November the 4th is the 181st anniversary of the Newport Rising. This is one of the most important events in the history of the working class of Britain. Far from being only a few unorganised troublemakers, the Newport Rising reflected the willingness of the mass of the working class in Britain to participate in an insurrection to overthrow the old order. The life of the working class in Victorian Britain was miserable. The factory was a dictatorship where workers and their families would be forced to work punishingly long hours for very little pay with fines being leveled for every tiny infraction. Working and living conditions were so bad that a popular prayer went from the loom, the factory in the mine, good Lord deliverers. The workers had no political representation. Those who owned no property didn't have the right to vote, a system that was maintained to protect the interests of the capitalist class. The ruling class feared that rather than limiting themselves to polite debates in Parliament, the workers would use any political power they gained to seize the property of the rich and put a stop to the exploitation of capitalism altogether. As the Duke of Wellington said of the workers demanding the vote, plunder is the object, plunder is likewise the means. In other words, the capitalists were terrified of the revolutionary power of the working class. This explains why they would do anything to keep them away from political power. Chartism was a mass political movement of millions of workers in Britain. Fed up with their terrible conditions of life and work, workers demanded the right to vote and to put their own representatives in Parliament who would act in their interests and not in the interests of the ruling class. As Bronteria Bryan, a leading Chartist explained, it was not the actions and the decisions of a few cruel individuals in Parliament that was needed to be remedied, but the question of which class they represented. Individuals, he explained, are but the chosen tools or instruments of these classes. The Chartist movement was set up to demand the fulfilment of the following six points. A vote for all men over the age of 21, secret ballots, no property qualifications for MPs enabling a worker to become an MP, payment of MPs, equal constituencies, and annual Parliaments. While these may sound like very reasonable demands even from the perspectives of the capitalist, in the context of the time angles explained, they would be sufficient to overthrow the whole English Constitution, Queen and Lords included. In 1839, the first petition was launched. More than 1,280,000 signatures demanding the Parliament accept the Charter were presented to Parliament. This was an amazing feat given that the population of Britain was less than 16 million at that time. However, many workers knew that the ruling class would never give in to their demands, no matter how many signatures they got. The real question was what should be done after the Charter was rejected. The Charter was not just a polite request for the vote, it was a catalyst which channeled the anger and hatred of the working class. Before the Charter was presented to Parliament, mass meetings were held in the industrial areas. Nighttime meetings became more frequent, illuminated by burning torches and addressed by speakers who captured the angry mood. As one Charter said, if that petition should fail, I could not attempt to say what would be the consequences. Rifles would be loaded, that would be the next step, no doubt, and I would defy the power of any government or any armed Bourbon police to put them down. This is exactly what happened. In July of 1839, the first petition was rejected in the House of Commons by 235 votes to 46. Immediately afterwards, Charter's rallies ended in clashes with the Army in Newcastle and a riot in Birmingham. The Charter's convention had planned to hold a general strike or national holiday as they called it in August. However, at the last minute, the wavering leadership put forward a proposal to postpone the strike. The confusion was worsened by a crackdown and arrests of leading Charterists. In the end, the general strike went ahead, but only in a localised, disorganised fashion taking the wind out of the sails of the movement. Nevertheless, in many areas, notably in Wales, the mood was becoming increasingly desperate. Let there be no blinking in the question, stated Hani. These are not the times to be nice about mere words. The fact is that there is but one mode of obtaining the Charter and that is by insurrection. Even before the position was presented, workers across the country had taken seriously the need to prepare for armed insurrection. Weapons were openly traded in street markets in most industrial towns. Military drilling took place across the country. John Frost, a Welsh Charterist, joined by a small group of Charterist leaders decided to take matters into their own hands. They made plans for a general insurrection in Yorkshire, Lancashire, Birmingham, Sheffield and South Wales, the heart of Charterism. This was not supposed to be a local uprising but a national insurrection. According to the plan, the country was divided into districts, then into groups of ten, a hundred and a thousand men with their own captains. Pike making and drilling became extensive while the authorities did not have the forces on the ground to prevent such activities. Pikes and possibly other weapons were secretly made and stuck piled in local caves in the Breckham Beacons. Towards the end of October, after a huge growth in Charterist numbers, the Charterist leaders in Wales decided on an armed attack on 3rd November, hoping to capture Newport. Henry Vincent, a leading Charterist, was being held in prison there and they hoped to free him. This was part of a much wider plan with uprisings planned in different areas of the country, particularly in Lancashire and West Yorkshire. The forces that they were assembling were viewed as part of a massive workers army that would spearhead a national Charterist uprising. On the day, the Charterist forces were formed into three armed columns made of around 20,000 to 30,000 colliers and iron workers. However, they did not reach Newport until the following morning, 4th of November. The authorities had been informed of what was happening and had reinforced the town with police, special constables and troops from the 45th Infantry Regiment. The authorities had rounded up local Charterist and held them at the Westgate Hotel in the centre of the town. The insurgents were informed about the prisoners held at Westgate. Rather than wait for reinforcements, they were sent to the hotel anxious to free their comrades. In the end, the early Charterist insurgents crowded around the hotel at around 9 o'clock in the morning, facing about 40 government troops who were waiting within. Then the troops opened fire. There were officially 20 dead with some 50 seriously wounded and many more injured. Thousands of insurrectionists were still stationed in surrounding hillsides and villages. However, the orders to advance never came. Skirmishes lasted for several days afterwards as more troops were sent to secure the town. There were rumours circulating that Yorkshire and Lancashire were to rise by the end of the month with growing fears among the ruling class from English Newport. In January 1840, it was reported that the Charterists in the county of Leicestershire were preparing a rising together with others in the north. However, the Charterists in the north of the country due to a lack of serious preparation failed to respond. Revolt's later broke out in Sheffield, Dewsbury and Bradford, but these were short-lived and were easily suppressed. Frost and the other insurrectionists were captured and sentenced to death, but due to the extremely high tensions and explosive situation in the country, their sentences were eventually commuted to transportation for life. However, although the Newport Rising ended up isolated and defeated, perhaps due to poor communication and decision and delays, the Newport Rising must be seen as the first generalised insurrection of the new industrial proletariat. It certainly was not over. The movement went on to found the first working-class party in history and to present two more petitions to Parliament. In 1848, a petition holding 5.7 million signatures, more than a third of the population was presented to Parliament. The Charterists were blocked from achieving their aim, and with the lack of any experience to go on, they had to blindly grope their way forward, making many mistakes. However, the experience of Charterism is vitally important and it remains the country of the British labour movement, and that of the whole working-class. In the words of Leon Trotsky, without Charterism there would have been no Paris Commune, without that, no October.


session of hacks for hybrid working. I'm so excited to be doing this, Maren and I. We've been talking about this for quite a while and so it's great to be finally here. I'm joined today, like I just said, by with Maren and we're going to be spending the next couple of weeks talking about hybrid working, hacks for hybrid working, our relationships with digital tools and everything that entails. And so I wanted to start first, Maren, by letting you introduce yourself and talk about who we are and why we're here. Oh, hi Lauren. Hi everybody. I'm really excited to be kicking off this week and hacks for hybrid working. I'm Dr. Maren Diegweil and I have been, yeah, I think having hybrid work experience for over a decade. And since 2017, I've led a completely remote and hybrid blended workforce. So I've kind of been through a whole transition from working in an office where we have a who makes coffee, rotor and a dress code in a very traditional kind of, you know, UK higher education kind of background to, you know, literally packing up the boxes of office equipment and closing the office door for the last time. And then, you know, entering the brave new world of the virtual workplace where we arrived a few years before 2020. And when so many of us had to adopt hybrid working and fully online working environment. And now I've kind of come out at the other end, you know, and I'm very mindful of, you know, it being really challenging, like even if you're super digitally literate and really good with technology and a big front of technology, working from home on hybrid working in general brings with it a whole new set of challenges and requires a whole new set of skills. So I'm really interested in, you know, working with you all for the next four weeks and exploring, yeah, how we can help. That's great. I have been, excuse me, I've been in a similar position, I think, over the last many years working in a remote and virtual setting too. So for those who don't know me, my name is Lauren Hanks. I'm the director of operations at Reclaim Hosting. And Reclaim Hosting is a small web hosting company that is entirely remote. So our growing team is, you know, distributed across the United States and we've got Jim in Italy. And at one point we did have an office location in Fredericksburg, Virginia, and it was actually a co-working space. And we were, again, just thinking about working even at that stage in different working models that make sense for folks. And we opened it up to the community and that was really exciting. But I think ultimately, you know, it just made sense for our team and the work that we're doing that, you know, we wanted to give folks the flexibility of working in their homes and working wherever they wanted in the world. So I've worked remotely from Spain. I've, and now I'm stationed in Florida with my husband and, you know, and so it's been a journey of trying to think about the best ways of doing good work in virtual settings. And so I'm really looking forward to chatting with you, Marin, and chatting with folks in Discord and throughout the Q&A times over the next couple of weeks about the pros and cons of that and really kind of, you know, reflecting on where we are currently and where we hope to be with our working habits. So definitely super excited and looking forward to it. So with that, Marin, should we chat first maybe about the welcome post and maybe how folks can participate over the coming weeks? Absolutely. So we very much hope that this course, which is designed to be an exploration of hybrid working and how it shapes our relationship with digital tools, will provide you with food for thought and practical resources and tools. As we explore what it means that hybrid working is here to stay, whether, you know, some of you might be here thinking, I'm just curious, maybe I'm looking for some new tools or some tips. Maybe others are looking for a hopefully post pandemic or increasingly post pandemic work-life balance and just thinking about sort of wellbeing or personal goals and progress when it comes to hybrid working or you might be in a position where you're supporting colleagues, academics or students to find a way around a kind of blended working environment. So we're hoping very much that the combination of the video sessions, which will be premiering every Monday 11 E.T. and the Q&A sessions, which are at the same time on Fridays, together with a whole lot of chat and learning together on the Discord hybrid working channel and also the resources that we provide will help you along this way. Before we go and talk about the course goals and learn, I know you'll want to jump in there and tell folks what to expect there. I just want to give you a little taste of what's in store for the next four weeks. So this week, we're going to focus on unpacking hybrid working. Next week, we're going to dive down a little bit deeper and think about our relationship to digital tools and platforms in the virtual workplace. Then in week three, we get into actually looking at the hacks. So we have a whole hybrid hacks bonanza planned for you, where there's lots to explore and have fun with. And then bringing this all together, all the things that we do throughout the weeks, we're going to help you set up your own hybrid working roadmap in week four and make sure you have a plan going forward of what you want to focus on. So each week, we're going to take one part of the map and complete it. And then at the end of the course, you should have a complete roadmap. Lauren, did you want to talk a little bit about the course goals and what folks can expect? Definitely. And thanks, Marin, for giving the outline. I think hybrid working or working in general looks different for everyone. It's not a secret that everyone has a different way that they like to learn and they like to work. And so when you pull folks into a hybrid or virtual remote setting, those working models are highlighted. So I'm really excited. I think over the next couple of weeks, I'm really looking forward to just spending time reflecting on our own personal working habits and also understanding our relationship with digital tools as they are now and thinking about the ways that they're impacting the work that we do. I'm also excited just to talk about connecting with others in virtual settings and making sure that we have hacks or tips in place to do the best collaborative work possible, or even the best personal work possible in these settings, and then also just making sure that we have a plan forward. So my goal, at least personally, is to walk away feeling like I've kind of cleaned up my own working habits, cleaned up how I'm using these digital tools to work for me, and also making sure that I've got good habits in place going forward using that hybrid working wheel. Right. I mean, I hope everybody else is going to jump in and share their hopes on the Discord channel. We'd love to know what your priorities are. So please use their Q&A during the session and also share your comments. We'll be picking them up throughout the week. One thing, before we move over and talk about the hybrid working environment and the plot side, I just wanted to make one more point, which is around how hard folk in edtech have been working for the last few years. It's been an incredibly tough period, and I think I'm not really sure I'm seeing the down time, or they're kind of like, oh, now we're good, but it's all achieved now. Let's build on that. Instead, for many people, it can be maybe not a continuation of a crisis, but certainly much more edtech at scale, which in some ways is great, but also means resources are very stretched. And also a lot of negotiation, I think, with folk who whose only experience of educational technology came through the pandemic. And I think many people didn't have an ideal experience during that period. So I think hopefully this course will provide you with a calm and supportive environment in which to kind of take a moment and just reflect and take a breath. Okay. What do you think, Lauren? Should we talk a little bit about gang sharing on the plot side? I know quite a few folk have already started jumping in. I think so. Yeah. And this is something that's been super exciting to watch. And I'm really looking forward to seeing it build over the next couple of weeks as well and just seeing how other folks are, what you're looking at each day, right? Because I think so many times when we're meeting in these sorts of environments, Mary, and I can see your background, I can see the plants and, you know, the frames behind you, but I'm not seeing what you're looking at each day. And so I think the spot could be a helpful way at that. That's right. Well, for everyone who has heard me before, you probably know that I have a little four-legged working companion, Posi, who is on this plot and a big part of my hybrid working environments. If you ever see me do like this during the recording, this is me batting off an open, enthusiastic puppy, who is now 18 months old, but she doesn't quite know that. Oh, someone joining us for the recording as well. Super well-behaved recording dog. Oh, awesome. Okay. So just to wrap up with the welcome post, I just want to make sure that we just touch base on what you can explore from that, if you haven't already done that. Have a look at building connections with virtual teams, which is where we have a little chat at the OER 22 conference earlier this year. I'm setting out some of our thinking and some of our inspiration, which ultimately informed the shaping of this course. And then one of the things I want to jump into a little bit later on in this session is for us to come round to exploring most of working, which is from leading virtual teams, which is a book I've written on hybrid working. And so hopefully we can explore it a little bit with folks today and see how that can be applied to their context. Absolutely. So yeah, I'm looking forward to getting into it as well. So did you want to start first then jumping right in today and chatting about the article that folks might have had a chance to read before today's session? And if not, we'll make sure that the links are all available as well. I think the article that we're discussing is when do we actually need to meet in person? Right. Yeah. Thanks, Lauren. And every week in our sessions, we are going to bring in some different perspectives and voices from different communities. So hopefully give you some inspiration to look outside of your immediate environment and have a little bit of a think about how what you do relates to what's happening across the sector or indeed in a different industry. So the article is really about thinking about that sort of old bubble of, does this really have to be a meeting? Am I just sitting here wasting my time? This meeting could have been an email. And kind of moving on from this kind of experience, which I think we can all relate to, to thinking around what sort of thought processes and decision making processes do you ideally want to have in place in order to decide can you meet online? Is it an email? Are you going to have to meet in person? And so the article goes and explores whether meetings are relationship based, for example, team building days or maybe conflict resolution or task based. So for example, developing a curriculum plan or delivery plan for a new course, considering how complex the objectives of the meetings are. And then it provides a really handy illustration where it sort of shows where, you know, if, for example, it's low complexity and the goal to be accomplished is basically information transfer. Maybe you don't need to meet at all. Maybe it could be an email or maybe it could be online. And then thinking about sort of how to make use of hybrid formats and then suggesting where value lies in meeting in person. And one of the reasons why we've included this in this week's sort of hybrid working unpacked is that I think it can be a lot more nuanced, the hybrid working experience than, you know, basically like you have a Slack maybe or a different instant messaging service and just kind of say, okay, there you go. That's it now. Problem solved. It's a little bit more complicated than that. And I hope this article can start us thinking around those considerations. So Lauren, do you want to jump in here and what are your thoughts on this? Yeah. Thanks, Marin. I read through this article a few times now because I think it makes a lot of good points, but I also have maybe some critiques based on my experience working in a remote setting and leading a virtual team that, you know, really does try to prioritize connection and striking that balance between, okay, less is more in terms of meeting and trying to avoid meeting just to meet, but also knowing that, you know, if done right meetings should be prioritizing that connection. And that's really important for that work to happen.  But I think one of the first things that I took away from the article was right in the beginning, I think the quote was without the ability to bump into one another in an office setting, you have to schedule every interaction. And that really resonated with me because that hits it right on the head in terms of how we have to think in our Slack environment. So to kind of back up for a second, reclaim is entirely remote. So we use Slack as our primary virtual office space. We do have email, but that's not something that we really try to use to connect. And then we also have Asana as our transparent to do list space, and we'll get into more of the tools and how we work with those next week. But I think for the purposes of where I wanted to start today, it was thinking about how we're scheduling that time for connection, because you're right, you can't just bump into someone in an office setting and say, oh, yeah, you know, how was your weekend? Or, you know, how did that go for you?  Like you can't have that same pulse on your team. And so that's really done through meetings for us, and also through Slack connections. And so I think one of the ways that I try to combat that idea of not meeting just to meet, but also knowing that it is important is to have helpful pathways in place for unscheduled connection. And for us, what has worked in the last many months, I would say, so Slack huddles, we're just recently introduced quite a while ago, but they've been really helpful for our team to just say, hey, you want to jump on a quick call and just, you know, talk about this or, you know, look at this issue together. We've also recently started doing kind of this impromptu working hour where there's no real agenda. It's not a meeting in the same way where we don't have things to get through. It doesn't have to be efficient. It's just a chance for our team to jump on a call and work alongside each other. And the conversation can go wherever it wants. And they're completely optional to join. It has nothing to do with, you know, again, performance or anything. It's just a chance to connect. And then we also try to you know, integrate different mediums of connection as well. So radio shows or podcasts, discord chats, we've even started doing Music Mondays where someone can control the podcast, or not the podcast, but the playlist for a while. Just again, trying to get at that idea that everyone connects differently. They learn differently and they work differently.  So, but listening to a playlist and tuning in and saying, like, oh, yeah, I love that song and sharing a gift and Slack or something. That is another way to connect to without being on a meeting. So I know that's kind of a lot. But Marin, I just wanted to throw that out as sort of a first maybe point of conversation just around scheduled versus unscheduled connections. I think that's a really important point and a really interesting insight into, you know, how you're trying to blend, blend those different modes of interaction. When you were speaking, one of the things that came up for me and that's also related to the article is that, you know, in higher end, I think there is a really broad spectrum of expectation but also ability. So I think we're seeing everything from folk who are kind of like scheduling meetings in person again, because that's what they used to do and they don't have to be online if it's safe to meet in person to, you know, institutions who are adopting kind of really quickly like policies to say, like, oh, you can now work from home like any day you choose, but you have to be in for this day. And I've had so many stories of folk who are like, I'm in my office, there's no one else here, or, you know, which kind of totally negates the whole point of going anywhere to connect with a beauty only person who choose Fridays, then, you know, there's no one there to connect with. And that is, I think, a really good example of why this requires thought, right? This isn't kind of going to be solved by in the long run, it's not going to be a good experience by not being designed properly and similar to, you know, how we design student interactions online. It's always, you know, we need to learn from virtual learning and for virtual working and really start to curate those experiences. And just before you jump back in, I think the big factor here is also skill and confidence level. So, you know, in order to be informal using technical technology or tools rather, you need to have a certain comfort level to kind of, you know, use different tools to jump in on radio shows or Slack channels. And these tools also need to be available.  And yeah, if you have some thoughts on this, please put them in the chat or share them with Discord. We'd love to hear your experiences there as well. Absolutely. And I think while folks are writing in, you know, one of the things that I was thinking about while you were talking, you know, I've taken meetings with folks from other schools that say exactly that, that they're in sort of this hybrid working schedule at the moment. And that means that their colleagues, you know, they're on alternating shifts about who goes into campus on what days. And so as a result, you more than likely are always still, you know, working with someone who is remote, right.  So yeah, I think that that's definitely the challenge. And I thought that the article did a good job of trying to, you know, elaborate just on how putting together and facilitating virtual events or hybrid events, especially is so challenging. It's something that Reclaim has really struggled with in the past.  But anytime we're running an in-person event, and Marin, I know you can probably relate to this, the question is usually, well, can I tune in remotely? And that, you know, it completely changes the game. And I think that the author of this article, you know, hit that on the head, basically saying that if done incorrectly, you can really sideline or alienate those virtual participants. And so until you have that done right, and you know you can do it right, it's, you know, it can be kind of a gray area for sure. That's such an important point. I wonder whether we just take a couple of minutes to think about the language we use to talk about these different ways of working. And I wanted to maybe share one of the documents we already put into this week's post, which is a document that we can use to start thinking about how we use these different terms and what different modes of working we're talking about. So I wanted to also use this to reflect on, you know, this really not being a new thing. Like digital technology is kind of incidental to working from home, which is, you know, historically speaking, a very long tradition. If you really think about, you know, like individual craftspeople or small industries over 100 years ago, working from home used to be a very normal thing. And having, you know, having your own workshop or specialism in your own and living there was not an unusual thing. So it's not a kind of completely new concept. But I think during 2020, in particular during the pandemic, it took on a very contemporary meaning. And it's worth, I think, stepping back from that and having a think. So throughout this course, we're going to try and use these different terms to describe different modes of working. So home working, the practice of working from home, hybrid working, working both at home and from office or from on campus, working as a virtual team. So this could be a whole blend of different modes of working. But the primary way of working is digital workflows and communications. I think Lauren, I think your team would be a great example of how you describe that. There's also distributed working, which folk who work for larger institutions in particular might really identify with. So if you have different campuses, this doesn't necessarily have to be, you know, facilitated by digital means. And if you think back about the old days of like the UK's Open University, for example, where, you know, mailed out assignments, constituted kind of work and study, or, you know, also radio and TV, it doesn't necessarily have to be digital technology that's used to facilitate distributed working. And then also remote working, which I think many of us are experiencing is all around a central hub, such as a compass or a company HQ. And I think it's important to consider whether this applies to you, as well as being a hybrid worker, because very likely if you're working in higher ed, you're working through to a central hub where things, people, resources are located. And a lot of institutions have policies that are kind of designed to envisage everybody being in the same place and working in the same way, rather than being able to reflect the kind of broad reality, which is much more messy and much more complex. So thanks for sharing that, Lauren. I thought it would just be helpful to kind of unpack that a little bit. What are your thoughts on those different terms? And what is your experience of that? Yeah. And let me just pull the visual back up because I find that it's helpful just to have something to reference while we're talking about them. I think, for me personally, the work that I am most familiar, I feel like I have worked in many of these modes at various points. I would say now I'm in the home working category for the most part. I work every day from my home office. That's where I am now. And so my commute is really waking up in the morning and going into the office or going to a dedicated work zone in my house. But I have also been in that hybrid working model where I've spent a couple of days working at our Fredericksburg office and then one or two days at home. Obviously, I'm a part of a distributed team and that folks are working across various locations, various time zones, and that's something you have to take into consideration as well. And then working as a virtual team right there with you as well. So definitely feel like I can relate to many of these just in over the course of years working for Reclaim. And they do come with their own challenges and benefits too. Well, we'd really love to hear what your thoughts are. Which of these modes of working have you experienced? What is currently dominating your experience of work? And Lauren, I think just before we jump into kind of a more practical part of this week's session where we're going to start actually working together and collaborating together. I just wanted to kind of ask, in terms of like how things have changed for you for the past sort of two to three years, what would you say is kind of like the thing that you reflect on that's sort of like a big difference? And just to share my example, I think before the pandemic hit, I think many people when I said, oh, I don't have an office or I'm based from home, they were like, really, you know, you're not, you're not, you're not somewhere, what's your address like, like registering a mailbox without a physical office address was quite difficult. So I think many people were, were quite sort of surprised. And even if they were familiar with the idea of home working, they didn't think this was a dominant or prevalent way of doing things. And now when I tell people that I'm working from home, they're like, oh, yeah, well, so do I, you know, and I'm basically, I've got my laptop, I've got the kitchen table, you know, there's dogs, kids, complete chaos very often. And or, you know, there could be like a bedside where I'm kind of sitting in this corner. And, you know, a lot of folks now have the sense that the sort of emergency response to not being able to safely go and co locate with other colleagues is kind of the reality of, you know, hybrid or home working long term. And I think that does worry me, because for a lot of folks, that is not the ideal situation. And there should be more support from an employer point of view, but also support for skills development. So that is one of the things that does kind of worry me at the moment. Yeah, I think you raise a really good point. And I saw that that kind of coming through the article even as well, like, I think the author at one point was saying, you know, instead of doing another meeting, the supervisor now records the updates for the week, and that gives folks the flexibility to listen to it as they're going on a jog or making dinner. And I immediately was, my red flags went up, because I think just because we have the benefit and the flexibility of being in a home working environment and don't get me wrong, that's great.  And then you're also switching off and leaving work, even if it's just leaving your desk or leaving your working zone or whatever that looks like. And so I thought that that's where that article was a little problematic because I don't want my colleagues or the folks, you know, if I've given someone directives for a project, I don't want them doing that while they're making dinner. Absolutely not, you know, so I think like having those boundaries are still really, really important. And I think also what you said just about knowing that, okay, we're going to have to ramp up our technical skills in order to use these tools, you know, for a successful working working environment. That's really important too. And I think over the summer in particular, we've spent more time as a team in that strategic space, thinking about time management, thinking about, you know, navigating and working on meetings, as opposed to just focusing on the content or, you know, the professional development technically, right? But actually spending time developing and improving on just how we're working. Because I think ultimately that does make us more successful, you know, employees on our own paths, but also as part of a larger team. And also, you know, personally with our mental health, I think that that's that that has to be prioritized and it can't be overlooked in these settings. So that's something that I, you know, I'm really excited to continue chatting about as well. I'm not sure if that's where your head goes with this type of conversation, but that's definitely where I'm thinking. I really hope that all of you, you know, joining in for this course will have similar thoughts and priorities, because that's what, you know, Hex for Hybrid Working is really all about. It's meant to give you ways to think about things, practical approaches, tools, resources to kind of start reflecting and starting to get a sense of which parts of how you currently work, work for you, not just today, but long term, and which don't. And there might be some aspects that you don't have much control over. There might be others that you do have some control over. So I think we're probably ready to jump in and talk about our practical exercise for the week, because this tool is designed to help you do just that. And it's called the Wheel of Hybrid Working. And Lauren and I are going to demo that for you now and share a template, which is also in this week's post and also talk you through every step of the way and how to use it and what you can do with it. So we hope that hybrid working will fit many of you, but this template does contain versions of all different ways of working. So if hybrid working doesn't feel the ideal fit for you, then just choose one of the other ones. And you can also try and do more than one, see if you get different results, if you have different reflections. But the way it works is the same for everyone. So we are going to use this example to just share how it works and what to do. You can either complete this template digitally and download it, either use it in Google Slides or PowerPoint, something like that. You can print it out. Hopefully you can adapt it in whatever format works for you. And if you want to take this completely offline, just with pencil and paper, you can absolutely do that too. We hope that some of you might feel comfortable sharing your thoughts and results with us on Discord. But also if you just want to keep it to yourself, the point is really that you should try and reflect for yourself as honestly as you can. So the wheel is divided into eight different areas. And many of you maybe come across a similar tool called the Wheel of Life or familiar with that. But the idea is really to reflect on different common areas that impact on the way we work and to try and give them a score. Now in this example that I've completed ahead of time, I've put some example scores in. And ideally we want you to assign a score from one to 10. Now if you assign a lower score, for example one, two or maybe three, that would present an area which is challenging for you or which might require attention. If you have a high score in an area, maybe a seven, eight, nine or even a 10, that would represent a way of working, which is currently working well for you, something that has a positive impact. And there's also a blank space for you to add your own categories. Eight categories is quite a lot to reflect on, so hopefully you won't need to add more. But if you have a burning category that you really want to add, and just please use the space provided and add one in. Now I want to say a few things about what it means to have a low score or a high score. So in the example I've shared, socializing with colleagues is a score three, and that's the lowest score on that board. Also collaboration, which is the category I added, has a low score, which is four. Now you might be an introverted colleague who is not so keen to do a lot of socializing with folk after work. You may be quite happy to be socializing on Slack and leave it at that. You might be quite happy with the score of three for socializing with colleagues if it's not an important category to you. A low score doesn't mean that you necessarily want to take some action. On the other hand, if, for example, work-life balance is super important to you, seven might be not a good enough score and you're like, oh, I think it's only a seven out of 10. I would like it to be a 10 out of 10. This is the thing I'm going to focus on for the next four weeks. The wheel isn't about judgment or performance. There are no right or wrong answers. If you give low scores across the board or high scores across the board, there's no right or wrong. The main purpose of it is to help you reflect on how you feel it's going and to just give you that moment to take a breath. In a minute, I'm going to come to you, Lauren, and see what areas you identified and what your scores were and see what you might want to share with us. Just to emphasize, we are going to be using this hybrid working wheel as part of our roadmap. In next week's sessions, we are going to show you exactly what to do and how to do that, but hopefully it will help you identify one or maybe two areas that you particularly want to focus on throughout the course.  What are your thoughts? Have you identified any areas you want to be focusing on? Yeah. In preparation for this course, I have to say that I've cheated a little bit and I cleaned up my workspace and definitely set the tone a little bit and knew that this is where we were headed this fall with this conversation. I've been thinking about my work-life balance and my physical and mental health and things like that and really reflecting a lot this summer in particular. For me, I would say that when I was taking a look at the working wheel, the commute for me was actually surprisingly low and that people might be like, Lauren, your commute is 10 seconds. How could that be low for you? I am a night owl. I do not like waking up in the mornings. For me, working from home has been great because I can sleep to the last minute, but I also know that I'm much happier if I wake up earlier and I start my day and I give myself time before work to make coffee or go on a walk with my dog to read the news or whatever. That is something that I would like to improve on in the coming weeks is just being really intentional on building that more into my schedule and actually making a commute, even if it's mentally to work. That's something that I'm particularly interested in doing. I also think for me the work-life balance has been tricky in the past because even though my day will end and I create those physical boundaries for myself and I leave this room and I do other things, I'm still thinking about work or that's something that has been a struggle for me in the past where I can't turn my brain off and then I'm thinking about my to-do list or what I'm working on the next day or things that I'm maybe just unsure about or something like that and I just mull through these ideas in my head and to the point where I'm still mentally exhausting myself even though I'm on my own time. That's something that I've really tried to work on particularly this summer and it's something that I am still going to be really focusing on in the coming weeks as well as just making sure that I'm setting up good habits towards the end of my day or at the beginning of my day where I feel like okay I've got a plan for the next day so there's no real reason for me to be thinking through all of these things on you know through the evening. I'm not sure if you can relate to that. Yeah I think everyone in the room can relate to that. I would be very surprised if there were a folk in a room said oh no I've never had that problem. I've never thought about work after 5 p.m. I would say like work-life balance is tricky so like you I've worked so hard at this and tried all kinds of different strategies for making sure work-life balance kind of does exist and has a balance but yeah the last few years I just feel like every time I figure it out there's like a new emergency or a new context in which you know I need to reinvent that all the time and one of the things that this really makes me reflect on is how much my approach to working in a hybrid kind of workplace is evolving over time. It changes a lot through circumstances you know in my life like last year when I had a puppy it was incredible like the amount of time that took like out of my working day and you know the amount of things that got destroyed not just the dimension but I think that was really tough and I also highlighted collaboration and I would be interested to hear what folks experience as that is so at the moment my in my team and my immediate team I have a whole range of colleagues who have started working with us very recently who've worked with us for many years so some of them have been you know seeing us through the pandemic some of them joined us beforehand and I think it's really difficult for folk to continuously upscale and adopt new tools like we're just about to adopt a tool like Asana and I already know that half of my team are going to be like really really I am so busy it's just really necessary that I'm learning a whole new workflow which is going to completely change how I manage every project and I think the bigger your institution the more work it is to kind of get that sort of collaboration in the tools for collaboration like across everyone and also to update it continuously. We are a Google Apps for Education user and you know boy is it unhelpful that they iteratively release updates without notice what I tell you on the data like hey did I hang out it's completely different and you're like oh my meetings just disappeared so thanks for that so yeah I think this is where you know big tech is super unhelpful in the virtual workplace. Well yeah so a couple of things to say to that one you know tool fatigue I think is just as real as needing fatigue where it's like oh you know everybody has this new platform that's just going to change the game and I you know I think you know some of them are very valid and have a real purpose but it has to be helpful for you it has to be a natural part of the work that you do and I think anytime you're talking about using a new tool or platform it needs to aid not take time to use you know where it's like if I've got to stop what I'm doing and go input data in here just to check a box that's that's efficient for no one right but if it's actually helping me you know by collecting things so I'm more efficient or something you know there might be a real purpose there but yeah I completely relate to the idea too of you know then okay you become ingrained with a tool and then suddenly they change their entire entire model and you know you realize that everything you were leaning on is now like you know feeling a bit rocky we're feeling that even with cPanel and WHM at the moment and that's something that we can talk about more next week as well where we're now faced as a team with okay all of our training all of our documentation is built on cPanel and WHM looking a certain way and they've completely thrown that on its head and so not only are we having to relearn where things are but we have to be experts enough to teach others and then we have to update you know so much documentation that it's just we have a mountain of work in front of us and so that's definitely something to think about when we're talking about collaborative tools for sure but I agree I think collaboration in general is something that I could probably you know do a better job you can always improve for that category for sure and I think reclaim as a whole does a great job of collaborating on projects in fact it's something that I'm really proud of because I think our teams can jump in on so many different projects and work cross-functionally which is wonderful you know but it can still be a challenge sometimes in virtual settings where you do feel rather isolated you know I look around by myself you know and so building that time to collaborate is an intentional choice as you said it's we have to be intentional about setting up working environments for these priorities. One of my favorite experiences of sort of you know collaboration fails is like a few years ago a colleague was showing me something on a spreadsheet and you know I'm a I'm a good spreadsheet user you know I'm not like amazing but I'm skilled and we were like online for like an hour sharing your screen talking about it I just couldn't do it and then in the end it turned out that he was just pressing a keyboard shortcut and he was like this is so obvious obviously you know that you press this button and I was like this is not a keyboard shortcut I've ever come across so keyboard shortcuts is one of those things where if you're sitting next to someone it's the most obvious thing in the universe but if you are remotely desktop sharing magic it is it is literally magic it just appears and you're like wait it can't replicate this and it's one of those examples where you know you can frustration and kind of you know miscommunication can so easily creep in and like someone leaves the meeting thinking well you know I'm really failing at this and the other person leaves thinking my god you know how can you not get this like and and you know these things can go wrong and spiral very quickly um so the question really just to come back to our hybrid working real and I know that many folk in a room will want to kind of share their own views and thoughts it's really to just think about the overall picture and once you've completed it reflect on the scores and just have a think and say okay which of these scores would I like to change um it may be a high score that you want to even get better it may be a low score that you want to increase or you may not decide that um something needs change but there's something you're really curious about or really frustrated about or something that you wish you could do something about even though within the practical constraints of your working environment or higher ed um environment you're working it's not as easy to change all that so in whatever mode you're completing this um do you try and pick one or two things that you want to focus on um and that's one of the things we're going to use for next week and I know Lauren we're nearly at the time where we're going to start our roundup and reminding folk of what's coming up next week so are you ready to jump into that sorry I can't hear you you know I I can't believe I did that I've tried really hard not to to at this point you know in the game but here I guess it's unavoidable but yes that sounds great I'm really looking forward to uh following along with the the working wheel over the next course of sessions um and looking forward to just continuing these conversations in the discord chat and also later this week as well um you know where we can just check in on how folks are getting along with that um and also just continue these conversations too around you know hybrid working in general and maybe we'll chat about the article and all good things so yeah you want to take us from here maren yeah definitely we want to encourage you all to keep posting on this blog site um I want to see pictures of coffee cups and dogs cats maybe you'll commute whether that would be a staircase or maybe it's a water campus or maybe something completely different um that makes your hybrid working environment special um I know of a few folk who've got craft items in and around their offices you know cushions maybe posters have sports equipment unreliably informed that at least two people I know have vinyl setups in their offices so you may decide that something that we haven't thought at all about is important to you and we hope that you'll share it with us so that we can all have a look at this sort of tapestry of hybrid working as it is developing yeah I have to say too I'm I'm really interested in seeing people's um desk layouts something that our our team at Reclaim talks about all the time I think Meredith put out a big blog post on it recently and I know Taylor just recently uh put out a tweet and he's got you know a vertical monitor and all of his radio you know things set up as well so um and Jim meanwhile is living in an arcade basement so you know I think everybody has their own setup and I'm really looking forward to seeing how people use um these tools to work for them so well I've got a small fun fact before we jump into what's in store for next week um the area around your desktop um that you're looking at is called a geekosphere and there's an interesting research article about that that I'm going to share on discord so if you're um into that sort of thing there is the research for you out there that I'll be sharing with you there are people watching this who are interested in that believe me so that's I'll be seeing you on discord and we can have a lot of conversation around that I'm looking forward to it great so what's up for next week so next week um we are going and focusing on tools and platforms um one of the things we've reflected on a lot when designing this course is how important the relationship is between us as human beings and digital tools particularly when it comes to hybrid working and virtual working so I know that Lauren you're really passionate about next week is there anything in particular you think folks will be looking forward to um so I just was writing this a little banner while we were talking here um but yes I'm super excited for next week this is kind of my bread and butter just thinking about how we're using these digital tools to work best for us and not just integrating a new tool because it looks pretty or we you know just because right we need to be really particular about what we're using I'm also excited just to you know think about you know how we're storing our data how we're you know if you think about cleaning up your office space it's just as important to clean up your virtual space too and so yeah definitely looking forward to getting into next week and just reflecting on how we're using digital tools to work for us and in case you know you're arriving here kind of super stressed from the start of term and you're like I really don't know what is this all about I need help well help is at hand because we have our weekly Q&A session coming up on Friday um so just drop in um we're going to be there to answer your questions if you have any problems completing the template we can help you with that and also if you just have any other thoughts comments questions um things you want to share do please join us on Friday I'm really looking forward to that conversation definitely and the thing I'll also mention too just because I know the hybrid working wheel can get into some personal concepts as well and so if you're wanting to ask a question but anonymously that's also fine too you don't have to put it in the public discord chat uh just you know write it to us privately or send it an email or in a twitter dm or somewhere else and we will highlight the question without highlighting you so that's something that I'm interested in and and you know continuing on this week as well absolutely um yeah feel free to share what you feel comfortable sharing and keep to yourself or share with us privately um what you don't want to be in a public channel but yeah keep those photos that you are happy to share um going on in our hybrid working spot sites awesome well thank you Marin uh for joining this first session we look forward to chatting with folks uh in the discord chat this week and on Friday so we will see you then thank you see ya


Hi, I'm Zor. Welcome to a new Zor education. Continuing building different graphs related to trigonometric functions, today's term is for secant. Secant is by definition, as you know, one over cosine of x. That's secant. Now, before addressing any individual problem which I have here, let's talk about secant itself very briefly. Now, considering this definition, and considering that cosine looks like this, where this is pi over 2 minus pi over 2, 0, y, x, pi, minus pi. One over cosine of x obviously has asymptotes where the cosine is equal to 0, which is pi over 2 plus pi plus 2 pi, etc., or minus pi minus 2 pi, etc. So these are asymptotes for then how it looks. Well, let's consider from 0, we move let's say towards the increasing argument x. At point 0, cosine is equal to 1, and obviously, inverse would be 1 as well. So this is a starting point. Our secant will grow because cosine goes down to 0 being positive, and this is denominator, which means one over cosine would go to plus infinity in this particular case. So let me just draw it this way. It goes asymptotically goes to this vertical line through pi over 2, and same thing goes here as well. Now, in this interval, everything really is similar except it's negative. So from minus 1, inverse to minus 1 is minus 1 obviously, and then it goes again since cosine goes to 0 being negative, one over cosine goes to infinity but again negative infinity. So it goes this way, and same thing here, and in this case on the positive side, so that's basically the graph of the second. Second is the black ones. Now, let's talk about properties. First of all, cosine is an even function. It doesn't change the value if you change an argument from positive to negative, and obviously, it stands exactly the same way for an inverted cosine, which is secant function is even. It has exactly the same value for positive as well as negative argument of the same absolute value, and that's why the graph is symmetrical relative to the y-axis. Now, does it have zero points? No, secant never equals to zero. It goes from either 1 to the positive infinity or from minus 1 to the negative infinity. So the range of this function is a combination of two intervals, this and this. Now that I'm using square bracket here and parenthesis here, meaning the end is not included because obviously the end is infinity. So it's a symbolical representation that obviously goes to infinity, obviously it's never reaching it. Same thing here. All right, so that's the range of the function. Asymptotes, yes. Asymptotes are where the cosine is equal to zero, which is pi over 2 plus pi times any integer number, positive or negative. Maximum and minimum? Well, there is no absolute maximum and minimum, but there is a local one. On each interval, there is either minimum on this interval, which is one, or maximum on this interval, which is minus one. Now let's talk about graphs. So the first example which I have is y is equal to second of minus x. Now, second is an even function, and as we were just talking about, which means second of minus x is exactly the same as second of x, right? So this is the same as second of x, and the graph is obviously the same. And as you know, the graph is something like this, where these are asymptotes. And this is minus pi over 2, and this is pi over 2. And this is 3 pi over 2. So that's the graph. That's simple. Now, how about second of 3x? Well, second of 3x, as I have explained in many previous lectures and in a general lecture about graphs of the functions, whenever you multiply an argument by 3, it means that the graph is squeezing towards the y-axis, which is, in this case, this one. So along the x towards y, towards 0, y, the simple explanation is if you have a function and point AB belongs to its graph, it means basically that B is equal to f of A. And then you have a function of 3x, then obviously 1 third AB would belong to this particular graph. Because if you substitute 1 third A as an argument, you will get f of A, and you know that f of A is B. So that would be B. So for each point AB of the original graph y is equal to f of x. There is a point with coordinates 1 third AB to the function which has a 3 multiplied by an argument. So this point 1 third AB is different from this one by its x coordinates 1 third, which means it's squeezed in 3 times. So if my asymptotes are p over 2 minus p over 2 and p over 2 and 3 over 2, then my new asymptotes would be, instead of p over 2, I would put p over 6 and p over 6 here and p over 2 here. So everything is divided by 3. So that's basically the graph. It's just changing the scale if you wish. So it looks exactly the same. Just asymptotes are spread apart, not at pi interval from pi over 2 to 3 pi over 2 to 5 pi over 2, et cetera. But it's spread at pi over 3 in 3 times less interval. So the asymptotes are at intervals of pi over 3. From minus pi over 6 to pi over 6, from pi over 6 to pi over 2, et cetera. But the general shape remains exactly the same. Next. Next is, instead of multiplying by 3, I will multiply by 1 third or divide by 3 if you wish. Well, obviously, the transformation of the graph is similar, but instead of squeezing, you have stretching. Because again, if function f of x has a point a b, then f of 1 third x has a point 3 a b. So this means that b is equal to f of a. And if you will substitute this into this, 3a into the x, you will have again a. And you know that f of a is b. So this particular point belongs to this graph, which means the y-coordinate is the same, but x-coordinate is three times further. Now, when I'm talking about further, I'm talking about stretching from the 0 point to the right and to the left. So again, my original asymptotes were pi over 2 and 3 pi over 2. Now, my new asymptotes would be spread three times further from each other, which means that this is supposed to be 3 pi over 2. This is supposed to be 9 pi over 2. And this is supposed to be minus 3 pi over 2. So the difference between them from minus 3 pi over 2 to 3 pi over 2 is 6 pi over 2, which is 6 pi over 2, right? Which is 3 pi, right? So used to be pi, now it's 3 pi, the distance between different asymptotes. And from 3 pi over 2 to 9 pi over 2, it's also 6 pi over 2, which is 3 pi. So these asymptotes are rarer, three times rarer. So that's the graph again. It's the same shape, just different scaling along the x-coordinates. OK. Next is, again, very much like it, but stretching would be instead of horizontal, it would be vertical. So the function is 3 secant of x. So now we are multiplying the function by 3, not the argument. Now what happens? Well, we used to have minus pi over 2, pi over 2, 3 pi over 2, minus 1, 1. Now what happens if every value of the function I will multiply by 3? Well, obviously the function will be stretched vertically. Now in this particular case, if I will use this example, what does it mean? It means that if I have a function 3 f of x, then a 3b would be a point of this function. Indeed, if I will substitute a into this, I will have f of a. But f of a is equal to b according to this. So the times 3 would be 3b, exactly. So what I'm saying is that if point a b belongs to this graph, which is b is equal to f of a, then this point belongs to this graph. Because again, 3b is equal to 3 times f of a, which is b. So it's 3b. Now what does it mean? It means that the graph is stretching vertically from the x-axis up and down. So this would not be 1. This would be 3. And this would not be minus 1. This would be minus 3. And the whole graph would go vertically a little steeper. But what's important is the asymptotes will remain exactly where they are. So the graph would be steeper. It will start from 3, and it will go three times faster up to the infinity, plus infinity or minus infinity. But it will be still within the same asymptotic boundaries. Next, secant of pi over 2 minus x. OK. Now, let me convert it slightly. Again, based on the fact that the secant is even function, which means it doesn't change the variable if I change the sign of the argument, I would rather use it as a secant of x minus pi over 2. So I inverted the sign. Now, what is this? Let's go back to this general function, general properties of the graphs. If I have minus c, what happens to the graph? Obviously, a plus c comma b point would belong to this graph. Why? If a b belongs to this, which means b is equal to f of a, that's given. Now, this point, a pi by cb, if you will substitute it instead of x, a plus c, and minus c would be f of a. And that's equal to b, exactly. So for each point of this graph, there is a point which is shifted to the right by c. Well, right if c is positive, if c is negative, it's to the left. So in this particular case, minus c, this is minus pi over 2, so everything is shifted to the right by pi over 2. What does it mean? It means that the graph actually remains as it used to be before, which is this is 1 and minus 1. But everything is shifted to the right by pi over 2. So this asymptote, which used to be at minus pi over 2, now will be at 0. So let me just draw another one. So now I will have a 0 asymptote. And then instead of pi over 2, it will be pi. And then 2 pi, et cetera. So these are new asymptotes. But other than this, from 1 and from minus 1, other than this, asymptotes, they direct. Basically, they restrict these lands of this. But other than that, behavior is exactly as it was before. So only shift to the right by pi over 2. So the asymptotes are changing, pulling the whole graph to the right. Now, a combination of all the above, just to make sure that everything is in place, as far as we understand it. So the combination is y is equal to minus 1 third secant of minus 3x minus 3 pi over 2. OK. How to deal with this? Well, we can deal with this in steps. We know how the graph is transformed on each elementary transformation of argument or function, et cetera. So let's just transform it in this way. First, I would draw secant of x. Then I would draw secant of 3x. Then I will draw secant of 3x plus pi over 2. Then I will draw secant of minus 3x plus pi over 2. And finally, I will multiply the whole graph by minus 1 third. Well, I can do it first by 1 third. And then minus 1 third. So a chain of these transformation will lead us to the final graph. But let's just summarize how it would look. Secant, we know what it is. Secant of 3x, we also actually did. It's squeezing of the graph horizontally along the x-axis towards 0 by a factor of 3. Then I add positive number, or subtract negative, if you wish, which means I'm moving to the left, the whole graph by pi over 2. Then I change the sign of the argument. But secant is even function, so it doesn't change the graph. So from here to here, there is no difference. Then I multiply graph by 1 third and we already did something like this. It means I'm squeezing the graph vertically by the factor of 3 towards 0 along the y-axis. And finally, I multiply it by minus 1. When you multiply the graph by minus 1, whatever was positive becomes symmetrically negative. Whatever negative becomes symmetrically positive. So graph is just turned this way. All right, I can do it relatively quickly, I hope, without much detail. So if you have, right now, we have from minus pi over 2 to pi over 2, pi 3 pi over 2, 2 pi. OK, so let's do this. And this is 0, obviously. So we start with, OK, this is minus 1, this is 1, and this is minus 1. So we start with this picture, that secant. Times 3 for x, that squeezes everything by a factor of 3, which means this becomes 2 pi, OK, let me just write it this way. This becomes 2 pi over 3, this becomes over 2, this becomes pi over 3, this becomes pi over 6, and this becomes minus pi over 6. So that's after this. Now we should move the whole graph to the left by pi over 2. So 0 was here. Now when we move it here, this would be 0. So the new graph would be like here. 0, and then you have pi over 6 to the right, and pi over 6 to the left. And these are new, wait a moment. Did I shift it? No, I'm sorry, I think I mixed that a little bit. Yes, that's not supposed to be 0. I started from this, this is, I didn't shift it yet. This is already a shifted variant. OK, let me start in the beginning. We should start with 0 and minus pi over 2 and plus pi over 2. And these are asymptotes, so it goes like this. Now this is pi and this is 3 pi over 2 and this is 2 pi. So the next is this. OK, now when I squeeze it, that's pi over 3. This is pi over 6. This is pi over 6. This is pi over 2. And this is 2 pi over 3. That's how I squeeze it by a factor of 3. Now when I move it to the left by pi over 2, so this point goes here. OK, so my 0 becomes an asymptote. OK, my 0 becomes an asymptote. So on the left and on the right, I will have this. And this is pi over 3 because asymptotes are now every pi over 3. Used to have asymptotes every pi, but now since we multiply by 3, every asymptote is the distance of pi over 3. So that's how it will be after this particular transformation. Now after this, nothing's changed because function is even. So if I change the argument, nothing changed. And all I have to do is multiply by 1 third, which means whatever used to be 1 now will become 1 third. And this was minus 1, so now it's minus 1 third. Because everything is squeezed in this way. Obviously, I didn't do it in a scale. My minus is definitely smaller than my plus. So this is my minus 1 third, so the graph is minus. So that's how the graph looks like. It's period is instead of 2 pi, the period is 2 pi over 3. The asymptotes are after each pi over 3. The minimum, local minimum is 1 third. And local maximum is minus 1 third. And these are asymptotes, so positive and negative, et cetera. And then the whole thing repeats, obviously. So you have something here and here. So that's the graph. Well, it might be a little more complicated. But in theory, the most important is to represent the complicated problem as a consecutive steps, each of them is not really complicated when you are familiar with this. OK, we have a couple of more problems related to graphs. This one is y is equal to secant of 2x plus secant of minus x. OK, so let's just add two graphs together. Now, we know that secant of x or secant of minus x is exactly the same thing. And we have pi over 2. Let's make it wider. Pi over 2 minus and pi over 2 plus. That would be pi. That would be pi over 4, 3 pi over 4, minus pi over 4, minus 3 pi over 4, and minus pi. So asymptotes of this guy are, as usually, from minus pi over 2 to plus pi over 2. And this is one. So that's this guy, this one. How about this one? We already talked about that the whole graph would be squeezed along the x-axis horizontally towards y-axis by a factor of 2. So let's just draw the second one. Now, it means that in this case, the asymptotes would be also squeezed in from pi over 2 to pi over 4. So these are asymptotes. And next asymptote was 3 pi over 2, right? 3 pi over 2 and minus 3 pi over 2. So everything is shifted. So we squeeze this one and let's squeeze this one. It would be 3 pi over 4, right? So that would be this one, another asymptote. And 3 pi over 4, OK? Now, what does it mean as far as our graph is concerned? Well, this piece would be here between these two guys. And this guy would squeeze in between these two. And this piece would also squeeze in between these two. So we have to add brown to red. OK, let's do it. In this particular area in between these two things, obviously we start with 2, because 1 and 1, we will add together would be 2. And then 1, the graph goes a very limited way. And another goes to infinity, which means we will have going to infinity relative to the same two asymptotes. Obviously, asymptotes would be the most frequent one. OK, this is this piece. Now, let's move on here. In this case, the brown one is very limited, but the red one goes to infinity. So on this side, the red one is limited, and the brown one goes to minus infinity, which means that the graph should be something like this. It's plus infinity here, and then gradually going down to minus infinity. If you add this red to this brown, in this case, the red prevails with a plus infinity. In this case, brown prevails with minus infinity. So the graph would go like this. And obviously, similarly, it will go the same way here, because it's an even function. So this red piece and these two are the sum of these two graphs. And then the story actually more or less repeats itself, because in this particular case, we have these two asymptotes. In both cases, both are minus infinity, which means that their sum would be like this. It's limited, somewhere limited in the middle, but goes to minus infinity, because either one or another component of this sum goes to minus infinity. And similarly here, well, et cetera. Then we will just spread it, and it will repeat itself more or less. Well, that's how it looks like. This is the sum of two sequence with different arguments, different multipliers, actually, because they have different asymptotes. But now the next problem is in some way similar, but in one particular way, it's different. And let me tell you which way. OK, one of them is x, and another is x plus pi over 2. So in this case, we have basically similar graphs, but shifted horizontally one relative to another, not squeezed, but shifted. So that's the difference. All right, let's see what happens in this case. So one would be from minus pi over 2 to pi over 2 like this, then to pi, and then to 3 pi over 2, then to 2 pi. So that's another asymptote, and that's another one. Here you have minus pi, minus 3 pi over 2, and minus 2 pi. That's another asymptote, and that's another piece. So that's how one graph looks like. Another graph is shifted to the left by minus pi over 2. So whatever was 0 here is shifted here. So the asymptote, which was pi over 2, will become 0. So basically, we have new asymptotes at these boundaries. And the new graph, which is shifted by pi over 2, would be like this. We shifted this, let's shift this one, and let's shift this one. So now we have to add dotted line and solid line. Well, let's do it. And again, as you understand, every asymptote will retain its asymptotic quality, because either one or another argument goes to infinity around it, and it's not defined. All right, so let's start from 0, let's say. When we go to 0 from, let's say, left, the dotted one goes to plus infinity, and this one is basically limited. And on the right from the 0, dotted line goes to minus infinity. So if I have to draw their sum, it will go to plus infinity here and minus infinity there. Let's go to this point. At this point, the dotted line is limited, but this one is plus infinity. So I have to round here and go up. Here, this one is plus infinity. This is limited, which means I have to go to plus infinity. OK, so these are my brown lines, which represent this graph and this particular piece. Next, let's consider this particular thing. Well, obviously, it's minus infinity and minus infinity, and this is something limited, so it goes like this. Very much close to this one. And on this one, on this side, this is minus infinity, and this is plus infinity, so it should go from here to here. And then similarly to this, it will be here. The function is symmetrical at this point. And then it will continue, basically, based on periodicity. So the complicated graph looks like this. And obviously, it's not defined in any point where you have an asymptote, either one or another. Well, these are exercises in graphing different functions, and I think it's very useful just to understand how the function behaves. There is one more lecture for cosecant, which would be next. And that would be the end of the graphs for trigonometric functions of this type. These are just properties of trigonometric functions by themselves, everyone separately. Then we might actually combine sine and cosine, tangent and cotangent, what happens with them. So it's all related to your understanding how the function behaves. OK, that's it. I do suggest you to reexamine the notes for this particular lecture at unizord.com and try again to draw these curves. And you know what might actually be helpful if you want? After you draw it yourself in this schematic fashion, you can use probably one of the scientific calculators which is capable of graphing functions, or you can find it on the computer some tool which can do exactly the same. And you can verify if the function like this does have the graph which looks like whatever you have schematically put on your paper. That's it. Thank you very much and good luck.


Hello friends, welcome to SSU redec, social decide and this is continuation of SSIS tutorial. So today we gonna discuss about containers. So what is container and what is sequence container. So let's start with container.  SSIS containers are controls that provide structure of the package and it support repeating control flows in packages and group tasks into a meaningful unit of work. In SSIS we have three type of containers. First is sequence container, then for loop container and last is for each loop container. So for each loop container is used the most. Today we will discuss about sequence container. What is sequence container and what are the real time use of sequence container. It is used to grouping logically related task together which makes it simple to divide the control flow in a package into group of tasks and containers that we manage as a single unit. So what is the purpose of sequence container. So here I have written six scenarios where we can use sequence container and that is very useful for developing our package. So first is grouping task so that we can disable a part of package that is no longer used. So what it mean go to on ssdT and here I would like to add one more package. Then I wish to rename this package with sequence container. Then here as we can see inside these containers we have three containers. First is for loop container, for each loop container and sequence container. We can drag and drop sequence container. Inside the sequence container we can use multiple data flow task. So this is our first data flow task and this is our second data flow task. Then this is our execute SQL task and this is our execute SQL task. So these four task is a label inside this sequence container. If we have a requirement where we want to disable all these task then there is no need to go to on each task and click on disable. We can simply disable our sequence container so that all these task will be disabled. As we can see once we disable then all these tasks have been disabled. Then our second narrowing the scope of the variable to a container. If we wish to create a variable and scope of that variable will be available inside this sequence container only then we can create. Our third is managing the property of multiple tasks into one by setting the property of the container. Like if we want to manage any property of these four tasks then there is no need to go to on each task and set the property. We can simply set the property of this sequence container then that property will be applicable for these tasks. Next is ensure that all tasks in the container must be executed before next task executed. So it ensures that once we execute this package our sequence container will be executed first. We have one more dataflow task and that is outside the sequence container then once these four tasks will be completed after that next dataflow task will be executed. So it ensures that our four tasks which is placed inside the sequence container will be executed first then our dataflow task will be executed which is available outside this sequence container. Next create a transaction across a series of data related tasks but not on the entire package. Let's assume we have a scenario where we want to use transaction and we don't want to use transaction on entire package. We just want to use transaction inside this sequence container then we have a option by which we can use the transaction for this sequence container and it will be available only for those tasks which is placed inside this sequence container. Bring event handler on a single container where we can send an email if anything fails inside the container. So what it means? Like we have four tasks and if any task will be failed then we want to send an email. There is no need to go to all these four tasks and send the property to send email if that task will be failed. We can only set the property for this sequence container if anything will be failed inside the sequence container then mail will be sent. So these are the scenarios by which we can use sequence container. Once we will discuss about the case study then we will see what is the real time use of sequence container and how we can use it. So thank you so much for watching this video. If you like this video please subscribe our channel to get many more videos. Don't forget to press the bell icon to get the notification of our newly uploaded videos. Thank you so much.


Now let's do some example exercises. We're going to stick to proofs for now. We've got to prove the associative property of the intersection of three sets. So if I have the intersection of A and B, it's intersection with C. I'm saying that would be the same as writing A's intersection with the intersection of B and C. How do we do that? Well, we take out what we have in our little box. The definitions that we've had before, and these are the two I want you to concentrate on. This is in our box. As human beings, we've decided that the intersection of two sets would be the set of all elements X such that X is an element of A sub 1, the first one, and X is an element of A sub 2. That's our definition. We've decided that. There's no need to prove that that is our definition. That is how we define it. And we said that two sets are equal if and only if one is a subset of the other and the other is a subset of the first one. That's in our box. Now, let's prove this. The way that we're going to go about it is just to start somewhere. We let X be an element of this first part of the equality. A's intersection with B's intersection with C. If that is so, let X be an element of that. Then X is an element of A's intersection with B and X is an element of C. All I've done now, I've used my definition. I've only used my definition. Then that is so, so that X is now also an element of A and X is an element of B. There, I've just unpacked it again and X is an element of C. Now, if X is an element of A and X is an element of B and X is an element of C, let's use some of the scenarios. I'm going to say if X is an element of B and X is an element of C, then what follows? Follows by the definition that X is an element of B's intersection with C. The other scenario now is now this. Then X is an element of A and X is an element of this. B's intersection with C, so that X is now an element of A's intersection with B's intersection with C. Now, it might not look that satisfying because what I'm doing, I'm actually just translating what I have there into language, into words. But be careful. What I'm doing is I have taken an arbitrary element inside of this first one and I'm unpacking that by definition. That is all that I'm doing. So if X is an element of that and X is an element of this now, that means this must be a subset of that. So A's intersection with B's intersection with C must be a subset of A's intersection with B's intersection with C. This must be a subset of that because I've started off with it being there. I've let it run through which now says that X is an element of this. X started here, so it means X must now be a subset of that. Now we can write conversely because what we have here is we've got to prove it in one direction and the other direction. We must also prove that this is equal to that. And how am I going to do that? Well, I'm going to say let X be an element of the second part, A's intersection with B's intersection with C. If that is so, then by definition, by our definition X is an element of A and X is an element of B's intersection with C. So that X is now an element of A and this means X is an element of B and X is an element of C. Now we have this scenario that X is an element of that and that and that. Let X be an element of these first two. If X is an element of A and X is an element of B, then by our definition it holds that X must be an element of A's intersection with B. That means so that X is now an element of A's intersection with B and X is an element of C. X is an element of C. And if that is so, by our definition that means that X is an element of A's intersection with B, it's intersection with C. So I see we started off there and now we are here. That means therefore we have that A's intersection with B's intersection with C must be a subset of this because X was an element of that first one. It is now an element of this so this must be a subset of that. Of A's intersection with B's intersection with C. Have I got that right? So this must be a subset of what we have here. And now we are going to use this second part. So if the one is a subset of the other and the other is a subset of that, therefore by this definition, therefore we have proven that A's intersection with B's intersection with C equal A's intersection with the intersection of B and C. There we go. So we have just used some of the definitions that we have had that we can take out. This can be proven. This is our definition. We are taking that out. It lives inside of our box. We can use them to do our proof. All we must remember is that what we are suggesting here is this implies the other. A's intersection with B's intersection with C implies that A's intersection with the intersection of B and C. So I have got to prove it in this direction and I have got to prove it in the other direction because what I have proven here is that this is a subset of that. What I have proven here is that this is a subset of that. And because they are subsets of each other, I can use the fact that they are now equal to each other.


What's going on everybody got Kyle and Sean here relating sports cards are an absolute football six box half case number seven This one is pick your team star got Adam L with the Steelers Alan K has the Browns We got Andre K with the Dolphins Brandon a has the Falcons boogie has the Falcons We have Christian F with the Rams Cory G has the Packers David C has the Texans Doug B has the Panthers we got Emmanuel L with the Saints and the Titans Gary H has the Jags Jason B has the Colts we got Jeremy H with the Eagles Joey Y Ravens Jonathan M with the Commanders Justin R with the Niners Justin L has the Bengals and the Cowboys Ken W with the Lions Kerry G has the Chiefs Matthew B has the Chargers Matthew R has Raiders and Giants Nathan J with the Patriots Ronald L has Vikings Russell K with the Seahawks Scott T Bucks Stephen S has Cardinals Stephen L has the Bills Wayne P has the Broncos Winshoe L has Jets and Stephen has the Bears Stephen Oh Good luck. Good luck here guys. Thank you. Tony grabbing one in upper deck We are down to seven in that get that going here in just a little bit Straugy Rinkaboom. Okay. I'm in I'm in You guys know I'm in on that good luck here guys box one six box half case number seven Our first two are sold out. We got two two spots left commit our Panthers in both of a Last two nine and ten will be from the same seal case as well Got you Preston. I'll try to say some say Some say for you. There's on the front man. That must be a new thing. They do I've been doing that in a couple products recently There's C-Mac on the base C-Mac and Travis Kelsey Now I would be the greens in this one sometimes sometimes though like the gold prism like gold prism sells really well The one-on-one still does better, but people really like the golds man There's one for the Cowboys the 16 that's gonna be a douche von nice rookie there low number to 16. I like those Duce Vaughan We have a Jason Seahorn to 50 on these signature standouts that will be for the Giants signature standouts g-men and Patch two color pasta 49 is gonna be a rookie force of Jaren Hall or the Vikings Jaren Hall Cooper Dejean Gulag from Iowa. He's supposed to be a first-round pick Cooper Dejean He is a freak We have a Desmond Ritter on the base and we have a Mack Jones for the Patriots Mack Jones We have a Reds 100 Jair Brown for the 49ers Jair Brown There is a Chase Brown on the triple relic RPA that one is a ball relic in three color patch Chase Brown to 99 bangles angles getting our first RPA and We have a Rokuwan Smith for the Ravens to 99 Rokuwan Smith heroes to 99 Ravens That would be kind of cool remarks Playoffs a Donriss though. So right wouldn't that be the buy Donriss got a base digs Have a rookie. Um, we'll let us to 275 Titans nice number to let us Steven Avila is gonna be rookie to 75 on the auto for the ramps Nick Bolton on the heroes 99 chiefs Chiefs And we have stargazing to 75 breeze all breeze the beast Thank You Michelle grabbing a personal get that going later on Stargazing to 75 box to I wouldn't mind that happen in the remarks Do you know how many car why how many cars that are numbered in at nine not exact fives or tens? I don't think I understand the question You know why so many cards that are numbered into nine I'm not sure you mean like 49 49 99. I don't know. I don't know why that is It's a good question. I'm not 100% sure why that is I get what you're saying now though like the 49 to 99 Set of 50 and 100. I don't know. That's a good question base Austin Eckler. We have Joe mixing To 25 rookie Clayton to nice one. They're Cardinals. It's the low number. We love sloms Cardinals to 25 Yeah, I don't know. That's a good question Tyler 50s unlucky or something to 399. We got an RPA Marvin mints rookie premier for the Broncos and triple relic to 249 It's gonna be DJ more or da bears Da bears there is hey, let's go sloms What else we got here? Baker bar the canvas Sam how Nice one here rookie to 50 is gonna be tank Dell one of CJ's favorite targets tank Dell the 50 and This will be a David car on the great iron grates throwback for the Texans David car Little throwback there in war room materials in 199 is a flowers They flowers third mini box That's true. They might say money went print one less serial number on there We're shot white Rookie to lead to a pillow to to 275 charges We have a scary terry on the veteran auto Commanders got a burners to 99. That's absolute burners of Christian Watson Absolute burners and we have introductions eyes on the prize of 75 of Clinton Johnson You rookie premier That's on the prize box three Some of the greats. Yeah, I don't know if they're our David cars quite a great But had now to plow slow snow. Oh, man So so my And never had to do that never had to do that. I'm not sure. I'm not sure how much we have left Jalen Hertz Got the 275 another tank Dell rookie for the Texans and Dante Hall on these signature standouts the 75 chiefs. He was fun to watch Dante Hall 75 standouts And rookie is gonna be the 49s a flowers to color patch It's Ricky's a and star gazing is to 25 a DJ more for da bears Da bears Mini box to yeah, that wasn't a bad roll. Also the cards came out. So that works Thank you Andre taking to an upper deck hockey When we add on that first one it is down to five down to five on that first one Thank you guys get that going after all of our absolute will end with the hockey tonight I Vontay Smith Marquis Brown Hollywood There's Michael Mayer to 75 that's gonna be rookie for the Raiders And nice and 99 on the five-way RPA is gonna be Anthony Richardson. There we go Colts Starting QB for the Colts very nice one there a little AR action who's got Indy that is It's gonna be Jason be very nice one there, sir rookie premier 98 and 99 AR Magda for you, Jason Got a groundhogs Jersey to 99 three color patch gonna be Kendra Miller And a really nice one there Magda for you Jason Roundhawks jibby jeep Devonte Adams back-to-back Raiders Got a sharpening to 100 rookie for the Seahawks One to 75 got iconic ink of Joe Cleco for the Jets Joe Cleco Forgot Paul asked me how this suggests we're a second ago. I forgot to look jets were 49 in this ball Jets were 49 if you're still watching Connick Inc. Cleco Dan Marino for the Dolphins on the Pro Bowl souvenirs Jersey to 125 Let's go Dolphins. Oh Dan Marino there. Let's go Pro Bowl for the AFC AFC box for Over it. Yeah, I went to uh, I went to visit my buddy a few weeks back or a few years back in Breckenridge And I was I busted pretty hard on the on my icy road. I was not happy about that Busted my butt It was not fun. Thank you Robert taking one in a ice hockey. I think we're down to four Not very nice it's not going at the end of the day Keenan Allen base There's an AR another numbered one this one's a 275 on the base I just won their Colts another AR go with the RPA Have a Jerry Judy standouts at 25 for the Broncos Jerry Judy and 99 a absolute burners Tony Pallett. So drippy. How we doing and rockouts of 100 Jamal for the Saints In guys, we do have a release day tomorrow with Sam starting at 10 a.m. Bowman University Basketball the first LeBron first LeBron in tops products looking for LeBron and brawny dual autos And a bunch of good college players can't complain Jeremy can't complain Montgomery Ken Walker Texans we have Dylan Horton to 50 rookie Got a great iron grates. That's Jamal Charles for the chiefs Jamal Charles on the greats auto. Thank you Stephen taking a couple of division spots Thank you Wong taking a Bowman University spot Justin taking the Panthers a number nine. So we'll keep on rolling Robert grabbing us down and A USC spot taking appreciate that the fact we have Jalen Heights and 99 Giants rookie You have a good bit of skiing so far. That's not not wrong do well on those jumbos tealaw base juju There's a jets to 100 that's going to be Aaron Rajas Rajas and we got another RPA this one's gonna be tank Dell nice one there Texans a bunch of tank coming out two colored or numbered already and an RPA Nice tank for the Texans On the CJ's favorite targets and a triple relics a 249 Cam Hayward Cam Hayward Steelers tools of the trade Ready box number five here. Thank you Ron taking a spot in upper deck two to go to go Appreciate that guys. We'll have two of those going tonight Same master case. There are two inner cases per per case on those will be from the same master case He is my boy. He is my boy. I'm hoping he gets drafted He doesn't get dropped up the box pick him up on a on a undrafted Got Odell Skaronski to 50 on the blue for the Titans and triple relic RPA to 99 is going to be Charbonnet So when there's Seahawks at a UCLA Zach Charbonnet And Groundhogs to 199 gonna be Jameer Gibbs This guy might have a good game against the bucks Jameer Gibbs is a beast this one there More worried about almond raw though, cuz our secondary hasn't been the greatest all year Almond raw is very good. Yeah, I do too. We hit one last night in personals Aaron Jones Kaboom Bateman Hinden Hooker rookie to 275 Lions Bill O'Brien going to Ohio State really Really Vaughn I did not see that that is interesting 75 I got juice Sanders rookie Otto for the Broncos and By storm the 75 is gonna be Quinton Johnston By storm haven't seen one of these yet charges Yeah, it sure does First pick in the drafts I'm sure that one-on-one will sell for a for a pretty penny Another redemption on the back Nick Chubb reporter. We have Trey Tucker to 75 rookie Raiders. Hello there Hello that So Brandon we doing a day, sir Who's a nice one for the Steelers? We have a two patch auto tools of the trade TJ Watts Where you go Steelers? Ball relic and two color patch very nice TJ Watts 23 at 25 To 199 can't nap salutes that'll be Antonio Gates Chargers on the Jersey Got a glass of Dan Marino. There we go Dolphins That is sweet Dan last Glass redemption for the Dolphins gonna be Dan Marino. That'll be Andre Andre got the Dolphins in this one very nice. Yeah, that's a that's a Sean card right there That's a Sean card right there glass of Danny Marino Very nice one there again. That was Andre with the Finneys and last box here this half case guys number six Really Jace, what'd you pull pull the Jenny? I still can't believe you guys pulled that blue Stroud. That is a That is a very big card at this point at this time. It might be five five digits in a in a ten or nine With how Stroud is selling That is a gigantic card It's true no matter what Mike Pittman Jordan love Devontae Smith to 100 on the red got a spectrum signatures. That's gonna be Vance Johnson for the Broncos to 199 Spectrum signatures. There was a glass Dan Marino Luke Sean was Sean was jealous Yeah, that's true You see Dan Marino though something's changed to 199 got a wardrobe materials Tyler Scott He's not mad at the throwback Dolphins. He's mad too at the moment. I think yeah Yeah, blue CJ from retail. It's it's a short printed blue. They make like 20 or 20 or 50 of them something like that They're not numbered, but they are about as hard to hit as you can you can get in anything That's hard to hit anything as you can get Dak Prescott base To 275 Zach Harrison on the rookie and To 199 Kalea can see and go bucks fire the cannons I Thank you Wong taking a few teams in a bowman chrome you basketball come on Groundhogs and 99 icky woods the bangles And Jackson Smith on the by storm to 100 The glass guards are really cool move when you get them redeemed. I like those glass cars a lot I've never had one, but they're very cool. I like the basketball ones football wands, right? Last pack here in this half case. We'll get number eight going right after guys Go right into it Lamar Jackson Kamara orange is gonna be a Dante formant to 75 da bears orange To 10 we got a five-way relic auto of Roshan Johnson right back to da bears When they're a glove relic three patches in a ball relic, you're nice one there bears Roshan action Championship fabric to 49 we got a Mike Evans can't guard Mike nice one there bucks Nice one there bucks. Thank you hunman grabbing a spot in upper deck ice Just two to go in that first one just two to go Alrighty guys that will do it that will do it for our first half case absolute number seven Do a quick hit recap here, and we will be on to number eight. Oh, you open up mega. I got you Genesis is are awesome, man. They are awesome. Oh No, it's not it's from the it's from the red and orange ones. It's not from the creams They have like the red orange and black ones So you 49 got Mike ickywoods to 99 to 199 Tyler Scott Tony O gates Jameer gifts to 249 Cameron Hayward to 99 Jalen Hyatt and Tony Pallett We had Marina on the um Pro Bowl jersey 299 Kendra Miller to 49s a flowers 99 was Christian Watson a 199 is a flowers to 49 DJ more Nick Colton Roquan Smith and to 49 Jaren Hall Rp to 10 Roshan and go bears Clea Kansy Vance Johnson Tj Watts to 25 To 75 Drew Sanders to 99 is Zach Charbonnet gridiron greats to ball Charles Jerry Judy to 25 to 75 is Joe Cleco Dante Hall and Terry scary Terry Had greats Otto David Carr 399 Marvin Mims of Vila Chase Brown Jason C. Horn to 50 got a tank Dell RPA and god damn arena on the glass go dolphins. Let's go dolphins. I'm told damn arena on the glass And our pay to 1 9 9 in the back is Anthony Richardson Very very nice there Alrighty guys that'll do it for case number seven or half case number seven in just a minute. We'll do half case number eight