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!
28 December 2008
14 May 2008
Living in two dimensions
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?
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?
13 April 2008
The number 25
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.
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.
30 March 2008
Elementary Mathematics
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
- and many more
For more information click here.
22 March 2008
Vacation Time
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
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)
15 March 2008
Elite or Outcast?
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?
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?
12 March 2008
Working the night-shift
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?
08 March 2008
The words 'Algebra' and 'Algorithm'
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)
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
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?
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?
06 March 2008
Time Flies (Continued)
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:
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
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
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
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.
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.
03 March 2008
My life today
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.
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.
01 March 2008
Scary Math?
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')
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
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
21 January 2008
2008
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!
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!
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