More than just Mathematics

Very clever

2010-09-08T21:28:00.003+02:00

http://jacksmix.wordpress.com/2007/05/30/some-funny-math-jokes/

The student and its teacher

2010-09-07T18:34:00.000+02:00

This picture reminded me of those times you admired your teacher/lecturer for being able to know all these amazing things, while you on the other end didn't have a clue what was going on. The image of the wizard is really fitting, perhaps some genuises are wizards...? Or family of wizards? I wonder...

swan200t.wordpress.com

Vectors

2010-09-04T15:52:00.000+02:00

I like vectors. It is a very good method to visualize the 3-dimentional world of maths. In algebra we learn all about its properties, the dot- and cross product, matrices etc. But where will I ever use vectors? Physics is one field in which it is commonly used to describe such thing as motion, forces, direction, etc.

Say for example that you have two forces acting on an object on the same point, but now you want to know what the resulting force will be, i.e. where will this object go and with what force or speed. Of course there are ways to calculate this, but why not make it fun? A very easy way to do this is to use vectors, where the length of the vectors will represent the magnitude of the force and the direction of the vectors, the direction of the force. Then you use a bit of geometry to create a rectangle from these vectors, the diagonal of the rectangle will then be the answer you are looking for. Clever isn’t it? This resulting vector is sometimes called the sum of the forces. There are many other applications for vectors, and although it isn’t always necessary to use them, it can make it easier by visualising the problem.

A vector space is a space where the elements are vectors. These spaces have nice properties and are used in many applications. It has a lot of theory behind it and was used in some cases to develop some very deep mathematics. Ever heard of a Hilbert space? It is just a complete vector space of which the norm is defined. Norms are defined differently depending on the space. I will discuss this some other time.

So for now, imagine you are a vector in your space (world) and think about what your direction is (where are you heading?) and what is your length (how great a impact have you made in this world?).

The emperor calls

2010-09-03T20:04:00.000+02:00

Due to recent comments on my blog (of which I have almost forgotten… I’m ashamed to say) I have decided that I owe it to everyone out there to keep this blog going. I’m considering the idea of it being the emperor of mathematics that is telling me to keep writing, that being the number 0 of course. Nobody messes with 0. If you get it crossed with you it will reduce you to nothing…
Well on a lighter note, I am still studying mathematics, having completed my degree and now studying towards a post-graduate honours degree. I still love it and am going to share with you, whoever you may be, whatever mathematics there is multiplying in my mind.

Time flies...

2008-12-28T21:26:00.002+02:00

Wow!
Such a long time and no writing. That's not good.
I still love mathematics. I guess I've been so busy with it, that I haven't had time to get to this blog.

But I'll definitely make more time for it.
I'm now entering my final year of studying, then I'll get my degree!
After that I'm not sure yet, but maths stays on my mind...
I also plan on moving, but we'll see.

Happy festive season!

Living in two dimensions

2008-05-14T09:10:00.002+02:00

Living in two dimensions would surely give rise to a monotonous and dull world. It would be flat, without texture (literally) and uninteresting. Maybe then we would all just be normal shapes, depending on species and size. Possibly there would still be colours, although it would have to be dull, because there is no room for shadows or splashes of light in two dimensions.

Every shape would move differently and the bigger the shape, the more careful it would have to move since it could easily get stuck between obstacles, which are made more complex because of the flatness that causes the shapes not to be able to see over anything. But then again, will they see? Or merely sense? Seeing would be a waste, they will only see lines and possibly colours, no depth.

Movement would be confined to the compass directions, no going up or down. There would be no wind, no rainbows, no rain, no water, no fire.

There would really be nothing to do, or would there? Trading three dimensions for two seems not to be a fair trade at all. Does it even make sense to think this way?

The number 25

2008-04-13T11:36:00.003+02:00

My favourite number!
I'm not entirely sure as to why... So I thought I would see what is interesting about it.

It divides into 100: 4 x 25 = 100
5 divides into it 5 times
25 = 5 squared
The root of 25 is 5
Reversing it, i.e. 52, it represents the numbers of weeks in a year
2 times 5 = 10 : A nice round number

I found some very cool facts on the web: click here

Considering all these facts, I still like 25 the most.

Elementary Mathematics

2008-03-30T10:19:00.003+02:00

Whilst elementary math may be the simplest and easiest of all mathematics, I believe it is the most important, because it is the foundation, it is the building blocks of mathematics. Without it one will never be able to do any other math.

Just imagine not knowing 1 + 1 = 2 or 1 x 1 = 1. Is there anything you will then be able to know and understand? Probably not.

Some methods used to teach elementary math:
- Flashcards

- Games

- Worksheets

- and many more

For more information click here.

Vacation Time

2008-03-22T07:10:00.007+02:00

I wish! But still, one can dream.
What I have in mind is waves, of the ocean.

Now I'm thinking, the next time I'm sitting on the beach staring out over the ocean, will this equation pop into my thoughts? I doubt it, but if it did: Will it be good or bad?

Well who likes to get those brainwaves going on vacation?
So it's probably a bad thing, unless you're very bored... which I doubt.

So how does the above mentioned equation work? This might give you some idea:

The wave equation is the important partial differential equation

that describes propagation of waves with speed . The form above gives the wave equation in three-dimensional space where is the Laplacian, which can also be written

An even more compact form is given by

where the first variable is the d'Alembertian, which subsumes the second time derivative and second space derivatives into a single operator.

The one-dimensional wave equation is given by

As with all partial differential equations, suitable initial and/or boundary conditions must be given to obtain solutions to the equation for particular geometries and starting conditions.

(Weisstein, Eric W. "Wave Equation." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/WaveEquation.html)

Elite or Outcast?

2008-03-15T08:21:00.001+02:00

At my university there are only a handful of people studying mathematics (literally). I now do not consider other courses containing a few math modules, I mean majoring in it.

So now I ask myself why? Are people scared, afraid? Do they have other plans? (That’s a good solid reason). Do they think they’re to dumb? (That’s just plain dumb, no pun intended.)

I always get the “WOW”-effect. Some people immediately place you outside the ‘normal’ students. Now what I want to know is where exactly are we put? And why?
An elite, not to-be-touched-and-get-into-conversation-with group?
Or an outcast, not to-be-touched-and-get-into-conversation-with group?
Neither sounds any good.
Why is different wrong in some people’s minds?

Go with the flow? I don’t think so.
Upstream is where all the gold is.

Now don’t get me wrong here, I don’t judge anyone by what they’re studying or by their career, all I’m asking is why I, as Applied Mathematics student, are often seen in a different light than others?

Working the night-shift

2008-03-12T20:34:00.003+02:00

So I have this amazing increase of concentration at night time.

I also have the need for eight hours of sleep per night.

On weekdays I usually get up at 5:30.

This math just doesn't add up?

The words 'Algebra' and 'Algorithm'

2008-03-08T16:41:00.002+02:00

Abu Ja'far Muhammad ibn Musa al-Khwarizmi (c. 780-850) was an Arabic mathematician whose book Hisab al-jabr w'al muqabalah (c.825) described the use of Hindu-Arabic numerals and the rules of basic arithmetic.

The second word of the book's title gives rise to the English word Algebra, and the word Algorithm is derived from al-Khwarizmi's name.

(Taken from: Poole, D. Linear Algebra: A Modern Introduction. (Second Edition), p.87)

In a Nutshell

2008-03-08T16:36:00.005+02:00

This is Scratch from Ice Age™, probably one of the most adorable animation characters ever. Your heart just goes out to this little squirrel as he struggles to collect nuts. He is definitely nuts about nuts.

Similarly, I am nuts about math. Luckily I don’t run around trying to get or catch it, but in a different way so many of it is indeed out of reach.
Considering what I know and what is yet to be learned and discovered, I almost feel like Scratch.
It’s kind of overwhelming (the amount unknown, not feeling like Scratch).

Yet, the ending may differ. Perhaps Scratch will one day collect all of his nuts (no pun intended!), but I don’t think that I’ll ever know EVERYTHING about mathematics.

And since it’s infinite, who does?

Time Flies (Continued)

2008-03-06T20:23:00.003+02:00

Where are the wings? I’m thinking.
What would we have done without time? Maybe it’s just one of those things that had to be discovered/found/created sooner or later.

Maybe you’re thinking: This is irrelevant to this blog, well think again.

What’s the mathematics behind time? Can time be captured into an equation or is it too vast (immeasurable, incalculable)?

After consulting a few sources I found the following:

The Question(Submitted January 16, 1998)
I have a question regarding sunrise and sunset. I realize that the winter solstice on 21Dec is the shortest day of the year. Since this date, the days have been gradually getting longer. Sunset has been getting gradually later as expected, however, sunrise continued to come later until the first week in Jan. My question is: what is the cause of this asymmetrical distribution of daylight between sunrise and sunset?
The Answer

This is due to a phenomenon called "the equation of time".
Solar day is the length of time between one local noon (when the Sun is highest in the sky) to the next. As it turns out, the length of the solar day is not always 24 hrs (its average over the course of a year defines 24 hrs). The solar day would always be 24 hrs if the Sun 'moves' east against the background of fixed stars at a constant rate (for convenience, astronomers have invented 'Mean Sun' to do exactly that). The real Sun moves at a variable rate, however,
Because of the tilt of the Earth rotation axis relative to its orbit around the Sun (the obliquity), the same reason as for the changing length of daytime hours.
Because the Earth's orbit is elliptical and so it moves faster at perihelion (around Jan 2) than at aphelion (Jul 3).
Both effects combine to create an offset in the time of local noon (and those of sunrise and sunset) by as much as +/- 16 min: this is the equation of time. Around winter solstice, the daily change in the equation of time happens to be more important than the daily change in the length of the day, causing the phenomenon you so keenly observed.
The equation of time is often represented by a figure 8. That figure is called an 'analemma'. There is an actual photograph of an analemma at http://sundials.org/links/local/pages/dicicco.htm, which was taken by Dennis di Cicco.

Koji Mukai, David Palmer, and Tim KallmanFor the Ask an Astrophysicist Team

(Taken from: NASA's Imagine the Universe)

Time Flies

2008-03-06T20:14:00.005+02:00

Just the other day I read on Yahoo Answers the question: “What is time?”.
It got me thinking, especially after reading a couple of the answers.

My opinion is that time is man-made. That without time everything would be disorganized and in chaos. Thus people invented time to make life easier – just like all the other things invented to simplify (and complicate at the same time) our lifestyles.
Time – as we know it – I believe is based on cycles. For example: the sun, probably the biggest time indicator except for our man-made clocks and watches.

Time goes by…
- We need yesterday for our memories.
- We need a now for our daily existence.
- We need a tomorrow for our hopes and dreams.
Structured. You see the pattern?

Maybe I’m sounding kind of negative about time, but that’s not it. I’m just analyzing and speculating.

In conclusion the thought:
If time does exists, define forever.

My life today

2008-03-03T19:46:00.001+02:00

Finally getting to the “more” in “More than Mathematics”.
Although it can refer to many things, I wish to now think of it as something different than math, just life in general.
Being a second year student may sound ‘great!’, but from personal experience I see it as:
- better as the first year (without question)
- hard work (lots of self-study)
- a preparation for my final year (which is the third year)
I generally don’t socialize very much, mainly because I have only a few good friends and they all lead very busy lives. I don’t mind, but sometimes I just feel like I want to get OUT! And usually I don’t because there’s no one available to go out with.
Thus, I spend a lot of time with my studies, which is not necessarily a bad thing, but I’ve lost the balance in life that I’ve maintained throughout my school years.
I realize that I’ve got to change my current lifestyle, I’m just not so sure how. Maybe (and hopefully) I’ll find a solution soon.

Scary Math?

2008-03-01T12:00:00.002+02:00

I found this logo at a math website and thought it looked kind of scary.

I think sometimes math really do seem scary. Just consider the fact that almost everything in the universe can be expressed as a formula...

But being scary it is also facinating and wonderful.

(Logo taken from 'Mr. Almeida's Math Class')

2008-03-01T11:46:00.002+02:00

WOW!
This year started with a bang! and is now in full swing.
This year I'm also into statistics and programming in addition to the math and I'm truly enjoying every moment. (Well, maybe not EVERY moment...)

Everything is real interesting and what I like about second year is that you more clearly start to see where everyting you learn will fit in with real life.

Of course it is hard work and lots of studying, but I'm sure in the end it will all be worth it. (Not meaning the end of the world, but merely the end of the year).

The more you learn the more you want to learn. This is actually true, believe it or not. Especially when you're really enthusiastic and want to ask questions such as: "But what if... ". That's real fun. It gets your mind working and you also start to realize and understand things you haven't before.

Conclusion:
Life without math would have been:
- Boring
- Incomprehensible
- Empty
- Ignorant
- Non-existent

2008

2008-01-21T20:41:00.000+02:00

A brand new year, full of new opportunities, experiences, lessons to learn (even math ones... )

Have a gr8 one, even on the days when things just doesn't seem to add up - just divide away all negativity and multiply with positivity and remember to count your blessings.

Cheers for now!

exp-function

2007-11-03T18:01:00.000+02:00

Two functions meet in a narrow street.

F1: Clear the way!
F2: No, I won't.
F1: Move over, or I will differentiate you!
F2: Ok, try it, I am the exp-function!

Available: http://www.primepuzzle.com/leeslightest/mathjokes.htm

Noah and his Ark

2007-11-03T17:58:00.000+02:00

The ark lands after The Flood. Noah lets all the animals out. Says, "Go and multiply." Several months pass. Noah decides to check up on the animals. All are doing fine except a pair of snakes. "What's the problem?" says Noah. "Cut down some trees and let us live there", say the snakes. Noah follows their advice. Several more weeks pass. Noah checks on the snakes again. Lots of little snakes, everybody is happy. Noah asks, "Want to tell me how the trees helped?" "Certainly", say the snakes. "We're adders, and we need logs to multiply."

Available: gopher://wiretaps.spies.com/00/Library/Humor/Jokes/math.jok

Definition: Mathematician

2007-11-03T17:54:00.000+02:00

"A mathematician is a device for turning coffee into theorems" -- P. Erdos

Famous curves - Lituus

2007-10-13T18:06:00.000+02:00

The lituus curve originated with Cotes in 1722. Lituus means a crook, for example a bishop's crosier. Maclaurin used the term in his book Harmonia Mensurarumin 1722. The lituus is the locus of the point P moving in such a manner that the area of a circular sector remains constant.
Roger Cotes (1682-1716) died at the age of 34 having only published two memoirs during his lifetime. Appointed professor at Cambridge at the age of 24 his work was published only after his death.
Cotes discovered an important theorem on the nth roots of unity; anticipated the method of least squares and discovered a method of integrating rational fractions with binomial denominators.

(1997. Available: http://www-history.mcs.st-andrews.ac.uk/history/Curves/Lituus.html )

The basics

2007-10-07T18:34:00.000+02:00

Ever think back to when you had your first encounter with mathematics?

Or what about those high school exams?

I think when some of us look back to those days we realize how little of mathematics we knew then (and still do). That was only a drop in the big ocean, with still so much that is unexplored. This is one of the many reasons why I love math, there's always new things to learn and discover, you definitely can never get bored or run out of ideas, there is always excitement.

Although some people would read my last statement and think: "Nerd!" or "Geek!", I feel obliqed to feel sorry for them, because there is this amazing,, incredible thing in life that they would probably never discover.

I am not saying that everyone should love or even like math, but it is definitely something which should be appreciated.

Mathematics is everywhere imaginable, it is infinite.

HAVE FUN

Pythagoras

2007-10-07T18:32:00.000+02:00

The picture below is indeed of Pythagoras.

For more about him please visit this link:

http://www-history.mcs.st-andrews.ac.uk/Biographies/Pythagoras.html

Who is this?

2007-09-28T21:19:00.000+02:00

Born: about 569 BC in Samos, Ionia
Died: about 475 BC

Mathematician: Ahmes

2007-09-23T07:42:00.000+02:00

Ahmes:

Born: about 1680 BC in Egypt
Died: about 1620 BC in Egypt

Ahmes is the scribe who wrote the Rhind Papyrus (named after the Scottish Egyptologist Alexander Henry Rhind who went to Thebes for health reasons, became interested in excavating and purchased the papyrus in Egypt in 1858).
Ahmes claims not to be the author of the work, being, he claims, only a scribe. He says that the material comes from an earlier work of about 2000 BC.
The papyrus is our chief source of information on Egyptian mathematics. The Recto contains division of 2 by the odd numbers 3 to 101 in unit fractions and the numbers 1 to 9 by 10. The Verso has 87 problems on the four operations, solution of equations, progressions, volumes of granaries, the two-thirds rule etc.
The Rhind Papyrus, which came to the British Museum in 1863, is sometimes called the 'Ahmes papyrus' in honour of Ahmes. Nothing is known of Ahmes other than his own comments in the papyrus.

Article by: J J O'Connor and E F Robertson
January 1997
MacTutor History of Mathematics
[http://www-history.mcs.st-andrews.ac.uk/Biographies/Ahmes.html]

Answer to integral

2007-09-22T12:43:00.001+02:00

This is indeed true and it is also a limerick:

Integral t-squared dt

from 1 to the cube root of 3

times the cosine

of three pi over 9

equals log of the cube root of 'e'.

(a limerick is poem with the 1st, 2nd and 5th lines rhyming and also the 3rd and 4th lines rhyming - just comes to show what one can do with mathematics)

Limits

2007-09-22T10:23:00.000+02:00

Introduction: Mathematicians

2007-09-18T19:22:00.000+02:00

The first mathematicians I’m going to take a look at are some of those who lived -500 AD. Yes, that’s a very long time ago, at the origin of the discovery of mathematics.
(Take note that it cannot be the origin of mathematics, because I don’t think there really is something like that, mathematics was always present, only people weren’t aware of it.)
I’m planning on then looking at the 1800’s and then again further back, to create some kind of oscillating effect.
I hope that those of you who will read it will find it interesting.

Mathematicians

2007-09-16T12:30:00.000+02:00

I will do my best to start publishing information and theories of mathematicians, especially those who contributed greatly to mathematics as we know it today.
I believe that it is important to know about these minds behind the ideas and theories, so that we can in a sense understand it better and also catch a glimpse of some truly dedicated mathematicians.
Althought there are many famous and well-known mathematicians, I also believe that there are many more out there who just wasn't in the right place and time to be truly recognised for the work they have done.
I also think that there must have been times when some mathematicians got credit for work which has already been done and proven by someone else who didn't make it public, or just kept it to themselves. Althought this is truly sad, we nevertheless can and will benefit from those proofs and theories, irrespective of who are known for it, and build on that to, hopefully, discover even more.

Life is a journey, and so is mathematics.

How does that work?

2007-09-16T11:47:00.001+02:00

A classic example of how one can easily be misled by mathematics when one doesn’t have efficient knowledge to know better.
2a = a, does in fact not mean that 2 = 1, but rather that a has a value that would satisfy 2a = a. Therefore a = 0 is the only possibility.

Question: Integration

2007-09-16T09:12:00.000+02:00

True or false?
To be continued...

Expand

2007-09-12T19:27:00.000+02:00

No, this is not how it is done.
Really.
Still don’t believe me? I guess then you’re still stuck with high school math?
Anyway, don’t we all just miss high school math? So carefree and fun! (Well, for some of us at least.)
For originality, I must give Peter 10 out of 10.

Proof: Mathematics is Art

2007-09-12T19:15:00.000+02:00

Prove by induction:

Note: Weird person: the way other people see for example mathematicians or artists.

Consider 1 weird person: This person is thus either an artist or mathematician.
Assume for k weird persons: Each one is either artist or mathematician.
Thus for k +1 people = k persons + 1 person: Either artist or mathematician.

Hence:
We have now proven that mathematicians and artists are not clearly distinguishable, and thus math and art are very closely related. Nearing infinity, they tend to be the same thing.
Now we can say that math is art. (Under the condition that our conclusion can never be commutative, i.e. art is not math!)

Mathematics is an Art!

2007-09-11T20:31:00.000+02:00

Creativity, Ideas = Art

When we think art, we think crazy people in weird outfits, with splatters of paint all over them, creating strange, often beautiful, images.

When we think math, we think weird people, wearing glasses, working out equations the entire day.

See the comparison? Weird people, wrong assumptions made by others, the creation of something great and beautiful...

By induction it can thus be proven that math is indeed an art. (I will provide the proof in the next post).

Definition of pi

2007-09-09T12:27:00.000+02:00

What is "pi"?
Mathematician: Pi is the number expressing the relationship between the circumference of a circle and its diameter.
Physicist: Pi is 3.1415927 plus or minus 0.00000005
Engineer: Pi is about 3.

(URL: http://www.primepuzzle.com/leeslightest/mathjokes.htm)

Definition of Mathematics

2007-09-08T13:52:00.000+02:00

Faced with the question of what the definition of mathematics is got me thinking... And to tell you the truth, I am still thinking.
Can such a vast field ever be pinned down to one specific definition?
Consider infinity, now try to capture that into one thing... Okay, so it's got a name, but the definition of that name is also kind of, uhm, infinite?
So many things still to be proven, discovered and studied, I don't really believe that there can be a definition of mathematics.
Care to differ? Feel free to give your opinion.
I found this definition at http://www.allnewuniverse.com/:
A great language and like any language may be used to describe emotions as well as ideas - truths and philosophies - facts and fiction. We must be very alert to distinguish what math is telling us. Math by itself is not fact!

How they prove that all odd integers higher than 2 are prime?

2007-09-07T11:09:00.000+02:00

Mathematician: 3 is a prime, 5 is a prime, 7 is a prime, and by induction - every odd integer higher than 2 is a prime.
Physicist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is an experimental error, 11 is a prime,...
Engineer: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime, 11 is a prime,...
Programmer: 3 is a prime, 5 is a prime, 7 is a prime, 7 is a prime, 7 is a prime,...
Salesperson: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- we'll do for you the best we can,...
Computer Software Salesperson: 3 is prime, 5 is prime, 7 is prime, 9 will be prime in the next release,...
Biologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- results have not arrived yet,...
Advertiser: 3 is a prime, 5 is a prime, 7 is a prime, 11 is a prime,...
Lawyer: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- there is not enough evidence to prove that it is not a prime,...
Accountant: 3 is prime, 5 is prime, 7 is prime, 9 is prime, deducing 10% tax and 5% other obligations.
Statistician: Let's try several randomly chosen numbers: 17 is a prime, 23 is a prime, 11 is a prime...
Professor: 3 is prime, 5 is prime, 7 is prime, and the rest are left as an exercise for the student.
Computational linguist: 3 is an odd prime, 5 is an odd prime, 7 is an odd prime, 9 is a very odd prime,...
Psychologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime but tries to suppress it,...

(www.workjoke.com)