Happy happy to do it. Thanks y'all for city staff are putting this together. For the citizens, this has been a project back and forth for a long period of time. And I know there was some. I'm citizen concern about certain areas and greenery and trees and other things. And I know y'all worked really hard to do as much as we can. In that part part of the neighborhood to make sure, but I do think it's an important project across the board. This is a state project. It may be in federal. Y'all, y'all clarify that. But providing safe routes to school for kids and there are kids that are walking to school in the middle of the street. And this gives them the opportunity to be not on the street walking to and from school. And so I just thank y'all for working with the neighborhood to. To limit anything that we might have to do with greenery and trees and other parts. And. And I'm sure you'll communicate with the neighborhood as we move forward. So, I appreciate that. Thank you, council member, Brendan, you ready to go? Brendan, are you connected? Oh, no, Brandon, are you connected? Can you can you hear us? Okay. He's having technical difficulties a bit. I said, are you there? Yes. Can you hear us? We could hear you. No, that's okay. Are you ready to get started? Jeff, are we recording this meeting? Yes, it's actually already recording. I wanted to make sure if we were the council member wanted to speak that we started the recording. So we're going. Okay. Just want to make sure that everybody's aware that we are recording. Okay, Brandon, you want to get started. Thank you presentation. Well, thank you everybody for attending the pre construction community meeting for safe routes to school for the Mary Lou Phillips elementary school. City project number 102 411 and council district three. My name is Brendan McKinnis. I'm the project manager. We also have Kim Lee Horn and associates as the project engineer and the contractor is North Star construction. I believe Mr crane may have already spoke. I missed that portion. Is that correct? Yes, correct. So, city staff, I guess I'm Brendan McKinnis. I'm the project manager. We also have Lissette Osavado, who is the program manager on this call. Hello, everybody. This is Lissette. Thank you so much for joining us this evening. Project engineer is Kim Lee Horn associates. Scott Arnold is on the call for them. And we have North Star construction with Luke and micro also on the call. The purpose of the meeting is to provide information about the construction of the safe routes to school project in the Philips area. The meeting will include information for the project limits, the project scope, typical construction process, project phasing and traffic control, as well as the project schedule and notification. If you have any questions, we'll try to answer them at the end of the presentation and we ask that those are put into the chat box. The attached map is showing the overall project limits of where we'll be expecting to see construction activities within the red box. On this page, this is the M L Phillips is highlighted in blue in the center of the picture. The light by light blue cyan color or existing sidewalks in the area, as well as the yellow lines are the proposed sidewalks that we're proposing to do as part of this project. The order the streets listed here are the anticipated order the contractor is proposing to progress through the project starting with all of place, working along Locke Avenue, working Bingham Boulevard and Edge Hill Road, Mary's Lane and finishing with Curzon Avenue. The project scope is approximately a quarter mile radius around the school. We will be constructing new sidewalks, driveway week reconstruction, curb ramps, replacement of non-compliant sidewalks, as well as signs and pavement markings, including crosswalks. The typical construction process will start with notifications. We'll be putting project signs out as well as door hangers on residents and stakeholders doors seven days in advance of construction activity. We'll follow up installing traffic control, having barrels and cones in the work zone. In the areas where we're working, the contractor will install erosion control to keep any materials outside of storm sewers and storm drains. They'll proceed with clearing the site in the area of the work, conducting any underground utility work and adjustments. They're planning on starting on driveway removals and replacements on the street as part of the first phase. When this is work is underway, it's typically around a seven day process from having the driveway removed to replaced, provided that we get concrete breaks for the driveways. But there will be a period of time the driveways will be replaced that you cannot access that area. They will follow up once they have the driveways in. They're going to be working on the 88 ramps and sidewalk constructions to tie into those driveways and tie into the street crossings. They'll proceed that with landscaping and sodding of the disturbed areas. They'll clean up the area, remove their traffic control and do all their final cleanup on the street as they're moving on to the next area. These are a few pictures from a previous job that we have done with the city of Fort Worth. The picture on the left is showing a driveway being reconstructed. The picture on the right is showing that same area showing how the sidewalks will be tied into those driveways. And they have the graded on each side of the sidewalk. And then these two pictures are representing the one on the right is showing the sidewalk as a finished product on the back of the curb. On the left on the picture on the right is the same as the previous two pictures showing it fully sodded in of that same driveway and sidewalk area being constructed after the contractor has left the area. Project scheduling notification. Currently it is estimated that the project will start in April of 2022. The project duration is 270 calendar days. With an estimated completion date of March of 2023. The contractor work hours will be from 7 a.m. to 6 p.m. Monday through Friday. 7 30 to 8 30 and 3 30 to 4 30. Closures are prohibited immediately adjacent to the school when it's in session. 9 a.m. to 5 p.m. on weekends they are allowed to work if they request. Permission in advance. Project notification. We will be putting out project signs 7 days before the start of construction. As well as placing door hangers on residents and businesses 7 days before construction. We're going to try to keep those closely moving with the work as it progresses down the streets. So you're the citizens are notified just prior to the work beginning. And the project schedule could be affected by unforeseen events such as utility conflicts or weather. So at this point I'd like to open it up to any questions anybody might have. Yes, sir. I'm going to call up on Ed chill. Unfortunately I could not get into the WebEx. I'm just here's a conference call. But where the outline is on the map that was on the flyer that was released. Are there going to be sidewalks at say on both sides of lock both sides of Ed chill. Both sides of curve on Curzon. No. The map of the area. So lock lock will have sidewalks on one side of the road, which was alternate depending on the location. Curzon will have sidewalks on one side of the road. On the west side of Edge Hill. And a little bit on the corners. You know, which was the other street that you had a question on. Well, that's where we live. Edge Hill. South of Cruz on will have sidewalk on the west side of the road on the north side of Cruz on the sidewalk will be on the east side of the road. Brendan someone in attendance would like for you to show the map again while you're explaining that please. Can you scroll back to that map? Yes. You repeat the information on Edge Hill, please. Yes. I'm going to get back to the map here. I think y'all should be able to see the map. Tell them what side of the street it's on. I mean, you can a little bit better on Edge Hill, but you said it alternates on lock Avenue. I don't see that. I don't see that. So I'll start with Edge Hill and I'll move over to lock so on Edge Hill on Edge Hill south of Cruz on the proposed sidewalk is on the west side of the road. On Edge Hill north of Cruz on the sidewalk will be on the east side of the road. On lock. Go ahead. Just saying thank you. Thank you. On lock Avenue from all of place to the text Boulevard. The sidewalk will be on the north side of the road at text Boulevard. It will transition to the south side of the road and it will be on the south side of the road from text Boulevard. All the way to Wrigley Avenue. There's another comment in the chat and asking question says, can you please tell us about the traffic control for the project that will happen while the sidewalks are being constructed. Thank you, Jen. For the traffic control during construction. The contractor will have barrels and cones along the shoulder in the lane while they're doing work. To keep safety of their employees doing the work and also keeping out people right adjacent to that area of work so you'll see barrels and cones as that work is completed those will be picked up the area cleaned up and it moved to the next work area. Did that answer the question on traffic control. I'm not sure Jay Parker you can unmute I believe and you can you can ask a question if that if that didn't help you or if you have a follow up question. I'm muted and I mean it does help some I guess my biggest concern is. It may be a different concern that with the sidewalks going in, I certainly think it's will be safer walking on this street. But there is tons of traffic on this street and people fly down this street just like they do on Edge Hill. So I don't know if I'm assuming that speed bumps that we have will not be painted or they're going to be a change in speed limit on the street. We have signs that say 20 miles an hour but it's never an enforcement of that. Do any of that get affected. We are not proposing to change any of those elements. There's another question in the chat from S Dillard and they're asking about the order of construction again. I believe you're at the correct sign. Can you please describe the order of construction again is the question. I think you're on the good slide to talk about that. Thank you. The proposed order of construction is to start on all of Avenue work up all of Avenue. Once they're complete or getting complete with all of to move on to lock Avenue. Work down lock. Towards Bingham and then they're going to work down Edge Hill. Then come back and do Mary's Lane and cruise on. Yes ma'am. My question is this. Are you going to do the driveways first and then the sidewalks after because my mom is handicapped and she's got to have access to the street either down the sidewalk in front of the house or the driveway. Are you going to do them one at a time. They they will be around the same time that if we know your address we can accommodate that access for you to make sure she always maintains access. Okay. And I have one other question. My controls for my sprinkler system is in the path of the sidewalk. Do y'all move those or do I get my people to do it. We the city is proposing or planning to adjust those as part of the project. Okay. In other words y'all will move them. Yes ma'am. We will move it just outside of the sidewalk limits. Okay. And you guarantee them because the gas company broke mine in two places and it wasn't realized until they were no longer here. And it cost me a lot of money to get it fixed. So I'm asking you. We will work with the contractor to make sure they're tested before the adjustment for operation as well as after the adjustment for operation. Okay. And when you start on my street which is Mary Lane I will talk to you at that point about access for my mother who is handicapped. Correct. Yes ma'am. Okay. Thank you very much. There's no other questions in the chat right now. Anyone is free to unmute and answer any questions or ask any questions and we'll try to help you.  Brendan this is Alan Conroy again. Yes sir. Okay. So our driveway we will not have access to our driveway during the first phase of the project. Did I understand that correctly? While they're rebuilding it there will be a period that access will not be able to be maintained. If you have a wide driveway there may be a chance to build it in portions. But most of the driveways on the project are fairly narrow which would not allow two phase construction. We have a double wide driveway street parking will be allowed. There shouldn't be a problem with street parking one hopes in that time. But I'm thinking with construction barrels and that sort of thing up it's going to get pretty tight on some of these streets. When driveways are closed and construction materials are out there and equip heavy equipment that sort of thing. Will there be additional police patrols or community patrols during that time at night? I can try to answer that question for you. My name is Buck Wheeler. I'm the commander for West Division. Yes sir. So are you asking during construction if we'll have extra patrol? Yes. Or the citizens. Go ahead. Or the citizens patrol or whatever would be appropriate. We can definitely it's really easy for us to alert the citizens on patrol or any community groups so they know. And quite often when there's construction projects as long as whether it's citizens or the construction usually we know about it. And we put it out to our patrol officers to keep an eye on do extra patrol in that area. So the short answer is yes. Well if there's construction we're going to know about it and we'll try to have a higher visibility. But it also it helps if citizens if if we see especially after hours on the construction site. If anybody sees any suspicious behavior people milling around the construction site. Definitely call us because construction sites a lot of folks will look at that as an opportunity to steal equipment as well. But the short answer is yes we'll definitely have higher visibility but feel free to call us and ask for more extra patrol that never hurts. Thank you commander. We call because I think that there's been an uptick in activity in this area already with stealing parts from cars. If they are on the street that is more likely to happen. This is officer that I'm your neighbor patrol officer. The uptick the uptick you're talking about is something I asked them to ask the originally north association to share with the group and that was just specific to some catalytic converters. As far as break ins or anything like that I haven't had an uptick in that. We did have a couple of catalytic converters hit over the last couple of weeks and that was just kind of a trend that we were seeing because of the value of the catalytic converter going up with some with some stuff going on overseas. Right. Yeah I mean I've definitely heard chatter about it in the neighborhood. I don't have a garage so I just try to back my vehicle and as close to the house as I can. I don't think it'll stop them but I have you know I also have cameras but it hasn't stopped them from trying to get into my car. No certainly not. No I mean people are going to try to get in. I mean you know they target that neighborhood and I can discuss that with you guys. I'm sure nobody you know everybody on here they want to discuss this project but you can call me. I'm your neighborhood patrol officer. I'm Officer Haddad. If you don't have my number if you want to jot that down now I'll give it to you and then we can discuss that in person but that's a<PHONE_NUMBER> and I'm your neighborhood patrol officer. Yeah I know who you are. Yeah we can catch up. Vernon there was one there's another question in the chat it's just and this may be for Jeff. It says it's asking where will this recording be available to watch again. So Jeff where can folks find the recording of this meeting. They'd be posted in two places. It'll be on our The City of Forwards YouTube channel. If you've ever gone to that it'll be listed on there but it will also be on our project page. Which I'm going to put the web address right into chat so everybody can have it. Or you can just search Phillips on the website and I'll show it that way too. Okay that's great and also I tried to put the neighborhood patrol officer's phone number in the chat. Could you please verify that and make sure I got it correct please sir. Yeah it looked like it was correct yes sir. Thank you. Thank you I appreciate that. So one other note I did put the project page link in the chat but one thing to note on that page is once construction begins in April we will be updating that page at least monthly. So you'll kind of have progress on where we are and what's next and what we just completed so you can go to that page anytime for an update. Or of course you can call the project manager if you have questions but this website would be a good place just for general high level detail on where we are on the project. I have a question. I'm on the phone call in so I can't see any chats or websites. Is there a way I can get the website for updates? So the web address is Fort Worth Texas all spelled out Fort Worth Texas dot gov. Okay. And then once you visit that if you go right in the upper right corner there's a search box and if you just type in Phillips it'll be one of the first pages to show up and that'll be the easiest thing since you can't see the link on the screen. Okay thank you. Sure. And on that if I got on there now I would be able to see details about what's going to happen and and timeline that kind of thing. The timeline isn't up there quite yet. I haven't been given that information but it'll be up probably tomorrow or Friday at the latest whatever we have but there's quite a bit of information on this project on that page at the moment. A lot of the stuff we did for the state for the funding is there so the environmental studies the manual the scope the plot the construction plans but not the timeline. So it's all on there some lot of detail for you to look at. Okay thank you. Thank you everyone.  No I'm still here. Okay I don't see anything else in the chat. So I guess we can take additional questions if anyone has any other questions or we could conclude the meeting Jeff or do we need to stay on here for a certain amount of time I'm sorry I'm not sure about the format. If there are any more questions we can we can stop the presentation. We always stay on a couple of minutes but if anyone has any other questions feel free to ask them if not will stop the presentation in the recording and stay on for a couple more minutes. Oh Brendan this is Alan Conroy again sorry to be a pain. I just remembered we have our address on both sides of our driveway stenciled in there. Will those be replaced. I will need to verify that in the plans but I believe that is a item that will be replaced. Okay so that would be on the website in terms of specs and that sort of thing. Yes. And I will I can verify and get get back with a answer for that. All right thank you sir. Jeff we're going to be able to see who's all in attendance and are we going to be able to contact Mr Conroy and give him that answer. No. If you do have a follow up please send a foot in chat your phone number or your email or your phone number or your email or your email address. Your phone number or your email or send a private chat message to Brendan or Chad with that information so we know how to reach out to you. Also here's Brendan's contact information yes. So if y'all have any questions my phone number is listed as well as my email address. And if Mr Conroy if you can just shoot me an email or a phone call that way I have a way to contact you I will get back to you. Yeah if you're a caller you might be able to take a picture with your phone also of this so you can have the contact information as well. Brandon we can go ahead and read your phone number. Yeah I was going to say the calling people can't see the screen so please read it out. My phone number is<PHONE_NUMBER> and that is Brendan McKinnis at Fort Worth Texas dot gov b-r-e-n-d-a-n dot m-c-i-n-n-e-s at Fort Worth Texas. I'll spell down dot gov. Are there any other questions? I have a question. I went to the website and I'm just wondering if I don't know what this means on the drawings it says ex row ex row with the blue highlights. What is that? That is the existing city right of way. Oh okay thank you. You're welcome. Were there any additional questions in the chat? No there are no additional questions in the chat. I'm trying to ask a question. That sounds like someone's just unmuted phone maybe. Okay. I think we're good then. Thank you to the representatives from the city for putting this together and holding this meeting. Thank you. Are you welcome. Oh for attending. Good luck gentlemen and ladies. Thank you. I think that should conclude our presentation. And I'll stay on the chat until about seven if needed or on the call to answer any questions if anybody has some. They're late. Thank you everyone have a good evening. Thank you.


Yeah, also, yeah, welcome everyone to the enterprise track of the commit, the expected to be Africa, and yeah, I'm super excited to introduce our first speaker, I think, you know, here is Madhu, so Madhu is a DevOps engineer at Demo's Cloud, oh, sorry, okay, okay, cool, I actually thought I mispronounced something, so yeah, Madhu is a DevOps engineer at Demo's Cloud, and Madhu will be speaking to us about this topic, which is basically reducing the attacks of issues in the top classes. Yeah, Madhu, the floor is yours, so please feel free to share with you. All right, good afternoon everyone, thank you for having me, let me know if you can hear me, all right, cool, so I'm just going to start presenting now, so yeah, good afternoon once again, welcome to our very first edition of Kubernetes, Kubernetes Days Africa, so I'm here to be talking about reducing attack surface using network policies. All right, so first of all, very briefly, my name is Manasi, and I work as an SRE at Demo's, at Demo's we work on infrastructural design, security and implementation, so yeah, for those of you who don't know what Demo's do, Demo's is a DevOps company that helps to guide other companies into their path of cloud adoption, so we offer a range of services from migration to cloud, to set up on infrastructure, and we also offer Google WorkSpaces as a service. All right, so cool, today we'll be talking about security, which is a very interesting first set of infrastructural management, and as much as most people don't like to hear it, it's one of the basic things, one of the major things that affect your performance, the performance of your application and the security of your application, so basically security is just ensuring you adhere to confidentiality of data, integrity of data and the availability of data to your customers, that's what basically security is, and yeah, we get this question a lot, how do you make your system secure, so there's no, I think before we just proceed, I just want to state this out that there's no single solution to security, you just have to keep implementing layers of security defenses, and that would improve your, the security of your system as a whole. All right, let's dig deep into this, nice, security, cloud security basically is you trying to implement a whole range of policies, services that's going to help you protect your data from the cloud, you want to protect your data from attackers, you want to ensure that your data is constantly available, and all these methods which you apply to help make all this possible is just basically cloud security, you've already been cloud secure, it goes from managing your IAM permissions, ensuring that the appropriate user has their appropriate permissions to set up firewalls, all of this, like all these, they constitute security in the cloud, and one of the major ways of improving your security is identifying ways which you can reduce attack surface, so basically an attack surface is what an attacker can do when he gains access into your system, so for example, when you're working to a compound, what can you do, you can, you see a lot of rooms, you can work into any of the rooms, so the number of rooms you can work into is basically like an attack surface, an attacker has access to when he compromises your security and gains access to your infrastructure, so one major thing to do in order to improve your security is just to try to reduce what this attacker can do, so we'll be talking mostly about kubernetes, so the basic components of the kubernetes is the pod, or the containers as most people would see, so yeah, what can a particular attacker do when he compromises your pod or your container, that's something we want to basically know, so one of the major things is he can have access to the qbpi server if the service account is mounted, so this is very important because the qbpi server contains, accessing the qbpi server means the attacker can have access to, you know, understanding what is deployed in your cluster, knowing the namespaces, knowing the applications you have, and everything about your cluster basically is available once you have access to the qbpi server, so you really don't want to give him access to your qbpi server. Another thing is if your pods are running in privilege mode, the attacker can have access to, you know, the underlying node that the pod is running on, we've seen cases of what we call container escape, so the person, the attacker can choose to, you know, compromise the node, which the particular pod is running on. Another thing is, you know, if you have access to a pod on the cluster, the cluster is also in network, so the pod can have access to, you know, other workloads and other components of your network, so if you have database on your network, you have other workloads running on your network, the attacker can, you know, have access to all of this once he compromises your pod. Another part, which is very important, is data exploration. When an attacker compromises a particular pod, he can be able to, you know, export data to another location and, you know, based on what data he needs and the data he has access to, that can be very dangerous when maybe he exports user information, or let's say credit card details, for example, to a particular location. So what can we do? We've been able to identify, you know, what this attacker can do once he has access to a pod. We want to be able to reduce the attack surface, so that's what we said basically what this talk is about. So we want to limit what the user can do once he compromises a particular pod. So most times, architectures are in such a way that we have funds facing applications and then we have applications at the back.  So we want to limit the pod or the services that this user can access once our funds-facing application is compromised, for example. So yeah, end-tas-network policies. So yeah, network policies are basically a set of rules, that determines how our clusters would communicate. So if a pod is in your cluster and you want to restrict it to be able to communicate only to a particular subset of codes, you know, for example, the case I gave earlier, you have your front-end, you have your back-end, I have your database, for example. The front-end communicates the back-end, the back-end communicates the database. You don't want a direct communication from the front-end to the back-end. So you can implement things such as network policies and these network policies would restrict the communication a particular pod can do when it is in the cluster. So you can also look at network policies like IP tables. For those of us coming from a Linux background, so we have IP tables are just like a way of setting firewall rules on VMs on Linux and network policies are like came to IP tables on Kubernetes. So why do we need network policies? Some people might say, okay, we have IP tables. We could probably just, you know, get an inspiration from IP table and do something around it. But one thing with Kubernetes is the IP addresses are quite dynamic. So your pod, when your pod spins up, it has an IP address that would change when it spins up again. And we know from deployments that this is bound to happen. So when you scale up, you scale down, new pods get created, all of these pods have different IP addresses. And yeah, that's why one of the major reasons why we needed something that is tailored to Kubernetes specifically. And yeah, another thing we have to notice is most people don't know this, but Kubernetes by defaults don't give you all the security features implemented. So you have to do this yourself. And by default, all the pods in every namespace can communicate to each other. So you have a test namespace, you have a staging namespace, you have a production namespace, staging can communicate to production. So that's how Kubernetes works by default. There is no isolation of the pod traffic at all. So yeah, now you see why we need network policies. So how does network policies just basically work? So network policies, they use labels. So from Kubernetes services and deployment, we've seen this when you're defining your deployment or your service, one thing you would notice is we use what we call selector labels. So selectors are just labels that target specific pod. That's the same thing with network policies. Network policies use labels. And these labels target specific pods to apply those policies to. And another thing you have to know with network policies is it is implemented by Kubernetes. So it is designed by Kubernetes, but it is implemented by your network plugin. So if your network plugin doesn't support network policies, then I'm sorry, you wouldn't be able to use this functionality. So if some example of network plugins that do this, you have Calico, you have WaveNet, you have Celium, and you have Qrout, and there are others. These are not just the four limited network plugins, but you have to be sure if you want to implement network policies, you have to confirm that your network plugin actually supports network policy implementations themselves. So you also need to know that network policies are namespaced. That means they are limited to namespaces. If you apply network policy in a particular namespace, it doesn't affect other pods on another namespace. Although you can have extensions, the basic network policies are namespaced. But as we've said, network policies are implemented by the network plugin. So Calico can choose to extend this by adding support for global network policies. But just know that network policies by default are namespaced, except you want to go opt-in for customized network policies offered by network plugins. Those ones offer other enriched features for network policies. So yeah, this is a quick link to a site you can use. It's built by Celium. And just it helps you design a network policy and visualize it properly so you can easily work with network policies. Cool. Let's look at the basic definition of a network policy. So we're not going to run through how to create a network policy, which is very important. So the first and important part of the network policy is the pod selector. So the pod selector determines which pods these network policies apply to. They are akin to selector labels on services or on deployment. So the labels you define as a pod selector target some specific set of pods and then apply this network policies to those pods. And the policy type. So we have two types of traffic. Traffic, we have ingress and egress traffic. So if we want to target only ingresses, there's traffic coming in. We specify a policy type of ingress. If we want to target traffic going out of the pod, we target egress type policies. And generally, you can also add both of them. You can define both ingress and egress policies for your network policy. So you can, after you've defined the policy type, the next thing is you need to specify the rule that this policy is going to use during communication. So as you can see here, your rules can have four basic types. So you can define an IP block. So an IP block is basically saying this is a particular IP. I want to limit the communication from O2. That's if you're using network ingress or egress. Namespace is just saying I want to limit communication to a particular namespace or from a particular namespace. This is very important. Like when you are deploying isolated environments, say you have a test environment and you want to isolate test environments from say demo environment and they're all on the same cluster. What you want to do is you want to limit traffic that can that can enter a particular pod in the test or in the demo namespace. So yeah, then pod selector, which are very granular. So this, sorry, this, this specifies the pods that you want to target, particularly like this is specific. You want to target a specific set of pods in your particular cluster. So when you specify this pod selector under ingress or ingress rule, any traffic coming to from that pod only will be accepted. So any other traffic that is going to any other pod or coming from any other pod would be dropped by the network policy. Another thing is pods. So pods are rarely specifying the pods that we want the policy to apply to. So for example, you have my SQL database and you know, my SQL normally listens on <IP_ADDRESS> for <IP_ADDRESS>. So you don't want the policy to allow access to other pods. So you limit the pods that it can communicate to. So yeah, as a rule of thumb, as a rule of thumb when you're creating your network policy, you should start with the default deny or. So what this policy just means is drop every traffic in your cluster or in that particular namespace, no traffic comes in, no traffic goes out. So once you've done this, you can now build up on this gradually and define granular network policies for your pod. So you want to do this because you don't want to miss out on any traffic.  You want to give granular permissions. You don't want to give access permissions. So by default, you first drop everything and then you give them specific policy definitions to allow specific traffic. All right. So yeah, I've talked about this briefly when I was talking about isolating environments. Network policies are very important in that they help you isolate environments. So environments, a couple people, a couple architectures would have them on staging environments on the same cluster. They can have staging like some can even have all three dev staging and production on the same cluster. So you don't want a vulnerability or an attacker to be able to access your production environment from your staging environment. That would be very weird and very, very insane. So you want to be able to shut down traffic from dev that is going to production from dev to staging. So yeah, you use network policies to isolate this particular traffic and it helps you isolate your environments properly. That is if you go for a multi-tenants kind of approach in deploying your cluster. Okay. So we're just going to see some basic demos. I'm not sure we'll be applying them. We'll just look at how they work. So I'm just quickly going to change this screen to another screen. All right. So all right. Good. All right. So I'm just going to share this again real quick. Um, I think, I can see. Can you hear me now? Yes. Yes. Yes. Well, nice. Good day to have a bad network. All right. So, um, yeah, so I'm just going to just quickly run through this. I think we've wasted a couple of time trying to resolve network connectivity issues. So, um, I was just talking about the default deny policy and we are just noting that, you know, when applying network policies, you want to start with this, drop all traffic first, then boot up on this. So from there, you can go on to, you know, allowing DNS because DNS is very important in Kubernetes. So, uh, then you want to allow DNS resolutions in the port. So this is the next one you go for. So as you notice, we are only allowing an egress policy. That means the port should only be sent, should be able to only send traffic to port 53. And you notice here we are not specifying any destination port labels or anything. That is because, as I said earlier, um, network policies are namespeed. So the DNS port is in, is in another namespace entirely. So we cannot target it from here. So all you can do though is we target port 53 and say, okay, let us allow all traffic from port 53 to go out of this particular port. The next thing you do then is you build up on this. You just build up, you keep building on these existing policies. So say you have a backend, a backend port like this, a backend deployment as this, very basic. Um, as you can see, it has these labels here that just say, let us target this particular backend and, um, you can now build up on this and create other policies. So here we are saying this is another policy that says, um, we should allow backend access to port. So this is, we are, we are selecting any port that has this particular label. This is, um, so if a port has this label and it's working, allow backend access set to true, we are going to allow it to be able to send egress to any port that has this tier called backend. So remember, we are, we are dropping both ingress and egress policies. So that means, um, we want to, if you want to create a network policy after, if you want to create a network policy, you have to allow ingress and you have to also allow egress. So I want to communicate to the backend port. So you first have to allow me to be able to send traffic to the backend board and you have to also set the backend to be able to allow traffic to come from me. So this is where we are setting traffic to go to the backend board. We are allowing any port that has this label to be able to send traffic to the backend port. And then, and in this policy now, what we are saying is we are going to target the backend port now and it should allow traffic from any port that has this label set. So this is just basically, um, something you can do. So by doing this already, we just limited who can communicate to the backend and the only part that can communicate to the backend is a port that has this label networking allow backend access. So you can set this label now in your front end port. For example, if we just go down to front end real quick, this is the front end manifest and you will see that it defines this for this particular label allow backend access. So this front end port now should be able to send traffic to the backend port. And yeah, this is a very basic example of, you know, building up on policies. So you do the same thing for your front end application. You do the same thing for your backend application.  And even if he tries to compromise your backend port, your backend port can send egress to any other traffic, apart from your backend port can send egress to any other services, except from the ones you've whitelisted that the backend should communicate to you. So you apply this granular accesses or this granular traffic permissions to reduce what port can communicate to you. You don't want everything to be visible to every other port on the cluster. This is very risky in terms of security. That's when you're talking about security. So yeah, I'm just going to roll back quickly to my slide and just run down through the remaining part of the presentation. Okay. So all right, cool. So that was just a quick rundown of basic policies and how you can build up on this. Very important, stability for deny, you allow DNS and then you build up on this for each individual service. We are running, if you're running critical systems, it's very important to ensure that you don't allow access to every port or you don't allow access to every infrastructure on your, on your, to every resource on your particular, on your infrastructure, for example. So yeah, let's talk policies are a holy grail in this aspect, but yeah, they have a couple of limitations. They don't enforce TLS, they don't love request, and they don't enforce policies on lookout rules. So you can just look at this and build upon it. There are solutions here. You can use link ID or elastic search to log and you can use link ID for the service mesh to enforce TLS and elastic search to elastic stack to, you know, log request on everything on your particular net of policies. So yeah, kubernetes as I've said earlier, they don't come pre-installed with security measures. So the additional security measures, which we're not really going to go into because this talk is mostly on net of policies, but you can check the link in the slide and then you will find all the security policies that you can apply in your, in your kubernetes cluster. And very importantly, you want to ensure that you've integrated security policies in your CI pipelines, scan your images for vulnerabilities, scan your kubernetes manifest that they adhere to best practices, and occasionally you want to scan your cluster as a whole to ensure that everything is fine and secured on your cluster. And as a final keynote, please remember that security is only important as a person implementing it. So if you, the person implementing it, make your credentials, you know, are free to everyone, you are definitely not going to be able to secure infrastructure. You are basically giving them the key to just go ahead and risk your attacking infrastructure for free. So yeah, you need help because security is a very wide thing. It's a very important part of your infrastructure. So if you need help around securing infrastructure, you can always contact Demos. We want SecOps, SecOps offerings and we will help you, you know, we, we want audits on your cluster and infrastructure and then we check where we can, we can help you secure your infrastructure better. So yeah, thank you for listening. I think that's the end of, of the slide, that end of the presentation. So yeah, this is time for questions. Yeah, exactly. Wow. Thank you so, so much, Madhu.  It's very important that you pay very key attention to the security aspect. So yeah, thanks a lot for that presentation. And yeah, this is question time, question and answers. If you have any questions for Madhu, drop on the chat section or the platform, if you are streaming live, free to also drop your questions on YouTube as well. Yeah, let's wait for an extra minute. And if we don't get any questions, then we move to the next speaker. But yeah, so basically, I have, I don't have any question, but I'll ask, can you willing to make your slides available to the attendees? Because I think, you know, the resources and information to just share is highly valuable and maybe it could be nice for the attendees to have access to them and then go back to those slides, you know, anytime you want. Yeah, sure. I'll be making these slides available. I'll be sending them to you as well. Awesome. Oh, nice. We just had a question here. Is there a link on how to get started with DevOps? Sorry, there is no link in the slide on how to get started with DevOps. I think you could probably check on GitHub. I like using the awesome list. You can check or some GitHub or some DevOps on GitHub and you can get to start it from there. Yes. Let me help out and just share the awesome DevOps for you. This is the name of the awesome DevOps. So yeah, from here, you can actually see helpful links to some of the tools and technologies you need to know. Yeah, thanks a lot, Madhu. I really enjoyed your session. It was really insightful. Yeah, and I know for sure my attendees are also excited and we get a lot from your session as well. So yeah, thanks a lot, Madhu, and we'll see you some other time. Thank you very much for having me.


A-15 Romeo is an H-64 attack helicopter repair responsible for the daily maintenance and functions as well as record keeping and inspecting the H-64 Delta model and eco-model Apache. The students today are working in the environmental control system, a system unique to the Apache responsible for cooling avionics components. For the first few weeks, students are taught the basics of maintenance practices as well as ensuring proper record keeping all leading up to culminating events in every single system of the H-64. H-64 trainers combined with adult teaching methods allow for us to do professional and competent maintainers ready to operate in any environment. To be a proficient maintainer, more than anything you need to have that integrity. Many times the aircraft will force you to choose the hard right over the easy wrong.


Hi guys, so we are here for another digital background exchange with Beagrob, Shell C, and Ayala Art. Hope I pronounced that correctly. If I didn't, please correct me. Anyway, so this year, as last year, we're all creating original works of art and then scanning them and turning them into something that's in a digital or printable format and exchanging them and then doing art with them. This is the one I created, and to be honest, it started out as a way to test some markers, pens, and crayons that I had in my stash. I was working on maybe purging some things and I just started making marks on a scrap piece of paper and it turned into this, this is one of four that I made for Spring 2020 and I love this one so much, I scanned it and made it into some artwork. The free, the download of which of mine is available to you all. The link is in the video description. If you're watching this on your TV, I know you don't have the video description. You need to get on a tablet or a computer, mobile device. I do believe you can find it from your phone. You can't get the link from your computer, but the link is in the video description, so really cool. Anyway, I also got these, now this one I believe is from Ayala Art. Isn't that pretty? This one is from Beagrob, I think. I could have these wrong, so it wouldn't surprise me and that one I know is from Chelsea. These are not printed in any special way. I have a very old HP inkjet printer. It's not a laser jet. They aren't printed on special paper. In fact, this is recycled paper. This is just plain ordinary printer paper. It's nothing special. So what I wanted to do with one or more of these today is show you all how I did this. These are some of my smaller watercolor palettes. This one is my floral and cobalt palette. When I want to limit my colors that I'm working with, I grab one of these when I'm watercoloring. This is like a bright, earthy, like I said, floral palette. When I was putting these together, I wanted to decorate the outside of the tin. I didn't really want it to be honest, sit and paint all of them because I have six of these. I have painted two, but the rest of these, these two included, these are prints done on printer paper with my old inkjet printer. You can see that I not only got them on here, but the ink didn't run, it didn't smear or anything like that. I'll show you the trick on how to do that right now. These particular square metal tins I got from Amazon. They look like this. Here's another blank one. You can see that it's dented. I love these little square tins. However, the seller on Amazon who has them, I have gotten, I don't know how many shipments from them, all of them come dented, every single one. I don't know if it's the way they're storing them or the way they're packing and shipping them, although I do think that way they're packing and shipping them is an issue because they're just putting them in a bubble mailer and they're thin metal. So they need to be in a box, but they never box them no matter what I've said. That being said, it is a cute tin and if you don't mind the dents and taking a chance on it getting dented, I will put the link for this in the video description. There is a similar tin at Paper Mart. I haven't ordered any yet, but I may just to see what the size similarity is because I do think I want to make some of these empty decorated tins for my Etsy shop, but I need to find a supplier first that can give me ones that aren't dented. So I may try to order some from Paper Mart. I haven't yet. I'll give you guys the link anyway and you guys can investigate on your own. But yeah, that's what these are from. Now you don't need to have a special tin for this. You saw this one I turned the camera on. This is an empty Dina Wigley scribble sticks box. I don't even have the scribble sticks anymore. I forgot I had the box. I sent the scribble sticks off to a friend because I never used them. There's nothing wrong with scribble sticks. I just never used them. So and then for a while, I had watercolor in here, which is probably why I forgot about it because it was in the watercolor palette container. Anyway, you can use this any metal tin will do. If you're going to use a tin like this, you might want to, you know, give it a coat of paint first, but maybe you don't care if it says this on the back, but you just want the lid to be something different. So we're going to work on that today. So I'm going to show you what to do. So the first thing we need to do is measure the size of our tin. Get out my paper cutter. This one is four and a half, seven and a quarter and plus an eighth, seven and three eighths. All right. So we want to pick a piece of paper to go on here. And I think I might use this one because I don't want to paint the whole tin. And at the same time, the colors in this would go with what's already on here. So let's do this one. First, let's take off the white edge of paper. Let's cut it to seven and three eighths of the other white edge. And then what did I say, four and a half? I lost track now already of what I said. Yeah, it's just a hair less than four and a half. So let's do four and three eighths. And then we'll test fit that to see how it fits. It needs to be just a hair shorter.  This is an old creative memories corner punch. I've had it for so long, it still works like a channel. Okay, so then I'm going to just again, we're going to test fit it. Yeah, I don't want it to go all the way to the edge, which it doesn't. So the next thing I'm going to do is I'm going to grab my E6000. So because this is a inkjet print, you don't want to use anything to glue it down or seal it. That's got too much water in it because the water is keeping away from the water is the key because if you have too much water, it's going to make the ink run. I'm going to grab something with a straight edge. Let's grab a gift card. Okay, we are going to put some E6000 on the lid here. As soon as I get it open. Okay, there we go. I'm going to run some E6000 around the edge. My E6000 is getting low. I need to get some more. Oops, so I need to start using the tube squeezer to get the glue out. If you don't have one of these tube squeezers, they're a handy tool. I can link that also in the video description. So then I'm going to just zigzag and run some across the middle, put the cap on so it doesn't leak everywhere. So now I'm going to put this down, eyeball it and get it in the middle. I start in the middle and work my way out. That'll prevent too many air bubbles. As the glue leaks out the edges, which it's likely to do, grab it with the edge of your gift card or whatever you're using and smear it on the top.  Now as you're doing this, if your paper moves around, you can, while the glue is wet, because this glue doesn't dry instantly, you can move your print around. Okay, it doesn't have to be a complete smooth even coat, but try to get some on most of the print and the E6000 will help seal the ink in so that it doesn't smear anywhere. So ideally now we're going to let that dry completely before we go on to the next step. Usually that's what I do, but for the sake of this video I'm not going to this time. It shouldn't make any difference, but I guess we'll find out. All right, I'll let me get the rest of the supplies and I'll be right back. Okay, the next thing you're going to need is some ranger glossy accents in clear. Now I don't know if other products would work with this. I have no idea. These are the ones I've tried. They're the ones I did these with and it worked just fine. I didn't pre-sand the tin on these. I didn't use any other kind of glue. I only used the E6000 and then the glossy accents. You should make sure it's dry, dry-ish before you do this next step, but like I said for the sake of the video we're not going to. I don't think it's going to make a big difference, but yeah. So the next thing that you want to do is cover it with something to clear coat it and protect the artwork on the print on the top. And also, can you see when you do the E6000 thing that it's kind of patchy? So the glossy accents will help smooth that out. Now you want to be careful not to put too much of this on because it'll just run over the edges and be all weird and just be a big mess. Let's zoom in. There we go. Okay, so I'm going to take this and I'm going to start about, I don't know, a quarter inch in from the edge. Oh, after I unclog it because it's got a clog. Let's see. It's handy also too, by the way, to have a pokey tool because if you get an air bubble, oh, didn't mean to do that. Unclogged it and got the needle tool out, which got stuck. All right, so about a quarter inch or so in from the edge. I'm going to run, start running my glossy accents. I'm not going to worry about doing a super thick coat. And as you can see, I'm not making sure, I'm not worried about making sure that there's no gaps. I'm just putting a decent amount on, but I'm not going too close to the edge. So then I'm going to take my, again, my straight edge and I'm going to start smoothing out the glossy accents, getting the air bubbles out and spreading it out. Because again, you want a thin coat. You don't want anything too thick. And you want to go up to the edge without going over. But I have a baby wipe in my hand, so if it does go over, then I will catch it. We'll also tilt it and see where it maybe needs some more, like right there. See, I spilt. I'll take the baby wipe and just do that. And I'm tilted again. Seems to be pretty good. Okay, then you let the whole thing dry, ideally overnight. And when it is done, you're going to be left with, when it's completely dry, something like this, it's not sticky. It's very durable. And pretty at the same time. And in the tin, you can use it as I have to store your watercolors. You could store pencils and pens in it. You could store paint brushes. You could use it as a travel art supply tin. Oops, let's go out the other way. You could do anything, but the point is that you've repurposed a tin. You've made it pretty. You've decorated it with your own artwork or someone else's. These would make great gifts for the creatives in your life. And yeah, they are a lot of fun and very easy to make. So yeah, I would love to see what you do with this and with the ideas the other ladies have with the digital art prints. Their links are in the description below. So pretty. That one is so pretty. So I didn't think I was going to like that one as much as I am right now. But yeah, anyway, I might have to keep that one. Probably not. I'll probably gift it to a friend. Anyway, as it's drying or once it's dry, if you find like right here, there's a little bit that's lifting. You can go back and put a little bit of glue under there and stick it down again. Ideally, that's why you want to wait for the E6000 to dry before you put the glossy accents on is not because you're worried too much about the one needing to dry before the other one's on there. It's just because you want to make sure it's stuck down. All right. Anyway, so that's it. Have a great time with that. I'd love to see what you do. If you want to start a conversation about it, you can join my Facebook group, A Life of Art and Self Expression. I'd love to have you over there. Again, the video description contains everybody else's links and the free download for the background I created. I hope you download it and have fun with it. You can do so many things with it besides just your standard journal page, so I'd love to see what you do with them in your art. Don't forget to like, share, and subscribe. Not only my channel, but the other artist channel that are involved in this project and support all of them how you can and the free content they provide you on Facebook and on YouTube and in the Facebook art groups. We all have ways to get support for the content that we provide, including Etsy shops and Amazon affiliate links and PayPal tip jars and Patreon and YouTube membership. There's so many ways. I have my own set of links. They're in the video description, so check it out if you have any questions. Leave them down or questions, comments, or concerns. Leave them down below in the comments below the video, or if you are connected with me on social media somewhere, feel free to DM me the question. All right, that's it for today. Don't forget the most important thing besides go out and play and make art. Do something nice for yourself because you deserve it. I'll see you later. Bye, guys.


Hey everybody this is Brett and today I'm excited to show you our very first 2021 Jeep Gladiator Mojave Edition in the limited edition color run Gekko Green. One of my favorite colors on the Wranglers and found out that we are getting one in Gekko Green and I said I have to do a video of this. So that's what we're doing, we're going to do a walk around here, we're going to check out the original window sticker, see all the options that this one has and just kind of show you the vehicle. This is actually sold so we do appreciate the person who bought it allowing us to do the video so thank you very much Mr. Customer. This one has the satin black hood. We shoot all of our videos in 1080p 60 frames per second so if you have HD capabilities on your computer, tablet, smartphone or television I highly recommend turning them on right now because it is your best way to check out the look, styling and options of the vehicle and especially a cool color like this. Look really good on an HD screen. So the Mojave package is meant for off-road, desert, racing, driving, you can see that it is desert rated, you get the Granite Crystal Jeep logos outlined in orange, the black Mojave lettering on the hood also outlined in orange that's kind of the theme because everything is orange trimmed on this vehicle, you get the painted and polished aluminum rims and it comes with the Falcon Wild Peak AT tires. These are LT28570R17s and they are definitely designed for sand and off-road usage. Comes with the 2.5 inch internal bypass shocks, the Fox shocks on there. You can see it does come with a lift kit from the factory also has the Fox shocks hydro jounce bumpers on here, you get the Kowal induction hood meant to keep your air intake above the sand, you get the orange powder coated tow hooks on the front and this one just has the normal halogen headlamps. Color matched fenders and color matched hard top pieces on this one, this one also comes with a Mopar fold up tonneau cover, you also get the rock rails with the Mojave package. We're going to take a look at the original window stickers so feel free to pause this, I'm not going to go through everything but just kind of some of the important stuff. 2021 Mojave, the limited edition Gecko clear coat, 3.6 liter 8 speed automatic transmission comes with the Jeep wave membership and heavy-duty Dana 44 wide front and rear axles, the 410 gear ratio. The limited edition Gecko clear coat is $395, leather trim bucket seats with sport bolsters are $1725. The customer preferred packaged cold weather group is $995 that gives you the heated seats, heated steering wheel and remote start, 8.4 radio and premium audio group is $1995 gives you the navigation system off road pages, alpine premium audio, serious guardian, five-year serious travel link and five-year serious traffic plus and automatic dimming rear view mirror. Jeep safety group is $995 gives you park sense rear park assist system and blind spot and cross path detection, LED tail lamps, adaptive cruise control and forward collision warning plus is $795. You get the bright sills, sill guards by Mopar which are those right there, they look really good. And then it has the hard tri-fold tonneau cover by Mopar which is $995 the automatic transmission is $2,000. And then this is new windshield with Corning grill glass is $195 and I will show you in just a second here on how you can tell if your windshield on your new Gladiator Wrangler has the Corning glass just by looking at it. So I'll show you that in a second. Remote proximity keyless entry is $695, body color freedom top is $2595 for that color match hard top. Cotton black grill is $195, the body color fender flares are $695 so between the hard top and the fender flares it's $3,200, $3,300 worth of color match stuff there. Wireless Bluetooth speakers $295, the 17 inch rims are $995 and it comes with a spree and bed liner by Mopar. This one MSRP'd for $63.85 I tell you to go to our website to see all the rebates and incentives but this one is sold and no longer on our website so you can't do that but if you want to check us out our website is in the upper right hand part of screen just to check out all of our inventory. Three year 36,000 mile bumper to bumper five year 60 powertrain. Miles per gallon 22 highways 17 city 19 average and then the crash test range only a front crash four and five stars and then rollovers three others are not rated. So we're going to continue with the outside walk around here. I always want to show these fox shocks in the back because they're pretty heavy duty and definitely made for off-road usage and just everything on this truck is pretty heavy duty to deal with the stress of off-roading. This one comes with the LED tail lamps you get the orange tow hooks in the back notice that that Jeep logo is outlined in orange as well there's that Mopar trifold tonneau cover pretty nice material there has the shock down assist spray and bed liner also has the LED bed lighting back here and it does have the case for the hard top pieces tailgate is really light it's also on a shock down assist so it's never going to slam down on you so that's pretty cool and as you go down this side just a really good looking color so I know I promised you I'd tell you about the windshield here has heated mirrors blind spot monitoring so if you look at the front here there's actually a little bit of there's a gorilla on the front of the windshield if you have the gorilla glass so there we go now it's in focus so if it has that then you know that you have the gorilla glass this is the first one I've seen with the gorilla glass and I'm pretty sure they just started offering that in 2021 leather seats you get the orange stitching the orange Mojave stitching on the backrest even the release right there is stitched in orange auto headlamps the steering wheels got the orange stitching you get kind of the copper orange surrounds on the air vents orange stitching on the door and if you're curious about Gacko green paint codes PFM that's where you find your paint code we'll take a look inside here show you all the options and the radio and everything get the seven inch LCD display and has a digital speedometer compass outside temperature display once again the heated leather wrap steering wheel there's your adaptive cruise controls your normal cruise controls Bluetooth and information center controls on the left and as always they have the audio controls on the back this one has the 8.4 4C radio which gives you the factory navigation system on it also AM FM and Sirius XM radio capabilities you have your heated seats and heated steering wheel controls and you can check out that backup camera what I love about the new backup cameras on the jeeps the wranglers and gladiators in particular is that they're HD super crisp super clear and really helpful on there you also have all your different apps including the off-road pages which are really cool those take a second to load up while those are loading up take note of this dash it's got it's kind of like a powder coated granite crystal or maybe mineral gray paint on there but it's it's got a little bit of a texture to it there your off-road pages you have your steering angle your transfer case your latitude longitude altitude whether your axles are locked or unlocked you have your accessory gauges and pitch and roll which is nice especially if you're off-roading with this vehicle down here your more tactile climate controls your heated seat buttons heated steering wheel buttons start stop capabilities that's your stability control that is your select speed control so if you're going slow you can or down a hill or something you can select that and set your speed power windows there's media center augs USB USB-C you have your axle lockers right there and then your off-road plus mode for speed I'm sorry four-wheel drive shifter eight speed automatic transmission you get a little gladiator logo on top stitched in orange and then the red button release right there keyless entry with the remote start has the flipper key I always like these keys ever since they came out in 2018 really solid key and chunky I guess is the word push button start and yeah just otherwise it's a normal Wrangler front end in here have your hard top pieces that come off SOS and assist buttons home link buttons for your garage door security systems and lighting systems and we'll take a quick look at the back seats and then we'll do one more final walk around on the gladiator here here's your wireless speaker so that's really nice it's portable it charges behind the backrest over there and you can hook it up to your bluetooth cell phone latch child safety system sliding rear window with the built-in rear defrost these seats fold down and then they also lock so like if you have the hard top off and you want to store stuff back there you can lock it so that nobody can get back there if you have valuables wallet purse whatever and then these seats also fold up you have your storage for all your bolts and everything and you get factory floor mats back here child safety locks on the back doors and now that I got all those lights on and check out the LED tail lamps there LED license plate lights and we'll just do one more personal or one more final walk around and I would personally like to thank you for checking out the video today and hopefully from this HD video you will have been able to get a really good idea of the overall look styling idea the color and the options on this particular gladiator thanks for checking out the video and to see more vehicles like this one you can go to our website right there www.summitauto.com full pictures and descriptions of every single vehicle from two locations all at summitauto.com and if you'd like to check out more HD videos you can go www.summitauto.com. Remember to like subscribe and share on this video and all the videos that you see there click the bell notifications you'll get updates on the videos we do each and every day here at Summit Automotive in fact in a second you will see a link to subscribe to our YouTube channel in the upper left a link to more gladiator videos like this one the upper right link to this vehicle on our website in the lower left and a link to one of our latest videos in the lower right click those checks out and we're super excited to be offering the 2021 and 2022 Jeep Wranglers and gladiators here at Summit Auto thanks again for checking out the video remember to like subscribe and share


Welcome back, we are proving that un is cyclic whenever n is power of an odd prime p. This is what we are proving, but to begin with our baby step is to show that up square is cyclic. We proved that up is cyclic for all primes p and using that we want to show that whenever p is an odd prime then up square is cyclic. So, we have the statement here on the slide for you. Remember that we are always taking p to be an odd prime. This is something that will remain in force now for this lecture and perhaps also for the next lecture. And I have told you the plan of this proof. So, let me just quickly go through that once. What we observed in the last lecture was that if you wanted to find a primitive element in up square then by going modulo p that element should better be a primitive element in up.  And so when I am looking for primitive roots modulo p square I should be looking in the residue classes of the primitive roots modulo p. So, what I do is that I choose a primitive root a modulo p and I check whether that is also primitive root mod p square. If it is not then we will do a slight modification and get a primitive root mod p square that is the plan. So, let a in the natural numbers be a primitive root in up. So, modulo p this element a is a primitive root. So, clearly first of all a is an element in up square. This is because if a is a primitive root in up then a is an element in up. So, a is co prime to p. Therefore, a is co prime to p square and so a is an invertible element modulo p square. So, a is our element in up square. Let the order of a in up square be d we want to check whether d is equal to pi p square pi p square is p into p minus 1. So, we of course have that d will need to divide pi p square which is p into p minus 1. But p minus 1 will also divide d the reason being that a power d minus 1 is divisible by p square would imply that p also divides a power d minus 1 and since we have started with a primitive root in up the order of a in up is p minus 1. So, p minus 1 will therefore have to divide d and d needs to divide p into p minus 1. So, the possibilities for d are p minus 1 and p into p minus 1. There are no other elements which are multiples of p minus 1 and which are also divisors of p into p minus 1. This is where we are using that p is a prime. If you show that the order of this element d cannot be p minus 1 then we are done. If d is not equal to p minus 1 then we are done. But this may not happen you may have d equal to p minus 1 if the order of the element a in p square is also p minus 1 then consider a new element b which is a plus p. So, first of all here b is also an invertible modulo invertible element modulo p square because the GCD of b with p is also 1 and so GCD of b with p square is also going to be 1. So, b is an invertible element further modulo p we have that b is same as a. Therefore, b is also a primitive root modulo p. So, all the discussion that we have done with a holds for the element b also which is that order of b modulo p square can be p minus 1 or p into p minus 1. And if you can now show that the order of b modulo p square is not p minus 1 then you have got a primitive root for p square. We show p square does not divide b power p minus 1 minus 1. This will tell order of b in up square is not p minus 1 and then we are done. So, we now need to only compute this b power p minus 1 minus 1.   So, in this binomial expansion we notice that the elements from here onwards are divisible by p. Of course, we do not have one divisible by p square. What we mean to say is that from this up to p power p minus 1, these are all divisible by p. This is not divisible by p by p square but it is divisible by p and finally we have a to the p minus 1 minus 1. a to the p minus 1 minus 1 this is divisible by p square. This is because the order of a modulo p square was p minus 1. So, we have among the right hand side the elements which are divisible by p square. So, this is divisible by p square together with minus 1 and this things are divisible by p square. So, when you look at this modulo p square the b power p minus 1 is exactly this p minus 1 a raise to p minus 2 into p. Here you have that p divides it this but p square it is not. So, we get it to be not congruent to 0 mod p square and therefore the order of b in u p square is not p minus 1 that is it. Then this b will have to be a primitive root modulo p square by the discussion that we have seen earlier. So, once again what we did was that we observed first of all that u p is cyclic. So, u p has to have a primitive element.  So, we will start with the primitive elements modulo p and check its order mod p square. We observed that there are only two possibilities p minus 1 or p into p minus 1. So, it is almost a primitive root modulo p square or it is only a primitive root modulo p and not modulo p square. If it is not you simply add p to it and then we see that by adding p to the element a that you started with we do get a primitive root modulo p square. So, what we now intend to do is to do this as an example for this very particular case. p is 2, p is 5, a is 2. So, 2 in u 5 is a primitive root or what is also called as primitive element.  So, this is exactly u 5. So, we have that u 5 with isomorphic to C4 and it is generated by the element 2. Now the question is is 2 primitive for u 25? This is the question but so for this we need to check whether 2 power 4 is congruent to 1 modulo 25. So, we know that the order of 2 in u 25 can be 4 or 20.  These are the only possibilities for the order of 4 modulo 25. Is this true? So, 2 power 4 is actually 16 but 16 is not congruent to 1 modulo 25. Therefore, the order of 2 mod 25 will have to be then 20 because this is not possible and hence 2 also generates the group u 25 which is isomorphic to C 20. So, if we were lucky and we had chosen the generator for 5 to be 2 then we will get that the 2 is going to further generate the element the group u 25 but you may make a small mistake and instead of 2 you may take a to be 7. So, observe that modulo 5 7 is congruent to 2 and therefore 7 also generates the group u 5. This is something that we already have but is it true that 7 power 4 is congruent to 1 modulo 25 because we know that order of 7 in u 25 it can be 4 or 20. If it is 4 then it is not a primitive root modulo 25. If it is not 4 then it is a primitive root modulo 25. So, 7 power 4 is 49 square and therefore when you go modulo 25 49 is actually minus 1 because 50 minus 1 is 49 and so this is 1 modulo 25. So, this tells you that the order of 7 in u 25 is actually 4 and so it cannot be this and then by the method of proof we would look at 7 plus 5 which is 12 this has to be a primitive element in u 25. This is something that you should check. So, what you should check is that 12 power 4 is not congruent to 1 modulo 25. So, once you check this then this will be proved. So, this is a very simple example which tells how we can compute the primitive roots. Once you know the primitive root modulo p you have a primitive root modulo p square which is congruent to the primitive root that you started with modulo p. You may ask how many primitive roots modulo p square can I get in this way? So, the question that you may ask is suppose I fix one primitive root modulo p. We know by our method of the proof that there has to be a primitive root mod p square which is congruent to the primitive root mod p that you have fixed. But among all those different p elements which are congruent to the same element modulo p how many are going to give you the primitive roots modulo p square? This is a very interesting question it is so interesting that I am going to ask you this question in the tutorial. But think about this question and we will see the answer in the tutorial. We now go to our next result which shows that if you have n to be p power e then un is cyclic and I will remind you once again because we are stating the theorem here for the first time that our p is an odd prime. Once again our beginning step will be the same step which we had for n equal to p square which is that we observed that to get a primitive root modulo p square we needed to start with a primitive root modulo p. Here if we are taking e to be bigger than or equal to 3 because for up and up square we are done then we have to start with a primitive root modulo p square and work with that in up power e. We will show in fact a more stronger result than we had in the case where n was p square. Let a in up square be primitive then a is primitive in up power e for all e bigger than or equal to 3. This is a fantastic result. It tells you that once you start with a primitive root modulo p square that element will continue to remain primitive modulo all the higher powers. That is a great result because now we do not have to work with cases. When we looked at the case of u p square and we started with a primitive root modulo p we had to deal with the possibility that the element will not remain primitive mod p square. There is no more such possibility. Any a which is primitive mod p square is going to remain primitive mod p power e for e bigger than or equal to 3 and the proof is using induction. Proof uses induction. To understand the proof clearly let us deal with the case p cube first. Here I am going to observe and will not repeat this observation that a is always primitive co-prime to the prime p. It is relatively prime with p and therefore it is an element in up power e. That is something that we are going to use. So, let us do the case of up cube. Let d be the order of a modulo p cube. Then once again as we have observed in the previous proof p into p minus 1 which is phi of p square will have to divide the order d and it will also divide p square into p minus 1 which is phi p cube. It will have it will be a multiple of this because whenever you have p cube dividing a to the d minus 1 you have p square also divides p cube and therefore p square divides a raise to d minus 1. And therefore d should be multiple of the phi of p square which is p into p minus 1 into some alpha for instance. So, therefore we have this. So, now d can be equal to this quantity or it can be equal to this. There are only two possibilities for d once again as we have noticed before in the case of u p square. So, here d will belong to the set p into p minus 1 and the set p square into p minus 1. We want to show that d cannot be this. This is the case that we want to remove. So, for that we use that since a is primitive mod p square its order in u p square is p into p minus 1. Thus p square does not divide a power i minus 1 for i 1 less than i less than p into p minus 1. This is one simple fact that we use. And now I show that if your d is p into p minus 1 then remember this is the order modulo p cube. Then you have that a power p into p minus 1 is congruent to 1 modulo p cube.  Further p square does not divide a to the p minus 1 minus 1 but p divides a to the p minus 1 minus 1.   This is because we are starting with the difference of these being divisible by p but not by p square. So, this alpha cannot have a p in its factor. So, therefore, alpha comma p has to be co-prime. And once we have this we have to now raise both sides to the pth power. So, using binomial expansion we have that a raise to p minus 1 to the power p which is nothing but a power p into p minus 1.  So, we have the binomial coefficient which is p. So, I will just put a summation sign here because all the remaining terms will have summation p choose i 1 to the power i and alpha p to the power. So, alpha p power i and 1 to the power p minus i and i goes from 2 to p. So, these are the terms where the powers of alpha p will keep increasing and you have the coefficient to be p choose i. So, we observe that in these coefficients you have a factor of p here actually you have a factor of p square here and you have a factor of p here.  But remember that alpha comma p is equal to 1 and therefore we have that this is not congruent to 1 mod p cube. So, the order of a modulo p cube cannot be p into p minus 1 and therefore order of a in u p cube has to be p square into p minus 1 which is what we wanted. So, we are proving that un where n is power of an odd prime is cyclic and what we have done is another baby step. Remember in this proof of un being cyclic where n is a power of an odd prime we did the p square case first and now we have done the p cube case. When in the beginning of the next lecture we are going to look at all the higher powers and use induction to show that such a un is cyclic. So, I hope to see you in my next lecture. Thank you.