Maths - Propositional Logic

A proposition is a statement which is either true or false, but it cannot be both true and false at the same time.
A question, exclamation or a command are all not propostions.

Logical Operators:

Unary Operator (Works with one value)   NOT  ¬    e.g      ¬P
^ AND
˅ OR
͢ ͢    Conditional (Always false when Q is false (When P͢  Q)) otherwise it is always true

<-> Only true if both are true or if both are false.



Implications relating to P -> Q

Implication: P->Q
If a student is female, then the student has brown hair.

Converse: Q->P
If a student has brwn hair, then they are female.

Inverse: ¬P->¬Q
If a student is not female, then they do not have brown hair

Contrapositive: ¬Q->¬P
If a student is not brown haired, they are not female.

TRUTH TABLES

P                Q                   P->Q                 ¬Q                  ¬P              ¬Q->¬P

T                T                      T                        F                    F                    T
T                F                      F                        T                     F                   F
F                T                      T                        F                     T                   T
F                F                      T                        T                     T                   T







Argument Validity

An argument is a set of compound propositions called premises together with another compound proposition that is suggested follows from the premises.
This is called a conclusion at the end.

The general form of an argument is  p1^p2^p3...pN) = Conclusion.

The conjunction of premises (and gate) is only true if all the premises are to be true. The argument is only valid when each premise is true!!

p1    p2    p3          C
T      T      T           T
at least one F      T or F


Example:
P - You read alot                                    Q - You are a brilliant conversationalist
R - You have many friends

The argument put forward is:
'If you read alot' = P, 'you will become a brilliant conversationalist' = Q. If you become a brilliant conversationalist, 'you will have many friends' = R. Therefore if you don't have many friends, you dont read alot.

The premises taken from the above arguments are:
p1 - If you read alot, you will become a brilliant conversationalist.    P->Q
p2 - if you are a brilliant conversationalist, you will have many friends.    Q->R
C - If you dont have many friends, you dont read alot.    ¬R->¬Q

p1^p2 = C
or
(p->q)^(q->r) = (¬r->¬p)


TRUTH TABLE


Where premises are true.
                                                    p1                      p2                                      C
P           Q              R                 P->Q                Q->R       ¬R     ¬P          ¬R->¬P

T           T             T                        T                    T             F          F               T
F          T             T                         T                    T             F         T               T
F           F              T                       T                     T           F          T                T
F          F               F                       T                    T             T         T                 T

To see if an argument is valid we must look at the rows of the truth table for which the premises are all true, and when all the conclusions are also true. If this happens (as above) we know that the argument is valid.





Contingency
e.g. (P v Q) -> ¬P

Propostions that are sometimes true and sometimes false, depending on P and Q values. With at least one T and at least one F appearing.
(P  v  Q) -> ¬P
      F
      F
      T
      T
Contains both True and False values in the conclusion.

Taughtology :
A taughtology is when all values in conclusion are True
e.g. P->( P  v  Q)
                    T
                    T
                    T
                    T
All final value ares true.


Contradiction:
 Is when all the final values are false.
P ^ (¬P  ^  Q)
            F
            F
            F
            F

Each final value is false. 

Security Technology

I am currently studying a module on Security Technology at university and will share what I am learning and understanding on here, it may or may not interest you but it will also help me with revision for my courses. It may appear basic to begin with but that is because we are all beginners to the course and they are breaking us in gently :P

If you have a read you may find that you do infact enjoy what you are reading and could ask me questions about it and find that you may want to do something similar to myself as I find it a rather interesting subject.

BioMetrics

BioMetrics litterally means the 'measure of life' which therefore means a way in which you can measure life, there are many different ways of doing this and it has been around for centuries - for example in the 14th century in China they stamped both palm and footprints onto paper in order to indentify people and used mainly to distinguish children.
In 1890 a man called Alponse Bertillon invented a way of keeping track of criminals by taking multiple body measurements, such as length of arm, skull etc. The problem was that Bertillonage was measured by many different people and with many different measuring tools, which made it near impossible to standardize the measurements in which would be taken and therefore result in lack of accuracy when the results when be taken from the same person again. It also had the issue that some people who attempted the technique would round up, whilst others would round down therefore could mean that the same person being measured by two different people could end up with completely different results, which therefore leads to mistaken indentity.

        An example of one of the measurements taken whilst using the Bertillonage technique


 Sir Edward Henry - Edward Henry worked for the Bengal police and was eventually promoted to Commissioner at Scotland Yard after using the Bertillonage technique throughout his career, but then introducing the fingerprint taxonomy which was the identification of others by their finger prints.

Along with the work of others such as Galton he realised that the constancy of peoples fingerprints could be used much like the Bertillonage technique, he noticed that each fingerprint of every person was different and had many features (also called minutia) such as loops, whorls and arches which refer to the patterns in which the skin on your fingers reflect.




There are also many other ways in which the biometrics of something can be recorded that arent neccesarily connected to human life, in order to roughly work out the age of a tree you can count the rings inside the tree and also with clams you can count the shell rings.

Use of Biometrics within technology

There are many many ways in which biometrics are used within everyday life such as your social security number, passports, medical records, dental records, drivers license, student ID, credit cards... you get the picture; These are all created and can be used for identification of a person.

The main reason for Biometrics in the modern day is for verification and security, verification defines if the person in question is actually who they say they are, this can be done via a password, PIN, signature etc. Whereas Identification is actually finding out who the person is I.E the forms you fill in whilst applying for passports and such.
It is infact rather easy to have your identification if it was just as simple as filling out a form, so therefore there are more accurate ways in which you can be identified and verified, such as a picture ID, but there are also more complicated ways which would be used in higher security situations, such as a bank vault... This ranges from fingerprints - in use with a scanner, Iris/Retina scanners which involve the use of infra-red lasers to read the patterns of the blood vessels within your eyes as they are unique to each of the people that use them because everyones blood vessel patterns are different to others.

Main methods of identification and verification are:
Fingerprints
Facial Recognition
Hand Geometry - finger length/width
Iris Scan - Front of eye
Retina Scan - Back of eye
Vascular Patterns
DNA - Blood, hair etc.
Voice Recognition
Keystroke Patterns

I should also mention that it is vital for all data that is being used for these processes is stored securely and to be encryted to maintain the high security level.

Stoke City 2 - 0 Fulham

Its been a while since I posted due to home issues and also because of work/starting university but I am now hoping to get back and post a few more a week now :)

It has been a while since I posted some information about my team Stoke City FC so I thought I would begin with the result at the weekend, it was a 2-0 win for Stoke over the decent side of Fulham. It was yet another home win which means if I am not mistaken that we have only lost one home game in the whole year at the Britannia Stadium (non-competetive); I was unable to attend the match because I was too busy serving coffee and scooping ice cream for people further down the road at work...

Despite losing away to the likes of Swansea and Sunderland our form this season has been brilliant with us drawing 1-1 with Man United (thats a win result for us!), beating liverpool and holding out for a draw with chelsea (also a win for us). We have also managed to win a few more less noticable games but nevertheless our season couldn't have got off to a much better start. The saturday game was an important victory because it means that we head into our european game on thursday with a winning mentality which is vital when playing against teams such as Dinamo Kiev and Maccabi Tel Aviv, it also means that we maintain our good league form and I am hoping that would could possibly be within the top 8 by the new year. Our last 3 seasons have been a matter of survival and Tony Pulis has been adamant that we reach the 40 point milestone in order to survive. However I now believe that we need to aim higher than that and by being in the top 8, it will help greatly to maintaining our place in the top half of the division.

We had Jonathon Walters score a goal for us against Fulham which is good news as you always need your forwards to be scoring when called upon, it is also brilliant that super Jon is keeping up his quality and ever increasing his popularity with our fans. Another goal which I think is vital is Rory Delap, he scored the second and I am delighted that he has finally been rewarded for his hard work and effort. Many people underestimate Rory and unfairly label him as a donkey used just for his throw, slow, poor ball distribution etc. However when played in his correct position he proved on saturday that he can pass the ball, help the flow of the game, put in important tackles when needed, is back to help when needed and also forward when attacking as an extra option. At his age of 35 for a central midfielder, Delap is old, but as the statistics show he was one of the players on the pitch that covvered the most ground in the entirity of the game. Another player I adore is Wilkinson but that is a whole other story altogether :P

Accumulator

Last week I placed two bets of six on several football teams to win, however the only team that actually pulled through out of the 12 I bet on was Stoke... I will bet on Stoke to win the majority of the time but I would like people to help me choose teams that you think will win. Even if you don't know who they are playing, if you comment below I will select that team to win in my next bet. It is mainly luck anyway :P

Thanks for reading

Greatest Albums of the Noughties

Here is a list of my opinion of the top 8 albums of the 00's
You may notice the large difference  in genres but hopefully you will agree with some of the albums I voted as my favourite.

8. Kano - London Town 

As a personal favourite of mine I have to include this album in my list :P This is a grime album which I feel captures the darker, underground world of the UK. Even if you feel you are not normally one to listen to this kind of music, this album really could suit all music enthusiasts. Kano is a very good lyricist and has a flow that you can enjoy listening too, aswell as doing his own twist on the famous 'Fightin' the nation' with interesting consequences. Even my 45 year old Dad now listens :D

 7. My Chemical Romance - The Black Parade

 Not normally a band that I would listen too, but due to my little brother buying the album I though I may aswell give it a try. I absolutely fell in love with the whole feel of the album, it is a dark album that really captures your soul with every song. Sometimes depressing but can definately contact different emotions that you would not normally expect from a rock/emo album. If you're feeling like you want to let everything out, this is the album you need!




6. Only By The Night - Kings Of Leon

The Kings Of Leon were always a fringe rock band that weren't always well known within the popular music scene, however with the release of this album they caught the eyes (and ears) of everyone. With songs such as 'Sex on Fire' it was hard for anyone to say that the KOL had hit the nail on the head with this album, reaching global heights that I'm sure even they couldn't imagine. The album really helped KOL move forward and become one of the most well known bands in the world.



 5. Invaders Must Die - The Prodigy

A band I have actually had the privilage of being at the front of a 60,000 strong crowd gig! This amazing album completely blows your mind and has the perfect tracklist to pump yourself up! They are a drum and bass band that I'm sure you will have heard of, or at least will recognise some of their songs instantly (no matter how old you may be ;P). The most recognised songs on the album are 'Invaders must die' - 'Omen' - and 'Warriors Dance'.

4. Hybrid Theory - Linkin Park

Linkin Park burst onto the scene with this amazing album of Rap-Metal. The combination of Mike Shinoda with his epic rapping skills and the raw metal talent within the band was relatively new to everybody and it worked a treat. A personal favourite of mine to blast through the headphones whilst walking down the street, with a number of different songs that can also calm down and let you listen to lyrics, and others that can make you want to jump up and down like a madman!

3. Kanye West - Graduation

American Hip-Hop music artist Kanye West's third album graduation reached #1 in the UK charts and sprung life into the music world. Unsurprisingly this album contained many tracks that would be used as mobile ring tones, be played in all of the clubs and therefore setting the standard for hip-hop artists around the world! It consisted of big hits like 'Good Life ft T-Pain' and the universally known 'Stronger'.

2. Whatever People Say I Am, That's What I'm Not - Arctic Monkeys

The 'Artic Monkeys' burst onto the scene with an instant classic, the single 'I bet that you look good on the dancefloor'. It had both parents and children alike dancing and singing without a care in the world, storming the UK album charts to #1. The album as a whole had a number of brilliant songs such as 'Mardy Bum' - 'When the sun goes down' - and a personal less well known favourite 'A certain romance'.

1. Standing On The Shoulder Of Giants - Oasis

The reputation of this band was not built just down to a few good tracks; as proven by this album Oasis show just how gifted they are with a brilliant number of rock anthems. Standing On The Shoulder Of Giants really did show the world how good Oasis were and how big they were going to be, the album consists of many beautiful tracks but my personal favourite would be 'Gas Panic' as my greatest rock song ever. Other great songs on the album consist of 'Go Let It Out' and 'F**king in the bushes'.

Book Review : 'She Stood There Laughing' - Stephen Foster

 This is a review taken from the website Ciao in which I wrote quite a while ago and just thought I would post it here. The book is written by a man called Stephen Foster who also was an avid stoke fan, however he passed away recently this year and I just thought I would post it on here again.
R.I.P

A book about the love of football between a man, his son and THEIR football club, written by Stephen Forster. I first read this book as a young boy, given to me by my Dad as we are both Stoke fans, It was a very entertaining read back than but after re-reading it recently I realised just how good this book is! The main plot of the book is about Stephen himself and the repercussions of following such a lowly second division team like Stoke City FC, paying sometimes hundreds of pounds to visit dingy parts of the country on foul rainy days to watch your team lose 5-0 to second off bottom in the league (you're team is bottom of course).
Hilarious throughout, as a football fan of any team you can really appreciate the thoughts and feelings that Stephens shares with us. I'm sure anyone who enjoys sports of any kind would enjoy the different views, ups and downs that are portrayed in the book. It tells of past trips he has had to endure, some that would make you want to cry with laughter - at the authors expense for following such as rubbish club! And others that will remind you of just how good it is to go and support you're team, no matter how good or bad the day goes.
Stephen Foster talks alot about his son, who he takes to as many games as he can. Both of them (at the time of writing) lived in Norwich, which is a good while away from Stoke making home games very hard for them to follow; but worse than that, his son has to go to school with the local Norwich fans (and man ure fans of course). The book also opened my eyes to not only how much I miss going to the Stoke matches (or any football matches for that matter) but gives me a close insight to how my father would feel when taking me to games. Throughout the book Stephen expresses his dismay in making his son follow the dark, lonely and sad path that is supporting Stoke City, however he states how it would not be the same without having someone to moan, grumble and discuss the matches with. I was the son that my father would turn to, to talk about Stoke with - someone to go through the pain with him!
Although it sounds as though both me and Stephen are making it seem like nobody would ever want to support this club, it is merely an overexageration that I'm sure football fans worldwide would be able to relate to. Overall the book is very interesting to read, including views from another fans point of view; gives information about the club Stoke City and is generally funny with dry humour throughout. I would definately suggest purchasing the book no matter what football club you support.
  

Album Review: Kano - Method to the Maadness

Kane Brett Robinson, better known as Kano realeased his fourth studio album 'Method to the Maadness' on the 30th of August 2010. Despite playing a massive part in bringing the UK grime scene forward, Kano has never really made it commercially and is not as well known as other grime artists such as Chipmunk, Dizzee Rascal and Tinchy Stryder; in order to change this it seems with the release of this album, Kano has evolved his music style with more of a dubstep/D&B style, whilst still maintaining his lyrical genius and amazing flow. The album includes songs produced by Chase & Status and features including Wiley, Damon Albarn, Ghetts and Vybz Kartel.

As of yet there has been three single releases from the album, one of which 'Spaceship' is produced by Chase & Status. You can really tell what Chase & Status have done in terms of the track, moving with the times and generating a dubstep feel; implementing this with Kano's talent makes 'Spaceship' my personal favourite of the album. Some people say that Kano is getting weaker lyrically recently, but this track alone proves that he is infact getting better with age. I would also say that this is the track that will appeal to most listeners as the best on the album, simply because of the well known producers and of the catchy chorus. The video features Kano sporting some extravagent yet stylish clothes in typical Kano fashion and reflects the song brilliantly - however could be seen as repetitive and boring by some and would appear to be have been created with a low budget. 'Get Wild' is the first single to have been released from the album and quite frankly is different from the rest of the album, it reminds me more of Kano's older tunes such as 'Buss it up - ft Vybz Kartel' which still shows that KA hasn't sold out his old ways for the commercial lifestyle. A feature on the track is Wiley, despite me being a big fan of Wiley I feel he is is simply blown away by the immense lyrical flow of Kano; the track on the whole is not one that would appeal to your typical listener as it does not just consist of a catchy chorus, but one that you can really appreciate the skill of the writer and the time/effort that has been put into it.

Other than these two tracks I don't really go back and listen to the other songs on the album, this may just be because I'm used to a bit more variation in Kano's albums such as 'London Town' whereas most of the songs on MTTM are similar to each other. Kano Performed his other single 'Upside' on the TV show Big Brothers Big Mouth and despite me trying (and I really did!) to like it, playing it over and over in my car - I just thought that it was not up to standard at all and not really worth the effort. I also have to include the fact that when I was encouraging my friends to listen to and enjoy the album, that one of them referred to it as like 'Ross's Noise' off the sitcom 'Friends' if you are familiar with it (the keyboard noises). On a whole I think the album is a success in Kano's career with helping him progress to greater heights and becoming more well known on the music scene. If I had the choice to get my money back for the album, I beleive I would still keep the album and that if you are wondering whether to purchase this; give it a try, its something different to what you would normally expect as it is, I believe is a result of Kano attempting to increase his target audience. I do however think that their will be another - better album not far away for Kano.

Carp Fishing for Beginners

I'll be making a series on youtube which will be for people wanting to begin carp fishing. I've done this because there doesnt seem to be many tutorials out there (useful ones) and I think that I can help people with different methods of carp fishing, all different tackle and equipment you will need and also small tips and tricks that I have picked up over the years (:

First video is here:

Not sure whether it will appeal to too many people but it is a start.


Oh and any subscribes/likes/comments would be greatly appreciated and returned