Here's a site to help those of us who are statistically challenged.
statistics help for Journalists: "Statistics Every Writer Should Know
A simple guide to understanding basic statistics, for journalists and other writers who might not know math."
statistics help
Tuesday, August 31, 2010
Removing GATE
A recent article in NY Times discusses the trouble with using SAT as the sole criterion for admission. This is actually one of the followups from several articles published on this issue in the Chronicle of Higher Education. This is based on the report by the National Association for College Admission Counseling. which discusses that tests like the SAT and ACT were never meant to be viewed in isolation but considered as one of the factors that include grades, essays and so on. But with the college ranking systems considering SAT as one of the main criteria for ranking, the colleges seem to have preferred the exam as the one of the major criteria of admission until recently. Now many colleges in USA have made SAT optional, though the major institutes like MIT and Harvard still require SAT.
This backdrop is interesting! considering that IISc is planning to drop GATE as one of the requirements for admission to its research degrees (masters and doctoral programs) in engineering. Under this proposal, the main criteria is the percentage of marks obtained by the candidate in the B.E/B.Tech examination and anyone who secures more than 70% marks in their undergraduation will be eligible for admission.
My opinion on the above has always been that we should not obsess with admissions tests like GATE for doctoral programs and we should take an expansive view of merit that would include GATE, the undergraduate scores, communication skills and motivation. However, for masters program, we need an all-India entrance exam just to screen the huge numbers. With nearly six undergraduates in engineering (and 2.5 lakhs of them expressing an interest in higher studies by writing GATE) with wide variations in the undergraduate marks awarded in each university, it would be nearly impossible to screen! them only by interviews.
statistics formula cheat sheet
This backdrop is interesting! considering that IISc is planning to drop GATE as one of the requirements for admission to its research degrees (masters and doctoral programs) in engineering. Under this proposal, the main criteria is the percentage of marks obtained by the candidate in the B.E/B.Tech examination and anyone who secures more than 70% marks in their undergraduation will be eligible for admission.
My opinion on the above has always been that we should not obsess with admissions tests like GATE for doctoral programs and we should take an expansive view of merit that would include GATE, the undergraduate scores, communication skills and motivation. However, for masters program, we need an all-India entrance exam just to screen the huge numbers. With nearly six undergraduates in engineering (and 2.5 lakhs of them expressing an interest in higher studies by writing GATE) with wide variations in the undergraduate marks awarded in each university, it would be nearly impossible to screen! them only by interviews.
statistics formula cheat sheet
Quadratic Formula Rap
If there's one thing my students learn by the end of the year and actually still remember in later years, it's the quadratic formula. The class where I introduce the formula goes down like this: First I tell them about the quadratic formula in a traditional way. I explain that now with the QF we can solve any quadratic equation, and do it much easier than we could with completing the square. I show them how to use it and they solve a couple quadratics themselves. I then tell them that for homework they have to memorize the quadratic formula overnight and there will be a quiz on it at the beginning of next class.(This is not my usual style) I always receive a chorus of groans. "But!" I interject "It will be much easier than you think. I've gotten someone to come in and help you all with this, let me go get him." I go into the hallway, put my tie around my head, half untuck my shirt and start a live performance of this. (my rapping name is SweenDawg, of course)
The live performance helps make it really fun for them, and I would highly suggest doing it if you decide to use a rap in your classroom. Any time I do a song in class (there are others) I typically do one "live" and then have a recording so I can play it for the kids multiple times and in later classes to help it stick in their memories. Now I realize this is not the most groundbreaking or new idea, but I want to stress its effectiveness and fun. The kids who have been generally uninterested throughout the year usually love this lesson the most and really get into it. Not only that, but I work in a small school and when I have students in later years they almost always remember how to solve quadratics without any prompting... or maybe just an "op-op-op" to get them started.
I also tend to plug the idea of making their own strategies when they have to memorize something, and how making a song is just one example of a memorization technique.
Shoutout to Mr. Mellor for helping lay down the track.
Have your own fun song that you like to do with your students? Tell me about it!
solving quadratic formula
The live performance helps make it really fun for them, and I would highly suggest doing it if you decide to use a rap in your classroom. Any time I do a song in class (there are others) I typically do one "live" and then have a recording so I can play it for the kids multiple times and in later classes to help it stick in their memories. Now I realize this is not the most groundbreaking or new idea, but I want to stress its effectiveness and fun. The kids who have been generally uninterested throughout the year usually love this lesson the most and really get into it. Not only that, but I work in a small school and when I have students in later years they almost always remember how to solve quadratics without any prompting... or maybe just an "op-op-op" to get them started.
I also tend to plug the idea of making their own strategies when they have to memorize something, and how making a song is just one example of a memorization technique.
Shoutout to Mr. Mellor for helping lay down the track.
Have your own fun song that you like to do with your students? Tell me about it!
solving quadratic formula
Rate-Time-Distance Word Problems
Or otherwise known as those dreaded train problems. These are always tricky for algebra students. Ask someone you know which problems they remember from Algebra I and almost all of them will have something to say about the train problems.
Train problems can be separated into two categories: same direction travel and opposite direction travel. Each are handled differently, but using a chart makes it easier to set up the equations. You also have to remember that distance equals rate times time or d=rt.
Here is an example. A train leaves the train station at 2:00 p.m. Its average rate of speed is 90 mph. Another train leaves the same station a half hour later. Its average rate of speed is 120 mph. If the second train follows the same route on a parallel track to the first, how many hours will it take the second train to catch the first?
Since the trains are travelling in the same direction, their distances are equal when the 2nd one catches the 1st. Therefore, to solve this equation, we set the distance of Train 1 equal to Train 2.
90t = 120(t-0.5)
90t = 120t - 60
-30t = -60
t = 2
The first train travelled for 2 hours before the 2nd train caught up to it. The problem asks how long it takes the 2nd train to catch the first. So it takes the 2nd train a half h! our less than it did the first train which is 1.5 hours.
Check back tomorrow for information on opposite direction travel.
solve algebra word problems
Train problems can be separated into two categories: same direction travel and opposite direction travel. Each are handled differently, but using a chart makes it easier to set up the equations. You also have to remember that distance equals rate times time or d=rt.
Here is an example. A train leaves the train station at 2:00 p.m. Its average rate of speed is 90 mph. Another train leaves the same station a half hour later. Its average rate of speed is 120 mph. If the second train follows the same route on a parallel track to the first, how many hours will it take the second train to catch the first?
Train | Rate | Time | Distance |
1 | 90 | t | 90t |
2 | 120 | t-0.5 | 120(t-0.5) |
Since the trains are travelling in the same direction, their distances are equal when the 2nd one catches the 1st. Therefore, to solve this equation, we set the distance of Train 1 equal to Train 2.
90t = 120(t-0.5)
90t = 120t - 60
-30t = -60
t = 2
The first train travelled for 2 hours before the 2nd train caught up to it. The problem asks how long it takes the 2nd train to catch the first. So it takes the 2nd train a half h! our less than it did the first train which is 1.5 hours.
Check back tomorrow for information on opposite direction travel.
solve algebra word problems
Custom Shape Tool -PhotoshopTools
The Custom Shape Tool creates custom shapes
How to use Custom Shape tool?
1.Choose the Custom Shape tool
2.Position the pointer inside the work area and just click and drag.
3.Next to Custom shape on the menu bar one arrow is there.Click that arrow.Option palette will open.
From Center - Used to draw th! e image from center.
- UnCon strained - According to our taste we can draw Custom Shape.But there is no need all the sides will be proportional to each other.
- Defined Size - Using this we can get What is the predefined size of image.We can't change or specify the size.
- DefinedProportions - Using this option we change the size.But all the sides will be automatically proportional to each other.
- Fixed Size - Using this option we can specify/change the height and width of the shape.But run time the size of the shape is fixed ie what we specified in the width and height column.
Drawing modes:
To create vector shape layers click Shape layers button
To draw paths (shape outlines) click Paths button
To create rasterized shapes in current layer click Fill pixels
Options:
- Create new shape layer - to create every new shape in a separate layer
- Add to shape area - to create multiple shapes in the same vector shape layer.
- Subtract from shape area - to subtract shapes from the current shape layer.
- Intersect with shape area - to intersect new shapes with existing one in the same layer.
- Exclude overlapping shape areas - to subtract overlapping areas.
shape areas
EPR Experiment (Designed by David Bohm)
Description of the paradox
The EPR paradox draws on a phenomenon predicted by quantum mechanics, known as quantum entanglement, to show that measurements performed on spatially separated parts of a quantum system can apparently have an instantaneous influence on one another. This effect is now known as "nonlocal behavior" (or colloquially as "quantum weirdness" or "spooky action at a distance"). In order to illustrate this, let us consider a simplified version of the EPR thought experiment put forth by David Bohm.
[edit] Measurements on an entangled state
We have a source that emits pairs of electrons, with one electron sent to destination A, where there is an observer named Alice, and another is sent to destination B, where there is an observer named Bob. According to quantum mechanics, we can arrange our source so that each emitted electron pair occupies a quantum state called a spin singlet. This can be viewed as a quantum super! position of two states, which we call state I and state II. In state I, electron A has spin pointing upward along the z-axis (+z) and electron B has spin pointing downward along the z-axis (-z). In state II, electron A has spin -z and electron B has spin +z. Therefore, it is impossible to associate either electron in the spin singlet with a state of definite spin. The electrons are thus said to be entangled.
The EPR thought experiment, performed with electrons. A source (center) sends electrons toward two observers, Alice (left) and Bob (right), who can perform spin measurements.
Alice now measures the spin along the z-axis. She can obtain one of two possible outcomes: +z or -z. Suppose she gets +z. According to quantum mechanics, the quantum state of the system collapses into state I. (Different interpretations of quantum mechanics have different ways of saying this, but the basic result is the same.) The quantum state determines the probable outcomes! of any measurement performed on the system. In this case, if ! Bob subs equently measures spin along the z-axis, he will obtain -z with 100% probability. Similarly, if Alice gets -z, Bob will get +z.
There is, of course, nothing special about our choice of the z-axis. For instance, suppose that Alice and Bob now decide to measure spin along the x-axis, according to quantum mechanics, the spin singlet state may equally well be expressed as a superposition of spin states pointing in the x direction. We'll call these states Ia and IIa. In state Ia, Alice's electron has spin +x and Bob's electron has spin -x. In state IIa, Alice's electron has spin -x and Bob's electron has spin +x. Therefore, if Alice measures +x, the system collapses into Ia, and Bob will get -x. If Alice measures -x, the system collapses into IIa, and Bob will get +x.
In quantum mechanics, the x-spin and z-spin are "incompatible observables", which means that there is a Heisenberg uncertainty principle operating between them: a quantum state cannot possess a definite va! lue for both variables. Suppose Alice measures the z-spin and obtains +z, so that the quantum state collapses into state I. Now, instead of measuring the z-spin as well, Bob measures the x-spin. According to quantum mechanics, when the system is in state I, Bob's x-spin measurement will have a 50% probability of producing +x and a 50% probability of -x. Furthermore, it is fundamentally impossible to predict which outcome will appear until Bob actually performs the measurement.
So how does Bob's electron know, at the same time, which way to point if Alice decides (based on information unavailable to Bob) to measure x and also how to point if Alice measures z? Using the usual Copenhagen interpretation rules that say the wave function "collapses" at the time of measurement, there must be action at a distance or the electron must know more than it is supposed to. To make the mixed part quantum and part classical descriptions of this experiment local, we have to say that th! e notebooks (and experimenters) are entangled and have linear ! combinat ions of + and Рwritten in them, like Schr̦dinger's Cat.
Incidentally, although we have used spin as an example, many types of physical quantities — what quantum mechanics refers to as "observables" — can be used to produce quantum entanglement. The original EPR paper used momentum for the observable. Experimental realizations of the EPR scenario often use photon polarization, because polarized photons are easy to prepare and measure.
quantum entanglement simplified
The EPR paradox draws on a phenomenon predicted by quantum mechanics, known as quantum entanglement, to show that measurements performed on spatially separated parts of a quantum system can apparently have an instantaneous influence on one another. This effect is now known as "nonlocal behavior" (or colloquially as "quantum weirdness" or "spooky action at a distance"). In order to illustrate this, let us consider a simplified version of the EPR thought experiment put forth by David Bohm.
[edit] Measurements on an entangled state
We have a source that emits pairs of electrons, with one electron sent to destination A, where there is an observer named Alice, and another is sent to destination B, where there is an observer named Bob. According to quantum mechanics, we can arrange our source so that each emitted electron pair occupies a quantum state called a spin singlet. This can be viewed as a quantum super! position of two states, which we call state I and state II. In state I, electron A has spin pointing upward along the z-axis (+z) and electron B has spin pointing downward along the z-axis (-z). In state II, electron A has spin -z and electron B has spin +z. Therefore, it is impossible to associate either electron in the spin singlet with a state of definite spin. The electrons are thus said to be entangled.
The EPR thought experiment, performed with electrons. A source (center) sends electrons toward two observers, Alice (left) and Bob (right), who can perform spin measurements.
Alice now measures the spin along the z-axis. She can obtain one of two possible outcomes: +z or -z. Suppose she gets +z. According to quantum mechanics, the quantum state of the system collapses into state I. (Different interpretations of quantum mechanics have different ways of saying this, but the basic result is the same.) The quantum state determines the probable outcomes! of any measurement performed on the system. In this case, if ! Bob subs equently measures spin along the z-axis, he will obtain -z with 100% probability. Similarly, if Alice gets -z, Bob will get +z.
There is, of course, nothing special about our choice of the z-axis. For instance, suppose that Alice and Bob now decide to measure spin along the x-axis, according to quantum mechanics, the spin singlet state may equally well be expressed as a superposition of spin states pointing in the x direction. We'll call these states Ia and IIa. In state Ia, Alice's electron has spin +x and Bob's electron has spin -x. In state IIa, Alice's electron has spin -x and Bob's electron has spin +x. Therefore, if Alice measures +x, the system collapses into Ia, and Bob will get -x. If Alice measures -x, the system collapses into IIa, and Bob will get +x.
In quantum mechanics, the x-spin and z-spin are "incompatible observables", which means that there is a Heisenberg uncertainty principle operating between them: a quantum state cannot possess a definite va! lue for both variables. Suppose Alice measures the z-spin and obtains +z, so that the quantum state collapses into state I. Now, instead of measuring the z-spin as well, Bob measures the x-spin. According to quantum mechanics, when the system is in state I, Bob's x-spin measurement will have a 50% probability of producing +x and a 50% probability of -x. Furthermore, it is fundamentally impossible to predict which outcome will appear until Bob actually performs the measurement.
So how does Bob's electron know, at the same time, which way to point if Alice decides (based on information unavailable to Bob) to measure x and also how to point if Alice measures z? Using the usual Copenhagen interpretation rules that say the wave function "collapses" at the time of measurement, there must be action at a distance or the electron must know more than it is supposed to. To make the mixed part quantum and part classical descriptions of this experiment local, we have to say that th! e notebooks (and experimenters) are entangled and have linear ! combinat ions of + and Рwritten in them, like Schr̦dinger's Cat.
Incidentally, although we have used spin as an example, many types of physical quantities — what quantum mechanics refers to as "observables" — can be used to produce quantum entanglement. The original EPR paper used momentum for the observable. Experimental realizations of the EPR scenario often use photon polarization, because polarized photons are easy to prepare and measure.
quantum entanglement simplified
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