What is mathematical research? And how is it done? Questions that have been on my mind for very long.
We know what researchers do:
- answering questions asked in the literature;
- discovering a new theorem;
- publishing an article in a journal ( i.e. Journal for Number Theory );
- writing a book;
- lecturing about their work and giving talks;
- being part of a research community.
Researchers are either employed by a university or by a corporation. University researchers have a commitment to teach and corporate researchers aren't free to chose their topics. Both are pressed to publish often in the best journals possible.
But -HOW- to they do it? What makes them successful in their field? Questions, I can't answer. Let's go and search for answers elsewhere. Starting with Manning, perhaps.
and this one:
Enjoy.
Tampilkan postingan dengan label video. Tampilkan semua postingan
Tampilkan postingan dengan label video. Tampilkan semua postingan
Senin, 20 Mei 2013
Rabu, 08 Mei 2013
Student Voice
Touching documentary from our local PBS, WGVU. They capture admininstrators, teachers, and student voices. Nicole, starting around 18, in particular, is full of determination and will.
When I see something like this, it drives me crazy that we can't convince our society to invest in these students, or the teachers that have answered the vocation to mentor them.
Watch Get Your Diploma. Get Your Dream. on PBS. See more from WGVU Presents.
When I see something like this, it drives me crazy that we can't convince our society to invest in these students, or the teachers that have answered the vocation to mentor them.
Senin, 18 Juni 2012
Mystery Teacher Theatre 2000
Welcome to our first episode. Recently, in the halls of School University, some teachers attempted some selfdirected professional development, encouraged by their principal and given hope by Sal Khan, a man described as "Bill Gate's favorite teacher" (from a TED endorsement), "very popular," "extremely popular," "an educational revolutionary," and being like "like a nerdy, South Asian-American Seinfeld." (I'm not making any of those up. The last is from Wired.)
Here's what happened.
So, obviously, as comedy improv actors we're a couple of math teachers.
We're very interested in your comments. What do you think of this video? Of the teaching? What did we miss in our commentary?
Dave was the instigator here, but is too smart to put it up at Deltascape.
Here's what happened.
So, obviously, as comedy improv actors we're a couple of math teachers.
We're very interested in your comments. What do you think of this video? Of the teaching? What did we miss in our commentary?
Dave was the instigator here, but is too smart to put it up at Deltascape.
Jumat, 04 Mei 2012
Open University M336 video lectures
#M336 #geometry #openuniversity
The Open University M336 course comes with 7 lectures on one DVD of about half an hour each, or almost four hours of lectures. The lectures are titled:
- Living with patterns
- Friezes
- Counting with groups
- Incidence symbols
- Lattices and wallpaper patterns
- Regular solids
- Octet for truss and comb
These lectures are additions to the booklets and excercises and are not meant to learn new material from, instead they reinforce what has been learned before.
So, although there is no entire lecture series covering the M336 materials you could easily create one by cherry picking lectures from the internet. For Group Theory you can use the first half of the Harvard Abstract Algebra course which covers group theory upto the Sylow Theorems.
For the geometry part you could use the MIT Course 'An Introduction to Crystallography'. This course contains 41 video lectures of which lectures 5 to 27 cover the material of the Geometry track in M336.
Link: Symmetry, Structure, and Tensor Properties of Materials MIT OpenCourseWare
The Open University M336 course comes with 7 lectures on one DVD of about half an hour each, or almost four hours of lectures. The lectures are titled:
- Living with patterns
- Friezes
- Counting with groups
- Incidence symbols
- Lattices and wallpaper patterns
- Regular solids
- Octet for truss and comb
These lectures are additions to the booklets and excercises and are not meant to learn new material from, instead they reinforce what has been learned before.
So, although there is no entire lecture series covering the M336 materials you could easily create one by cherry picking lectures from the internet. For Group Theory you can use the first half of the Harvard Abstract Algebra course which covers group theory upto the Sylow Theorems.
For the geometry part you could use the MIT Course 'An Introduction to Crystallography'. This course contains 41 video lectures of which lectures 5 to 27 cover the material of the Geometry track in M336.
Link: Symmetry, Structure, and Tensor Properties of Materials MIT OpenCourseWare
Kamis, 03 Mei 2012
Escher's imaginery workplace
#mathematics #art #Open University #m336 #Escher
The Scream by Edvard Munch was sold for USD 120 million. I didn't like it yesterday and I don't like it now that I know it's perceived value. My favourite artists are Escher, Kandinsky and Dali, their work inspires me, and I am truly impressed by what they have created, art needs beauty. M336 brings group theory and geometry together through visual symmetry, or the symmetry Escher used in a lot of his work. I browse a lot through work of Escher as a result of M336 studies. Recently I came across this sensational video. A must see, really.
( A short movie inspired on Escher's works and a free vision on how it could be his workplace. )
This is another video by Eterea.
( A short movie about numbers and geometry. )
The Scream by Edvard Munch was sold for USD 120 million. I didn't like it yesterday and I don't like it now that I know it's perceived value. My favourite artists are Escher, Kandinsky and Dali, their work inspires me, and I am truly impressed by what they have created, art needs beauty. M336 brings group theory and geometry together through visual symmetry, or the symmetry Escher used in a lot of his work. I browse a lot through work of Escher as a result of M336 studies. Recently I came across this sensational video. A must see, really.
( A short movie inspired on Escher's works and a free vision on how it could be his workplace. )
This is another video by Eterea.
( A short movie about numbers and geometry. )
Rabu, 21 Maret 2012
M336 - Group Theory - Fundamental Theorem of Abelian Groups
#openuniversity #m336 #video
One of the theorems that is discussed in the group theory track in the Open University Course 'M336 Groups and Geometry' is the Fundamental Theorem of Abelian Groups. Early on in Group Theory it becomes clear that there is a connection between group theory and number theory in Langrange's theorem and the Sylow Theorems ( also part of M336 ) but only after studying the Fundamental Theorem of Abelian Groups you'll get a notion of the depth of the connection between Group Theory and Number Theory.
MathDoctorBob ( his YouTube alias ) made a short video lecture on the topic. Precise as always.
One of the theorems that is discussed in the group theory track in the Open University Course 'M336 Groups and Geometry' is the Fundamental Theorem of Abelian Groups. Early on in Group Theory it becomes clear that there is a connection between group theory and number theory in Langrange's theorem and the Sylow Theorems ( also part of M336 ) but only after studying the Fundamental Theorem of Abelian Groups you'll get a notion of the depth of the connection between Group Theory and Number Theory.
MathDoctorBob ( his YouTube alias ) made a short video lecture on the topic. Precise as always.
Jumat, 09 Maret 2012
Math Memoirs
There's one of my favorite math teaching videos up in Keith Devlin's most recent blogpost. (Thrilled that it's now on YouTube with several other of her interviews.) It's from the wonderful Marilyn Burns, who has really done more for math education than anyone in recent decades. Her stuff was good enough to get word of mouth sharing before there was an internet. (Dan Meyer is quite reminiscent of her in several ways.) Devlin uses the video to make the point that apparent understanding is not proof. A better assessment can uncover the truth, and Burns is excellent at questioning to get an accurate picture.
As a novice teacher I quickly found that the students giving an answer did not tell me whether they understood or not, and I moved to asking for how they got it. It took me years, however, to get to understand that how is better, but also does not get at understanding. It's their thinking that I want to hear. Then I should ask for it! Unfortunately, even spoiled university teachers don't have time to sit down and interview students over all of our major objectives. I can, however, ask questions to which I really
Dave Coffey found this excellent solution by Carl Barnard, a high school student, to the painted cube problem that crossed the line to be a memoir. We often introduce the idea of a memoir by having our students read it and comment on it. (Here's my most recent version of the workshop; Dave was almost certainly the original writer of it.) It's a start to learning how to communicate your thinking. While it's important and beneficial for any math student to do this, it is unbelievably crucial for math teachers, and a big part of pedagogical content knowledge to me. Most students on end of term evaluations comment that this is an area where they grew significantly.
I wanted to experiment with what this looked like in elementary school, so I asked my daughter to give it a go. These are from the summer between her 4th and 5th grade. She was a bit precocious with her writing, but had had pretty traditional math instruction. (And not interested in talking with me about to a large extent.)
Just writing the method. A first attempt at memoir. I supported with a kind of questioning framework.
She was game enough to try twice more.
This is the sort of information that I want from an assessment. I get so much more an image of what ideas she has about number and operation. And it is far more interesting reading than traditional assignments where I'm looking for what I expect or not.
As a novice teacher I quickly found that the students giving an answer did not tell me whether they understood or not, and I moved to asking for how they got it. It took me years, however, to get to understand that how is better, but also does not get at understanding. It's their thinking that I want to hear. Then I should ask for it! Unfortunately, even spoiled university teachers don't have time to sit down and interview students over all of our major objectives. I can, however, ask questions to which I really
Dave Coffey found this excellent solution by Carl Barnard, a high school student, to the painted cube problem that crossed the line to be a memoir. We often introduce the idea of a memoir by having our students read it and comment on it. (Here's my most recent version of the workshop; Dave was almost certainly the original writer of it.) It's a start to learning how to communicate your thinking. While it's important and beneficial for any math student to do this, it is unbelievably crucial for math teachers, and a big part of pedagogical content knowledge to me. Most students on end of term evaluations comment that this is an area where they grew significantly.
I wanted to experiment with what this looked like in elementary school, so I asked my daughter to give it a go. These are from the summer between her 4th and 5th grade. She was a bit precocious with her writing, but had had pretty traditional math instruction. (And not interested in talking with me about to a large extent.)
Just writing the method. A first attempt at memoir. I supported with a kind of questioning framework.
She was game enough to try twice more.
This is the sort of information that I want from an assessment. I get so much more an image of what ideas she has about number and operation. And it is far more interesting reading than traditional assignments where I'm looking for what I expect or not.
Japanese Precision
I don't know how this art is called in Japan, but it is awesome. It is not dance, it is not mathematics, it is both!
Rabu, 22 Februari 2012
Abstract Algebra E-222 video 26 Rings 2
#maths
Watched lecture 26 of the Harvard Abstract Algebra series. - What can you say about the complex number $z$ if $(2+i)z$ must be an integer?
These lectures were recorded in 2003 and are basically saved for all generations to come. Imagine that the lectures of Gauss were recorded on video! Euler and Gauss will be remembered forever by their name and picture, but the great mathematicians of today and tomorrow will be remembered by their video lectures.
Watched lecture 26 of the Harvard Abstract Algebra series. - What can you say about the complex number $z$ if $(2+i)z$ must be an integer?
 |
| Prof. Gross ... "ideals in the Gaussian integers $\mathbf{Z}\left[i\right]$ of type $\mathbf{Z}/p\mathbf{Z}$". |
These lectures were recorded in 2003 and are basically saved for all generations to come. Imagine that the lectures of Gauss were recorded on video! Euler and Gauss will be remembered forever by their name and picture, but the great mathematicians of today and tomorrow will be remembered by their video lectures.
Senin, 20 Februari 2012
Abstract Algebra E-222 video 25 Rings 2
Every word counts in mathematics.
The polynomial $x^2-1=0$ has ( thus ) two roots: $(1, -1)$. However, if we consider the coefficients of the polynomial as elements of the ring $\mathbf{Z/8Z}$ then the polynomial has four roots: $(1, -1, 3, -3)$.
In lecture 25 professor Gross explains how the division and Euclidean Algorithm can be applied to polynomials in Polynomial Rings over a field.
Every non zero single-variable polynomial with complex coefficients has exactly as many complex roots as its degree, if each root is counted up to its multiplicity. ( Fundamental theorem of algebra, Wikipedia )
The polynomial $x^2-1=0$ has ( thus ) two roots: $(1, -1)$. However, if we consider the coefficients of the polynomial as elements of the ring $\mathbf{Z/8Z}$ then the polynomial has four roots: $(1, -1, 3, -3)$.
 |
| $x^2-1$ has $4$ roots... |
In lecture 25 professor Gross explains how the division and Euclidean Algorithm can be applied to polynomials in Polynomial Rings over a field.
Sabtu, 18 Februari 2012
Abstract Algebra E-222 video 24 Rings 1
#M336
Just watched a video where Benedict Gross introduces Ring Theory. I don't think you can learn Ring Theory ( or any mathematics for that matter ) by just watching a video.
But if you watch prepared you can pick up a lot from this professor. In this first lecture he explains why there is such a field as Ring Theory in the first place. Where did it come from? And most of all: what are the important topics we have to watch in this field? ( I.e. Ideals and Unit Groups ). You may wonder why I gave this post the M336 ( Groups and Geometry ) hash-tag, it is because Rings and abelian Groups ( and Number Theory ) are intimately connected and one of the objectives of M336 is the classification of all abelian groups. - By the way, the word is abelian group and not Abelian group despite the fact that the word abelian comes from Niels Abel. Writing a name lowercase is the highest possible honor in mathematics. ( So I have been told... ).
At the end of this lecture he mentions that Group Theory is a really hard subject and all that. The thing with Group Theory is that it has to sink in quite a while before it clicks and opens up to you.
Just watched a video where Benedict Gross introduces Ring Theory. I don't think you can learn Ring Theory ( or any mathematics for that matter ) by just watching a video.
In the business of commercial education, in programming for example, teachers are often confronted with students ( sent by their employers ) who expect to leave as a qualified programmer just by hanging in their chairs during the course. Needless to say they leave as empty headed as they came in.
But if you watch prepared you can pick up a lot from this professor. In this first lecture he explains why there is such a field as Ring Theory in the first place. Where did it come from? And most of all: what are the important topics we have to watch in this field? ( I.e. Ideals and Unit Groups ). You may wonder why I gave this post the M336 ( Groups and Geometry ) hash-tag, it is because Rings and abelian Groups ( and Number Theory ) are intimately connected and one of the objectives of M336 is the classification of all abelian groups. - By the way, the word is abelian group and not Abelian group despite the fact that the word abelian comes from Niels Abel. Writing a name lowercase is the highest possible honor in mathematics. ( So I have been told... ).
 |
| $(\mathbf{Z/nZ})^{\times}$ has $\phi(n)$ elements |
At the end of this lecture he mentions that Group Theory is a really hard subject and all that. The thing with Group Theory is that it has to sink in quite a while before it clicks and opens up to you.
Rabu, 08 Februari 2012
Riemann Hypothesis ( Video )
Very well done video about the history, and the implications of the RH.
Sabtu, 28 Januari 2012
[Video] Deriving Binet's formula for the Fibonacci numbers
One of those formulas every mathematician loves ( I think ):
$$F_n = \frac{1}{\sqrt{5}}( \phi^n - (1-\phi)^n )$$
Here's how MathDoctorBob explains it.
Although I like The Doctor's videos ( I wished the real doctor would show up accusing me for abusing his name but taking me for a ride in his phone box anyway ), I wouldn't like to have Doctor Bob as a tutor in class, I simply wouldn't be able to catch up and I am not the audible type anyway. I like to read a bit, play and think a bit, read a bit, and so on. Every person has its own unique style of learning that works for him. Part of studying is discovering your own learning style.
Oh, and I think this formula beats the one of Binet ( although strictly speaking not in closed form ), because it fascinates me that the Fibonacci numbers are actually -in- the triangle of Pascal.
$$F_{n+1} = \sum_{k=0}^{n} {n-k \choose k}$$
$$F_n = \frac{1}{\sqrt{5}}( \phi^n - (1-\phi)^n )$$
Here's how MathDoctorBob explains it.
Although I like The Doctor's videos ( I wished the real doctor would show up accusing me for abusing his name but taking me for a ride in his phone box anyway ), I wouldn't like to have Doctor Bob as a tutor in class, I simply wouldn't be able to catch up and I am not the audible type anyway. I like to read a bit, play and think a bit, read a bit, and so on. Every person has its own unique style of learning that works for him. Part of studying is discovering your own learning style.
Oh, and I think this formula beats the one of Binet ( although strictly speaking not in closed form ), because it fascinates me that the Fibonacci numbers are actually -in- the triangle of Pascal.
$$F_{n+1} = \sum_{k=0}^{n} {n-k \choose k}$$
Selasa, 03 Januari 2012
Example of a Galois Group of order 8 ( Introducing Math Doctor Bob )
Regular readers must have noticed my interest in Abstract Algebra, of which I am currently studying, in different ways, the topic of Galois Theory. If you have chosen a different route in mathematics ( computation, statistics, and so forth ) or if you are at the early undergraduate level you may have difficulty picturing what Galois Theory is -all about-. I am trying to communicate that idea by summarizing the popular introduction to the field 'Fearless Symmetry' which basically introduces Galois Theory to the general ( but educated ) public. ( Currently working on part 7 out of 23). But as they say, one picture says more than a thousand words. For those that want to get an idea, fast and easy, and *now*, I recommend the following video ( mini lecture ). Don't expect you can master the subject by watching a ten minute video but the ten minutes are well worth it. The video lecturer is 'Math Doctor Bob', who uploaded about 600 mini lectures on various mathematical topics.
See also:
- Fearless Symmetry
See also:
- Fearless Symmetry
Sabtu, 31 Desember 2011
More Alan Turing
( Although I have read more Fearless Symmetry haven't done a new summary yet. )
Anyway, I have selected two Alan Turing videos. First a clip from Nottingham Trent University in the series FavScientist.
Then the great Derek Jacobi as Turing in a clip from the docu drama Breaking the Code.
Anyway, I have selected two Alan Turing videos. First a clip from Nottingham Trent University in the series FavScientist.
Then the great Derek Jacobi as Turing in a clip from the docu drama Breaking the Code.
Senin, 26 Desember 2011
Minggu, 11 Desember 2011
Sabtu, 10 Desember 2011
Video lectures on Theory Of Automata, Formal Languages and Computation
NPTEL released a new series of video lectures featuring Prof.Kamala Krithivasan from the Department of Computer Science and Engineering IIT in Madras on the Theory of Automata, Formal Languages and Computation. The first lecture in the series is called GRAMMARS AND NATURAL LANGUAGE PROCESSING.
Jumat, 30 September 2011
Fraction Sense
Watched a nice video about Dor Abrahamson talking about how math is, or should be, about making sense.
In this video he describes a device to let students play with a proportion, and I thought it would be simple enough to do in GeoGebra, so... here you go! I'm pretty happy with the sketch, it's clean and the controls should be simple enough for young students. Close means within 5%, and Wow! is within 1%, so it's easier with a large unit. There's a lot of research supporting introducing fractions with a comparison model before the typical part-whole model, so it's nice to have a tool for that.
Available as a GeoGebra file or dynamic webpage. I've mostly stopped embedding GeoGebra files on the blog because it adds to load time significantly, it seems faster as a separate webpage.What other fraction representations would you like to see in a dynamic representation?
EDIT:
Made this before GeoGebraTube! I've updated this a little with a practice mode and more sensible checking. Here's the Teacher page (download) or the Student page (applet). Also have made this multiple choice fraction estimation applet.
In this video he describes a device to let students play with a proportion, and I thought it would be simple enough to do in GeoGebra, so... here you go! I'm pretty happy with the sketch, it's clean and the controls should be simple enough for young students. Close means within 5%, and Wow! is within 1%, so it's easier with a large unit. There's a lot of research supporting introducing fractions with a comparison model before the typical part-whole model, so it's nice to have a tool for that.
EDIT:
Made this before GeoGebraTube! I've updated this a little with a practice mode and more sensible checking. Here's the Teacher page (download) or the Student page (applet). Also have made this multiple choice fraction estimation applet.
Rabu, 08 Juni 2011
Graphing Stories: Balloon and Tower
Yeah! I have rarely been so excited to get an email. "We just pulled your Graphing Story out of the oven!" The only downside is that my name is prominent, when I really just incited other people to make them. But I'm still geeked. Huge props to Dan Meyer and BuzzMath for doing this.
First, the Balloon. Filmmaker - Anna Minnebo, Balloonist - Gregg Minnebo.
Second, The Towers of Hanoi. Stacker/Graphist - Eric Thuemmel; Camera - Monica Leneway. In the original he just got the fourth stack complete on the 15th second, but it just barely gets cut off here. He was quick.
Still to come: four simultaneous tower builders... can understand why the graph for that is a special problem.
First, the Balloon. Filmmaker - Anna Minnebo, Balloonist - Gregg Minnebo.
Second, The Towers of Hanoi. Stacker/Graphist - Eric Thuemmel; Camera - Monica Leneway. In the original he just got the fourth stack complete on the 15th second, but it just barely gets cut off here. He was quick.
Still to come: four simultaneous tower builders... can understand why the graph for that is a special problem.
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