decided and I requested, we requested Professor Pathak to take on this responsibility and IIT Bombay took on this responsibility and in three months time there has been a sea change in our confidence in the project and now today we are symbolically going to launch the low cost Akash device. I have to also mention the fact that not only is this now Akash 2 which is version 2 of Akash where the processor is now 800 MHz. The life of the battery has been increased I believe for three hours and of course it has a capacitive screen which is of much greater quality. So the result is that this new version of Akash in a sense is again is a step forward in fulfilling our dreams to be ultimately be able to supply a tablet to millions of our children, not just to our children, not just to our student community in technical institutions and in universities but Akash will be a low cost access device for the public at large to be able to deliver public services to the citizens of this country and these are the solutions that will ultimately change India. These are the solutions that will empower India.  Akash is no longer a device that consumes content through the efforts of IIT Bombay. Akash is a device that creates content. That content has been created with unique applications and you can actually now have programs in Python, in C and this is of enormous value to our student community. All in all I think that this is yet another step where we are delivering for the people of our country and of course it is a symbol of the level of collaboration and cooperation that occurs between institutions, whether it's Amrita or IIT Bombay. It's not just institutions but we are seeing individuals rise above themselves and collaborate with each other and with institutions with one aim in mind that let us make a national effort to make India the nation that it deserves to be. We cannot let history control us. The future is within our grasp. We must in fact make sure that we are able to use the imagination and use the tools and the innovative capabilities that we have to be able to realize that future. It is not a matter of us dreaming. The dream is becoming a reality and these are two steps in that reality. I'm also given to understand that we are now in the, you know, 170 centres have been set up or 168 centres have been set up and ultimately the aim is to set up about 500 centres in one go so that every educational institution becomes a centre and there should be connectivity with each engineering college wherever it is located in India. This really is the ultimate dream that we are looking at. I am now connected to St. Ravius College in Kanyakumari. What a pleasure it is to be with you. Good morning everybody. Good morning sir. We are very thankful to you. We are really honored to have an interaction with you and we really thank the ministry and IIT Bombay for empowering teachers to improve the quality of education to the remote corners of our nation. Really we are from a remote corner like Kanyakumari where we can't have access to high quality education which is available in IITs and higher institutions but through ICT. We thank you sir. You have made it possible to us. Thank you. I just want to ask anyone of the students can respond to it. What is your feeling today sitting there? Do you think that you have a new opportunity at hand and that this is going a long way in actually empowering you as you go forward as a teacher? I am really happy to attend this workshop because regarding the research we can understand so many things how to work on research and how to improve our knowledge and so this workshop will be very much helpful to us. That's what I am feeling. Thank you. You know I have always felt as a human being that unless I continually empower myself through lifelong learning I will stop growing. I am sure that you have all come here with that mindset. Is that correct? Can somebody respond on that? Do you believe that there should be lifelong learning and these kind of programs should be done on a continuous basis to empower yourself in times to come? Good morning sir. We feel that continuous learning for engineering college teachers is very much important because such type of programs will be very much helpful for us. Even if you want to learn something from the book it will take so much of time but when we hear from professors like IIT professors then easily we can grasp and we need continuous education is very much needed and I request you to continue such effort in future also sir. Thank you sir. Thank you. Good morning sir. So it is a privilege to talk to you sir. Good morning. Good morning to you all. On behalf of School of Engineering RQ University, Rajkot we are heartily thankful to the Ministry of HRD for sponsoring the two-week mega workshop on Introduction to Research Methodologies. Sir on this occasion I would like to introduce our Executive Vice President, say, Dhanis Bhai Patel, our Registrar, Sevalal Bhai Ramani, Vice Sun Seller, Dr. Ramamohan Rao, Ph.D. from IISC, Dr. C.D. Sankhar, our Dean's School of Engineering and all the participants, all the 100 participants who are going to participate in this mega workshop on Introduction to Research Methodologies. Sir, we are very much happy with the model and the way the workshop is going to be conducted and we would like to thank to Professor D.B. Patak and his team for making an effort success. Sir, we are very much proud to be a remote center, one of the remote centers where more than 10,000 teachers are participating and taking the knowledge from the expert faculties of IIT Bombay. Sir, thank you very much sir and over to you sir. I just wanted to mention to you that, you know, research in metrology is one of the most important issues that confronts our country because our farmers don't get information on time and as you know that the rain seemed to have failed us this year at least in the first month. The expectation is that rainfall will be about 96% today with a margin of error of 8-9%. So if the rainfall is about 90% we are in real trouble and therefore we need to constantly inform our farmers out there when the monsoon is going to arrive, when they should throw their seeds, when they should change to another crop. So research in met is one of the most important aspects of that need to be addressed as a nation and therefore you teachers out there participating in this program are participating in a novel. This is a novel initiative of the ministry to empower you in researching issues relating to the met. Over to you. Yes sir, you are very much right sir. And this kind of workshop will help all the participants to do the quality research and the application oriented research sir. We have the privilege of hosting 5 IST workshop so far. Sir, you will appreciate that in Srinagar institutions like IIT and ISE are still a distant dream but through this workshop we have got so well connected to adopting the best teaching and learning practices that Professor D.B. Patek has become like a household name among the teaching faculty in Srinagar. Sir, I like to put a couple of suggestions today. One of the suggestions would be sir, so far we have been able to create a larger group which spans over number of institutions. Now it is time to create a number of clusters within this group and each institute is associated with a cluster so that we are able to create a manageable unit within this larger group. The immediate advantage would be that there would be better exchange of programs like faculty or on research which would directly accrue a lot of benefits to the students. Sir, my second suggestion would be at MCIT also there are very good initiatives which are coming forth under your leadership especially projects like NKN, projects like national skill development initiatives. I believe we can use such platforms for adding not only adding numbers but producing quality numbers under our flagship programs. Third thing sir, we as an institute are still a large part of NKN. Formerly we were DOACC, now we are NILIT Srinagar. We would request your good self sir that we should be also brought under NKN and sometimes we would like to host you in Srinagar sir, Srinagar has a great weather and we have a great tourist season this time. So we are looking forward to sometimes hosting you in Srinagar. Thank you very much sir and over. Yeah, yeah, yeah, I'd love to have some Gustava and Tabak Madh when I come to Srinagar. Yeah, no, no, no. I think you have very good suggestions. I think these should be moved forward through cluster mode. Good morning sir. This is Dr. Gokhale, director of VNIT Nakhpur. We have been associated with the CD program of IIT Mumbai for a real long time. VNIT Nakhpur is a sister institute of IIT Mumbai and we have been closely associated for past 10 years and the benefits are for everyone to see. In the 10 years we have improved our research publications in a great deal. The research project proposals from various government funding agencies, the faculty receiving their PhDs and so on and so forth. So the benefits are plentiful and this particular effort that has now been firmly rooted into the technical education is the most welcome change. Earlier you know IIT Mumbai was concentrating more on the IT, ITAs but in the recent times the expansion in the other engineering disciplines has been really creditable and we have about 50 teachers sitting over here for 10 to 15 days and continuously working towards it. The best part of it is that the teachers are now made to sit as students in the classroom and the rigor in all these programs has been really wonderful because the value addition that teachers carry with them when they go back to their colleges is really phenomenal and we thank you as well as IIT Mumbai for this particular initiative. I am basically from IIT Madras and I was associated in a remote way with the NPTEL program. Now virtual laboratories also they could be brought in into the foray and technical education would be significantly improved right across the nooks and corners of our country. We are extremely grateful to you for the continued support in this particular initiative as well as being a participant in this particular program. Thank you very much sir. Good day. Thank you. Thank you very much. I think this is very important. You know this particular program has been very popular because in this particular workshop that we are taking up today I believe there were 12,000 teachers who registered and there was not enough space to accommodate 12,000 so that we were able to accommodate I believe only 9,000. So I think despite the you know with the kind of things that IIT Mumbai has been doing over the years by training 1,000 teachers for workshop we have reached a situation where more and more teachers want to take the benefit of this program. This shows the enormous reach of this program the empowerment through this program and how keen teachers are to empower themselves and this is a very positive sign and I am delighted to be in touch with me and IIT Nagpur and be in the midst of you today so good luck and all the best. Thank you. Thank you sir. Thank you very much honorable minister for interacting with some of our centers. I am sure that they are excited by your encouraging words. Over to you sir. If I may suggest that I want to hold for the country to see the version 2 of the Akash. Akash version 2 in which you have included several applications in which you have included several applications and I congratulate you for it. This has a you know a processor which is 800 megahertz it has about a much larger battery life it has a capacitive screen and it's really a super product I want to symbolically not just show this to the people of the country but also hand it over to you for you in turn to hand this product over to the directors. Thank you very much congratulations. Thank you so much honorable minister both for your kind courtesy in interacting with a large number of teachers. As you rightly said we are privileged and honored to have initiated this program and we now feel a part of a very large teachers community in this country. More importantly thank you very much for unviling Akash to a large number of my colleagues here including research students, undergraduate students and even summer interns coming from other institutions have worked very hard for last three months as instructed by you we would now be symbolically handing over these tablets to directors and principals of four select remote centers. As you are all aware we have planned to use our relationship with all the remote centers to do field testing of these tablets because although we have done a lot of work there is no end to the number of useful applications that can be continuously developed and more and more useful contents that can be created for this tablet. Towards this end we wish to use the creative talents of large number of students and teachers across the country from all the engineering colleges. To begin with we have roped in the support and partnership of our remote center colleges. We believe that after the testing the tablet production would start sometime by July end or August but starting with the next academic year we will be delivering these tablets and working closely with the engineering colleges. I am very proud to announce a partnership with SEALAC who had joined us in this program. Unfortunately Professor Rajat Muna could not come but Mr. Zia Sakeb is here the director of Mumbai unit of SEALAC. Thank you very much Zia for coming here. They are the ones who are helping us in rigorous lab testing of the AKAS tablet. As you know we want to make sure that the tablet that reaches the hands of students and teachers works absolutely fine. In cases such as such embedded devices particularly when it is not a commodity item but an item made to specifications it is important to go through such iterative testing to ensure that all the production processes are correctly geared up to produce only the best quality product. Thank you very much Zia and through you I would like to thank Professor Rajat Muna, Professor Amin Kumar and his team who are helping us in this testing. However from the samples that we have received and the extraordinary work that has been done by my colleagues here I would after this event I would like to show a small demonstration of a film but before that I would like to request Professor Sukhatme, the President of the Function and Professor Devan Khakkar to kindly hand over tablets to the four principals who have come here to receive them on behalf of the minister as instructed by the honorable minister. May I now request our friend directors of the partner institutions to come forward and receive these tablets. Professor Sahasrabudde, director College of Engineering Pune Thank you so much friends for having come here and thank you very much for agreeing to collaborate with us for the future activities just for the benefit of all the participants across the country I would like to now demonstrate the additional capabilities that have been built by a large team of IIT professors and students and as I said some students from other engineering colleges in fact we have that team here which is a set of people who have built some of these applications Professor Sahasrabudde I think there is one student who is from COEP who is doing internship here can you say hello to your director there are people there are 110 summer interns from all nook and corners of the country there are in fact some from VNIT there are several from our remote centers themselves I would also like to Pan, can you show Professor Kavi Arya will have the robo that you had very briefly seen in Naunch's hand has been designed at IIT Bombay for the last two years in the YI Yantra lab which Professor Kavi Arya leads and you will soon see a demonstration of how we have made Akash capable of controlling that robo and collecting a video stream from that robo we have Srikant is here can we show Srikant and his team yes they are the people who have developed the programming environment on Akash see many of us consider Akash or such tablets only to be excess devices and we forget that these are actually full-fledged computers to emphasize the fact that these are computers and they can indeed be used at least for learning programming and even running your programs the team led by Srikant has been working in fact they work with Professor Madhu Berlour and Professor Kannan Mawgalyar and it is curious that the programming environment has not been constructed by project engineers and researchers from CS department but from chemical engineering department aerospace department and such place that merely shows the strength that you have so we now have programming capabilities on Akash there is a team which has been creating interactive lessons they have created a tool called proximity I would like to show Parak Tiwari and his team this tool permits video lectures to be converted into interactive lessons so that people can directly jump to a desired theme in a lecture and go to a point of their requirement they we propose to convert most of the NPTEL lectures and these workshop lectures insanely all the workshop lecture materials released in open source so that will be easily accessible to people we also have another killer application called clicker application which is used for conducting quizzes in classes there is a team led by Rajesh Kushalkar and others who have created this particular application I would now like to show a very short movie of 6 minutes in which we have tried to capture please forgive me for very amateurish attempt this is not a professional film we just wanted to consolidate and show people at one point this is the team which designed and developed the proximity application which was originally meant for desktop publishing of interactive lectures these lectures now can be seen and heard on Akash we will now see an application which permits students to see the video recorded lectures the proximity tool permits editing of video recorded lectures to create interactive lessons for example this is one lesson that has been created people can move over to any point in this lecture the spoken tutorials created by the second team are also available and accessible on this the lectures and tutorials that you just heard were stored on the SD card which you can see protruding a little bit from this tablet it is also possible for this tablet to connect on Wi-Fi to a backend server and the same lectures can also be heard directly from a server so here for example is an NPTEL lecture which is located on the backend server the Akash is connecting to the server through Wi-Fi our team has prepared interactive lessons so even on this lecture it is possible to go to any one particular topic directly this is the team which has developed the clicker application on Akash tablet it is the same team which was involved in the development of original clicker application on the clicker devices which were designed at IIT Bombay we will now see a demonstration of using clickers for collecting responses from students in a classroom for quizzes which a teacher might pose this application permits a teacher to conduct a quiz in the class what you see is the quiz module which is being controlled by the teacher clicks here to conduct the quiz a quiz appears here the teacher will set a default time for students to answer the quiz and will launch the quiz when he launches the quiz the quiz question will be available on the Akash tablet and the student can answer this question by clicking on to the right answer that he thinks is the correct answer after the time that has been set all the answers from various Akash tablets and the answer of different students will be collected and once the quiz time is over I can view actually the result so for example I seem to have answered it correctly because the responses that my answer was correct meanwhile here you can the teacher can see responses from all the students I have to choose the question number these are the responses that come from different students against their ideas I can also see a bar chart here is a demonstration of the programming environment that has been built by Professor Kannan's team and Professor Madhu Bello's team on Akash tablet in this we have actually created a Linux environment on top of Akash Android operating system and provide for C programming interface for example so here is some sample code the traditional program which when executed prints hello world here is the execute button this will compile that C program and execute it you can see the hello world coming out as the output there are many exciting environments such as C++ and Python which have been built but perhaps the most useful for engineers and scientists is the open source Sylab Sylab is a tool which is equivalent of the well known industrial product called MATLAB and it is used extensively by engineers so here for example is the code written in Sylab which when executed will produce a milk dock image you can actually write the code on the fly and execute it here we now show an exciting engineering application where a robo is being controlled by the Akash tablet the robo itself has been designed in IIT in Professor Kaviariya's lab this is the team of summer interns that you see who have programmed the Akash tablet to control the robo as well as to get the video stream coming from the camera mounted on the robo to be displayed on Akash tablet this is the robo that you see there is a Wi-Fi camera which is mounted on top we will now see the operation of this camera and the robo by using the Akash tablet so this is the robo control application as you can see on the Akash tablet they have given a small control on the right by which the robo can be moved this moves forward, this moves backward this can turn the robo left so you can see that the control is very refined here and the video stream is being obtained by this Akash tablet using a Wi-Fi connector I hope you can you can see the potential of this tablet while the applications that have been built by that large number of teams in IIT Bombay are impressive I would take all of this to only indicate the possibilities and these possibilities obviously can be exploited only if a large number of talented researchers students, teachers across the country work on creating applications and contents which are useful for our own use as the minister said I would like all of you to appreciate for example that if the school children in the country have to use tablets like this then they must be able to use this tablet for educational purposes in their own native tongue in Gujarati and Tamil they should be able to use those fonts visibly on the Akash tablet they should be able to create contents what it means is therefore there is a huge potential for us to develop targeted applications for all segments of the education in fact while our mandate is to empower engine college teachers and students using this tablet the ministry has agreed to my proposal that this empowerment will also involve some 20-25 students at each engineering college working on specific application development and content development which in turn will span the entire educational spectrum more specifically we are looking forward to a large number of applications and contents being developed by the talented students of these partner institutions which will be directly useful for school education in various Indian languages across the country I think they have a robo setup here our young team of interns from other institutions is very keen to show how the robo functions can somebody focus on the robo please and see that yes you can see the video stream which is being continuously collected from the robo thank you very much young people let's give them a clap they have done an excellent job with this the last job for me is to offer a vote of thanks there are just too many people to thank and my job is made doubly difficult because honorable minister introduced Akash in addition to the workshop for 10,000 teachers we are doing these workshops as you already heard are not new we have been conducting this structured workshop for more than two years and you heard from some of our partnering institutions that they are very effective a whole lot of effectiveness of these workshops comes from a large number of people working behind these workshops to begin with it is the expert faculty members who offer these workshops who offer the academic contents of these workshops who interact constantly with the participating teachers to solve their problems to enlighten them with their own experience and I must first thank all the teachers who participate in these workshops as expert faculty from IIT Bombay well there are many but one particular remark of one of the remote centers we said that they are glad that these workshops are not computer centric or IT centric well the credit goes to my colleagues from other disciplines in the institute led by professor Gayathonday can we see professor Gayathonday here he offered the first non computer science program in thermodynamics and that program became so popular in fact as the coordinator I keep looking at the feedback from the participating teachers which we see on the moodle and there were several people who started addressing him as god of thermodynamics that was a unique title but more importantly he liked the support system of these workshops so much that he called his colleagues in the mechanical engineering department and said that conducting workshop does not put any additional administrative load on the heads of the participating teachers faculty since then the mechanical engineering department has been contributing to a very large number of conduct of workshops under so we have had heat transfer for example we have a coordinator from photovoltaic cell professor Chetan Solanki here can we see Chetan Solanki thank you Chetan in fact we have we have a number of such professor Sudarshan is here the database guru of the world who happens to work for professor Sandeva in fact you just saw one of his lectures converted by our tool into interactive lecture session so thank you professor Sudarshan I will of course have ample opportunity to thank the faculty members who are participating as experts in this particular workshop but needless to add such faculty members make a lot of difference over the coming years it will be our endeavor that we should be exposing to our large number of teachers not just the expert faculty from IIT Bombay but expert faculty from all over the country from any institution because all institutions small or large have one or two extraordinary people there and this technology should permit them to address the participants from any place that we have so professor Karmalkar next time when you talk to our participants you may not have to come to Bombay you can do so from IIT Madras itself the next in line of course is a large backend team which works tirelessly to make these workshops successful so I would like to just show the glimpse of some of the leaders here Dr. Mukta Atre she is the workshop manager most of you would be interacting with her Mrs. Jaya, Gaitanya Jaya is here she is the finance minister of the project it is extremely difficult to spend a single paisa she makes so many conditions and makes my life miserable but does manage to conduct the workshops in assigned budget we have Kalpana Kalpana Kannan is the in charge of all our contents so after the workshop the contents would go on to this we have Mahendra behind who many of you would recognize the logistics name behind us I can see Professor Santosh Narona who is going to teach in this workshop but we will thank you later Santosh we have two advisors who have been with us for a very long time Mr. Avinash Aute he is also an alumnus of IIT Bombay ex TCS after retiring from TCS he started doing some social work I invited him to do social work for these workshops instead so he has been with us he handles the entire design and implementation of all back end systems all back end computer systems we have Prakash Vaidya here he has been an expert embedded system designer and in fact he also designed the earlier clicker systems but his other passion is proof editing and if you see the documentation coming out to be in a reasonably good shape it is because of his extensive proof editing while we have a large number of staff members here next to him is one young lady Firuza Firuza can you raise your hand she works as a research associate and concentrates on the correctness of technical documentation what is remarkable about her is when she was studying in school she started writing books her first book on HTML programming she wrote when she was 11th standard and she has now written by the time she finished her MSC IIT she has written some six books they are of course for school and college children but when she came to me wanting to join as a programmer I said you would be better as a technical writer rather than programmer and she has agreed to join I can tell you I have just taken this as one sample instance but I am very proud to say that hundreds of members of my team and all other teams who have worked tirelessly all have this kind of passion and some unique capability which they bring to the table I just coordinate and take the credit at the end we have of course we have already seen now let me come back to the Akash tablet when we got this project it was very obvious to us that the most important thing is not the device but the applications and contents that go with that device to this end it was impossible to very quickly develop applications all of those who have done computer software development particularly with embedded system would know that you cannot do miracles overnight so what I did is I tapped into the large pool of already done work in the institute you have already seen the glimpses of Kavyaariya's work on Robotics this robo control incidentally which the interns were able to do so quickly in six months was done because there is a whole lot of open source control software which Kavyaariya's students and researchers have already done and these people could build on top of it in exactly the same fashion Prabhu Ramchandra and Prasabh Madhu Belvedur have been working on FOSSI for a long time so the work that they have been doing has culminated into getting this iLab and other packages here the proximity work and the clicker work has been going on the department of computer science for the last two years we had a meeting in the department of computer science with our faculty colleagues and I am going to conduct such a meeting with the rest of the faculty here when I invited them to participate it is amazing how every one of my colleagues in the department said look we do this can this be used in a car we do this can this be done in a car that is when I realized that if the same environment is extended to first 168 colleges and then to 500 colleges where the creative talents of teachers and students can be brought to bear on the further development there is no reason why all the educational contents that you need for India cannot be created by Indians in India I want the engineering colleges to spearhead this thing last but not the least I will mention in the context of these applications the spoken tutorial application which was these are ten minute video tutorials but the audio can be in any language so these are not video films these are actually screens which move around like your slides but the audio is a explanation in any language so we construct first a spoken tutorial in English and then we hand it over to other people we can do the translation of English into Hindi Telugu, Malati and so on they conduct these workshops across the country and in fact we expect the participating teachers in these workshops also to take that forward and ask their students in turn to work towards that direction I think I can speak endlessly on both the Aakash tablet and the workshops but it is just about 11 o'clock at the end of the session so let me do the thanksgiving at the end for the people who have come all the way from long distances Prasasarapudde, Prasachalpa, Prasitopkar, Prasapandit thank you very much for coming here Prasasya Sarkip, thank you very much for making it to us all my faculty colleagues I understand that there are some representatives of the media also who have joined us thank you very much for coming at such a short notice and I must thank my PRO for doing an excellent job because only yesterday evening we got the news from the ministry generally one does not thank one's own close friends and senior colleagues but I think it is only proper that I thank Prasasukhatmay for sparing time and coming here to preside over this function well I know how much he loves IIT and the work that goes on at IIT Bomb so I am sure that if I had not invited as a chief guest he would have quietly walked in and sat in the corner because he has been supporting our efforts particularly my efforts for decades here Prasadevan Khakkar of course is our leader and it is under his able guidance that all of us work I just told you something about Prasarangan Banerjee's office in general the office of Dean RND exactly the same thing applies to my director's office let me just give you one incidence when we wanted to rush through the final processing of the purchase order of Akash there was a certain date before which we had to open the bank guarantee for us to start receiving the tablets in time and some signatures were required as you know in the process by the time the file reached the deputy director's office the office was closed and the deputy director had gone home and the some activity had to be done next day so when I called him he says no problem Farthak just come home I went to his home but my director could sign the file only after his deputy director has seen and signed so I called my director it was already 8 o'clock in the night and you know what my director said he says Farthak whatever time you come you will find me in my office that is the greatness of my leadership here sir and we are very proud of that in my own department when we started working on this large project Prasar Sannayal spent considerable personal time in discussing this with several senior colleagues helped us to appoint a appropriate purchase committee which could apply it's not just some senior professors people were experts and give correct advice indeed without this great leadership at the departmental level at the level of dean and at the level of the director if we did not have it believe me I would say it is impossible for any other institute to complete the purchase process of this magnitude in one month we were helped tremendously by the administrative departments as well as I said no paper ever waited either in the office of the deputy director or material management so Mr. Borkade is here and his colleague Roy we have Dr. Ramesh our deputy director finance and accounts I don't see Chabuk Swar ah he is here he is the auditor let me tell you it is extremely difficult to get past him he is worse than Jaya my finance minister Mr. Borkade read thousand pages of documentation overnight in order to ensure that there is not a single squiggle left in the process we are very thankful to you sir for helping us to move ahead with the Akash and of course with this great support and with the greater support and research from my friends in the other engineering institutions we will take both the Akash and the workshops to greater heights thank you so much thank you one and all please join us for high T outside this thank you


In the previous video for lecture two, we introduced the idea of sets, that is, we have established what is a set in the mathematical sense. And we mentioned that when it comes to sets, things like order and repetition don't matter, the only thing that matters for a set is membership. Is this object an element of the set or not? So for our logic video in lecture two today, we really need to emphasize how does one prove whether an object belongs to a set or not? There is actually a proof template that we're going to begin with. So we're going to start writing some proofs and these are usually fairly elementary proofs to the most part. And let me kind of explain what makes these things so important, but also what makes these things so simple. For most of us, if you're given two pictures of plants, like the ones you see on the screen right now, I bet you could probably correctly identify which of the pictures is that of a tree and which one is not a picture of a tree. Take a moment, pause the video if you need some more time, but decide amongst yourselves as you're watching this, which of these two pictures, the one on the left or the one on the right, which is the picture of a tree? I've probably given you more time than is necessary, but the object on the left, I imagine most of us were very able to quickly identify that that is a tree. Now if you're curious, this thing on the right is not a tree, it is a flower, it's a lily, it's a pretty flower there, but it's not a tree, it's not a tree. There are characteristics of a tree that distinguish it from other plants, and we as humans can recognize those characteristics. We can identify whether a plant belongs to the category of trees or not, or using what we would say is that this picture, this tree that's illustrated on the screen there, it belongs to the set of trees. If we take all of the trees in the world, this plant on the left here belongs to that set. Deciding that this is a tree is the same thing as proving it belongs to a set. In mathematics, we have to do the same thing. Does this object belong to the set or not? Does this plant belong to the subcategory or the genus or whatever? It's all about classification. We often have to decide whether a mathematical object belongs to a specific set or not. Take for example, we have to decide that the number two belongs to the set of integers, but we also can decide that one half does not. When I say decide, I mean, we made a determination there, right? It's not like our choice. Like, I feel like one half is an integer today. No, no, no. There is a definition of the set of integers, and then we have to determine whether does two match that property? Yes, it does, so it belongs to the set. Does one half satisfy that property? No, so it doesn't belong to that set. Every set has a mathematical property which determines whether an element belongs to it or not. In order to determine whether a specific element belongs to the set or not, we simply need to check if the defining membership property of the set is satisfied with its object or if it isn't. And so I should mention that this defining membership, I said that for a reason, right? The defining membership of a set is equivalent to checking a definition. Definitions, mathematically we talked about in lecture one. Sets and definitions are basically the same thing. If you're given a definition, we can define the set of objects that satisfy that definition. For example, we can say that x is equal to the set of trees. There is this biological definition of what a tree is, and so we can then use that definition to define a set. And then once the set's defined, anything that satisfies the definition then belongs to the set. But conversely, given any set, we can make a definition to mean all the things that belong to that set. So it goes hand in hand. The notion of a set and a definition are essentially the same thing. Checking membership of a set is really just checking a definition. All right. And so let's do some examples of such a thing. Now, one strategy for determining whether an object belongs to a set or not is the so-called brute force property, the brute force strategy, brute force algorithm. We alluded to this earlier in lecture two here. And the idea is if I list every member of the set, then I can check, does this belong to the set or not? Because if I can list every member, then that'll take care of it. Now, this is going to work well if you have a small set, right? A finite set with not very many elements. Once these things start to get too big, it becomes way too difficult for a human to check. But you could use technology or computer or a program of some kind. But even still, there's a limit to how well these things can compute them as well. Now, let's look at set A right here. We're going to take the set of all integers such that the absolute value of the integer is less than or equal to four. Now, I want to make a comment about this here. This is set builder notation that we saw in part one of this lecture here, where the first part before the vertical line represents a typical element, an arbitrary element. Really what it's doing, it's defining what we would call the universe. The universe are often referred to as the universal set. Okay? So what this means is that we're going to take all elements that belong to some other set, and we're only going to consider those. And the reason for that is when you talk about absolute value, it makes sense to talk about the absolute value of natural numbers, of integers, of rational numbers, of real numbers. And it even makes sense to talk about the absolute value of a complex number, although in that context, it's usually referred to as the modulus or the magnitude of the complex number. But it is the natural extension of this notion of absolute value. So if I don't specify the universe, then it might be a little bit confusing. Like what objects belong to the set? And so again, a set has to be well-defined. There has to be a clear rule to decide to determine whether objects belong to the set or not. Now, be aware that the rule has to be clear and unambiguous. That doesn't mean it has to be easy. It could be a difficult rule to check. And we'll see an example of that one at the end of this video. But we do have a rule. And so we sometimes have to specify a universe, a universal set to determine where do our objects live. And so in this case, our objects live within the set of integers. So we want all integers whose absolute value is less than or equal to 4. So I can actually list all the elements of A here. So you can take, for example, negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3 and 4. Knowing properties about the integers, I know that these are the only objects, the only integers, which will belong to the set by this property. So we actually listed all of the elements. This is brute force approach. Now I can decide who belongs or not. I know that the element 2 belongs to the set because I listed them all. I also know that the element 5 does not belong to the set. Now, I don't necessarily have to list all the elements to check these. I could just have them take the numbers 2 and 5 and check their absolute values. The absolute value of 2, of course, is 2. The absolute value of 5 is 5. But using this property, it's a very simple property, I'm able to then list every element that belongs to the set. Now let's change pace a little bit because I want to then dig into this idea of a universal set a little bit more. What if we change the universal set? What if we take the exact same set from before? So let me make sure they're both on the screen here. If we take the exact same set from before a, that is, it's the same set because it means the exact same property. Let's take all numbers whose absolute value is less than or equal to 4. Let us now change the universal set to the be the real numbers. So when you read this set here, this is the set B such that we want all real numbers whose absolute value is less than or equal to 4. Well, this is clearly going to contain all nine of these elements we saw before. There's some new things that belong there as well. Like so three still belongs to the set. We've enlarged the set here, but we also gained things like Pi, right? The irrational number 3.14159, etc. That number has an absolute value which is less than or equal to 4. So Pi belongs to the set. We can also grab something like the negative square root of 2. That belongs to the set as well. The negative square root of 2 is approximately 1.4142. And so when you take the absolute value of the negative square root of 2, you get the positive square root of 2. So that belongs to the set as well. But on the other hand, if you take something like 11 halves, right? Maybe it's easier to see it as a decimal. 11 halves is 5.5. That has absolute value greater than 4. The number is bigger than 4, so it's absolute value greater than 4. So the fraction, the rational number 11 halves does not belong to the set B right here. There are lots of numbers that belong to the set, but there's also lots of numbers that don't belong to the set. I should also mention that the number 1 plus I does not belong to the set B. Well, why doesn't it belong to the set B? I want to mention that if you take the complex modulus of this number 1 plus I, this is equal to 1 squared plus 1 squared inside the square root, of course. The idea is to take the complex modulus of a complex number. You take the square root of the sum of squares where the squares are going to be the real part and the imaginary part. So real imaginary part of this number 1 and 1. So this becomes a square root of 2. Be aware that the absolute value of the square root of 2, excuse me, the square root of 2 we were talking about earlier, 1.4, it is inside this range here. This is a complex number whose modulus is in fact less than equal to 4. But it's not included because 1 plus I is not a real number. The universal set dictates that we only are accepting real numbers. So when we work with these sets to deciding whether something belongs to a set, there's really two things you need to consider. One, you need to check, does the object satisfy the property? But you also have to make sure that does the object live inside the universe of consideration? If it's outside that universe, then it's irrelevant whether it satisfies the property or not. So that's how you check whether an object belongs to a set. Is it within the universe and does it satisfy the property? Does it satisfy the definition? Speaking of definitions, let's give us a very important definition when one talks about sets here. This is the definition of cardinality. The cardinality of a set is the number of elements that belong to that set. And if the set is called A, we typically denote the cardinality of the set as, well, looks like the absolute value of A, but A is not a number. It's not a real number. It's going to be a set. And so this is the notation we use to denote the cardinality of the set. So this is the number of elements that belong to the set. Now, some people use different symbols for cardinality. Like some people use like N of A, but this is very uncommon in advanced mathematics. There's other symbols you can use as well. This is actually quite universal for mathematicians. Now, in like college classes or even high school classes, if students learn about sets, they might use other notation because they're afraid the students won't be able to distinguish this notation from absolute value. But in advanced mathematics, there's so many mathematical ideas and so little notation that you can use that we have to overload symbols all the time. That is reuse symbols to mean different things. How do you tell the difference by context? Because the thing in between the vertical lines is a set and not a number, I know it's not absolute value. You're considering the cardinality. How many elements belong to the set? Now, if this cardinality, that is the number of elements turns out to be a natural number, which be where zero is included in that. We call this a finite set. How could the cardinality of a set be zero? Well, the empty set contains nothing. The empty set has a cardinality of zero. This is actually one of the reasons to justify why the natural number should include zero. The natural numbers, you could define them to be the set. We could define the natural numbers to be those numbers which are cardinalities of finite sets, which include zero in that situation. Now, if a set is not finite, then we call it an infinite set. Be aware that many of the sets we've considered are already infinite. We know our infinite, like the set of natural numbers is infinite. The integers are infinite. The rational numbers are infinite. The real numbers are infinite. The complex numbers are infinite. These are all examples of infinite sets. Now, from the two sets that we were considering on the previous slide here, like remember A was the set of integers whose absolute value was less than equal to four. There were nine elements in that set, so it's a finite set, nine's a natural number. On the other hand, the set B, which is the set of real numbers whose absolute value is less than equal to four, that's actually an infinite set. We couldn't list every single element. We started to describe them, but we can't get all of them. There's too many because it's an example of an infinite set. Before we end this video, I want to introduce one more example that illustrates a very important point that even if a set has a very simple property that defines the set, it can still be very difficult to determine whether an element belongs to the set or not. And therefore, we might not know how big the set is. We might not know its cardinality. It might be infinite or finite. We don't know. Maybe even empty if the property is difficult here. So the example we're going to do is talk about the set of perfect numbers. Now, let N be a natural number. I want you to notice we're starting to use this mathematical notation here. Remember, this symbol is the set of natural numbers, which does include zero. This symbol right here means set membership. So N is an element of the set of natural numbers. So we would read that as let N be a natural number. So we say that N is a perfect number if the sum of all of its divisors is equal to two N. So the sum of all of the divisors of that number, positive divisors here, since we're only talking about natural numbers, we don't include negative numbers as possibilities. We won't worry about negative divisors here. So we want the sum of all of its positive divisors to equal two N. That makes it a perfect number. So let me give you an example of one. Six is a perfect number. One can show that the divisors of six are one, two, three, and six. One divide six, two divide six, three divide six, and six divide six. No other natural number is going to do that. This right here is the set of divisors of six. Now, if we add together all four divisors, we get the following. One plus two is three, plus three is six, plus six is 12. 12 is two times six. Six is an example of a perfect number. And in fact, it is the smallest perfect number. You can check that every natural number less than six is not a perfect number. We'll give an example of one in just a second. With some more experimentation, you could try seven, eight, nine, 10. With enough experimentation, you could show that the next perfect number is actually 28. The divisors of 28 are one, two, four, seven, 14, 28. Given the prime factorization of 28, you could actually come up with this set of divisors, right? 28, you could factor as like four times seven. Seven is a prime number, so it doesn't factor anymore. Four would factor as two and two. So you can list the prime factorization of 28 is two squared times seven. And then, looking at all the possibilities, you have to make a decision like which factors are you going to show up there. You know, one is when you take no prime factors. Two shows up when you only have a two. Four shows up when you have two twos. Seven, two and a seven, and four and seven. I'm not going to go through all of this right now, but we can actually, if we have a prime factorization for an actual number, we can come up with a set of divisors. There's an algorithm that exists for that. Keep that, keep a pin in that. We'll come back to that in a second. So once we have the set of divisors, we can then sum them together, add them.  Hopefully I said all of those correctly. But anyways, 56 is two times 28. So even if I said my things out loud incorrectly, I hope I didn't. 28 is in fact a perfect number. It's the second, it's the second perfect number. In fact, if you were to go with calendar, a very important mathematical holiday is actually perfects day, perfects day. This would be in the United States, this would be June 28th, because they are the first two perfect numbers. June 28th also sometimes referred to as two pi day, because 6.28 is 3.14 times two. And so much like on pi day, you get a pi to celebrate the number pi on perfect day or two pi day, you eat two pies, which would be just perfect there. All right, so we have two perfect numbers found already, 6 and 28. Let me convince you that not every number is a perfect number. Take for example, five. Five is not a perfect number. Five is actually a prime number. And so it's only divisors are one and five. And if you add those together, one plus five, you get six. Six is not the same thing as 10, 10 being two times five. So five is not a perfect number. And in fact, I could generalize the argument I just had on the screen right here. I could actually show that no prime number is a perfect number. It's not just five that every prime number is going to be imperfect, not perfect for the following argument. This is what a proof is. A proof is generalizing a specific case.  The only thing I know about P is that it is a prime number. All right, then its set of divisors is going to be the set one and P by definition. That's what a prime number is. It's a number other than one whose divisor whose divisors are just one in itself. This gives more reasons why we don't include one as a prime number for one. The set of divisors is just one. But for prime numbers, the set of divisors always has a cardinality of two. That's what made one so exceptional. It's the only natural number whose set of divisors is cardinality one. Prime numbers all have cardinality two. So I know exactly what those are. You're going to have one plus P. The sum of divisors is one plus P. Is it possible that one plus P could equal two P? Because that's what a perfect number means. The sum of divisors equals twice the P. But this is just a linear equation. We could solve this from our algebra training here. If I subtract P from both sides, you're going to end up with one equals P. But remember, P is a prime number. And by definition, prime numbers are not equal to one. So we get a contradiction if this was a perfect number. So what we can infer from this is that it's impossible for a prime number to be a perfect number. And so no prime is perfect. And that gives us a very nice proof of this here. So we can prove that prime numbers are not perfect. And it turns out there's other proofs you could provide to show that certain numbers are not perfect. And so if we summarize what we've seen so far, it's not too difficult to determine whether a number is perfect or not if we have a set of divisors. If you have the divisor set, it's pretty simple. Just add and divide by two. Now, admittedly, for very large natural numbers, finding their set of primes turns out to be very, very difficult. That is, it's a difficult computational problem. I alluded to the fact earlier that if you have a prime factorization of a natural number, it's actually quite simple to find its set of divisors. But it turns out that's where the problem is. Factoring large numbers to find their prime factorization is actually a very, very hard problem. If one goes deeper into number theory, we could talk about why is prime factorization a computationally difficult problem. That goes beyond the scope of this course, but I do want to mention that things in cryptography, which is the mathematics of security, that how you can use your credit card online safely, has a lot to do with this problem at hand, that there exists computationally difficult problems. And so eavesdroppers and hackers can't necessarily solve these problems in a short amount of time, and this creates security. Factorization natural numbers exist as a computational difficult problem. Now we're of course talking about numbers which have prime factors that are like hundreds of digits long, millions of digits long, maybe. So that's not going to be within our scope here, but I just want to make mention that assuming we can find a prime factorization of a number, that itself is a hard problem. Then we could check whether you're perfect or not very quickly. But that's something to be to acknowledge here that prime factorization is hard. So this is a computationally hard problem to check for an arbitrary natural number, whether it is perfect or not. But it turns out for even numbers, there's an awesome proof that one can prove we're not going to prove it. But we can prove the following one could get even if we're not going to that if n is an even number. If n is an even number, so it does have to be divisible by two, notice six and 28 are even numbers. If n is an even number, then it turns out n is perfect if and only if n can be written in the following form. That's two p minus one times two p minus one, where in this situation, p is a prime number, and the number two p minus one is likewise a prime number. These are referred to as the Marysine primes, a very important family of prime numbers. Among other reasons, it's connections to perfect numbers. One can show that every perfect number, every even perfect number can be factored in the following way. I want you to consider the numbers six and 28 that we've seen already, right? Six factors as two times three, which two is of course a power of two. In this situation, we're going to use p equals two, two is a prime number. Notice that two to the first is same thing as two to the two minus one power, and three under the hand, this is equal to two squared minus one. That satisfies the formula. If you look at 28, which is four times seven, in that situation, I want you to be aware that four is two squared, so that's going to be two cubed minus one, like so. And then if you consider over here, two cubed minus one, that's seven, so this factorization matches up with these two perfect numbers, six and 28. We have our first two Marysine primes, three and seven, and so using Marysine primes, we can actually construct perfect numbers. And so this dramatically simplifies the problem for even perfect numbers, that the difficulty of finding them comes down to the difficulty of finding these so-called Marysine primes, which it turns out that also is still a very difficult problem. It's unknown how many Marysine primes there are. Currently, there's only 51 known Marysine primes, and as such there's only 51 known perfect numbers. It is unknown whether the set of perfect numbers is infinite, because we know that the number of even perfect numbers will coincide with the number of Marysine primes, but it's still an open conjecture, an open question in number theory, how many Marysine primes are there, at least at the time when this video was recorded, it was unknown. And then there's another very interesting question when it comes to perfect numbers. Is there such a thing as an odd perfect number? The theorem we mentioned before was only about evens. So even perfect numbers aren't one-to-one correspondence with the Marysine primes, but for odd ones, it's unknown.  And I should mention that this involves, of course, the digital age, where people have written programs, very good programs that their algorithms go beyond the scope of this video here, very good programs that then search for odd perfect numbers and they haven't been found. And so if they exist, these numbers have to be gigantic because, well, we've searched all the small ones, right? We're looking at numbers with like millions and billions of digits, but at last we can't find any odd perfect numbers. Now, that doesn't mean they don't exist. Maybe they're just very elusive. Maybe they're hanging out with Bigfoot in the California mountains somewhere. I don't know. The problem is we don't know they don't exist. Most conjecture there's no odd perfect numbers, but there yet doesn't exist a proof that shows they don't exist. Just because we can't find them doesn't mean they don't exist. There are many examples in mathematics where it took a long time to find the first example of something. And sometimes it took so long that people believed they didn't exist. And then someone was like, aha, a great mathematical discovery happened because someone found something that people believed didn't exist. One such example is the existence of non-Euclidean geometry. People for hundreds of years believed that all geometry was Euclidean, but one of the greatest discoveries of all mathematical history was the discovery of non-Euclidean geometry, proving that something existed that people believed didn't. Is there an odd perfect number? I don't know. It would be pretty awesome if someone found one or also equally awesome if someone proved they didn't exist. And so I present the examples of perfect numbers as just an example. It has a very simple definition. Numbers whose divisors add up to be twice the number, but the membership of the set is very difficult to determine. We don't know if the set is infinite or finite. We don't know if there exists some members. It's at least 51. And we have no idea if odd numbers belong to the set or not. How could such a simple set be so difficult to understand? Well, this happens all the time in mathematics. It sounds scary, but it's actually wonderful and exciting. Mathematics is a great, beautiful puzzle that's waiting to be solved. And mathematicians like you are exactly the type of people who will solve these problems in the future.


إنه جميل أن نرى that the Creator is inviting people to the right path, taking them away from the Hellfire and get them into paradise. Now before we go the procedure of entering Islam by Shahada, I just want to say something that shall benefit you and all of us. Our Prophet صلى الله عليه وسلم سيدنا محمد he told us that he said that souls are soldiers and the souls that share the same things they get together and the souls that they don't share things take they run away from each other so we know that we are a body this body is created from the low thing which is the mud and there is a soul came from up from الله سبحانه وتعالى to elevate this body now الله سبحانه وتعالى the Creator he knew that your soul share with more than one billion Muslims the same concept the witness there is only one God since their soul have this الله guided you to this path now when you enter the Islam there are circles and there are souls in the circles that get together the first circle is the circle of Islam which is submit to the Creator knowing the things that Creator asked you to do and we probably think that I say don't do it as the first circle the circle above that is circle of Eman believe which is the soul will depend on the Creator they believe the unseen we worship him and we know there is paradise we never seen them we believe in all prophets before us we never seen them we believe in Allah the Creator we never seen him so this is believe in the unseen and these people they live in on this earth in country equality because they know that Creator choose them to enter this path and taking good care of them in this dunya in this life and the life after and there's a circle higher than this which is called ihsan perfection which is where you saw will do things with perfect things by knowing that you are being watched by the Creator every second in your life you know he is with me he's witnessing me so I do things in the so there's people of that level third level and they get together you'll see yourself that your your friend is people of of Islam or Eman or ihsan and there is another hidden circle circle of love the lovers they worship the Creator not to enter paradise not to run away from the high fire that's because they love Allah they love God they love the messenger they love all messengers and that circle of love you see people who are lovers they get in together but you want to avoid the circle of the devil because he wanted to get you down with him and that's all of us we need to be aware of that that's why there is a advice by ابن عطال السكندري he said ملّم يردك حاله ويدولك ع الله بقاعده don't have a friend or close companionship the one who just looking at him you have energy to do good and just if he talk he directly to God so your soul and we thank God because he wanted you your soul to join this billions of Muslims and you'll be brother to them فهذا هو يوم your luckiest day in your life now we proceed insha'Allah with the procedure so I'm going to say that in Arabic which is witnessing there is no God except Allah and we see that I say the Muhammad ﷺ he's the last and the servant the last messenger and the servant of God okay say after me اشهدوا واشهدوا اشهدوا ان محمدا رسول الله ستقين اشهدوا اشهدوا ان لا إله إلا إله واشهدوا ان محمدا رسول الله اشهدوا ان لا إله إلا إله واشهدوا ان محمدا رسول الله رسول الله الله واكبر الله واكبر الله واكبر لا إله إلا الله الله واكبر الله واكبر ولله الحمد شكرا لكم now I want to tell you something that all of us wish to be in your situation because Allah erased all the bad things in all your life everything erased what doesn't matter how bad it was but Allah سبحانه وتعالى he kept all the goodness for you everything you did good your smile your mother your father the thing that you did is still your book so your book now clean from everything bad and it's filled with everything good and all of us wish to have this so keep it like this and keep on learning go with the Islam the first one the Salah the prayer the fasting and so on and then move from it to Imam to Ihsan and so on ما شاء الله everybody الحمد لله MCC to you so for the BJP in this mode believe what the props also said to us as Amut Arif said if there's any sins that you've done they've been erased and any good deeds that you have are there so he's visiting with us from Texas I'm very honored that he choose our community for the privilege of this Shahada may Allah bless you those that were here for the next drama will be starting momentarily in 50 minutes in the prayer hall


So last week, Republican lawmaker from Texas, Ronnie Jackson said something that somehow flew under the radar. And I think the reason why it didn't get picked up by the press is because it's not necessarily surprising. But still, what he said was the quiet part out loud. He said that Republicans would effectively rig the elections in 2022 and take back the house easily. And I'm paraphrasing this isn't his exact words, but basically he explained very clearly how gerrymandering is going to be used effectively by Republicans to give them power once again. And you'd think that this should further, you know, make the push for the For the People Act be that much easier, like Democrats can point to this and say, look, Republicans are already admitting that they wanted gerrymander their way to victory. Let's get the For the People Act passed, call mansion, call cinema, tell them to support it. But it's not because again, this kind of went under the radar. And David Daley of The Guardian does a phenomenal report where he actually brings it into perspective and explains that this individual isn't lying. They don't have to do much gerrymandering to take back the house in 2023. In fact, given the Republican Party's ruthlessness and willingness to do whatever to maintain power, they're going to do that. So let's get to the article here. In Washington, the real insiders know that the true outrageous are what's perfectly legal and that it's simply a gaffe when somebody accidentally blurts out something honest. And so it barely made a ripple last week when a Texas congressman and Donald Trump's former White House physician said aloud what's supposed to be kept to a back room whisper. Republicans intend to retake the U.S. House of Representatives in 2022 through gerrymandering. We have redistricting coming up and the Republicans control most of that process in most of the states around the country. Representative Ronny Jackson told a conference of religious conservatives that alone should get us the majority back. He's right. Republicans won't have to win more votes next year to claim the U.S. House. In fact, everyone could vote the exact same way for Congress next year as they did in 2020 when Democratic candidates nationwide won more than 4.7 million votes. The Republicans and narrowly held the chamber, but under the new maps that will be in place, the Republican Party would take control. How is this possible? The Republican Party only needs to win five seats to wrench the speaker's gavel from Nancy Pelosi. They could draw themselves a dozen or more through gerrymandering alone. Republicans could create at least two additional red seats in Texas and North Carolina and another certain to in Georgia and Florida. Then could nab another in Kansas, Kentucky, Tennessee and New Hampshire. They won't need to embrace policies favored by a majority of Americans. All they need to do is rework maps to their favor in states where they hold complete control of the decennial redistricting that follows the census, some of which they have held since they gerrymandered them 10 years ago. Now they can double down on the undeserved majorities that they have seized and dominate another decade. If Republicans aggressively maximize every advantage and crash through any of the usual guardrails and they have given every indication that they will, there's little Democrats can do. And after a 2019 Supreme Court decision declared partisan gerrymandering a non-justiciable political issue, the federal courts will be powerless as well. So if you're wondering why Republicans refuse to support the For the People Act, even Joe Manchin's compromise, it's because of things like this. They are counting on gerrymandering to be their ticket to victory come 2022 and beyond. And just think about this. If they are able to redraw district lines in this way, which they likely will be able to, that's 10 years of them being in control, surpassing the IPCC's deadline to actually meaningfully tackle climate change. So I don't really know what to say. I think that the solution is obvious. If the For the People Act is not passed, Republicans are absolutely going to dominate the next decade. Or I should say continue to dominate because they've been pretty dominant in state legislatures and at the local level. But what the For the People Act would do, even if it isn't perfect, even if it isn't a panacea and it's not going to save democracy, it would create independent commissions that redraw districts on nonpartisan grounds. So it actually doesn't account for who's going to win this seat. It just looks at the populations and does it in a nonbiased way. Republicans don't want this to be the case because they're counting on gerrymandering to win. They're deeply, deeply anti-democratic and in everything that they do, it shows and it's not just that they're anti-democratic. I mean, we've covered the videos of Republicans calling for Donald Trump to be reinstated with the military coup, Marjorie Greene calling for her political opponents to be jailed. They're outright authoritarian at this point. The Republican Party is a threat to democracy and now they're not even hiding the fact that they don't care, that they are vocally antagonistic towards the prospect of democracy and enhancing democracy in the United States. So it worries me that a lawmaker can essentially say the quiet part out loud and admit that they want to gerrymander their way to victory and then like nobody pays attention to this. Democrats should be using this to further fuel their push for the For the People Act. They should be blasting this quote on every single news network screaming at the top of their lungs and the fact that they're not highlighting this is a failure on their part and really it speaks to the factlessness of Democratic Party leadership. But I mean, look, if we actually allowed Republicans to effectively rig elections by redrawing districts so there's a lot more safe seats, then I mean, what does that mean for future generations and the planet? I mean, it may be the case already that we've passed the climate tipping point as some scientists are suggesting, but still it's not just about climate change.  Not that, you know, Democrats are super willing to help out working people, but I mean, it just, things get that much worse when we have this party that has gone insane, that is deeply authoritarian, taking control by any means necessary. So I mean, I don't know what else to say. If, you know, people don't see this as an issue regardless of what team they're playing on, then there's no hope for American democracy.