http://www.writingfun.com/ – a fantastic writing website I used while on practicum

Some more pages I found by Jenny:

http://www.teachers.ash.org.au/jeather/jennyindex.html

http://www.amathsdictionaryforkids.com/

HelperTeam.com est un forum Algérien d’entraide en Mathématiques.

Le forum utilise vBulletin, et ne se limite pas qu’au Maths, on peut y trouver l’actualité des voitures, sports… et on a la possibilité de répondre aux sujets sans être enregistré !

Alors si vous bloquez sur un problème de maths, vous savez qui contacter

Exercise 7.12: Let be the sum of independent rolls of a fair dice. Show that, for any , .

Solution: Let be a Markov chain on state space consist of states: , where the chain reaches state if and only if .
The transition matrix is for and . The claim is equivalent to

We know that if a Markov chain has an irreducible, aperiodic transition matrix and an invariant distribution , then for all of the state space.

We will prove the defined above is irreducible, aperiodic and then find the invariant distribution of (it will turn out that as we need).

Exercise 7.21: Consider a Markov chain on the states , where for we have and . Also, and . This process can be viewed as a random walk on a directed graph with vertices , where each vertex has two directed edges: one that returns to and one that moves to the vertex with the next higher number(with a self-loop at vertex ). Find the stationary distribution of this chain.(This example shows that random walks on directed graphs are very different than random walks on undirected graph).

Solution:

While listening to the Liberal Party of Australia disintegrate under the weight of a ‘leader’ who hasn’t read Machiavelli and a bunch of old white guys who think that they were elected for their scientific opinion, I began to think about Simpson’s Paradox.

It’s pretty cool. Take the 1998 Federal Election. The Howard Government had a twelve seat majority in the Lower House (so more than 50% of the seats) but only got 49.02% of the two-party preferred vote (so less than 50% of the votes).

It’s easy to see why this might happen. Imagine two political parties — the Optimes and the Populares — are attempting to be elected into a parliament with only twenty seats. For each seat, there are one hundred voters who are all very good people and do not lodge invalid votes.

Imagine that the Populares win their seats with 100% of the vote for those seats (that is, for each Populares Party seat in the parliament, 100 votes were lodged for the Populares Party). Also imagine that the Optimes Party only win their seats by one vote (that is, for each Optimes Party seat in the parliament, 51 votes were lodged for the Optimes Party and 49 were lodged for the Populares Party).

After a gruelling televised broadcast probably involving Koshie and some sort of Eureka Tower of Power, the Optimes Party gains eleven seats of the twenty and so forms government.

There were 2,000 votes cast in this election (20 x 100). The Populares Party scored 1,439 of them (9 x 100 + 11 x 49).

That’s 71.95% of the total vote and yet they won’t form government. Yay, democracy!  Let’s spread it across the Middle East!

When we add more parties to the mix (as we end up doing in the Senate due to the extremely nonsensical process by which we ‘elect’ senators), we can end up with situations where a person who has the support of fewer than 10% of the votes in their district can block the plans and designs of parties with greater support.

In the last election, it was a Ruddslide in favour of the ALP. This included their plan for an ETS. The ALP attempts to bring an ETS into fruition. Minor parties who do not have the broader support of the voting public block it. Yay, democracy! Let’s spread it to the Middle East!

Sure, the ETS is probably a bad idea. Its reasoning seems to run along the lines of ‘We need to do something; this is something; ergo, let’s do this.’ This post is not attempting to justify the ETS — and I’m rather against attempting to use market mechanisms to deal with pollution — but it does show that we have somehow transformed ‘Democracy: it’s the rule of the people’ into ‘Democracy: it’s the rule of whoever won an arbitrary game with no necessary connexion to the needs or desires of the population.’

This week in my maths set we have been focusing on percentages. We discussed where they might come across percentages in real-life contexts.

I decided to try some different ways to gather data and so created a simple PollDaddy survey with yes no answers so that we could then look at the results and calculate the percentages etc. This nearly didn’t work as 97 people took the survey. 3 more and the maths would have been a bit too simple. The children were amazed by the fact people from Israel, Malaysia, Spain and Poland took part in the survey.

At the beginning of the week we played Family Fortunes – points being rewarded on the basis of the percentage for each answer. We then thought about creating our own Family Fortunes game. Using Etherpad I created a couple of questions and opened it up to my PLN to contribute answers for use in a future lesson.

Today I had hoped to set up the school’s Wii and play the bowling game from Wii Sports where, on successive bowls, more pins are added. Unfortunately I teach my math set in the one classroom that does not have the correct leads. So instead I found a bowling game online – www.smiliegames.com/bowling

Five children came to the front and took turns bowling. We recorded how many pins they were aiming at and how many they succeded in knocking down. Children then calculated the percentage for their Strike Rate. Usually this was easy – 8 out of 10 for example. But when a child hit 4 pins on their first go it then became out of 6 and calculating the percentage became trickier. We then took the results for each child, totalled up how many pins they bowled at during their game, how many they actually knocked down and then calcualted their strike rate as a percentage.

I really like the way tools such as Etherpad, PollDaddy and Wallwisher allow me to gather data to use in the class. The children seem to respond well to the fact the information has been gathered specifically for them and it means I can tailor the data to suit the lesson.

Many thanks to all who took my survey and has contributed to the Family Fortunes etherpad.

Teacher

To a small community, to a big nation

They lend a very strong foundation

They guide us against right and wrong

 They teach us the anthem and also the national song.

Geography tells me where I stand?

It names the river, the barren land

With Languages everyday new word I learn

 The power to express my heart’s churn.

History they bring alive

 Civic senses make us strive

 Matters related to finance and money

Is taught to us through Economy.

Hyacinth it is; I know

‘Cause Botany made me see them and glow

Zoology made me see the smallest of being

 The diseases I could identify, the remedies I could think.

Life’s tough calculation

Was taught through Maths and Stats

Chemistry made me see the logistic chemical reason

 As to why some people are thin and some very fat.

 The mystery of gravity, the history of circuits

 Was taught to me through Physics and Electronics

 Across the continents, strangers I met

 ‘Cause Computers taught me to handle the net.

Importance of health and fitness

 Relaxation for mental and physical stress

 Was taught to me through Physical Education

My inner beauty, I could express.

 You took out the best in me

 You made me a winner in life’s run

 I can’t thank you enough TEACHERS

‘Cause you made learning real fun.

၁။ ေသြဖည္ျခင္းဆိုတာ ပံုမွန္ပဲလို႔စဥ္းစားရင္
1) Deviation is considered normal

၂။ ကို္ယ့္ကိုယ္ကို ျပည့္စံုတယ္ လံုေလာက္တယ္ လို႔ထင္တယ္။
2) We feel complete and sufficient

၃။ ပ်မ္းမွ်ခ်စ္တတ္သူေတြ ေပါ့။
3) We are “mean” lover.

၄။ တစ္ဦးတည္း အဆက္မျပတ္ လုပ္ေနတယ္။
4) Statisticians do it discretely and continuously.

၅။ အၿမဲတမ္း ၉၅ % ေတာ့ မွန္ေနတာပဲ။
5) We are right 95% of the time.

၆။ တစ္ေယာက္ေယာက္ ရဲ႕ ေနာက္ကြယ္က ျဖန္႔ေဝတဲ့ ကိစၥေတြကို တရားဝင္ သံုးသပ္ေပးတယ္။
6) We can legally comment on someone’s posterior distribution.

၇။ ပံုမွန္ေတာ့ မဟုတ္ဘူး။ ဒါေပမယ့္ ေျပာင္းလို႔ရတယ္။
7) We may not be normal but we are transformable.

၈။ ေသခ်ာပါတယ္လို႔ ဘယ္ေတာ့ မွ ေျပာစရာမလိုဘူး။
We never have to say we are certain.

၉။ ရိုးရိုးသားသားေျပာရရင္ သိသိသာသာကို ကြဲျပားတယ္။
9) We are honestly significantly different.

၁၀။ ဘယ္သူမွ ဒီအလုပ္ကို လာမလုဘူး။
10) No one want our jobs.

ဆီေလ်ာ္ေအာင္ ဘာသာ ျပန္ထားျခင္းျဖစ္ပါတယ္။ တစ္ခ်ိဳ႕ ဟာေတြက ဆိုလိုရင္းကို ငဲ့ ၿပီးဘာသာျပန္တာ ျဖစ္တဲ့ အတြက္ တကယ့္ အဓိပၸါယ္နဲ႔ ေတာ့ မတူပါဘူး။ မွားတယ္ထင္လည္း ကိုယ့္ ဟာကိုယ္သာ ျပန္လိုက္ပါ။ စာရင္းအင္းပညာရွင္ ေတြကေတာ့ သေဘာက်ပါတယ္။ အျဖစ္က အဲဒီလို ျဖစ္ေနတာကိုး။
ြြreference:
http://statistica.miur.it/ustat/People/Turchetti/tenreasons.htm

A nice puzzle from Tanya Khovanova’s Math Blog

Which of the shapes below is the odd one out?

Is being the only thing that isn't different more different than being different?

So as I have stated in my cryptically named “About the author” page, I am a maths student. It should, however, be clarified that I am the worst maths student in the history of the universe. This is because maths holds little interest for me. Don’t get me wrong, I find some of the ideas and theories fascinating, not to mention the pretty pictures you can make. However it’s all very well being interested in something someone is telling you about, but when you actually have to do it yourself it can lose its charm faster than a man in a bar taking his pants off before he’s even told you his name. This is how I feel about maths. I did a module last semester which was pretty much just an overview of about 20 different topics in maths. Great. This semester I am doing an in depth look at the workings of Linear Algebra and Complex Analysis. Oh joy. These subjects fail to grasp my interest so spectacularly that I find myself doodling, day dreaming and giving my lecturers alternative personalities to stop my eyes exploding just to add some variety. To give you some idea of just how hard i’ve had to work to distract myself from the maths I will list a few of the names that my lecturers are now being known as by myself and, rather worryingly, some other people too. In no particular order, we have; Grandpa Bell, Quickie, Naughton The Awesome, Dr No, Tranny, Gerbil Woman, Kenny ‘The Falcon’ Combover, The Hoff and Lube. These lecturers vary from the good and interesting (Naughton The Awesome), the loveable but shite (Grandpa Bell), to the just fucking annoying (Gerbil Woman).

As you can probably tell, i’m not usually in the best of moods while in lectures, however nothing in life annoys me as much as the 3 people who sit in front of me (apart from early rising seagulls of course). There are some people that irritate you on sight. Don’t try to deny it, its a human thing to be. However some people do so little change that feeling that its hard not to stab them in the head with a fork. These 3 are like that. Over the course of the semester I have learnt their real names due to the unfeasible volume at which they speak, but in order to protect their privacy, and to satisfy my vindictive nature, I have decided that they will get new names just as our lecturers have. To me they are now Big-head, Boring and Gay.

A little about each. Boring is as her name suggests. She rarely says anything, choosing to defer to the somewhat larger personalities of the others. Gay is also as his name suggests. Now do not misunderstand me, I am not a homophobe, I have some good friends, and even relatives, who are gay. No problem. However this guy seems to have decided to base his personality on Graham Naughton without the comedy. Now its probably because i’m a horrendous person, but I just cannot stand happy people. It is fine to be happy some of the time, it’s not my favourite state of being becuase i’m a miserable bastard but if you like it, go for it. Don’t let me stop you. However, there are some people on this Earth that are happy so often I want to kick their dog just to provoke a negative reaction. This is the kind of person that Gay is. It’s often difficult to stop myself sticking my pen in the back of his head. Speaking of which, I challenge anyone to spend more than 5 minutes with the trio’s ring-leader, Big-Head, without strangling her. This is a girl who is seemingly without any spacial awareness or volume control. She is called Big-Head because, drum roll, she has a big head. Never let it be said that my naming isn’t original. Now this head is not just normal “my what a large sandwhich” big, it’s “fuck me I didn’t know that much space could be occupied by one thing” big. Added to which she has a stupid frizzy hairstyle which looks as though she styled it by sticking a pair of scissors into a plug socket. With all this i’m suprised she only takes up one chair. Now I am not one to be annoyed at someone simply from the enormity of their features (except if you count jealousy towards porn stars but anyway) its the fact that the gigantic head/hair combo literally blocks my view of the entire front of the lecture hall. No seriously, it does. I cannot see any of the 6 boards at the front which must be at least 20 feet high by 30 feet wide. Its incredible. At first I was simply awed by the size of it, but more and more i’m realising that I might have to take notes if I want to pass these classes and she gets in the way of that a lot, as if I needed another excuse to not concentrate and fantasize about being spiderman more. Not only this but I have never met another person who was so spatially unaware. One time she leaned her head back and rested it on my desk, literally covering half my pad! And not only this when I moved the pad from under her head and her head hit the desk with an audible *thunk* she didn’t even notice! Unbelievable! Another time she got to lectures and absently put her coat over my desk and then didn’t move it the whole lecture! I was literally forced to share what little space I had with a fucking coat! Now i’m not the kind of person who has it out with people, I prefer to stew in silence and rant inside my own head (an extension of which is this hence the rant going on now) so i’ve not said anything yet but it’s getting close to my breaking point. So if you are watching the news and see that someone has been arrested for beating a girl with a huge head to death with a lever arch file you know not to bother checking this blog for a while.

Stay tuned for more of the Adventures of Big-Head, Boring and Gay in the future, or failing that, more rants about pointless things. Good Pie.

I just read a wonderful article on Discover magazine. The article centers around Kwabena Boahen (and other members of the school of Carver Mead) in creating electronic circuitry modeled more after the human brain. The main claim is that these types of neurocircuits have the potential in significantly lowering the power consumption for computing. If the claim were correct, though, it will imply there are certain nontrivial relationship between the voltage applied to a transistor and the noise experienced.

The idea, I think, if I understood correctly just from the lay explanation, is a trade-off between error rates versus power. Let us consider the completely simplified and idealized model given by the following. A signal is sent in at voltage . The line introduces thermal noise in the form of a Gaussian distribution. So the signal that comes out at the other end has a distribution , where the Gaussian family is defined as

Definition 1 (Noisy signal)

(Note: our definition is not the standard definition, in particular our Gaussian is centered at ! This definition makes calculations later simpler, as we shall see.)

In other words, for a given signal , the output is a random variable . Let us suppose we have a sensitive instrument to measure the output in analog. Given one reading, we will interpret a positive voltage as the initial signal being , and a negative voltage as it being . So there will be times with a positive signal was sent and our reading, due to the thermal noise, indicates that a negative signal was received. In other words, error!

To reduce the error, there are two things we can do: one is to increase in the input voltage. Assuming the thermal noise does not depend on the input voltage, the increase will shift the center of our Gaussian signal further away from the origin, which in turn reduces the error (since an erroneous signal requires the thermal noise to overcome the original signal, if the signal is bigger, the noise spike has to be bigger too. But the probability for a large enough noise spike decreases rapidly as the required size gets bigger). The other choice is to send the same signal simultaneously through several pathways, and average their readings. By averaging multiple noisy readings we can get a more accurate measurement.

Mathematically choice one means that we shift from to , and the corresponding signal readout follows a new distribution of . What about choice two? From basic probability theory, we learn that the sum distribution of independent random variables is obtained by the convolution of their corresponding distributions . So let us do a computation:

(Note: if one uses the Fourier transform, the above equality can be proven in just one simple line…) This implies that sending the same signal down channels will result in a total signal readout on the other end with probability .

Now, let us evaluate the error probability. Assuming that the initial input has positive voltage, the error rate due to the Gaussian noise can be found by integrating the probability density from minus infinity to 0. So if one reads a signal probability of , the error rate should be

What does this tell us? Under our idealized situation, this shows that doubling the input voltage has the same improvement to the error rate as quadrupling the number of transmissions. Now, under the assumption the power consumed by an electrical appliance is proportional the the square of the voltage (this is true for the resistor), this means that both options will give the same power consumption for the same error rate. One might have expected this result based on the principle of “there’s no free lunch”.

Obviously, this also indicates that our simple model is insufficient to describe the phenomenon mentioned in the article. Two ways that I can imagine this happening is that (1) the power consumption is “worse” than squared of the voltage due to non-ideal behavior of the physical systems and (2) the real thermal noise is not Gaussian, and has a nontrivial dependence on the input voltage. Both, I think, are physically reasonable, yet neither, I think, is sufficient to explain the massive power saving it is claimed in the article.

But this article got me thinking more than just the physics. Another point that was brought up is the representation of data digitally. Consider a scratchy phonograph. This is an analog representation of data. Even when the phonograph is old and scratched, we can still play it back and mostly hear what is going on. If the phonograph were really scratched, we may not be able to hear the parts that are quieter on the original recording, but the loud parts will still come through. The point I want to make is that in an analog recording, increasing levels of noise makes the lower amplitude portion of the original signal less visible, but the most significant high amplitude signals will not be obscured as much. But now consider digital storage of data. The information is stored in sequences of bits. Each individual bit, however, can represent a value of any power of two. For example, in a modern 64-bit computer, each unit of storage (this is not strictly true, but let’s pretend that it is) consists of a 64 slots, each taking the value of either 1 or 0. But each individual slot among the 64 represents a different weight! The lowest (or the right-most when you write it out) slot represent a value of 2 to the 0 power, or the value 1. The highest (or the left-most) represent a value of 2 to the 63rd power, which is bigger than 8 billion billion (American notion of billion, or 9 zeros). The problem now is that each of the bits is on equal footing: an error is as lightly to affect the 2 to the 63rd power bit as the 2 to the zeroth power bit. Now imagine the number stored represent your savings in your bank account: this means that a thermal error that changes the value of one single bit could as easily change your savings by 1 cent as by the US military budget.

This is partially why it is so important in modern computing that the error rates must be limited as low as possible. Unlike a physical/analog process where noise can be tolerated because the signal degrades gracefully (meaning that the large-scale structure is maintained: an analog television broadcast where the noise is high can still be watched even though there is a bit of snowcrash), a digital process without redundancy with high levels of noise can be problematic because the noise is allowed to disturb the large-scale structure (in digital TV broadcasts, the signal basically has three qualities: clear, mosaic-like blocky, or lost). An error is as likely to be insignificant as catastrophic.

MATLAB for Research and Teaching
2pm – 5pm, Wednesday 25th November 2009
Clore Lecture Theatre, Huxley Building

Simulink for Research and Teaching
2pm – 5pm, Wednesday 9th December 2009
Clore Lecture Theatre, Huxley Building

The purpose of this seminar series is to provide staff and post graduates at Imperial College with the opportunity to gain a deeper insight into MATLAB and Simulink technology which is available on campus.
These events will consider applications highlighting many of the latest features and capabilities. Presentations will be delivered by The MathWorks engineers with many years of experience in applying methods and tools in industry and academia.

In this post, we shall consider an NP-complete problem, namely that of determining whether a simple path of length k exists in a given graph, G = (V,E).

Formally,

LONGEST PATH PROBLEM

Input: undirected graph, G = (V,E), integer .

Parameter: k

To find: Does G contain a simple path of length, k?

(Note: length refers to edge length here. In particular, a simple path of length k has k edges.)

The problem has a natural extension:-

EXTENDED LONGEST PATH PROBLEM

Input: undirected graph, G = (V,E), integer .

Parameter: k

To find: All pairs of vertices , such that there exists a simple path of length k between i and j in G.

=======

This article is based on the seminal paper on Color-Coding by Noga Alon, Raphael Yuster, Uri Zwick [1995]. The method of random orientations is mentioned in the paper prior to a description of the color-coding approach.

=======

We concern ourselves with the Extended Longest Path problem.

Consider the adjacency matrix, A of input graph, G. (A is an matrix, with 0 / 1 entries, which we interpret as integers.)

We have, iff there exists an edge .

(Note: represents the entry at the row and column of matrix A.)

Consider the matrix, .

iff there exists a path of length two between i and j in G. (Why? Verify for yourself.)

Generalizing, we can make the following statement for the matrix .

iff there exists a path of length k between i and j in G. (Why? use induction to prove this.)

Question: Do all paths represented in the matrix entries correspond to simple paths of G?

In other words, is the following statement true:

iff there exists a simple path of length k between i and j in G.

–

By a little observation, it can be seen that for the matrix entry to be non-zero, the path between vertices i and j need not necessarily be simple. In other words, the path may contain cycles.

Hence, we can not infer from the fact of having , the conclusion that there exists a simple path of length k between i and j in G.

—

How do we fix this problem?

Consider a graph, H that does not have any cycles (i.e. acyclic graph). Clearly, all paths in H are necessarily simple. (For a path to not be simple, the path needs to contain a cycle, which is precluded by the fact of H being acyclic.)

Let B denote the adjacency matrix of acyclic graph, H.

We can make the following statements:-

iff there exists a path of length k between i and j in H.

And since all paths of H are necessarily simple, the above statement is equivalent to:-

iff there exists a simple path of length k between i and j in H.

Therefore, if the input graph is acyclic, raising the adjacency matrix to the power k solves the Extended Longest Path Problem.

—-

Question: How do we obtain an acyclic graph, H from the given input graph, G?

Prior to answering this question, we shall digress briefly to the look at the notion of a Directed Acyclic Graph (abbreviated as DAG).

—

Consider an undirected graph, G = (V,E) on vertices. We shall construct a directed acyclic version of G.

Let be a permutation of the vertices i.e. , ( is one-one and onto, i.e. bijective.)

Call the directed version of G as . The vertex set of is V (same as G). For every edge of G, we have a corresponding directed edge in .

For each edge of G, add edge to iff .

(i.e. Orient every edge of G from the vertex having lower value to the vertex having greater value. )

Claim 1. is acyclic.

Proof. Assume to the contrary that has a cycle, .

Hence, we have the following inequalities:-

…

.

From the first inequalities, we obtain:-

, which is contrary to the inequality.

Hence, is acyclic. QED.

==

Claim 2 (Converse of Claim 1.). Given a Directed Acyclic Graph, G = (V,E), we can obtain a bijection , such that for every edge , the following condition holds:.

Proof-sketch.

Given any directed acyclic graph, G = (V,E), we have:-

such that .

(In other words, we can find a vertex in V, which has no incoming edges.)

Assign for one such vertex, v.

Remove from to get a new directed acyclic graph. Find a vertex, u that satisfies the above condition in this new graph, assign .

Proceed in this manner until all vertices are assigned a value under the function, .

End of proof-sketch.

===

We can now return to the question raised prior to the discussion on directed acyclic graphs.

To restate:

Question: How do we obtain an acyclic graph, H from the given input graph, G?

Solution: Take a random (What does “random” mean?) permutation . Create an directed acyclic version of G as outlined in the preceding discussion. Call this graph, .

(By “random”, we mean a permutation selected uniformly at random from the set of n! possible permutations of the vertex set, V.)

Denote the adjacency matrix of by B.

As seen earlier, we have:-

iff there exists a simple path in between i and j in $latex  G_{dir} $ of length k.

Since every simple path in is also a simple path in G (Why is this true?), we have:-

If , then a simple path between i and j in G of length k.

Question: Is the converse of this above statement true?

In other words, is the following statement true:-

If there exists a simple path between i and j in G of length k, then .

Answer: No.

The above question can also be rephrased as:

Are all simple paths in G carried over into ?

(Take a simple path, p in G, and figure out for yourself how the edges of p need to be oriented for path, p to exist in . In particular, what does this imply about the values of the vertices along the path?)

==

Now, we can ask the question:

Question: What is the probability that a particular simple path, of length k in G gets preserved in given that we take a random permutation, to obtain from ?

Solution: There are only two ways in which path can get preserved in -

either as the directed path, ,

or as the directed path, .

Path exists only if .

Path exists only if .

Note that we are not concerned with the values of any of the other vertices of G.

Hence, we obtain the following:

Probability that a particular path, p in G, of length k, is preserved in = 2 / (k+1)!.

(How do we get that?)

===

The above probability implies that to preserve any particular simple path of G (having length k), we need to take an expected number of (k+1)! / 2 random permutations.

===

Running time of the algorithm:

We can state the expected running time of the algorithm. We need to perform the following steps.

1. Given a particular random permutation, .

Raise the adjacency matrix, B  of to the power k.

This can be done via matrix multiplications, each of which takes time. (Here is the exponent for matrix multiplication . )

2. Repeating the same for an expected number of random permutations.

3. Keep track of of the pairs of vertices, for each of which we need to output a boolean Yes or No value (corresponding to whether or not a simple path of length k exists in G between that pair of vertices.) (Note: n = |V|).

Initialize all values of this global list to No at the beginning of the algorithm. For each permutation, if the matrix entry, and if the value corresponding to pair (i,j) is listed as No in the global list, change it to Yes.

Hence, the expected running time of the algorithm is . .

(We have ignored certain polynomial (in the size of the graph) factors in the running time. That is justified owing to the “supremacy” of the (k+1)! term over other factors.)

Les épreuves corrigées de l’année 2009

Maths is a good subject. We have it 4 times in the week. We have it in G block. Mrs Han is our teacher and she is a very good one that is nice as long as you behave yourself. Why we have maths is probably so we can add, subtract, multiply and divide really big numbers or really small numbers or so that if we need to use it in a job we have the skills.

In maths we have to solve problems mostly out of the textbooks or off worksheets. When worksheets or stuff from the textbooks we must complete a certain task or part of a certain task or more than one task. If we completed it she would give us some more work to do. If we didn’t finish it we had to come back at lunch time to finish the work. We also got homework for stuff like numbers and other topics in the subject sometime homework was a worksheet or a page from a book full of questions and that you needed to complete. We also had to pay attention to the teacher so that we don’t get any thing wrong and we get most of the questions right.

In Maths I learnt that you have to be a hard worker. You have to be a nice person and how to add, subtract, multiply and divide really big numbers and really small numbers. Sometimes you need to keep quiet so that the teacher can finish what see needs to say or do. Overall I think that if you like work, teachers or if you like solving difficult problems maths is the subject for you.

Matthew