But some are professional universities like CMU, we are medical professional universities. So we, our students are mainly medical professionals. And we have some universities that are technical universities. So we'll focus on the technical training of the students. And some are competitive universities. So they will have a general knowledge course and have a lot of knowledge course and prepare for their math degree or doctoral degree. So today we have six different universities in Taiwan. We will share how we do the books and how we are facing the pandemic, although we didn't actually shut down lockdown or the whole wide. We have all normal life, but we still got some friends in the pandemic. So we have some doing. So they will show their experience during the time. So first, I will later go to the university to share their experience. So I will. Located in the metropolitan area of northern Taiwan, which is essence location. And Chile is a vocational and technical university in Taiwan with full enrollment. Even there is the low birthrate in Taiwan. As the campus is located in the core district of New Taipei City, we have over 11,000 students in full-time undergraduate division and department of continuing education in the limited space. All the time, we make effective use of online internal and external resources to comprehensively promote e-learning. But the speed become faster due to facing the COVID-19. So we must provide the immediate learning resources and course model that could be suitable for the emergency and during the epidemic. Therefore, we set up two blended course types of distance courses and MOOCs to satisfy the demand of students of different educational systems. In addition to promote our systems in university, we have also promote our e-learning energy and experiences by tutorship, lecture or industry education cooperation cases to spread our professionals. At first, let's see how are the distance courses of our university promoted. The Ministry of Education in Taiwan specifies that the implementation of distance courses in colleges and universities refers to the teaching method of asynchronously, synchronously or physically providing courses by a mixed instructional design with over half of the total hours of regular credit courses in single course. We already have asynchronously LMS, synchronous system Google Meet and physical campus to implement distant courses for many years. And we have set up the distance course application process based on the Ministry of Education policy. Through the three levels review, after approved, teachers could offer the distance course. From the table, you can see that the number of students taking the distance courses in our university from 2016 to 2020 has been over 8,000. The students participate in the asynchronous courses by Chile LMS and the synchronous online courses via Google Meet so that they acquire rich online learning experiences. But this year, facing the epidemic, we have set up existing distance courses. We start up the learning and teaching project for COVID-19 prevention. If the outbreak is notified, all courses don't need to follow the application process to apply. Each course should provide online course no matter synchronous or asynchronous activity immediately. And we work with external experts, also friends, to create the guide for distance courses learning and teaching website. We provide teachers and students so that they can self-learn online. Further, we open the website for public so that all universities in Taiwan could use the resources. The epidemic came suddenly. Teachers also need to prepare and redesign their courses. In order to improve all teachers, not only just who offer distance courses preparation and readiness, we design and provide systematic training courses for teachers regardless of online teaching process. What you see on the screen is the status of our training courses for teacher. And we also provide a teaching for dummies to teachers to reduce their anxiety. In response to the epidemic, this year we handled 12 workshops for teachers. 511 people trained. In addition, we also trained 32 e-learning seed teachers to help guide teachers whose skill is insufficient and provide more counseling channel. Next, let's move to massive open online courses. We support MOOCs from 2018 to the present. We increase the deductible credits year by year as shown on the screen. On the campus, MOOCs are open to all the students and the students who take the class are shown in the figure. Up to now, we have opened over 20 MOOCs and every course provides rich contents which last for 8 to 9 weeks with online learning activities. The number of students taking the class have been accumulated to over 20,000. Why we could do this smoothly? That's because we have the systematic six phases to promote MOOCs including course plan and design, course development, course launch, promotion, facilitation, operation and evaluation. Take a course as an example. First, we convene a kickoff meeting before the course development to determine the course need of the learning courseware by the initiator of the course, the teacher and the learning development team. Next, we enter the stage of course planning and designing. Design the learning objectives in the course structure. As shown in the picture, instructional designer will discuss with teacher or subject matter expert to design the activities include online discussion, quiz, and assessment, etc. After confirming the course structure we find out the contents requiring courseware development. Before the development of courseware, we review whether the contents infringe upon any intellectual property according to the review mechanism. The intellectual property right mechanism is shown in the figure. After confirming the course structure and the contents of courseware we design the courseware scripts with the teacher or subject matter expert, just as the screenshot shown. After the scripts are finished, the team refers to the content characteristics of the courseware to record video or audio by multiple approaches. As shown in the picture, next we enter the stage of post-production. According to the diversified pattern of courseware, we use this different software to present the contents in a richer way and conform to the learning demand. During the development process of courseware and after the courseware is produced, we use our review mechanism through internal and external experts and users review and continuous revision to ensure the quality of the courseware. Next, let's see how do we apply MOOCs in a diversified way. In order to ensure that the students know well about relevant information of MOOCs, we turn to physical and online promotional methods as well as the mechanism of online services. Particularly in order to guide the learners to successfully study and finish the course we apply professionally facilitating skills to offer the learners with rich learning experiences. The questionnaire and evaluation results of every course is the basis for us to discuss and improve the courses continuously. We apply MOOCs on the campus and launch them to the worldwide platform of Udemy for overseas learners. Besides, we also offer MOOCs on the platforms with different properties such as OpenEDU, Taiwan Life, Golf Alliance and EN Public Affairs Park. It's because that we have professional MOOCs mechanism of credit acceptance. As you can see on the screen, the flow chart of the MOOCs mechanism have effectively improved the efficiency of our university's MOOCs promotion. Meanwhile, by the ways of tutorship and lecture, we transfer the typical experiences to internal and external institutions. For example, we assist Taiwan companies such as Industrial Technology Research Institute, ITRI, Ooptronics Corporation and Inventac, community universities and junior colleges to establish e-learning teams, develop online courses and to cultivate the learning lecturers. In addition, this year we have also made a major breakthrough, that is, for freshmen, we use live broadcast with asynchronous assessment activities to handle freshman prerequisite courses to improve students' online learning readiness. What you see on the screen is that our principal is opening the live broadcast course and we broadcast live teaching to 1,489 freshmen. And we have also imported international e-learning trends, established producer mechanism not only e-learning instructional design, media production, e-facilitating. We cultivate new team functions, planning and execution at the level required by the enterprise. We also give MOOCs to high school senior so that they can learn in the summer vacation before going to university, achieve the completion criteria to obtain a certificate of completion and apply for credits after enrollment. This year, there are 1,023 high school senior students who have completed the course. 286 learners have completed the course. The completion rate is 28%. I am glad to have this opportunity to share our experience with you. Thank you for your listening and welcome contact us. The next presenter is from CJ University. Can you see her? Yes. My name is Jay Wen Liu. I'm currently the director of the Center for Faculty Development and Instructional Resources. Today I would like to talk a little bit about the current status of the online courses in CJ University. The title of the course is Global Education is Changing and e-learning is also under innovation. As you may know or you may not know, our CJ University was established by a foundation called CJ Foundation, which is considered one of the biggest charity foundation in the world. Because of that, our education is emphasizing on humanity and also the benefit of the society. We want our students to have kind of a service spirit and will become a great student in the world. As we all know, we are under threat of the pandemic of COVID-19. We need to get back to the general when the pandemic was just started and we were on holiday, actually, winter holidays. Our government did a very quick decision to postpone the semester after the start of the semester for two weeks and the student hasn't come back yet. Our CJ University has done a very quick and effective job. We initiated a project meeting very quickly because this project meeting is assembled by myself and the leader of the department of digitalized learning and teaching and also the director of the curriculum of the university. I was the director of the curriculum of the university and also the head of the department of digital learning is also the curriculum director as well. We communicate in very effective ways and we focus on three aspects. One is for the teacher, one is for the student and one is for the administrative staff. For teachers, we emphasize the training support and we integrate some new technology into their teaching and we give them training courses. That for students and the CJ University recognized a form of credit for online courses. For administrative staff, we support them and we also train them to be kind of with the digital ability and we optimize the administrative execution and also the student can learn after they graduate from the university and the teacher can learn after they receive this training. Then they can connect the international network if they have a kind of ability. And for e-course, we print in the CJ University and we have four major series of courses and one is sustainable development kind of courses and we have several courses entitled sustainable self-life and environment energy issues and international aid courses of social economy issues and food and globalization issues and we have a series of courses for this. And for effective education we not only emphasize liberal arts education and also general education, we also have kind of professional education courses. For example, we have five chemistry courses that include physiology, nutrition science and nitrogen metabolism and also molecular biology. These kind of very, very specific professional courses. And then we also have kind of application kind of courses, medical applications. We have course of course school of health data, interpretation of clinical laboratory data, blood transfusion, medicine, heart disease, kidney disease, emergency medicine and these kind of courses. And also I mentioned before we are a university with humanity in mind. So we have human service courses. For example, we have past thinking, psychology and past mental strength, also humanities or social service, a volunteer work service kind of courses. And then we also provide courses for improving students or personnel's helping still. And as I mentioned before we have department for doing this and we have staff in this department for doing this. And we provide systematic support and we reward the staff and we reward the teacher, take part in online learning. We provide training and resources for the courses. Then we have some great job and we have received quite a lot of certifications and awards. For example, we received awards from Ministry of Education and we also have kind of a recognition in other organizations which certify the courses, online courses of course. Then we collaborate with corporations to do their training courses. Of course we will receive certificate fees and we will have kind of a profit sharing kind of a mechanism to share the profit with the university, the department and the project manager. And we also remodel our studio over the years. And we are now focusing on massive open online courses, development and implementation. And we build up learning foundation using the learning courses. We provide courses to high school students and they can get the credits. When they get into the university, then they can use their credits for the university degree. And we also promote self-study, okay, MOOCs, credits for university students. The students can take MOOCs courses of the university or other university and we recognize their credits. They can use these credits for their graduation. And we also emphasize our effort on globalization issue and social influence. Okay, we incorporate SDGs and we also provide, which is a very unique, provide education assistance program for refugee. As you can see from the corner of this slide, our students using online long distance tool to assist the refugees in Turkey. They are Syrian refugees now in Turkey and we give them online learning exchange kind of opportunity. And we cooperate with overseas city education center to do this job and we provide a monthly course for them. And they are very happy about that. And then we also provide opportunities if possible for enrolling in the city university. Basically, this is the end of my talk and I would like to finish my talk with some more. That is let's keep up with e-learning and create new connection with the world. That's our purpose and maybe also your purpose as well. Thank you very much, Indy, for your listening. Thank you. Okay, thank you for the university. And our next speaker is for Ivan University. Hi everyone, true. I'm from National University I'm the center for digital learning division director. Now I want to share the experience and what we do during the pandemic. We have all heard about the city and the university. How they doing I think we will feel very impressive that they doing so much in my experience. First of all is that during this period the student and the teacher they are worried about how to distance teaching and distance learning. So the first thing is what we do is we share the experience in e-learning to all the teachers and students and make them feel safe feel convenient in teaching and learning. First we use the LMS to do the asynchronous online learning. We have so many material, for example video and the examination or some documents LMS in NIU. So we just let the teacher know that they can use LMS to do the distance learning. Not only share the document to students but also they can teach on the LMS. Second, we try to share the experience to use web and video conferencing software such as run and WebEx or Adobe Connect. For example, NIU use the teams to teach and to use the software to record the video and to share with students that they cannot come to Taiwan. So we not only the training course but also for a teacher we share how to teach online because maybe some teacher they never use such software to teach online. So we share the experience and we teach them step by step to do how can they use the software. For example, run or teams to teach how to record the course, how to interact with the students and how to examination using such software. And I think the most important policy we do is use the teams for teaching. We use the Office 365 account for all the students and teachers in our University, National Iran University. I think this made more convenient for teacher to have online courses because when they open the meeting online the students are all there so they can very easy just one step to have their course online. So if the student cannot come to the classroom they can also learn online system. And till today in our school there are also many teacher and student they use teams to teaching and learning. Please forget about the last sentence that the Ministry of Education do not like them but today we use them. This is what we get. This data from the teams, they can see that course meeting we grow up very rapidly during the march and get higher. We can see that in the April meeting it's so much. What's this about because I will mention later that in our school we have rehearsal how to distance learning all the school. We prepare for the very awful. That teacher and student cannot come to campus so we practice in the campus that if the student have to stay at home how can they do it. So we practice in the classroom in the first week that's the March 22 to 28 and then we practice all the campus that student can stay at home and not go to the school at the April to April 18. And we can see that the practice is very successful. So all the teachers and students all have practice about distance learning by our teams. And we also encourage the usage of OYA and MOOCs. We just as Judy and Tiji we have so many MOOCs. So we encourage the teacher that they can use their MOOCs or they can use other teachers MOOCs or other schools MOOCs. We just use the video or the video of OCW and we can see that this is the data that we can see that 2019 and 2020 we can see is the growth of the OYA that we can see. This is months, six months statistic. We can see that there are so many new user during this period.  So that's the experience that we share to you that what we do in national university. So thank you everyone. Thank you. Thank you Professor Zhu. This is from Da Ye University. Yeah. Alright. Let's welcome Professor Zhu from Da Ye University. Yeah. So wait a moment. Yeah. Yeah. I would say that there's one question from others. Mentioned that what kind of models we are using for course design or teaching design. Anyone online please check on the question and think about your interest and we will discuss that later. Thank you. Hello. Welcome to join the impacts of the MOOCs in higher education during the pandemic. A Taiwan experience session. I am working for the center of teaching and learning that is in Da Ye University and then I will talk about our case. Da Ye University school badge symbolizes a thriving tree and green is used to recognize the image of the tree. But first let's see how are the distance courses of our university promoted. The Ministry of Education in Taiwan specifies that the implementation of distance courses and colleges and universities refers to the teaching method of asynchronously synchronously or physically providing courses by mixed instructional design with over half of the total hours in single course. We already have asynchronously LMS synchronous system, Google Meet and physical campus to implement distance courses for many years. And we have set up a distance course application process based on the ministry of education policy through the three levels review after approved teachers could offer the distance course. But this year facing the epidemic in addition to the existing distance courses we start up the learning and teaching project for COVID-19 prevention. If the outbreak is notified all courses don't need to follow the application process to apply. Each course should provide an online course no matter synchronous or asynchronous activity immediately. What you see on the screen is the status of our training courses for teacher and we also provide a teaching for dummies to teachers to reduce their anxiety. Next let's move to massive open online courses. Courses can be divided into four categories business cultures, language and law. The business course focus on accounting and costing. The cultures course focus on tourism culture. The language course focus on Japanese and Chinese. The law course focus on our brooded and tele-property rights. This is the statistics of the number of participants. There are six courses with more than 500 students. The courses are open-ended, dominated by the general public and not limited to learning. We have this opportunity to share our experience with you. Thank you for your listening and welcome to contact us. Okay, thank you for my university. Next we have Miss Ding. You can share your slide. They changed the slide. We have several panelists that are unable to participate online. They give us the videos. They will watch the video afterwards. Thank you for joining us. We may begin. Hello everyone, and welcome to join our new session. I'm Ho-Yi Ho, and I'm working at National University of Kaohsiung Center for Teaching Online Development. In the following six minutes, I would like to start by a brief introduction to how we work together and then I will move to what we did during the pandemic. Finally, I will talk a bit about our next steps. So, let's start. The National University of Kaohsiung is located south of Taiwan in accordance with the government industry development policy. We are expected to assist to upgrade and transform traditional industries in technology and management. So, NUK is a very young university that was established in 2000, only 20 years. We have five departments in total and 227 faculties and up to 3,000 students in total. So, as you can see, NUK is also a quite small university. So, our e-learning at NUK contains three main strategies including most digital teaching material and distance courses. However, it is interesting that we started our e-learning by MOOC since 2013. Not like all universities since more books on distance courses on the campus. So, the NUK MOOC started actually only from 2013 until this year we already have had 31 courses in total in which 21 language courses including Thai language, Vietnamese language, Indonesian language and Japanese language and six history related courses, three environmental sustainability courses and one arm design. So, we do also have 17 active courses since 2013 up to 20,000 students. So, the current on campus and off-campus learners took all courses and the average completed rate is 10%. Besides MOOC, we also encourage our faculty to make a digital teaching material until this year 12 teachers which is about 23 courses. But interesting, only a few teachers works on distance courses which is only two teachers and four courses in these years. So, to sum up, the applications of e-learning at NUK is more focused on digital material in a fully classroom. So, even an application of MOOC at the campus relevant traditional distance teaching on learning of other university. But this year, facing the epidemic therefore this year facing the pandemic we actually move to a synchro readiness teaching on learning in particular for those teachers have already had the digital material. So, for those teachers who has no digital materials will also challenge a series of training activities to help them and students in deal with the synchronous synchronous and synchronous teaching on learning. So, it is interesting to find out that the distance course has increased rapidly which is we never expect before. So, learning from the experience of the pandemic for our next step of e-learning at NUK we will actually rearrange our e-learning blueprint and strategy now. The main purpose is surely to establish a system to understand the learning of e-learning. And also we are looking for more possibilities in applications of MOOCs. They are always a lot of things to do. So, let's move on together. Thanks. Okay, thank you, Paladin. All right. Yeah, we have nine minutes left. So, I have to, this one, that's me. Thank you during the pandemic. Okay. Actually, before the pandemic, we already got the strategy of doing the MOOCs or the digital learning parts. The team enjoying OCWC, which is the previous version of the OED in 2007. And then we joined the OCWC in 2008. And then when the MOOCs come up we joined OCWC in 2014. Yeah. Okay. And right now we are producing the MOOCs and we also have a digital initiative which allows the team of students can take the MOOCs and become their credits. And also because some MOOCs need money to buy the certificate, so we provide the digital initiative funds for them so they can pay for their certificate. It's like an investment. And also, TEMI MOOC is not only on digital learning but also on the local MOOC platforms such as E1, Scherkel, OpenEDU. All right. And during the pandemic, we find out several questions about this. Such as, we will need to probably need to do a lot of next content. And also some issues on how to deal with education, or we can benefit from that. And also for teachers, they have to do the e-teaching and for our students, they have to do e-learning. And also, probably a bigger problem is the national localization part because all the international travel events, so we have to do here, like we do right now, do the virtual things. And also, and we find out that our teachers have got the most problems like this. You probably don't recognize the Mandarin characters, the Chinese characters. These are all mentioned about the videos and how to synchronize learning and how to produce your videos. So, you know, their problems are probably the most content how to create it. So, we provide the so our production team will come in and help our teacher to do that. However, it seems not enough. We have to try to do it by yourself. So, we will have a lot of support for them so they can do the e-teaching. We put on the website and they then know how to make it quickly and easily. And if they have more needs, they can come to us and we will give them some help. Also, we have many MOOCs that for them so they can do the flip classroom and also we provide them to have more resources to study. And also, for the MOOCs, we do provide the focus that the MOOCs the pharmacist or clinical medical skills. All right. And by the benefit, we because even though Taiwan doesn't exactly have a lot of moments however, because we are medical university our students in hospitals. When the pandemic, the hospital is the frontier. So, we kind of not allow our students to do the internship so we do provide a virtual internship so they can decrease their hours in the hospital so that we will provide it in VR360 and if you want to experience that, you can go to connect. I have put on our landmark tool VR360 so you can bring that but the way here we are doing the hospital. Okay. And also, TNU has partnership with COSERA and the future. We provide free MOOCs to the students during the pandemic. So, we allow a lot of TNU students can take courses from COSERA and future and also in future we provide free courses to everybody in the world. So, after we put this in the university in my university, they have chosen a lot of, a lot of looks and finish them. But the future is quite good and we feel that if students get free certificates, they really want to learn. That's a very interesting finding. All right. And for our stats for the results in TNU because we've been doing it for a very long time. So, most of these teachers, they tend to use the synchronized format rather than the synchronized format. So, 70% of our courses are delivered by the synchronized format. So, after the screen the matter that the pandemic was very clear. And before we are going to our staff faculty to do the education in the fixed weekend, the fixed week, that's a requirement. So, this is the result right now we calculate and we want them to have at least some stress of the teaching. So, if the new norm is normal this is a new normal. So, we want them to have some kind of real experience in teaching. Okay. And then we also do some quality assurance of these courses. So, we monitor their activity in the LMS so that, yeah, so we will keep on with graphic and keep our monitoring. So, this is the experience of TNU. So, I think, yeah, we have almost time up.  So, it's like using the means and using the you and to do the classroom. So, how is our panelists? We have just one minute. Thank you to respond to it. Anyone want to respond to it? Because in TNU, we do a synchronized format, mostly. Yeah, because they have already got a lot of videos. So, they can put on the LMS and lay down students to study. So, they don't have, they just spend a little bit of time to do synchronization. Because most of them are like patients. Anyone want to respond? All right. Anyway, yeah, so glad to have you here. And I have one thing to mention. Today we have six university and the two are from Taipei, which is northern Taiwan. And the two are from the eastern Taiwan. And the one is from the middle Taiwan and the one is from the southern Taiwan. So, we basically want to cover all the Taiwan. Anyway, thank you very much for a participant with us. If you have any question regarding the topic, you are welcome to discuss or you can connect on the website. And, yeah, just the recording can start. All right.


Welcome to JSA TV, the newsroom for tech and telecom professionals. I'm Jamie Scott of Kataya here at the lovely Honolulu PTC 2018 with my good friend, Mr. Rob Barlow, CEO of Wire IE. Rob, welcome again to JSA TV and PTC. Thank you, Jamie. It's a pleasure to be here. And I know last time you guys gave us an update about 2017. But here now, kicking off 2018, what's in store for Wire IE? Well, more of the same, our success in 2017 was really predicated on our reliability. 2.17 mean time to repair hours across a network that's 160,000 kilometers long from Port Hardy, Vancouver Island to Gander, Newfoundland. It's quite an accomplishment supporting critical infrastructure for Canada and provincial provinces and large oil and gas and industrial. So for 2018, we're really working on unleashing that potential. We have some indigenous projects on the way, really trying to connect the unconnected. I think it's something that we have an obligation to do as a company. And as a culture, if you can't be part of the digital economy, you are actually disadvantaged. So Wire IE is taking its trusted, vault-like network and going to be using that as we go forward. Well, I love that, the vault-like network and serving those that are underserved or hard to serve in those critical locations as we experience growth across the continent. So tell us a little bit more about Wire IE solutions. So basically, we're a robust, high-availability network that uses fiber and microwave. It's certified by the Metro Ethernet Forum, Care Ethernet 2.0. It's really interesting that that certification is something that today is just assumed as table stakes. Quality, though, when it's not there can really make your network less desirable, specifically when things go wrong. So with large industrial applications specifically and government, the technology that we use is reliable and trustworthy and actually something that keeps them out of the newspaper if something goes wrong or reduces costs from a support perspective because we can fix things quickly. And it's not just in metropolitan areas. We take this type of quality to underserved markets. And so what makes Wire IE unique? Why are you an alternative? Well, really, we're extending metropolitan areas in underserved markets. Our partners are working together with us. They have some critical enterprise and government contracts. They use our network to fulfill those. It's important that Wire IE be recognized as somebody who is taking the consistent look and feel of your assets in metropolitan areas and having the same experience in underserved markets. And for those of our viewers who are interested, where can they go to learn more? They can go to our website, www.wireye.com. Wireye.com. Thank you, Rob, for joining us. And thank you, viewers, for tuning in to JSA TV.


The USS Stetum participates in its fourth and final carrot exercise during its deployment. The exercise features the first tactical free play of the carrot series and will force both navies to push their limits. We learn how to act as a warfare commander and that requires us to have a level of tactical proficiency that we usually don't have to demonstrate and so it forces me and my crew to grow and become better tactically as well. There's no defined script during the free play exercise and that means the ships have no idea what threats will present themselves until they happen and it gets the five inch team training on how to overcome weapon malfunctions. The guns needed on the ship to fight the fight and if the gun's broken can't fight it so we got a 60 casualty as fast as possible just to get the gun back in the game and that's why it's so important.


Hi guys, so today's video is going to be on why I chose to become a nurse instead of choosing to go to med school and become a doctor. I have mentioned this in previous videos, so if you've heard the story, I'm sorry. But a lot of people ask me, you know, why didn't you become a doctor?   In high school I did very, very well, I was in the top like 1% of my class, I got all A's, I did honors classes, I graduated high school, I had over 40 college credits to give you kind of like a little background information. So I was very involved, knew a lot of people, everyone was like you should be a doctor, you have a good personality, you have the smarts to do it, whatnot, and I was like yes, I'm going to. But probably my junior year in high school, I started to think about what doctors actually do versus what nurses do, and nothing against doctors because I think there's so many wonderful doctors out there and I really, really appreciate what they do. And I wanted to do a job where I was more involved at the patient's bedside. Doctors typically write orders and the nurses are the ones who carry out those orders. The doctors don't spend a whole lot of time at the bedside, again it really depends on the doctor or the type of field that you're in, but the nurses are the ones who are there 99.9% of the day and are the ones holding your hand when you're crying, who are the ones who are explaining things to you, giving you the medications, putting in your IV, explaining things like really being involved. And I realized like that is what I wanted to do, I want to be involved. I don't necessarily want to be the one who's writing the medication orders, I want to be the one who's giving up. And so then I decided okay, I want to pursue nursing. Another good reason why I chose nursing, a couple reasons. One, it's usually a little bit more conducive to family life and we eventually want to have kids. And two is that I knew that going into nursing, I would spend three, four years, you know, however long it took, and that I would have a career afterwards. I would be a nurse afterwards and I would be able to make X amount of money when I graduated. If I decided to go to do pre-med and then go on to med school, if after that four years of doing pre-med, if I decided, and this is not really for me, I want to do something different or I just don't really want to go on to med school or I didn't get into a med school, I would be stuck. I would not really have a whole lot of job opportunities with just having a pre-med bachelor's degree because I mean I could teach possibly but really like nursing would just open up so many more opportunities. Another reason is I knew that if I became a nurse and wanted to expand my education to become more like a doctor, I could get my nurse practitioner. Now not saying that those are identical because there are some differences but nurse practitioners can ultimately do a lot of what a doctor can do. So that was another influence is I knew after I graduated, I would have a solid career. I would be able to still work and have a family. I would make enough income to support my family and that if I still wanted to expand my education, I could become a nurse practitioner. So those are the reasons why I chose to become a nurse instead of a doctor and again if you're pursuing to become a doctor that is wonderful, that's great. We need more doctors, we need more great doctors and you know, same for nursing. I personally, I tell people this all the time, I may have not said this in my videos but I am so so happy with the career choice that I made. I could not have picked a better career choice for myself, for my needs, my personality and I love caring for people. I love the medical world, I love critical thinking and I love being there when people are experiencing some very, very tough emotional times. And so I'm super happy that I chose nursing and I hope, I only could hope that everyone who goes into nursing can feel the way that I do about nursing. Now I know that's not always true but anyways, I hope you guys like this video, make sure you give it a thumbs up and subscribe to my channel and I'll see you guys next time. Bye.


Tell me about your anxiety and where it came from.  My anxiety comes in the form. It is funny how everyone's anxiety comes in these weird. Mine is super high stress levels, cortisol, pulsing through my body, but not, I don't recognize it until I crash. I do this really wild thing that I've only learned through my old lady that I'll be humming along like I'll be doing this and this and this and go to this thing and have to go to this thing and meet this thing and I'll be like, I'll emotionally get so amped up and like rude, I'll start to be rude. Is it, does it feel good when you're in it? No, no, but it's like I'm keeping up. Do you know what I mean? I feel like I'm, it feels like when you're in a dream and you, when you can't punch or you can't run and you're stuck, that's what it feels like when I'm going through like a, like an anxiety moment. Not an anxiety attack, but just like a heavy anxiety. You have chronic anxiety. It seems like you have anxiety. All the time. Like you wake up with it. Yep, yeah. I mean, it doesn't, it's crippling.  Huh? It's a crippling. I have a cane. You walk around. He's got my cane. Your anxiety cane? My anxiety cane. What happens is I will crash. I'll have, I will literally physically go to bed. Like I'll be running, running hot and I'll sit on the couch and I'll wake up like three hours later. Really? Yeah, it's the craziest thing. I had to ask a doctor about it because I got kind of concerned that I was like, did something bad, is something wrong? Have you missed things because of it? Like you were supposed to be somewhere and you was like, I had anxiety. No. And then I fell asleep. No, that's the problem is because I'm so worried about that I'll make it those. But the moment that I know I have a minute to like, all right, I don't want to do that thing till later tonight. And if I sit on the couch after I'm kind of pacing and panicking and talking out loud how annoyed I am, I will genuinely crash. I'll actually fall asleep. Anxiety. I mean, dude, I didn't realize how anxious I was until I started dating Katie. Are you like a foot popper? I'm kind of like, I shut down and I try to like, like she gave me the example of when we're out in public. I try to make sure that she's okay. Everyone's okay.  We're in a ball game. We're at a concert. Like you don't have to, you can just go. You can just be a part of it. But I'd be like, and then I can't talk. Like she can hear my, we'll play a video game sometimes and we'll both be on a headset and she'll hear my breathing and she'll be like, dude, relax. Cause I'll be like, it's like, I don't even know I'm being anxious. I just like go into this stage where I'm like, like rocket league, something ridiculous. Something where we're literally playing to relax and I'm getting anxious cause I want to do well. Cause it's against people pleasing. It's the fucking, all this like adding up. I didn't realize that it was making me so anxious. Also, I'm a pod head. So I thought I was like. Cool. Pod heads are the most anxious people by and large. I've been really discovering that the last like two months.   And you're like, yeah, I do. And then Katie one time was like.  It's like, no, I'm not. You're constantly on edge.  And now even more so, cause it went sideways. But I had never had, she was the first person in my life that put the word anxiety on it. Where she was like, you know how anxious you are?   And then I started being like, I am. And then she noticed it. Now what are you going to do? You can't smoke weed ain't going to help. Well, now it's even better just like learning how to relax naturally and being, you know, I meditate now. There's just like a lot of stuff that I do where I'm like, well that, yeah, I'm a big old puss. Big old do my breaths in the morning kind of puss. But I didn't notice it with my stand up until she noticed it. I did. Shane Gillis was, did like five sold out shows at Caroline's and he was like, dude, do guess it. Like it'd be awesome.  This song, you know, it's cool. It's my friend's show. It's all sold out. No stakes for me.  And then I went into my bits and I was doing it like this and I, but in my head I'm like, oh, it's time to do the bits. Now I got a really, now I'm going to kill.  And I got off stage and Katie was like, why'd you get so anxious? And I was like, what do you mean? I did my bits and she was like, dude, you were killing. And then you went into like, hopped up, did you ever go to here? I went to here and then I did this. And I was like, oh, that was pure anxiety. Pure anxiety of like, I have to do well.  And I'm like, nah, but I was, yeah. And so it's that anxiety of like robotic almost. And so now I'm aware of that every time I'm on stage, I'm like, hey dude, this isn't a big deal. This is fun. Yeah, relax, chill out. You don't have to do well. Yeah, you can do okay. And if you have fun watching comedians that have fun on stage made me realize how much I'm not having fun on stage. Like Chappelle, you watch Chappelle on stage and you're like, oh man. Never seen him.  I see that with like Sean Patton. I see that with Ali Sadiq. Like Ali Sadiq, I just watch him and I'm like, this is such a guy that's just in it. He's just present, he's in it and he's having fun. Same with Shane. Yeah. And I watch him and I'm like, Nate. I'm like, damn, you guys are all just having a blast. And I'm up there like this.  Well, it's hard if you have to, I not like have memorization issues, but like I want to remember, my bits are good. And I like doing them and I like when they work. And I can do crowd work that's funny and I just don't see it as more valuable than my bits. But I know what you mean. But I always used to watch Patrice and Big J and they do this thing where it's all one thing.  That was so cool to watch because I kind of knew what was the pre-planned stuff. But how you got there were organic. It just looked so smooth. And I love that. And I realized that I was like, are you guys having a good night? Good. Dating is very difficult with apps.  Just relax. But that's all tied to the anxiety. One of my blocks is anxiety.  And it's like, I have a joke about it in my hour right now.  And that's why you can never really let your guard down ever.   But then the stuff you didn't worry about is what happens. And you go, see, I knew it. Like I say on stage, I go, I think COVID was my fault. Like that was the one thing. Like did anyone else feel like that? When everything shut down, like I knew I forgot something. I knew it. I just didn't. The stove. Yeah. It came from your stove. Yes. Everything locked down the week after my first special came out. And I was like, wow, I was worried about everything else but this. Happening. Nothing is ever as bad as you think it's gonna be. Even bad stuff. But I would say, mom dying, as bad as you could have imagined. Never occurred to me. Right. Never occurred to me once. So there's no. I believed in Jesus. Jesus was gonna take care of me. Yeah. I think that there's a hierarchy of anxiety. So you were at some point, you're probably worried about succeeding. You succeeded.  No, no, no, no. Full amount of anxiety, now it's just proportion in different ways. It's just like, no, I'm gonna give 10% of that success anxiety to. My agent. There you go. Or I'm gonna worry about my relationship with someone. Whatever.  That's a great one for women. It's number one. Number one for women, black mold. Aging, murder, black mold. Yes, yeah. Let's go with our first block, right? You ready? High anxiety stress. Yeah. I've known you for 15 years. You seem not, uptight, you like things a certain way. So tell me about high anxiety and stress. My problem is I'm constantly thinking. I'm never in the moment. I've been trying to do meditation over the last five years to kind of calm my mind down. But especially with kids, I'm always thinking if they could get hurt doing that or I'm thinking six months, 18 months ahead, career-wise. Never really enjoying being present. Right. So the anxiety comes from, it's like a lot of worry for me. Yeah. So that's what the anxiety is. It's not like I'm stressed out. It's more that I wish I could stop thinking so much and just being. Well, that's knowing what I know about From Your Act and the little bit I know about your life. You, how old's your dad? 76.  So they didn't enjoy anything. You know what I mean? It's like you're, it's that joke you do about your dad. Like I've been depressed since I was 12 or whatever. Like that wasn't a thing that they had. Like as a way to be. My parents didn't enjoy anything. Enjoying, what are you talking about?  So like you then have, by all accounts, things could not be going better for you. Yes, they're going really well, but. Hold on, there is a better. I hear a better. With all that's going on. See, I enjoyed the kind of ride to where I'm at right now more than where I'm at right now. Because I feel a lot of pressure.   You know, I was surprised that I started to sell out. I go, wow, we sold out or does it? Now it's a little bit more of a pressure to get the people to come and to sustain that. And I put a lot of pressure on myself to try and do that. And I am now just taking some time off. Are you really? Yeah. The anxiety, stress, is it from expectations you put on yourself? Yeah, it's not from childhood.  I take after my mother that way. But the anxiety came more from, here in a nutshell, it's like you're successful, you make money, right? I've never been in this position before in my entire life as far as, you know, when I was making $70,000 a year at the Four Seasons Hotel as a waiter, I knew every year I generally will make around that amount of money. I had my rent, I had, oh, I could go to a dinner that was maybe expensive, but I could only do that once in a while. All right?  Well, I mean, I could go back to waiting tables right now. Yeah, no, I believe it. If you got any shifts that you need picked up, the greater LA, I mean, we need a certain level of establishment. So now I'm dealing with money that I really never dealt with before. And it's like, sometimes you don't know, and I'm very conservative with it, just because I don't know how tomorrow could be my last show. And then what I got's gonna last 30 years. So that's kind of the challenge for me right now is to not pine so much over money and where it's spent and it's not like I'm tight.  What am I saving for?  I don't know, I'm being like, who am I now? I could dial it tomorrow.  No, I'm with you though, like what am I doing? Why am I doing this?  I just, I gotta figure out what the hell my goal is in regards to socket money away. Yeah, I guess for me right now it's more of a safety blanket than anything else. Yeah, didn't you think that once you got to a certain level, you would relax? No, I'm getting to this level now of like just thinking about it because I was working so much. I just put my head down when the pandemic hit.  I'm like, plus kids too, it's another thing. And there's another block on there which relates to kids. But once you have a family, a wife and two kids, you know, it's just ain't me anymore.  So that puts another level of stress on top of what's going on. And how, what about overthinking? Have you done anything to help yourself with that? So I, I'm in therapy, which I've never really considered. I mean, not that I've never considered it, but you know, again, growing up where I grew up, therapy was no, no one I knew went to therapy. Nor should they have. And it's nice just to have, and it's a half hour a week on the phone. You only are doing a half hour? Half hour. I've never heard of anyone doing a half hour. Do you find it helpful? It's nice. It's nice for me. It's nice. And this is the type of therapy, not necessarily that we're dissecting a lot of things. It's just more like me talking some of my, what's going on in my life out, getting it out in the open, just talking about it, throwing it up to someone who doesn't really have a stake in the game. Yeah. And regardless of what the therapist says to me, I just find it therapeutic to throw up. Of course. Hey, did you like that? Did you like that? Yeah, did you like it though? You want more? Don't want to work? Would rather watch videos of me grab acid with people?  This is like when the weatherman says there's a high pressure system coming in. I'm not really used to the green screen.


We'll buy a cup of coffee or drink of their choice really and then they have the opportunity to pay it forward and give back. There's approximately 50 to 60 people every day who are being served those meals at the soup kitchen so we know that we're taking care of a lot of people and just wanting to give back in our own community.


Welcome to Scrum Mastery Challenge, the Agile Coach Game Show. I'm Geoff Watts. And in this game show, I've set a number of challenges for four agile coaches and one teenager, with next to no agile experience, to test their agile knowledge, their creativity, their estimation abilities, their construction knowledge, and interpretation of agile values, in hope that it'll make some great entertainment, while also providing some interesting insights for the agile community. Over the course of eight episodes, you'll watch Sam Whiting, Christina O'Hanion, Helen Meek, Paul Goddard, and my daughter, Freya Watts, undertake various challenges, none of which they have any idea about until they turned up. I hope you have as much fun watching these episodes as me and the contestants have making them. Make sure you're subscribed to the YouTube channel, because that's the best way to stay in touch and to be the first to know when each episode is released. Get in touch, comment, tweet, whatever. Let us know what you like as the series progresses.


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This lecture is part of an online course on Lie groups, and will be about Lie algebras. So the problem with the Lie group is that it's kind of complicated. For example, if you look at the group gln over the reals, this is the matrices with non-zero determinant, and the determinant is really quite a complicated function, and it's quite difficult to visualize what the set of matrices in the set looks like. I mean it's a fairly complicated topological space with non-trivial homology groups. And the idea is to replace the Lie group by something rather simple, which is a Lie algebra. And the Lie algebra is easy to visualize because it will just be a vector space with some extra structure. So it's a linear object, and we can use linear algebra to study it. So the informal picture is as follows. Suppose you've got a Lie group G, so it might be a circle. What we do is we pick the identity element, and we look at the tangent space. So this is going to be the Lie group, and the Lie algebra will be the tangent space at the origin. And the informal idea is the Lie algebra sort of gives you the, describes the elements of the group that are close to the origin. So if you look at the neighborhood of the origin, then you can more or less identify this with a bit of the Lie algebra near the origin. So the idea is the Lie algebra sort of tells you what the Lie group looks like near the identity element. So the problem is, of course, we can always take the tangent vector space of a Lie group, but this doesn't tell us anything very interesting. It's just a vector space. We want to put some structure on the Lie algebra to capture most of the structure of the Lie group. So to do this, let's first of all recall the connection between first-order differential operators and vector fields and infinitesimal automorphisms of a manifold. And for simplicity, I'm just going to take the manifold to be euclidean, ordinary euclidean vector space. So first of all, what does a differential operator look like? Well, it's just going to be a sum of functions fix1 up to xn of the partial derivative with respect to xi. So that's a first-order differential operator. The order is, of course, the highest derivative that appears. So if you had a second derivative of xi, that would be second order and so on. And first-order differential operators are more or less the same as vector fields. So if you've got some sort of manifold here, we can consider a vector field on it, which you can think of as a little pointy arrow at each point. And if this manifold is r to the n, then a vector field gives you a first-order differential operator because at each point you can take the derivative in the direction of this vector field. And if you write down coordinates, you see that's just essentially the same as a first-order differential operator. So vector fields are just a geometric way of picturing first-order differential operators. Finally, we can think of this as being an infinitesimal automorphism. So if you've got a vector field on, say, r2, it will have a lot of vectors looking like this. And we can think of this as being an infinitesimally small automorphism of r2. What we do is we just push each point an infinitesimally small amount in the direction of the vector field, whatever infinitesimally small amount means. So, but informally, a vector field is sort of a bit like an automorphism that just moves everything an infinitely small distance. So what we want to do now is to discuss how to put an algebraic structure on first-order differential operators. And this will later turn out to be essentially the lee bracket. So let's suppose we've got two differential operators. Let's make the first order. So d is going to be sum of fi times d by dx i. And let's make e equal to sum of gi d by dx i. So here fi is going to be a function of x1 up to xn, which I can't be bothered to write out, and similarly for gi. So here we've got two first-order differential operators. And we want to find some sort of algebraic operation we can do with them. Well, we can multiply them together. So de is now going to be sum of fi d by dx i. So this is going to be a sum over i and gi d by dx j. And if we work this out, we can see that's the sum over i and j of, well, first we've got fi g j d by dx i d by dx j. But then we also have to move the d by dx i past the g j's. So we've got plus fi delta gi over delta xi times d by dx j. And you see this is the product of two first-order differential operators is in general not first-order because this is second-order. However, if we multiply them in the other order, we see we get something very similar. So first we get the same expression here. So that should have been a j.  And what you notice here is the second-order parts of these are the same. So d and e do not quite commute, but they almost commute in that if you just look at the highest-order parts then they commute, but there are some lower-order parts that don't commute. And what you notice from this is that d e minus ed is first-order. It's just this bit which is a first-order operator minus this bit which is another first-order operator. So here we've got an algebraic operation on first-order differential operators. We can't multiply them, but we can sort of take what's called a commutator. And what we do is we define the le bracket to be d e minus ed. So this will be essentially the operation we have on the le algebra of a le group. We can't multiply two elements of a le algebra, but we can take their le bracket. So I said here that if you've got two first-order operators, the le bracket is a first-order operator. I'm just going to have a little exercise. It says if d e have orders m n, then the le bracket d e has order m plus n minus 1. So roughly speaking, differential operators are trying to commute. They commute if you just look at their leading terms, and the thing that causes them to fail to commute are terms of order less than the leading order term. So this is just the special case where d and e both have order 1. Next, we can ask what identities are satisfied by this bracket of two operators? Well, it's obviously not commutative in general, because d e is not equal to ed for most e and d, and it's not associative that d e f is not equal to d e f in general. So what identities does it satisfy? Well, there's one obvious one, which is that d e is minus ed, which is completely trivial if you just look at the definition. And there's a more subtle one due to Jacobi, or I know I've mispronounced it, but this is the standard pronunciation in English-speaking countries. So the Jacobi identity says that a b c plus b c a plus c a b equals zero. And it's easy to remember these because these are just the three cyclic permutations of these. They all rotate a, b and c. And this is actually easy to prove. It's true for any associative ring. I'm saying associative because we do actually have a non-associative product here. If we define a b to be a b minus b a, then you can check this identity holds. And if you haven't already checked this, you should do so because as someone said everybody should check the Jacobi identity for themselves once in their life. And are there any others? Well, you can find some other obvious identities just by taking combinations of these two identities. So you can ask are there any other identities which are not consequences of these two? Once it turns out to be no, we have actually found essentially all the identities satisfied by general the algebras. So a Lie algebra is a vector space over the reals with a bilinear map taking d and e to a bracket d and e satisfying conditions one and two. So that's what it's going to be in this course. In general, you may notice there's no particular reason if you're an abstract algebraist why this should be a vector space over the reals. You could perfectly well take it to be a module over some sort of commutative ring, but we will start off the case over the reals or sometimes the complex numbers. So that's what a Lie algebra is. Now we have the following problem. Let's find the Lie algebra of a Lie group. And I'm first going to give a sort of abstract way of defining the Lie algebra over a Lie group as motivation. And then what I'm going to do is to try and calculate what it is explicitly. So here's the sort of abstract version. What we do is we take a Lie group. Let's call it G. And we take the identity element and we look at the tangent space at the identity element. So this will end up being the Lie algebra. And we're going to look at vector fields on G. And a vector field is going to be got by taking a little tangent vector at each point. So it might look something like this and so on. So in general, there are an awful lot of vector fields on G, at least if G has dimension greater than zero. But what we're going to do is we're going to take a look at the left invariant vector fields. And what we do is we notice that G acts on itself by left translation. And what we can do is we can ask for the vector fields that are fixed by this translation. And these are pretty easy to work out because suppose we pick a tangent vector at the identity, then at any point G of the group, this vector field has to be invariant under multiplication by G. So we just transport this vector field to this other point here. So the left invariant vector field is uniquely determined by its value at the identity. So the left invariant vector fields correspond to just tangent vectors at the identity. So they form a finite dimensional vector space, at least if our lead group is finite dimensional, which it will be for the moment. So vector fields correspond to first-order differential operators. And as we've just seen, the first-order differential operators on any manifold have this nice lead bracket. And this is preserved by all automorphisms of your manifold, in particular preserved by left translation. So the left invariant vector fields are also closed under the lead bracket. Well, the left invariant fields are closed under the lead bracket, and we can identify them with tangent vectors at the identity. So the lead algebra of G has a lead bracket. Given by, if you take two vectors here, you first of all turn them into left invariant vector fields. Take the lead bracket of those and then restrict back to the identity. So this gives us an abstract explanation for why the lead algebra of a lead group, its tangent space at the identity, has a lead bracket operation. Well, we can compute it in one trivial case. Suppose we take the group to be just a vector space under addition. Well, then G is just acting on itself by translation. So the invariant vector fields, well, left invariant and right invariant are the same in this particular case. Well, what do they look like? Well, they just look like sum of a i delta by delta x i where these a i are constant. And the lead bracket of any of these is always zero. And if the lead bracket is always zero, we see that the lead algebra is abelian or commutative. And obviously, abelian lead algebra is not terribly exciting because they're really just the same as vector spaces. You're just saying the lead bracket is always zero. So that's a rather trivial case. What we'd like to do is a more interesting case where the lead bracket isn't zero. So let's try and work out the lead algebra of the general linear group over the reals. So here the identity element is just as one's down the diagonal. And the tangent space, well, this is the tangent space at E, can be identified with all n by n matrices over R because this is an open subset of the n by n matrices. The tangent space at any point can be canonically identified with this. So suppose you've got a vector x in MnR. What does the corresponding vector field look like? Well, what we have to do is just move an element according to this vector field, roughly speaking. So what we want to know is what is d of f at some vector a in the general linear group. So here f is going to be a function on gln. And in order to know what the vector field does, we need to know what it does to any function f. And we can define a vector field just by taking f of a times 1 plus epsilon x minus f of a over epsilon. You notice this is more or less the usual rule for a derivative, except we're taking a derivative in the direction of the vector field x where we've moved it to a by something that commutes with left translation. Or we can think of this as being the lowest order term, or at least the lowest order non-zero term of f of a times 1 plus epsilon x minus f of a, which is equal to epsilon times something plus higher order terms. And what we want is this term here. Well, now we can now take two different vector fields. So suppose x and y are vector fields and they correspond to differential operators d and e. Then we want to compute what is e df at a point a.  So we take this and we want the lowest order term, because this will be epsilon delta times something plus higher order terms. So here what we've done is just plugged in the definition for the two vector fields x and y. So we're looking at 1 plus epsilon x giving you one of the vector fields and 1 plus delta y giving you the other. So we just get this complicated expression. And we can look at d e of f, and this will be something similar with x and y inverted, of course.  And we want, and this is going to be delta epsilon times something plus higher order. And this something is going to be the value of this at the matrix A in the general linear group. And since we are ignoring all higher order terms, you can change A to any sum of higher, you can add any higher order terms to A without changing this.  So this will be equal to, sorry, minus f of A. And this is equal to delta epsilon of xy minus yx times, sorry, this is just the differential operator corresponding to vector xy minus yx. You can see there's xy minus yx. So this shows that the lead bracket of differential operators corresponding to matrices x and y is just xy minus yx. So we get the same bracket of x and y, whether we consider x and y as matrices in the associative ring of matrices, or whether we consider x and y as corresponding to left invariant vector fields on the lead group. So now we can work out the lead algebras of various lead groups. For example, gln, the lead algebra, is just n by n matrices over the reels with the lead bracket given by xy equals xy minus yx. Now if we've got a closed subgroup of the general linear group, the tangent space at the identity is just a subspace of mnr. And it's not very difficult to check that the lead bracket you get is just the restriction of this bracket. And this makes it very easy to work out the lead algebra of any closed subgroup of gln. So let's do a few examples. Suppose I take the special linear group r. Then I want to know what is the tangent space. So the special linear group consists of elements such that the determinant of A is equal to 1. Now the tangent space at the identity will now consist of matrices x such that the determinant of 1 plus epsilon x is equal to 1 plus higher order. Where epsilon is some very small number. So if we expand out this determinant, sorry I should have said 1 plus order epsilon squared. And if we expand out this determinant, the determinant of 1 plus epsilon x is 1 plus epsilon times the trace of x plus epsilon squared times something complicated. So we get the condition that trace of x should be equal to 0. So the lead algebra of the special linear group is just n by n matrices of trace 0 with the lead bracket given by that of course. And we can do the same thing for say the orthogonal group. So let's work out the lead algebra of the orthogonal group.  So the lead algebra, we just have to figure out the tangent space of these. So this will be matrices x such that 1 plus epsilon x times 1 plus epsilon x transpose is equal to 1 plus things of order epsilon squared. So here we're sort of approximating x by 1 plus epsilon times the tangent vector. And if we expand this out it's 1 plus epsilon x plus epsilon x transpose plus epsilon squared times something we don't care about. So if this is equal to 1 to order epsilon squared, we find the condition x plus x transpose is equal to 0. So the lead algebra of the orthogonal group consists of n by n matrices such that the sum of x and its transpose is equal to 0. There's an alternative way of finding the lead algebra. So the alternative approach is in some ways simpler but it doesn't give quite such a good explanation of why the Jacobi identity holds. The alternative explanation is you define x, y to be the lowest order term of a commutator A to the minus 1 B to the minus 1 AB. Here we're thinking of A is equal to 1 plus epsilon x or roughly equal to that and B is approximately 1 plus epsilon y where x and y are tangent vectors and A and B are elements of the group which we will take to be the general linear group over the reals. It'll be a little bit easier if we just choose explicit coordinates. And if we work out A to the minus 1 B to the minus 1 AB, we see that it's approximately 1 minus epsilon x, 1 minus delta y. Let's make that a delta because I want to keep the epsilon's and delta's distinct times 1 plus epsilon x times 1 plus delta y. And if you work this out it's equal to we get an epsilon delta times x, y minus y, x plus higher order. So these are of order epsilon squared times something or delta squared times something and so on. So this gives a simpler calculation of the Liebracket. However the Jacobi identity isn't so obvious from this approach. If you want to get the Jacobi identity use the Hall-Vitt identity which says the following. It says that x y to the minus 1 z with exponent y times y z to the minus 1 x with exponent z times z x to the minus 1 y with exponent x is equal to 1. So let me explain this here. x y for elements in a group is defined to be x to the minus 1 y to the minus 1 x y. And x to the power of y is just the conjugate of x with respect to y. This is notation sometimes used by group theorists. So you can check this by brute force. Let me leave this as another exercise because you really don't want to watch me checking this. And as you can see this is formally very similar to the Jacobi identity. And if you use the definition of the brackets in the previous sheet of paper and apply this expression you can deduce the usual Jacobi identity for the Lie algebra. So next lecture we will be discussing the relationship between the Lie algebra and the Lie group in more detail using the exponential function.


Imagine if I fell and you'd walk in and be like, what are you doing? I'm gonna just be stuck out here. You're like, nothing. Nothing to do with you. There's light in here. Uh, whoo, it's hot in here. Do you really want to go in somewhere?  Are we live? We're live. Hi y'all.   Yes, it's live. So anyway, what I'm doing right now is, okay, let me back up. I lost a shoe to the game today. Well, technically I lost the shoe. This, it was over there. I should have left it, but it, RIP, look at this mess. Woo! So we thought we would do some couple little just tips to help you save your chanclas. And what chanclas are, are sandals in Spanish. Flippy floppies. Flippy floppies. So, normally when you're doing these countertops and you get these drips, and normally you do the drapery, which is awesome. It's good. I figured out it's good to make these a little bit longer than normal, not just, you know, cut it off right here. Make it go longer so that it does drip down. And then that way you can lift this up, fold it onto itself.  And you can also put a piece of paper down as well. But I thought of something really fun in the kitchen.  Like if you want, put down a second layer, then start your pour. So then all this first, like that second layer gets all the resin on it. You can peel that up after you're done doing what she's doing.  And what she's doing here is an acetone. Yeah. Is that gonna eat those gloves? What do you do? You put acetone in your hand and it smooths out? Yeah, you just rub it down. I could also take the heat gun and hit it which actually I probably should do. I used the rag the first time around and it left stuff on there. Left some fuzzies. So I'm actually gonna hit it with some heat real quick. Nope. Okay, kids, don't say this one. Can you let your shipping person know that Jacqueline Porter placed an order and haven't seen the shipping notification? Okay, we're gonna have to deal with all the shipping stuff. Like, you can't address that right this second. And our shipping people come in on different days.  I think she goes into... Austin should be there today. Austin should be there. We're gonna zoom in on what we're getting rid of. There's like extra grip here going on here. You can also, won't the sweatshirt? Yeah, but you'll see that pink grip. Oh, yeah. What we can also do is spray paint it. I would go down. I wouldn't go sideways like that. And don't cook your resin. Just get you a little, just enough heat on there to soften your resin up. This is about, what, two hours? Three hours after? A few hours after, yeah. And all she's doing is just pushing, giving a little pressure on there and smoothing out those. Look at that. Don't breathe in acetone, by the way. JJ just said that. Isn't that what they use in nail salons? Yeah. And you're right, the flood coat will conceal it as well, but it might make it harder on yourself. You should heat some of that up so it's kind of smooth that out, right? Is that what you should be doing, or no? I'm asking, so I don't know. I haven't had some heat on it. So it doesn't get like that. That doesn't look very smooth. Not my thing. I just don't want it to get too heated to where it melts. Goopy, we could have done this a couple hours ago, but. I think it'll be fine with the flood coat, too. I wonder if you could probably take one of those paint sticks and smooth it up. That looks good. And then the flood coat will cover. Yeah. I need to do this one last part. The other ones are pretty flat in terms of drops. So on the last video, we went over other pro tips, countertops. Lori, we went to Venice Beach yesterday and it was beautiful. We went down the boardwalk. You guys, we went and bought two shirts. And, okay, we went to this t-shirt place, right? We went and bought two shirts. I got an LA with the skateboard on the front, just like a cutout. Just like literally just a cutout. Like how I make on my sticker machine at home. It was a LA with how you cross the the A and the L with the skateboard. And then on the back, it said VB with a little surfboard, but it was just a barely like a silhouette on both sides. And then Erica got a tank top with long or a Venice Beach on it and they said, you get a free pair of shorts or a shirt, but you have to pay for the logo. So we get it and the price was $159 for two t-shirts and a free pair of shorts. I was like, what is, what did I just pay for? No, I'm talking, we went to a t-shirt stand, like a souvenir stand, like a building, not like, not like on the sidewalk. Like it was, you know, a store. So other pro tips. We base painted this with pink and white before we added the resin. So you can kind of see some of the pink in here. And definitely the light pink that's on the, but back splash that's on the wall, the light pink, that was all pre-painted on there. And then we put resin over it to make it look right. But working with resin is really hard to do vertical things on a vertical surface. So that along with when we added these like darker lines, they're not just vertical drips. Right now they have that slight motion because we waited till the resin thickened before adding those on there so that there's some direction and it's not just gravity. Yeah, it looks so good. I was afraid it was gonna be too much pink because obviously she has all the pink, but man, this really like, it looks great. I can't wait to take all this tape off and all the paper. I think it's gonna look nice and clean. Also, the awesome like white lines have a shadow. Oh, thank you. She put her makeup on today with the murder. I was watching murder. I'm gonna know your tips. So we put the thick white stark lines on last as well so that it won't move quite as much, but where it is moving, it's looking pretty natural. Also, also this building, okay, we're in West Hollywood. There's Hills. Yeah, we're on a pretty steep hill. So this unit is not exempt from that. So there's, everything's, you can see this sputtering right here. That is from... It's shifting. The shift. However, that tends to look more natural. I mean, look at that. That looks crazy. So it's giving the piece some unified movement as it's relaxing and shifting like that. As long as you have enough masking down to prevent. Yeah, like we always say, always, always do your prep work and always, always prepare for the worst. I guess that would be the best way to put it. Always put down way too much. We could probably put down another foot, probably another two or three feet that way. Always prepare for the worst because you never know. You could be filling your bucket. You can be filling a cup with resin from your bucket and spill it. And you do not want this to go, you know, on somebody's hardwood floors and like these. And it looks like she's about ready to redo these. So maybe, I don't know. But there you go. I know, I think she's gonna be happy with it. Like it looks just like the sample. And she is very, she's very easy going, super nice. Just, you know, she was like, I love what you did. She found us on Google, which was awesome. What you doing here, babe? There was a something and so I had to pull it out and then nothing is going to stop that thing. Arlene, we haven't done the gold yet. We're gonna let this dry up a little bit. Maybe in the morning, we'll take the gold because we want the gold to be a little bit more relevant. We don't want it to, you know, when you take the spray paint and you put it in the resin and it just kind of spreads like it blooms out. And we don't want those big pieces of bloom. We just want it to be just inside of the rose gold there. So we're just going to hand paint just little sections of the gold. So it stays gold and then flood coat it. And we're going to pull the gold veins up onto the back splashes and the front splashes to make them look more fluid and flowy with everything else we got going on. No, Derek, Derek asks, do you put anything in the, hold on, you putting anything in the flood coat? Diamond dust from stone coat. We are not putting anything in the flood coat. If the client comes back and says they want more or less something and we come to an agreement, sometimes we'll add something into the flood coat. She wanted subtle sparkle, which is why we used Milky Way in this particular piece. You can probably see some of it right there. It's a very fine green sparkle as opposed to diamond dust, which is a little bit thicker grain, which is still beautiful. But...  You want it to be a, you want it to be strictly the countertop resin so that it's, for one, you're not getting any contamination of pigment or... It's really important to have nothing in your flood coat because that's going to be what protects your surface from if you put a hand down. If you, some people use acrylic pigments and those sometimes aren't light fast and if there's nothing to protect it from the light, then even if your resin is UV resistant and your pigments aren't, it could yellow. So the pigments that we use are titanium-based, the white is, so we're not going to have that issue. However, you really want the last thing you put on to be resin. Even if it is just a glitter additive like diamond dust or Milky Way, you really want it in nothing but resin flood, in my opinion. Yeah. This is all just how you do, so. I love it. Looks good, looks good. All right, well, let's go get some food. Yeah, if you have any questions, leave them down in the comment box below. I haven't checked the red phone or not in the studio to check emails, but we are, we have someone coming in today to send out orders, so that. Thank you very much for that. So yeah, follow us on other social media things I would show you, but I don't have my handy-dandy pop-ups. So just look on our other videos for our other social media to see what we're doing live and in real time and the kind of one another. We never tell them it's going through and we will see you tomorrow. Bye. I said, bye.