Possible New Horizon

I got really excited today – Dr. Davis recommended a link to me (knowing I was a previous music major) A couple of papers written by Dmitri Tymoczko.  He did a wonderful job of geometrically showing chord structures.  I was very impressed with how he presented the music theory with math – visually.  A lot of my frustration has been wanting to present to the class and elsewhere as he does – visually (geometrically) – algebraically and analytically – and auditory – as I watched sandpiling and fractals and cellular autonomy and chaos – I wondered what it would all sound like to hear what we see and see what we hear.  As I have been studying Fourier analysis and wavelets – I have found myself thinking and wondering how to merge it all – to be able to hear spectrum’s that we cannot see and see spectrum’s that we cannot hear – way back at the science museum – I learned that we see such a tiny portion of what out universe looks like – there is such a large spectrum – we s”see” so little of it – same with auditory – can a computer show us more? Can those waves be transformed into something we can see?  Are we able to use filters for this?  can we choose to see ultra violet?  Microwave – we can see things with night goggles that pick up heat – EMF machines pick up electro-magnetic waves – is there a program or way of collecting all these different spectrum’s of information onto something we can see or hear or even feel – and laughingly I thought smell – does a supernova smell?  Silly question – but yet – someone can be having a bbq – I can smell it before I see it – same with burning campfires – smell does travel …. kind of funny questions – I”m sure I’m not the first to ask – but as I am studying more practically – learning Fourier Analysis and Wavelets – and geometrical representations and analysis of music and sounds – I hope that I can find answers to these questions – whether it be from somebody else – or through research – well,

June 25, 2009

I made a little more progress with MatLab today – created two m-files with Alfa’s help – I guess I was getting confused – I was actually trying to create a program that would create a transform matrix – instead of just adding input vectors and keeping the matrix the same – but, I got a much better understanding of creating a function and then calling it from the command window – I had a couple of notation issues that needed clearing up too.  So, my goal for the week-end is to actually work through the text and follow the mathematics in MatLab – I have begun to create a flow chart of goals – so that I can create smaller steps so that I at least can see progress visually – by being able to check off accomplishments – I have felt like I have been learning a lot – but not really producing a lot – this has led to a lot of frustration and guilt – so, I think if I can see the progress – it will help create some confidence and sense of accomplishment  … I think now is a good pt. to start posting code on the MatLab page – I have created different pages to help organize my thoughts and research.

June 24,2009

JUNE 24, 2009

 

Starting to work with transforms in MatLab

starting with linear combinations – sums and difference

 

represents the components with matrix notation

x(0),x(1),x(2),x(3)

 

going to replace this signal with four other numbers y(0) = x(0)+x(1)

y(1) = x(0)-x(1)

y(2) = x(2)+x(3)

y(3) = x(2)-x(3)

this transform can be inverted

 

add y(0) + y(1) = 2x(0)

sub y(0) + y(1) = 2x(1)

 

the inverse transform uses addition and subtraction like the original and then divides by 2

x(0) = 0.5(y(0) + y(1)) x(2) = 0.5(y(2) + y(3))

x(1) = 0.5(y(0) – y(1)) x(3) = 0.5(y(2) – y(3))

 

matrices displays the detail of the transform – x(n) for the inputs -y(n) for the outputs

 

June 23, 2009

 – getting further understanding of signals and Fourier Transforms – Series –

 

wavelet stuff – internet vs. book – went to school library today – found a couple of books to help – doing research for my research – found this very helpful compared to internet searches – Dr. Kim also loaned me a book on wavelets – between her book – which is very theoretical – and Gilbert Strang’s book – which is very hands on – feel like I have a good foundation on which to build further.

 

Fourier Transforms – read some to get a deeper understanding

 

Some applications of wavelets – signal analysis – data compression – i.e. pictures, music,videos,medical equipment, finger prints – face recognition – voice recognition, etc.

 

definitions of amplitude,frequency,period and angular velocity

formulas that show the relationship between time, frequency, amplitude,angular velocity

 

Fourier Series Formula

 

sound – difference between a sin and cosine wave auditory

combine them – harmony?

 

Radio – getting a signal vs. static “noise” – compare to visual signals

 

Read – “Who is Fourier? A Mathematical Adventure” by Transitional Collage of LEX

pages 1-77

Gilbert Strang Lecture from MIT Open Courseware Computational Math and Engineering – lecture 1 and 2

Beginning Matlab reading – tutorial and exercises

 

http://faculty.olin.edu/bstorey/Notes/Fourier.pdf

 

http://www.mathworks.com/moler/exm/chapters/preface.pdf

 

http://chaos.swarthmore.edu/courses/Phys50L_2006/Matlab/MatlabExercises.pdf

 

 

 

 

 

 

Results from 6/15/09

- It was a revitalizing day – the Discover magazine article from May 1, 1995 was very helpful to me on a couple of different levels – some of the key things that interested me – were …

1.) pattern recognition vs. meaningless background “noise”

After last semester – I understood a bit more than in Jan and Feb. – and have a different approach when learning further – I felt like I got a deeper understanding of Heisenburg principal beyond a memorized definition – the way it was explained – led to greater understanding – a long toned “C” compared to a cymbal crash – I still would like to know Fourier analysis better – and compression techniques.  Oh, will have to continue later…

Summer Session

Today – very happily finally understood a powerful technique!  I can now laugh at how the obvious alluded me

I found my final report for the semester frustrating – I had a difficult time with LaTex.  Now I understand the frustration with programming also -

I would plan everything and then type it as a whole – left with finding errors all at once.  Dan wandered by and gave me a little project to work on – the concept of the day for me was – go line by line – a lot easier to find errors when only dealing with one at a time – now, I understand Gary’s suggestion about working based on success rather than tackling things on a large scale and feeling like a failure – it clicked – smaller steps and goals – as Dr. Wang stated – a journey of a thousand miles begins with one step – now I understand it is all the small steps that add up to the thousand miles.

Yesterday – was the first day of the summer workshop.  I was quite excited to read a Discover article on Ingrid Debechies and wavelets – I had wondered if I should have pressed through with the study of wavelets – instead of letting fear take over – I happily revisited the topic after meeting with Dr. Gottlieb and discussing goals (she had remembered the article and suggested it to me) it brought back enthusiasm and curiosity – a new energy – but, also a greater understanding of researching and organizing time and information that I learned over the spring semester should make a big difference

Hind’s Sight 20/20

Wow, it seems like this semester has been very up and down.  There are many things that I would have done differently.  There was a lot of learning and figuring things out – it all seemed very random and felt very over-whelming at times.  I was having a difficult time organizing information – both, in my head and in my blog.  Initially I wanted to explain step by step with a lot of pictures.  But, it slowed me down – I was trying to program my own pics.  Now I would use other’s pics first – then I would go back and work on it on my own.  I tend to be a visual learner – and figured that that would be the easiest.  I also had a goal of presenting it in the manner that an average person without that much background in math would be able to understand it.  I have noticed that that was a feature of some of my favorite presenters.  They were able to take what they knew – as complex as it was – but, they were to present it in such a way – that it did not seem as complex – it is a personal goal of mine – to be this way.  Now, I realize that the ability to break things down and explain things to a non-math person – is difficult at times – but, that is my goal.

     I have also learned this semester to overcome a great deal of fear – I am just now at the point where I feel settled and functioning in CSUMS – I am now comfortable speaking with my advisors.  Not sure why it took so long – but, I am happy to be gone with that fear.  I learned that my fear was unjustified.

     I have finally figured out how to organize my blog to present things that I am learning and have learned.  That was another huge lesson that I learned.  Preparing for the poster presentations was a very good experience on many different levels.  The Laptop I was using kept crashing every time I went to print my presentation – I was trying to print it without saving the file because I lost the majority of my visuals after I saved the whole poster – I later learned that it was a software issue – to my relief – I did not damage the Laptop.  At UMASS Amherst – I noticed that Elise and Dan had glitches – I was so impressed at how they responded – they taught me a lot.  I am not able to change things by increasingly becoming panic stricken – they just seemed to go along and take it in stride.

     I have enjoyed interacting with everyone in CSUMS – I am learning a lot about math and computer programs –  and I am enjoying learning on my own and from others.  I have definitely learned to keep everything in my blog – it will  be accessible in the event of glitches  I guess I felt silly writing things like – today I created a line and then a square in MatLab.

       I baby sat for a friend twice last month.  A beautiful 8 month little girl.  I have been able to observe her learning process.  She understands more than she can speak.  She only says a few words – but, seems to get her message across with what she knows.  She has recently learned to say – bye-bye.  I giggled when she said bye bye to her food – but, realized she wasn’t able to say – “I do not want anymore” or “I’m full”.  She communicated with what she knew – with what she had.  My goal is to do the same …

building my tool box

I still want to know more than I know But, I am a bit more peaceful with the new approach I have been taking.  Initially – I felt like the more I learned – the less I knew – I kind of felt like  I was falling into a black hole !

I finally stated – “I don’t know anything” – so I started from the absolute beginning with programming and how I did my Math – I no longer assumed I new definitions or methods – I also realized that I needed to know things well enough – so that they were part of me – this seems to have revolutionized my thinking and approach…  kind of like a proof I guess.

So, for the last couple of weeks – I have been learning about the finite difference method.  Alpha had given me a worksheet to work on in MatLab and Mathematica.  I began to notice through presentations – that Neil had stated his original problem that he was going to be working on – but, when he presents – he is learning by tackling smaller problems to build his tool box.  That was encouraging.

so, what I have been working on and hope to present tomorrow is a little history and information about Poisson – Lagrange – finite difference – stencils – weights – and accuracy problems – I have completed stencils for 3,5, and 7 finite difference weights for the Lagrange Polynomial.  And am now working on creating a function for MatLab to create the matrices.

I have been spending time “unfreezing” myself.  I narrowed down to focusing on just MatLab and Java.  After talking to Daniel – I realized I was expecting too much of myself.  By trying to learn programming 5 languages at the same time.  Also – a help in this process was Dr. Kim.  I was so afraid of failure and appearing stupid – she was so free in asking questions and saying things like “can you slow down” when we were going over one of the worksheets for MatLab in the CSUMS class.  So, I have been asking a lot more questions and starting a new way of approaching things.  My frustration with MatLab was that everything seemed mystical to me.  Pulled out of thin air.  “I often felt how would I know that command ?”  I realized that a lot my frustration – was having gaps in my learning – so, it felt unstable.  So, I have literally gone back to the beginning.  Most students that I talked to have learned MatLab and programming by pieces.  They needed to do something and just figured things out on a case by case basis.  For whatever reason – I was getting frustrated by this process.  I felt like I was doing things – but, not really understanding them deeply.   So, I just declared myself to really not know anything.  I restarted there.  Freeing and humbling – but, necessary. 

 In order to work on the poster project – I read an analysis book – suggested by Alpha.  Read up on Poisson and finite difference.  Also have been learning about the 1D Poisson in PDE class.  In this project – I am seeing that a lot of  things are connected mathematically – seeing how even though it felt like seperate classes and seperate topics – they really weren’t – it was all interconnected. 

To alleviate the gaps I was feeling in programming – things like what different kinds of loops there were and which ones to use when.  So, basically understanding not just “what” to program – but “how” to program.  I went and got really basic programming books.  I have been going through MatLab Demystified step by step – doing each example – just increasingly building knowledge and becoming comfortable with syntax and programming in MatLab.  I guess I have basically gone back to basics and slowed down a bit.  I am finding this helpful as far as to my overall goal.  Initially – it was very slow – but, I am noticing more speed and comfort.  Yesterday in class, we started to work in Python.  Instead of thinking – oh, no, another programming language to learn – I was able to realize – gee – by learning the process and overall structure of programming – the rest is just syntax changes – it helped me a great deal.  Also incorporated in all this learning is learning and training the voice recognization program.  But, instead of feeling like “information overload”  and panicking at how much there is to learn and do – I decided to relax with it and enjoy the process of learning it all.  So, this week will be spent finishing the Matlab worksheets that we were given in class – with the voice recognition program – working on my poster – and  adding to the powerpoint presentation.  OH, – and continuing to read my programming for dummies book

Powerpoint Presentation

Wow – what a difference a week made

Alfa really helped me to narrow things down.   I was kind of feeling lost and without a road map.  Lots of new terrain to traverse – it seemed very large and I felt very small.

  I have been reading up on Finite Difference Method and working on programming in Matlab, Java, Octave and C.  I began working on a PowerPoint Presentation for two reasons.  1.) I tend to be a visual learner so – I believe that I would be a better presenter – with graphics.  I was frustrated by my programing skills not being where I wanted them … but, in waiting to catch up – I was feeling like I was making no progress … so, 2.)  I forced myself to just sit down and figure out PowerPoint.  It was not as difficult as I thought – to my relief – but, I also discovered that part of my problem was that I wanted perfection and completion before I presented.  It was causing me to be stuck.  By jumping into  PowerPoint and just getting a rough kind of out line helped me tremendously.  I was able to just leave a few slides with “insert math from LaTex here” – and to just move on – so, the ideas were there for me now and the rest to fill in the details  So, kind of a map really.  I found it was not as much work as I thought and totally doable for me to present on Monday – wow – progress for others to see  instead of it just being  just in my head.  I am going to be adding pages to my blog to categorize and organize information – power point, Matlab information,bibliography, questions I have, observations as I get results,hypothesis’,conclusions.     Happy Day! – a quick draft of the power point presentation is located on a page called “Power Point”  it did not save in presentation form – so, unless I find out differently – I will present in power point for this next presentation and place the slides in this page as a gallery.