Tuesday, April 7, 2009
Wednesday, October 8, 2008
Humility in Mathematics
As it is, I tutor in the math center at a local community college. There are many different kinds of people here from varying backgrounds and all at a different level of comprehension. Yet there is a single ability that could be valuable for them all to learn. This is humility.
The term humility is very general and I would like to clarify that I am referring to being humble with the math itself specifically. Learning mathematics is a personal struggle, potentially gratifying, which requires humility to the discipline itself for efficient progress. I came to experience this phenomenon while I was still in high school, and it was then that I began to understand the purest of joy, which is math itself...
I say that to study and to learn math, be it algebra, trigonometry, calculus, etc., one needs to approach the material in the right state of mind. This is one of patience, one of curiosity, and one of hope. I have found that seeking to humble oneself before the discipline truly brings these things. Surely when you do this then there is no room for frustration. This is not so difficult to do, but I do recommend that when attempting to study your math that you do so on a full stomach. Don't be hungry. Your brain needs the fuel to function.
When I watch someone get frustrated (and I have, hehe, many many times) I can see that this creates a mental block that becomes enormously more difficult to overcome then the learning of the math itself. Thus, if you want to experience the joys of being able to understand math concepts and really feeling the beauty of its purity, then you have to be humble. You cannot reject it without truly attempting to alter your perspective first.
You might be wondering what it looks like to be humble. I am thinking that it is more important to be able to understand what it FEELS like, but this is more difficult to describe. I am going to try and describe it what it looks like.
Someone who is humble accepts the material for what it is. There is no questioning of its usefulness, no negative reasoning of why one might be required to learn it.. there is only the math and the acknowledgement that it is what it is. Next, there is the humility to read and TRY to follow the logic. Humility is trying to learn, it is trying to understand. Someone might get caught up in a step and get frustrated because they cannot see where it goes. If they are not humble then they might curse the author of the textbook, glare at the nearest math department personnel, and give up. If they are exercising humility, and thus patience, then immediately some attempts to look at it from different angles may occur or some other method to at least make progress in the efforts to TRY. Being humble is all about doing the work, reading the textbook, and opening your mind to the possibilities of mathematics.
Ultimately, humility is simply having an open mind and hopeful curiosity to the cryptic secrets of the realm of mathematics.
One of the most gratifying experiences of my life was that first day when I could truly feel the greatness of learning math and all the wonderful physical and psychological implications. I associate this with my humble desire to know and to understand the nature of mathematics.
Don't forget! If you need some math help just visit my website!
www.algebraist.org
Elementary Algebra_Algebra_Trigonometry_Pre-calculus_Calculus_Differential Equations
The term humility is very general and I would like to clarify that I am referring to being humble with the math itself specifically. Learning mathematics is a personal struggle, potentially gratifying, which requires humility to the discipline itself for efficient progress. I came to experience this phenomenon while I was still in high school, and it was then that I began to understand the purest of joy, which is math itself...
I say that to study and to learn math, be it algebra, trigonometry, calculus, etc., one needs to approach the material in the right state of mind. This is one of patience, one of curiosity, and one of hope. I have found that seeking to humble oneself before the discipline truly brings these things. Surely when you do this then there is no room for frustration. This is not so difficult to do, but I do recommend that when attempting to study your math that you do so on a full stomach. Don't be hungry. Your brain needs the fuel to function.
When I watch someone get frustrated (and I have, hehe, many many times) I can see that this creates a mental block that becomes enormously more difficult to overcome then the learning of the math itself. Thus, if you want to experience the joys of being able to understand math concepts and really feeling the beauty of its purity, then you have to be humble. You cannot reject it without truly attempting to alter your perspective first.
You might be wondering what it looks like to be humble. I am thinking that it is more important to be able to understand what it FEELS like, but this is more difficult to describe. I am going to try and describe it what it looks like.
Someone who is humble accepts the material for what it is. There is no questioning of its usefulness, no negative reasoning of why one might be required to learn it.. there is only the math and the acknowledgement that it is what it is. Next, there is the humility to read and TRY to follow the logic. Humility is trying to learn, it is trying to understand. Someone might get caught up in a step and get frustrated because they cannot see where it goes. If they are not humble then they might curse the author of the textbook, glare at the nearest math department personnel, and give up. If they are exercising humility, and thus patience, then immediately some attempts to look at it from different angles may occur or some other method to at least make progress in the efforts to TRY. Being humble is all about doing the work, reading the textbook, and opening your mind to the possibilities of mathematics.
Ultimately, humility is simply having an open mind and hopeful curiosity to the cryptic secrets of the realm of mathematics.
One of the most gratifying experiences of my life was that first day when I could truly feel the greatness of learning math and all the wonderful physical and psychological implications. I associate this with my humble desire to know and to understand the nature of mathematics.
Don't forget! If you need some math help just visit my website!
www.algebraist.org
Elementary Algebra_Algebra_Trigonometry_Pre-calculus_Calculus_Differential Equations
Friday, September 26, 2008
Graphing Calculator Fun!
I am in a light hearted mood tonight..
If you ever find yourself sitting in math class (algebra I or II, trigonometry, pre-calculus, calculus, etc.) and have a graphing calculator handy then I have a few cool little tricks that you might find fun!
Graphing a Smiley Face : )
I am using a Ti-84 but any graphing calculator will work.
Now, to do this.. I recommend starting with the general equation for a circle.
(x-h)2 + (y-k)2= r2
Remember; 'h', 'k' and 'r' are constants.
Texas Instrument calculators will only graph a function entered as a function of x. So you must solve for y.
y = ± √[r2-(x-h)2] + k
The ± gives us either an upside down (+) half circle or a right side up (-) one.
Now, in this form we get to choose some numbers for h, k, and r that give us the desired result on the calculator screen. Each equation will only graph half of a circle and thus you would need the oppisite (negative) equation to complete it... if you were, for example, making the eyes then you would need to do both the negative and the positive. I highly recommend playing around with the numbers to get a feel for it yourself and then designing your own smiley : )
Otherwise here are a few equations that you can plug in to calculator and get a nice smiley face.
To remove the axis you must change the settings format.
Standard window settings:
Xmin: -10 Xmax: 10
Ymin: -10 Ymax: 10
Xscale:1 Yscale: 1
y = + √[4-(x-4)2] + 2
y = + √[4-(x+4)2] + 2
y = -1/2√[30-(x)2] -3 (note: I added the 1/2 in front so as to stretch in the horizontal direction, or the along the x-axis)
Try to be more detailed.. create different kinds of eyes or try to make a nose to match. And when you are done, remove the axes to seee your handiwork in all its glory!
If you ever find yourself sitting in math class (algebra I or II, trigonometry, pre-calculus, calculus, etc.) and have a graphing calculator handy then I have a few cool little tricks that you might find fun!
Graphing a Smiley Face : )
I am using a Ti-84 but any graphing calculator will work.
Now, to do this.. I recommend starting with the general equation for a circle.
(x-h)2 + (y-k)2= r2
Remember; 'h', 'k' and 'r' are constants.
Texas Instrument calculators will only graph a function entered as a function of x. So you must solve for y.
y = ± √[r2-(x-h)2] + k
The ± gives us either an upside down (+) half circle or a right side up (-) one.
Now, in this form we get to choose some numbers for h, k, and r that give us the desired result on the calculator screen. Each equation will only graph half of a circle and thus you would need the oppisite (negative) equation to complete it... if you were, for example, making the eyes then you would need to do both the negative and the positive. I highly recommend playing around with the numbers to get a feel for it yourself and then designing your own smiley : )
Otherwise here are a few equations that you can plug in to calculator and get a nice smiley face.
To remove the axis you must change the settings format.
Standard window settings:
Xmin: -10 Xmax: 10
Ymin: -10 Ymax: 10
Xscale:1 Yscale: 1
y = + √[4-(x-4)2] + 2
y = + √[4-(x+4)2] + 2
y = -1/2√[30-(x)2] -3 (note: I added the 1/2 in front so as to stretch in the horizontal direction, or the along the x-axis)
Try to be more detailed.. create different kinds of eyes or try to make a nose to match. And when you are done, remove the axes to seee your handiwork in all its glory!
Monday, September 22, 2008
What is my blog all about?
I am here to simply reflect upon the beauties and sorrows of mathematics. To inspire within each of my readers a sense of ultimate truth that is possible to be easily grasped. Am I going to teach you how to do your homework? Yes and no.
In my later entries I might go over some really good study habits that I have accumulated and put together over the many years I have spent learning and teaching math. But truly I will be posting my thoughts and reflections on various perspectives of mathematics, as a discipline having grown and evolved throughout history. Actually, my site, algebraist.org, is being set up to assist with your homework needs. If you have a question to ask me then post it on my site and I will gladly get back to you!
http://www.algebraist.org
Hopefully I will be able to make time to address some common concerns and new age issues. Some examples would be common math disabilities or the latest arguments concerning the necessity to learn fractions.
Also, I love to read. Consequently, I read a lot of math books. When I finish one I will post a little summary and review on its works. Check back weekly (or perhaps even daily) for new posts!
In my later entries I might go over some really good study habits that I have accumulated and put together over the many years I have spent learning and teaching math. But truly I will be posting my thoughts and reflections on various perspectives of mathematics, as a discipline having grown and evolved throughout history. Actually, my site, algebraist.org, is being set up to assist with your homework needs. If you have a question to ask me then post it on my site and I will gladly get back to you!
http://www.algebraist.org
Hopefully I will be able to make time to address some common concerns and new age issues. Some examples would be common math disabilities or the latest arguments concerning the necessity to learn fractions.
Also, I love to read. Consequently, I read a lot of math books. When I finish one I will post a little summary and review on its works. Check back weekly (or perhaps even daily) for new posts!
Sunday, September 21, 2008
Pure Math Joy
Of the many questions pertinent to life there is one I feel that, at some point or another, every person has asked. Why do we do math?
The answer? Pure Math Joy! We do it because we love it.
Pure math joy is that euphoric feeling of excitement and accomplishment you get when you personally solve that equation for x. It is learning and applying a series of irrefutable truths that organize and make some sense to the confusing chaos of everyday reality. This euphoric feeling is natural and in many ways therapeutic. This is why we do math, and in so doing, our efforts have granted us the miracles of modern genius.
I find that math stimulates the mind and spirit to new levels of awareness, enlightenment, and perspective shifts. It grants one power and understanding. This alone should make it valuable enough to be pursued and explored. Yet it is the simple joy of being productive that taps our inner being (whatever it is that you believe in) and connects with us that makes math such a grand discipline.
This blog is ultimately dedicated to my high-school Pre-calculus and AP Calculus teacher. Without her I would never have taken higher level math in college and discovered the joyful depths of pure mathematics. It is in her great spirit of enthusiasm and the spirit of all math teachers everywhere that I write this blog.
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