I was looking to understand more on positive definite matrices and a couple of theorems. I found a nice summary of positive definite matrices, their properties and role in quadratic minimization on the web here. Another link here. Another here.
Also an ultra-quick summary of Linal.
Showing posts with label Resources. Show all posts
Showing posts with label Resources. Show all posts
Sunday, May 4, 2008
Thursday, April 24, 2008
Lessons from the teaching assistantship experience
I. Introduction
I have been a teaching assistant in udub for about 2 quarters (including this one) and I find it to be a rewarding experience and a continual learning experience too. My job is to hold quiz sections twice every week where I go over examples to better explain concepts from the lectures and also give students some practice problems. I also help out with some grading. Believe me, this is not an easy job at all but at the same time it is a fulfilling and creative job. When you develop new, ingenious ways to communicate ideas and concepts to students and they "GET IT", that's awesome - that's why its fulfilling, that very feeling of having given your all into the job gives you back a feeling of fullness.
II. Key elements
From my limited experience , the key elements I have found for a successful quiz section are:
1) Know the content thoroughly and anticipate potential questions: You have already taken the course you are TAing, that's why you are qualified to be a teaching assistant. But knowing the concepts on the surface isn't enough, you got to be able to explain them, analyse them from all angles, think of potential questions students might come up with and see if you can answer them comfortably. To be able to explain content requires different preparation than just knowing the content and hence sufficient effort needs to be put in here depending on your knowledge of the subject.
2) Get to know the students, atleast their names: This is important, since your ideal quiz section is one where students are involved in it and find it interesting and useful. Knowing their names makes it easier to engage them and increases their participation in the quiz section. Eye contact is also important, you need to make them feel comfortable. These things come easily for some people who are more sociable than others. I am more of an ambivert and hence had to put some effort to get this connection thing going.
3) Make the quiz section interesting: Depending on the composition of the class, students may or may not be able to follow the class easily. If they follow the class easily, they would expect more than other students, who would be content with practicing problems related to the homework or quizzes. I try to bring in one or two examples from outside the book that the students can relate to, find interesting, and also helps their understanding of the concepts.
Cracking a joke or two now and then will also help lighten up the mood.
Variety is the spice of life, but it can also spice up the quiz section. This is something that keeps me interested too. I try out different things every quiz section, see if it works and imbibe it into my "teaching model" if it does.
4) Organize the quiz section well and incorporate time management:
Organizing or structuring the quiz section well gives the students a good idea of what's coming next, sets expectations (which isn't necessarily a great thing) and keeps them involved. Last quarter I was always on time for my quiz sections. But this quarter, I need to wake up by 7am and go to the quiz sections by 8:30am. I have had problems with the bus not coming on time and traffic signal delays. So basically, I don't have a time-window for uncertainities such as delays. It's good to be efficient but not at the cost of coming to quiz sections late every now and then. So I realized that early and am catching an earlier bus that gives me enough breathing time before I begin my quiz section.
It's also good to have a schedule of what you are going to do when during the quiz section, so that the quiz sections are efficient and the students get more out of it. Ofcourse, you have to decide the level of efficiency since being too efficient might come at the cost of rushing through the quiz section.
So that's a good summary of what I think has helped me out in the quiz sections.
III. Challenges
1) It has not been easy at all as I mentioned earlier. I wasn't given an agenda of what's to be done in the quiz section last quarter. A few examples and asking students to work out problems was what I was told. You know, just following those instructions isn't going to give you the greatest quiz section at all. When you realize that, your learning process begins. You begin experimenting, infact what you are doing is you are researching your teaching skills through experimentation!! Isn't that wonderful to be able to research your teaching skills on the fly, without reading any papers!
2) Feedback from students was my main motivation for improving the quiz section. Ofcourse, I would get feedback from students even when I didn't ask for it and sometimes, in a rude manner. Dealing with such cases was also a challenge.
3) The main challenge I would say is coming up with a basic, working, "quiz section model" that is good as it is, but can be improvized. That working model, is what I have described in the second section above.
I have been a teaching assistant in udub for about 2 quarters (including this one) and I find it to be a rewarding experience and a continual learning experience too. My job is to hold quiz sections twice every week where I go over examples to better explain concepts from the lectures and also give students some practice problems. I also help out with some grading. Believe me, this is not an easy job at all but at the same time it is a fulfilling and creative job. When you develop new, ingenious ways to communicate ideas and concepts to students and they "GET IT", that's awesome - that's why its fulfilling, that very feeling of having given your all into the job gives you back a feeling of fullness.
II. Key elements
From my limited experience , the key elements I have found for a successful quiz section are:
1) Know the content thoroughly and anticipate potential questions: You have already taken the course you are TAing, that's why you are qualified to be a teaching assistant. But knowing the concepts on the surface isn't enough, you got to be able to explain them, analyse them from all angles, think of potential questions students might come up with and see if you can answer them comfortably. To be able to explain content requires different preparation than just knowing the content and hence sufficient effort needs to be put in here depending on your knowledge of the subject.
2) Get to know the students, atleast their names: This is important, since your ideal quiz section is one where students are involved in it and find it interesting and useful. Knowing their names makes it easier to engage them and increases their participation in the quiz section. Eye contact is also important, you need to make them feel comfortable. These things come easily for some people who are more sociable than others. I am more of an ambivert and hence had to put some effort to get this connection thing going.
3) Make the quiz section interesting: Depending on the composition of the class, students may or may not be able to follow the class easily. If they follow the class easily, they would expect more than other students, who would be content with practicing problems related to the homework or quizzes. I try to bring in one or two examples from outside the book that the students can relate to, find interesting, and also helps their understanding of the concepts.
Cracking a joke or two now and then will also help lighten up the mood.
Variety is the spice of life, but it can also spice up the quiz section. This is something that keeps me interested too. I try out different things every quiz section, see if it works and imbibe it into my "teaching model" if it does.
4) Organize the quiz section well and incorporate time management:
Organizing or structuring the quiz section well gives the students a good idea of what's coming next, sets expectations (which isn't necessarily a great thing) and keeps them involved. Last quarter I was always on time for my quiz sections. But this quarter, I need to wake up by 7am and go to the quiz sections by 8:30am. I have had problems with the bus not coming on time and traffic signal delays. So basically, I don't have a time-window for uncertainities such as delays. It's good to be efficient but not at the cost of coming to quiz sections late every now and then. So I realized that early and am catching an earlier bus that gives me enough breathing time before I begin my quiz section.
It's also good to have a schedule of what you are going to do when during the quiz section, so that the quiz sections are efficient and the students get more out of it. Ofcourse, you have to decide the level of efficiency since being too efficient might come at the cost of rushing through the quiz section.
So that's a good summary of what I think has helped me out in the quiz sections.
III. Challenges
1) It has not been easy at all as I mentioned earlier. I wasn't given an agenda of what's to be done in the quiz section last quarter. A few examples and asking students to work out problems was what I was told. You know, just following those instructions isn't going to give you the greatest quiz section at all. When you realize that, your learning process begins. You begin experimenting, infact what you are doing is you are researching your teaching skills through experimentation!! Isn't that wonderful to be able to research your teaching skills on the fly, without reading any papers!
2) Feedback from students was my main motivation for improving the quiz section. Ofcourse, I would get feedback from students even when I didn't ask for it and sometimes, in a rude manner. Dealing with such cases was also a challenge.
3) The main challenge I would say is coming up with a basic, working, "quiz section model" that is good as it is, but can be improvized. That working model, is what I have described in the second section above.
Thursday, January 17, 2008
The "Clicking problem" in laptops (mine's a Dell)
Does your laptop "click" incessantly when you are doing even mildly intensive work such as opening documents or running a small software?
Does your laptop "beep" every minute or two when it's idle (This problem might be exclusive to dell laptops).
Well this problem has got to do with your hard-drive's power saving features (unless your os starts to crash - Then it might be a mother board problem). If your computer's pretty ok except for the "incessant clicking and ocassional beeps", do visit this forumpage.
It gives you a step by step procedure to minimize the noise due to those "clicks".
To summarize the solution in the forum page:
1) Install Microsoft .net 2.0 version from here. If you have an earlier version of .net, uninstall it before installing version 2.
2) Install NHC (Network Hardware Control) from here. Note: users of Dell laptops such as Dell Vostro, Dell Inspiron, etc use the Dell bug fix version on the same page. The other version would give you an error when you try to install it.
3) Run the installed NHC 2.0.
4) You should see an icon to the left of your desktop icons that looks like a big battery.
5) Double click the icon.
6) In the window that just appeared select the Settings tab
7) Click Show all NHC options and settings
8) Now select the Hard Disk tab, and under Advanced Power Management select the highest setting: Max. Peformance Mode
Voila ~ you are done!
Now you can enjoy blissful sleep when your laptop is idle(a.k.a those painful beeps vanish). Also, if you want to work in a very quiet place, the "incessant clickings" would become incessant whispers that are hardly noticeable.
Enjoy the peace and be peaceful :-)
Does your laptop "beep" every minute or two when it's idle (This problem might be exclusive to dell laptops).
Well this problem has got to do with your hard-drive's power saving features (unless your os starts to crash - Then it might be a mother board problem). If your computer's pretty ok except for the "incessant clicking and ocassional beeps", do visit this forumpage.
It gives you a step by step procedure to minimize the noise due to those "clicks".
To summarize the solution in the forum page:
1) Install Microsoft .net 2.0 version from here. If you have an earlier version of .net, uninstall it before installing version 2.
2) Install NHC (Network Hardware Control) from here. Note: users of Dell laptops such as Dell Vostro, Dell Inspiron, etc use the Dell bug fix version on the same page. The other version would give you an error when you try to install it.
3) Run the installed NHC 2.0.
4) You should see an icon to the left of your desktop icons that looks like a big battery.
5) Double click the icon.
6) In the window that just appeared select the Settings tab
7) Click Show all NHC options and settings
8) Now select the Hard Disk tab, and under Advanced Power Management select the highest setting: Max. Peformance Mode
Voila ~ you are done!
Now you can enjoy blissful sleep when your laptop is idle(a.k.a those painful beeps vanish). Also, if you want to work in a very quiet place, the "incessant clickings" would become incessant whispers that are hardly noticeable.
Enjoy the peace and be peaceful :-)
Saturday, November 10, 2007
Becoming a successful researcher
The following articles address the following questions:
1) What does it mean to do good research?
2) What are the important factors in doing good research?
3) How does one successfully and confidently do a Phd?
4) How important is it to have a good and compatible advisor?
Article1
Article2
Article3
Article4
Other articles on becoming a successful researcher (including problems faced by junior faculty)here.
1) What does it mean to do good research?
2) What are the important factors in doing good research?
3) How does one successfully and confidently do a Phd?
4) How important is it to have a good and compatible advisor?
Article1
Article2
Article3
Article4
Other articles on becoming a successful researcher (including problems faced by junior faculty)here.
Saturday, March 17, 2007
VRP
A good site on the web that summarizes the problem features, formulations and solution techniques to the VRP(Vehicle routing problem) and its variants such as VRPTW(with time windows), SVRP(stochastic), VRPPD (both pick-up and delivery), CVRP (capacitated), PVRP (periodic), SDVRP (Split delivery),MDVRP(Multiple depot), etc...
Also a nice bibliography of the algorithms and solution techniques for VRP and its variants can be found here.
Also a nice bibliography of the algorithms and solution techniques for VRP and its variants can be found here.
Sunday, March 11, 2007
Writing a research proposal
I took this seminar course whose aim is basically to give you a set of tools to guide your research and fine tune the way you conduct research. Three take homes I got from this seminar are:
1) When to reference and when not to reference when you write a paper
2) Giving a presentation: What needs to be taken care of, the good and bad of a few case presentations.
3) Research proposal: Writing one effectively.
I will just discuss the third take home. Here's a good article on writing a research proposal. Find a pdf version here.
To summarize the article:
There are two things to writing a research proposal - a) The writing part of it b) The content and structure part of it.
The writing part is similar to writing any document - The document should be coherent, have a flow, should be concise and also be easily understandable to the targetted audience.
The content can be summarized as follows and is very similar to the structure of a thesis:
a) Abstract - What is it that you propose to do in your research summarized briefly in a paragraph.
b) Introduction - i) Should clearly define the objectives of the study or research to be conducted
ii) Should establish the context of the study and its significance and/or contribution practically(application) and theoretically(model/technique development/formulation of the problem, etc).
iii) The main problem features should be described and the scope of the problem clearly delineated.
c) Literature review - Should include all contributions from literature relevant to the problem area. The contributions should not be rambling but should be expressed concisely though effectively.
d) Solution Methodology - Should be described in the context of what is in the literature. Should narrow down a few solution techniques and the pros and cons of this subset of techniques should be briefly described.
e) Data - What data do you think is required for this problem. How are you going to get it(Experiments/data collection, etc).
f) Discussion - Summarize the research briefly. Discuss the pros and cons of the solution methodology adopted, data to be used, etc.
Usually a research proposal is made to obtain grants and funding for the research. So a research proposal should be written in a manner that highlights the significance of the research and its contribution. Hence the emphasis on both the 'writing' and the 'content'.
1) When to reference and when not to reference when you write a paper
2) Giving a presentation: What needs to be taken care of, the good and bad of a few case presentations.
3) Research proposal: Writing one effectively.
I will just discuss the third take home. Here's a good article on writing a research proposal. Find a pdf version here.
To summarize the article:
There are two things to writing a research proposal - a) The writing part of it b) The content and structure part of it.
The writing part is similar to writing any document - The document should be coherent, have a flow, should be concise and also be easily understandable to the targetted audience.
The content can be summarized as follows and is very similar to the structure of a thesis:
a) Abstract - What is it that you propose to do in your research summarized briefly in a paragraph.
b) Introduction - i) Should clearly define the objectives of the study or research to be conducted
ii) Should establish the context of the study and its significance and/or contribution practically(application) and theoretically(model/technique development/formulation of the problem, etc).
iii) The main problem features should be described and the scope of the problem clearly delineated.
c) Literature review - Should include all contributions from literature relevant to the problem area. The contributions should not be rambling but should be expressed concisely though effectively.
d) Solution Methodology - Should be described in the context of what is in the literature. Should narrow down a few solution techniques and the pros and cons of this subset of techniques should be briefly described.
e) Data - What data do you think is required for this problem. How are you going to get it(Experiments/data collection, etc).
f) Discussion - Summarize the research briefly. Discuss the pros and cons of the solution methodology adopted, data to be used, etc.
Usually a research proposal is made to obtain grants and funding for the research. So a research proposal should be written in a manner that highlights the significance of the research and its contribution. Hence the emphasis on both the 'writing' and the 'content'.
Tuesday, March 6, 2007
Fundamentals of Optimization
Here are the lecture notes of the course I just finished. Coming from an engineering background, I found this course to be really tough to start with. The 'toughness' didn't change, only I got used to it. The course was graded entirely based on 8 assignments (one every week), which were more an extension of the notes rather than being a completely new devil. I still don't have the big picture or the take-home from the notes, since this course involved pre-requisites such as Linear Algebra and a good enough exposure (supposedly years!) to elements of analysis and advanced calculus, which I didn't have. So most of my time was spent getting a 'feel' for the subject, including notations, concepts et al - basically the 'language of mathematics'. I am still uncomfortable looking at the level of math in the course, but hopefully with more exposure to these kind of courses and materials, I should begin to understand and enjoy the subject more thoroughly.
This is one of a kind course in that it goes into the fundamentals of the subject. Many people (me included) use the word 'optimization' loosely, but hardly realise that there is a whole theory(as I gleaned from this course) that lays the basis for all the algorithms and optimization techniques being widely used in various engineering, science and health disciplines.
A note on my course-mates: Most of them were studs in the field(grad level math course machi)
who left me amazed on their depth in the subject as was evident from the questions fielded in the class. Through this course, I have been fortunate enough to have the experience of knowing first hand how tough Math can be (I had strange opinions on Math before coming here). I might get away with a 3.7 or 3.8 in the course, but you see these assignments were very instructive and guiding the student onto the methodology and analysis required to solve the problems. Ofcourse, I had to understand the theory before attempting the assignment, but as I said earlier the big picture is still missing. I have the bits and pieces from each of these chapters, only I need to piece them together in the coming future.
As a final note, this course(the last course taught by the prof) was taught by a highly knowledgeable prof who was very precise and exact in his development of subject(something new to me since we engineers make a lot of assumptions whenever we can) and as a result, has sort of aroused my interest in optimization theory. Let's see where I can go from here.
This is one of a kind course in that it goes into the fundamentals of the subject. Many people (me included) use the word 'optimization' loosely, but hardly realise that there is a whole theory(as I gleaned from this course) that lays the basis for all the algorithms and optimization techniques being widely used in various engineering, science and health disciplines.
A note on my course-mates: Most of them were studs in the field(grad level math course machi)
who left me amazed on their depth in the subject as was evident from the questions fielded in the class. Through this course, I have been fortunate enough to have the experience of knowing first hand how tough Math can be (I had strange opinions on Math before coming here). I might get away with a 3.7 or 3.8 in the course, but you see these assignments were very instructive and guiding the student onto the methodology and analysis required to solve the problems. Ofcourse, I had to understand the theory before attempting the assignment, but as I said earlier the big picture is still missing. I have the bits and pieces from each of these chapters, only I need to piece them together in the coming future.
As a final note, this course(the last course taught by the prof) was taught by a highly knowledgeable prof who was very precise and exact in his development of subject(something new to me since we engineers make a lot of assumptions whenever we can) and as a result, has sort of aroused my interest in optimization theory. Let's see where I can go from here.
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