About M381 mathematical logic or how to study an Open University booklet

How to study an Open University booklet? Well, don't if you have an alternative classic source. Study the source first, then go back to the booklets and do the exercises. Just because the TMA questions are modeled after them and the model answers are written in that style. Remember that your tutor wants to get through your work asap. The more they look like the model answer the better. The rule is 'when in doubt it is wrong.' Tutors are NOT professors, so don't expect them to be.

Studying the source is essential. Because that's what the authors of the booklets used when they wrote them. You should be able to write these booklets yourself and sooner than you think. Besides, the vast body of mathematics is written in source classics, not in the form of OU booklets or lecture notes. - ( An Open University booklet is roughly comparable to a set of lecture notes brick university students get, I suppose. )

Take for example the M381 mathematical logic booklets. What a Layman would understand as Mathematical Logic is called Propositional Logic and is covered early in the track in the MS221 course. The title of the course 'Mathematical Logic' is thus somewhat confusing. And it is not just the title that is confusing. I noticed on the forums that students considered the M381 logic part rather 'difficult'. The principal author of the booklet is Alan Slomson, now a professor in Mathematics at Leeds University. ( A host of other names are listed in the credits including Jeremy Gray: Wise Beard Man, the face of the OU ). Anyway, the source book is: "Computability, an introduction to recursive function theory" by Nigel Cutland.". ( I checked all available books on Mathematical Logic, I have no doubt that this is the book that was used. ) The thing is that the material in the course booklet looks a bit fuzzy, somwehat unclear, rather difficult to be honest. Well, it isn't. Not if you read Cutland's original first. Then you recognize what they ( Slomson ) are -trying- to explain. It's just the presentation in the booklet that makes it foggy. It would have been better if they simply have used Cutland's book ( like Apostol's in the Analytical Number Theory course ) and write a Reader's Guide. In a Reader's Guide you can use informal English to explain things while for the formal math definitions you can refer to the book. - ( Under Slomsons wings another book on Computability has been published by Brian Cooper : Computability Theory. Here too you'll find Cutland's URM and a lot of his original examples. )

Despite my occasional criticism I feel quite at home at the Open University.

The Open University and MathCad

I wonder if there is any university out there in the world where the professors choose MathCad for their students. The answer is of course No, N-O. Only managers or others on the receiving end of the kickback pipe can take a decision like that. - MathCad is a joke. If I had known on beforehand how bad MathCad was I would not have chosen to study mathematics at the Open University. I am very serious about this.

Think twice if you are still deciding. And go elsewhere if you have an option.

What I am complaining about is the following.

I do my TMA's in four rounds. First I solve them with Mathematica. That part is easy and fast. Then I typeset the answers in LaTeX because most ( not all ) tutors don't really understand what they are marking. They insist a presentation a toddler can understand. This round is time-consuming but I like to become proficient in LaTeX so who cares. Then in the third round I descend down to the gates of hell. In that phase I have to redo the answers in MathCad. This is Guantanamo Bay Home Edition. Then round four: the psychiatric ward. Because the OU does not accept electronic delivery I have to PRINT sometimes up to 100 pages of which 80 come from MathCad. I call this insanity.

Thanks MathCad.

Linear Programming ( M373 )

A series of 24 video lectures on Operations Research of which the first 12 are on Linear Programming. These 12 lectures cover more or less block 2 of course M373. The lectures are easy to follow since they go in a slow ( but steady! ) pace with lots and lots of examples. TIP!

More here: NPTEL

As usual Mathematica can be your virtual math coach through the commands:
- Maximize
- Minimize
- LinearProgramming
( See the Mathematica docs for more. )

Spirograph 1

from Robert S Donovan @ Flickr

I have always loved Spirographs.  When I inherited my sister's I was in heaven - I think the exact box pictured here, supposedly from 1968.

Seeing this tumblr entry with an animated Spirograph picture when I had a few minutes sorta free, inspired me to finally put together a sketch.  So I thought I'd share it.  It's definitely good for experimenting to see if you can figure out what is going on.  Very fun to make.  The webpage lets you see the patterns, but doesn't give nearly the control that the GeoGebra file does.  It succeeded insofar as you can make some pretty pictures, and I didn't have to cheat by parameterizing the curves..

I'm interested in developing some lessons on ratios that could be visualized in interesting ways with the curves traced. If you have feedback on the sketch or on the lesson idea, I'd love to hear it.

The View menu should allow you to refresh views in the applet below, but it can get hung up.  I sometimes have to click pause several times before it pauses.  As I said, on this one I recommend the GeoGebra file, if you're going to do any serious playing around.



Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Study Wisata Ke Jogyakarta

Kamis, 19 Mei 2011 MGMP Matematika SMP DKI Jakarta sore itu berkumpul di Stasiun Gambir untuk melaksanakan Prgram Kerjanya melaksanakan Study Wisata ke SMPN 5 dan SMPN 8 Jogyakarta. Rombongan yang terdiri dari 100 orang akhirnya tepat jam 20.45 meninggalkan Stasiun Gambir menuju Jogyakarta dengan kereta api Taksaka II.
Tujuan dari Kegiatan ini adalah untuk lebih menyambung tali silaturahim sesama Pengurus MGMP baik dari tingkat Kecamatan sampai tingkat DKI Jakarta, serta untuk mencari masukan dari sekolah lain di luar DKI Jakarta.

Kurang lebih jam 05.00 pagi rombongan tiba di stasiun kereta api Jogyakarta dan diteruskan menuju Grage Ramayana Hotel untuk cek in dan persiapan untuk melaksanakan study wisata ke SMPN 5 dan SMPN 8 Jogyakarta.
Setelah sarapan jam 08.00 rombongan dibagi menjadi 2. Rombongan 1 menuju SMPN 5 Jogyakarta dan Rombongan 2 menuju SMPN 8 Jogyakarta.
Admin yang ikut di rombongan 2 menuju ke SMPN 8 Jogyakarta. Begitu antusias SMPN 8 Jogyakarta menyambut rombongan dari MGMP Matematika Jogyakarta. Kebetulan sekali pada saat yang sama, juga datang rombongan dari MGMP Matematika SMP Bandung, sehingga kegiatan Study Banding ini semakin terasa. Kemudian diisi oleh presentasi dari Wolu
Kegiatab berakhir jam 11.00 dan dilanjutkan menuju Surakarta. Ditengah perjalanan berhenti di Masjid di daerah Prambanan untuk melaksanakan Sholat Jum'at.
Sabtu, 21 Mei 2011 sesuai jadwal acara Rombongan mengadakan wisata ke Dieng. Karena perjalanan yang lumayan jauh, jam 07.00 pagi itu rombongan sudah meluncur menuju kawasan Dieng. Hingga jam 19.00 rombongan baru kembali ke hotel.....
Rombongan kembali ke Jakarta minggu, 22 Mei 2011 jam 10.30. Dan alhamdulillah jam 19.00 rombongan sampai di Jakarta dengan selamat dan membawa kesan dan kesan yang berarti demi kemajuan Matematika SMP DKI Jakarta.
Maju terus matematika, maju MGMP Matematika SMP DKI Jakarta...

Lihat Photo

Social media for mathematicians: Math Overflow

I wouldn't be surprised if ( research ) mathematicians were so ( Asperger / social anxious / Nerd / whatever buzzword you like ) that they stay away from Facebook. - The quality of Facebook is that you meet people that you wouldn't have met otherwise, because they are completely out of all the circles you are in. - Anyway, a place where research Mathematicians ask questions ( in a way programmers do for example ) is the site Math Overflow, it is set up like Stack Overflow, a well known site for programmers. Registration is open to anyone. Only questions on the graduate and research level though. No place to search for help with TMAs but a fascinating place to get a feel for what it is like on the frontline of our science.

Math Overflow ( Research )

Math Stack Exchange ( B.Sc. students )

Equivalence classes in Mathematica

An equivalence relation like 'has the same remainder after division by 5' partitions a set in equivalence classes.

The relevant Mathematica function is GatherBy[ set, equivalence relation] -> {equivalence classes}:

In[5]:= GatherBy[{1, 2, 3, 4, 5}, Mod[#, 5] &]

Out[5]= {{1}, {2}, {3}, {4}, {5}}

In[6]:= GatherBy[{49, 33, 11, 1, 2, 3, 4, 5}, Mod[#, 5] &]

Out[6]= {{49, 4}, {33, 3}, {11, 1}, {2}, {5}}

Or when using the equivalence relation 'Is Odd?' on the same set:

In[7]:= GatherBy[{49, 33, 11, 1, 2, 3, 4, 5},OddQ]

Out[7]= {{49, 33, 11, 1, 3, 5}, {2, 4}}

Olimpiade Matematika 2011

Istora Senayan, Jakarta - 4, 5, dan 7 Juli 2011

Klik di sini untuk Download formulir pendaftaran (Pdf)

LATAR BELAKANG

Pesta Buku Jakarta (PBJ) merupakan media pertemuan antara penerbit dengan konsumen; siswa, guru, orang tua, sekolah, perpustakaan, dan sebagainya. Melalui PBJ, penerbit dapat memamerkan buku-buku yang telah diterbitkan dan konsumen dapat berinteraksi dengan penerbit dan penulis, serta memperoleh informasi mengenai buku-buku terbitan baru.

Dalam rangka menyemarakkan PBJ 2011 dan sekaligus mendorong semangat belajar dan kompetisi di lingkungan siswa dan sekolah, maka Panitia Pesta Buku Jakarta 2011 bekerja sama dengan Yayasan Peduli Matematika Indonesia menyelenggarakan OLIMPIADE MATEMATIKA SD, SMP, dan SMA 2011.

TUJUAN

• Mendorong semangat belajar dan kompetisi bagi siswa-siswi
• Menyediakan ruang bagi siswa menguji kemampuannya di bidang matematika
• Mendekatkan penerbit dengan siswa, guru, dan sekolah
• Mencari masukan dalam rangka pengembangan kemampuan siswa di bidang matematika

PESERTA DAN PERSYARATANNYA

Siswa-siswi SD Kelas 3, 4, 5 & 6, SMP Kelas 7, 8 & 9, dan SMA Kelas 10 &11 negeri dan swasta tahun ajaran 2010/2011

KATEGORI

Olimpiade dibagi menjadi 4 kategori, yaitu:

• A (untuk SD kelas 3 & 4)
• B (untuk SD kelas 5 & 6)
• C (untuk SMP kelas 7, 8 & 9)
• D (untuk SMA kelas 10 & 11)

RUANG LINGKUP SOAL

• Bilangan, Aljabar, Geometri dan Pengukuran, dan Statisika dan Peluang
• Soal-soal yang diujikan merupakan soal nonrutin (problem solving) sesuai dengan standar Olimpiade Sains Nasional (OSN)

TIM JURI

Tim yang dibentuk oleh Yayasan Peduli Matematika Indonesia


TEMPAT DAN BIAYA PENDAFTARAN

Tempat:Yayasan Peduli Matematika Indonesia
Jl.Kartini Raya (Ruko 2F), Depok 16431
Telp. (021) 7099 1162, 7721 7672; Fax. (021) 7721 7672
Contact Person: Albert Simbolon (0812 8554 630), Sukarjo (0813 1596 5162)

Waktu: 16 April 2011 - 16 Juni 2011
Biaya: Rp25.000,- per siswa SD atau Rp 35.000 per siswa SMP/SMA

TEMPAT DAN WAKTU PELAKSANAAN

Ruang Anggrek Istora Senayan Jakarta
4 Juli 2011 (SD Kelas 3, 4, 5 & 6)
5 Juli 2011 (SMP Kelas 7, 8 & 9)
7 Juli 2011 (SMA Kelas 10 & 11)

Pukul 10.00 - 12.00 WIB

HADIAH DAN PENGHARGAAN

• Medali dan Total hadiah uang sebesar Rp20.000.000,- (dua puluh juta rupiah)
• Hadiah diberikan kepada tiga orang siswa dari setiap kategori yang memperoleh nilai tertinggi

Penyelenggara:

Bekerja sama dengan:


Yayasan Peduli Matematika Indonesia

10 Daerah Dengan Nilai UN Terbaik

Persentase kelulusan pada satuan pendidikan SMA/MA/SMK tahun ini mengalami kenaikan lebih dari sembilan persen. Berdasarkan data Kementerian Pendidikan Nasional (Kemdiknas), 1.461.941 peserta ujian nasional (UN) SMA/sederajat tahun ajaran 2010/2011, 1.450.498 atau sama dengan 99.22 persen siswa lulus, sementara 11.443 atau sama dengan 0.78 persen siswa lainnya tidak lulus.

Tahun lalu, dari 1.522.195 peserta UN, sebanyak 1.368.938 atau sama dengan 89.93 persen siswa lulus, dan 153.257 atau sama dengan 10.07 persen lainnya tidak lulus. Berikut kami berikan ringkasan 10 daerah dengan rata-rata nilai akhir, nilai UN dan nilai sekolah terbaik.

Data Kemdiknas memaparkan, 10 daerah dengan persentase nilai akhir terbaik tahun ini adalah Bali (8.40), Sumatera Utara (8.17), Bengkulu (8.08), Jawa Barat (8.08), Jawa Timur (8.05), Sumatera Selatan (7.96), Sulawesi Utara (7.94), Lampung (7.91), Riau (7.90), Jawa Tengah (7.89), Sulawesi Selatan (7.84).

Sementara itu, 10 daerah dengan rata-rata nilai UN terbaik adalah Bali (8.31), Bengkulu (8.07), Sumatera Utara (8.05), Jawa Barat (8.03), Jawa Timur (7.86), Sumatera Selatan (7.80), Sulawesi Utara (7.66), Lampung (7.67), Riau (7.91), Jawa Tengah (7.70), Maluku (7.69). Sedangkan 10 daerah dengan rata-rata nilai sekolah terbaik adalah Bali (8.51), Bengkulu (8.35), DI Yogyakarta ( 8.35), Sulawesi Utara ( 8.340, Jawa Timur (8.32), Lampung (8.25), Sumatera Selatan (8.25), Sumatera Selatan (8.19), Jawa Tengah (8.16), Sumut (8.16), Jawa Barat (8.13).

Sumber : Kompas.Com

M381 Exam setup

Today I received pack 2 of M381 materials and read some interesting news about the exam setup. ( Open University ) course M381 has two fairly independent tracks: Number Theory and Mathematical Logic. The TMA's are thus mostly 50/50. The exam however has a different setup.

The exam consists of 16 questions.
Questions 1-8 cover Number Theory. ( My educated guess is 1 questions for each book / topic.
- divisibility
- prime numbers
- congruence
- Fermat / Wilson theorems
- multiplicative functions
- quadratic reciprocity
- continued fractions
- linear Diophantine equations.
Questions 9-16 cover Mathematical Logic. ( My guess is as follows )
- computability
- primitive recursive functions
- Church's thesis
- formal systems
- formal proofs
- formal number theory ( 3 questions )

All questions are marked and ranked. The nine best results are used to count your grade for the exam. There is one restriction however you can't use more than six questions from one subject. So if all number theory results are better than the logic ones than they take the six best nt questions and then the best three from logic.
eaxc
If, and I suppose it is, ( isn't it always? ) an extremely time-constrained exam then there are quite a number of strategies to follow for sequencing the work at the exam. I will have to think about that when the exam date comes closer, I suppose. A lot depends on my self-

SSLC പത്താം ക്ലാസ് പാഠപുസ്തകങ്ങള്‍ (Updated Links)

ഈ വര്‍ഷം പത്താം ക്ലാസിലെ പാഠപുസ്തകങ്ങള്‍ മാറുകയാണല്ലോ. ഐടി ഒഴികെയുള്ള എല്ലാ പുസ്തകങ്ങള്‍ക്കും മാറ്റമുണ്ട്. മെയ് ആദ്യ വാരത്തില്‍ പത്താം ക്ലാസുകാര്‍ക്ക് കോച്ചിങ് ക്ലാസ് ആരംഭിക്കുമല്ലോ. പക്ഷെ ഇതേ വരെ പാഠപുസ്തകങ്ങള്‍ സ്ക്കൂളില്‍ എത്തിയിട്ടില്ലെന്നോര്‍ത്ത് നമ്മുടെ സഹപ്രവര്‍ത്തകര്‍ ആശങ്കയിലാണ്. (അതെല്ലാം കൃത്യസമയത്ത് എത്തിക്കാനുള്ള നടപടികള്‍ തകൃതിയായി നടക്കുന്നു). പക്ഷെ, ഇന്റര്‍നെറ്റിന്റെ കടന്നു വരവോടെ വിവരവിനിമയം അതിവേഗത്തിലും കാര്യക്ഷമതയോടും സാധ്യമായി. പത്താം ക്ലാസ് ഗണിത പാഠപുസ്തകത്തെക്കുറിച്ച് ഗണിതാധ്യാപകരുടെ ആശങ്ക ദുരീകരിക്കാന്‍ വേണ്ടി പാഠപുസ്തകകമ്മിറ്റി ചെയര്‍മാനും മാത്​സ് ബ്ലോഗിന്റെ പേട്രനുമായ കൃഷ്ണന്‍ സാര്‍ ഒരു അവലോകനം നടത്തിയിരുന്നു. അതോടെ ഗണിതശാസ്ത്ര പാഠപുസ്തകത്തെക്കുറിച്ച് ഏതാണ്ടൊരു ധാരണ അധ്യാപകര്‍ക്കു ലഭിച്ചു. അതോടൊപ്പം ഇതരവിഷയങ്ങള്‍ കൈകാര്യം ചെയ്യുന്ന അധ്യാപകരും മറ്റു വിഷയങ്ങളുടെ പാഠപുസ്തകങ്ങള്‍ ആവശ്യപ്പെടുകയുണ്ടായി. ഇപ്പോഴിതാ, അധ്യാപകരുടെയും വിദ്യാര്‍ത്ഥികളുടെയും സഹായത്തിനായി സ്തുത്യര്‍ഹമായ വിധത്തിലില്‍ എസ്.സി.ഇ.ആര്‍.ടിയും സി.ഡിറ്റുമടക്കം ഇടപെട്ടിരിക്കുന്നു. ആദ്യഘട്ടത്തില്‍ മലയാളം മീഡിയത്തിലുള്ള പാഠപുസ്തകങ്ങളുടെ പി.ഡി.എഫുകളാണ് എസ്.സി.ഇ.ആര്‍.ടി ലഭ്യമാക്കിയിരിക്കുന്നത്. മറ്റു മീഡിയങ്ങളിലുള്ളവ വൈകാതെ തന്നെ ലഭ്യമാകുമെന്ന് പ്രതീക്ഷിക്കുന്നു. പാഠപുസ്തകങ്ങളുടെ ലിങ്കുകള്‍ താഴെ നല്‍കിയിരിക്കുന്നു.


Std X (Malayalam Medium) 2011
Malayalam AT

Malayalam_BT

Tamil_AT

Tamil_BT

Kannada_AT

Kannada_BT

English_Part_I

English_Part_II

Hindi Reader

Arabic Reader_General

Arabic Reader_Academic Schools

Urdu Reader

Sanskrit_General

Sanskrit_Oriental

Science_I_Mal
Amughum, Chapter-01, 02, 03, 04, 05, 06, 07, 08

Science_II_Mal
Amughum, Chapter-09, 10, 11, 12, 13, 14, 15, 16

Science_III_Mal
Biology Amugham, Chapter-01, 02, 03, 04, 05, 06, 07, 08

Social Science_I_Mal
Cover Aamughum Chapter-01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 12, 
 

Social Science_II_Mal
Aamughum Chapter-01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 12, 
 
Mathematics_Mal_Part_I
Aamughum Chapter-01, 02, 03, 04, 05, 06,
 
Mathematics_Mal_Part_II
Glossary, Aamughum Chapter-07, 08, 09, 10, 11,


Information Technology (Malayalam Medium) :
ICT Text Book Std X

Kerala Health & Physical Education Curriculum- Teachers Handbook - Part I - Part II - Part III

എസ്.സി.ഇ.ആര്‍.ടി യ്ക്ക് കടപ്പാട്

Algebra's Tiling

I don't think algebra tiles or blocks are a panacea for what ails student algebraists, but I do think they are powerful.  Even though as a mathematician I am pretty comfortable with symbolic reasoning, at heart I am a visual thinker.  Having a way to visualize algebra opens up many possibilities for learners, even when they had a good symbolic understanding beforehand.  The goal for me is not to replace symbolic manipulation, but support the concepts.

I designed the activity for students that may have not done a lot of investigation before.  So it starts with a lot of modeling, and then letting them try.  Students did an amazing job.

Even before doing the mental math (making the point that even number operations can be visualized, plus setting the context for the follow up activity), I asked the students to take a  look at the blocks to see what they noticed. Mr. Boeve had had the students play with the blocks the day before, which is an excellent idea.  They noticed corresponding dimensions, colors, different designs.  These were the tiles from Algebra Lab Gear, so there's 1/2 x blocks, 1/4 x blocks, 5 sticks and 25 sticks.

None of the students had seen the visual multiplication before, but they were willing to give it a try.  They made connections as to why the pieces represented what they did.  The verbal connection, x squared, was biggest, but then a few students recognized the x times x relation.  They picked up the symbol to picture representing quickly, and that gave an opportunity to talk about how there are many different ways to write things in math.  They had 2x+3+1x+2 and 2x +3 +x+2 and 3x+5.  We introduced what mathematicians call simplifying, which they connected to fractions.

I raised the problem of negatives - how could we show negatives, because algebra has a lot of those.  They thought we could have two color blocks, or use some kind of design.  How could we do it with the blocks we have?  Maybe we could separate the positives and negatives.  Nice thinking!

Sometimes I think of mini-lessons like these as equipping the students for problems.  The problem list offered practice, light extension and serious problems.  After 15 minutes to do their choice, which they loved having, we came back together and I asked if there were any they wanted to see me do?  They suggested problems, and if there was a student to explain them, they gave it a try.  One of the themes throughout was "give it a go."  I made sure to ask some students who had incomplete or incorrect thinking so we could talk about that, too.  Because the whole situation was different, it helped with making that safe.

In discussing the subtraction problems, they got to three separate ideas: taking away, zero pairs, and adding the opposite.  The students exploring these ideas were able to give reasons for why it made sense with the blocks.


We just worked with the document camera, but if you want virtual algebra tiles, there's the National Virtual Manipulative Library tiles, a two color version from the Michigan Virtual University, and NCTM's Illuminations Algebra Tiles.  None of them are ideal, but all are serviceable.  It's very possible to make homemade algebra tiles, and there was a good article about that in the Mathematics Teacher: "Algebra for All: Using Homemade Algebra Tiles to Develop Algebra and Prealgebra Concepts," Annette Ricks Leitze and Nancy A. Kitt, September 2000, Volume 93, Issue 6.

Thanks to Mr. Boeve and his classes for the nice opportunity!  Jill Beauchamp came along for experience with the algebra blocks, and she was a great support to the kids, so thanks to her, too.




Playing With Blocks

Photo credits: Eamonn @ Flickr

Solving linear congruences ( NOT the M381 way )

In M381 Number Theory Unit 3 I read "...The way to become proficient at solving linear congruences is through plenty of practice at applying the above strategy. ..." - What did I just read?!

Well. This is NOT how it should be done. You need as much 'strategies' for solving linear congruences as you would need for solving a linear equality equation in x. There is a simple formula that solves -any- linear congruence equation.

a x ~ b mod m <=> x = Mod[a PowerMod[b, -1, m], m] where a, b can be ( negative ) fractions. ( Understanding the formula only requires understanding Greatest Common Divisors and the Euclidean Algorithm or one of its improved alternatives )

Example.
7 x ~ 41 mod 101 <=> x = Mod[41 PowerMod[7, -1, 101], 101] <=> x ~ 78 mod 101
Since:
7 * ( 78 + 101k ) - 41 = 505 + 707k which is clearly a multiple of 101 for any k.

Jadwal Study Wisata Ke Jogyakarta

Berikut jadwal Study Tour MGMP Matematika SMP DKI Jakarta :






Jadwal Jogya

Link Terkait : Undangan Study Wisata Jogyakarta

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TMA week ( Pomodoro style )

Studying mathematics at the Open University means that you have to send in a Tutor Marked Assignment ( 10 questions on which I spent as little as 5 hours but there were TMAs that cost me 40 hours ) per 7.5 study-points. So, if you do 60 points in a year you have to do 8 of those ( and one or two exams ). Unfortunately it is not allowed to publish any TMA questions on the Internet.

Today and the next thee days until Saturday are for M381 TMA02 ( Number Theory and Mathematical Logic ). Although I haven't planned to complete the TMA by then I want to see how far I come now that I have almost three weeks of Pomodoro experience. The drop in posts to my blog is definitely a result of my implementation of the PT. - I can say that the Pomodoro Technique is fully compatible with GTD, one could argue that PT fixes GTD so that it effectively cures procrastination. ( That the PT is compatible with Hubbard's Management Methods and Techniques is a no-brainer. )

More later...