Stats Notebook Index Set Up Lookin Hella Fine

ACADEMIC PHRASE BANK MASTERPOST: CONNECTING WORDS FOR ESSAY WRITING

Addition

To begin with, 

In the first place, 

Firstly, 

The first reason

Additionally

Furthermore, 

Another reason why

Secondly, Thirdly, 

Next, 

Pursuing this further, 

Also

Lastly, Finally

In the same way,

Comparison

Similarly,

In the same way,

Likewise,

As with,

Equally,

Contrasting

On the same contrary,

However,

Nevertheless,

On the other hand,

Even so

Alternatively

At the same time

Otherwise

Instead

Conversely 

Result

Hence

Therefore

Accordingly

Consequently

Thus

As a result

In consequence 

For this reason

For this purpose

Time

Meanwhile

Presently

At last

Finally

Immediately

Thereafter

At that time

Eventually

Currently

Subsequently

In the meantime

Importance

Importantly

Especially

Above all

With attention to

Example

For example

For instance

That is

Such as

As revealed by

Illustrated by

Specifically

In particular

For one thing

This can be seen by

An instance of this

Literary

Clarifies

Conveys

Depicts

Demonstrates

Determines

Displays

Emphasizes

Establishes 

Explains

Exemplifies

Highlights

Illustrates

Indicates

Potrays

Represents

Shows

Signifies

Suggests

Beginnings/Causes/Effects

Affects

Generates

Ignites

Impacts

Imposes

Influences

Initiates

Introduces

Involves

Launches

Leads to

Presents

Promotes

Prompts

Results in

Summary

In conclusion,

To sum it all up,

To summarize,

In the final analysis

You can see why …

Finally,

To wrap it all up,

Therefore,

In summary,

In short,

In brief,

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This makes me sound stupid but what does a feynman diagram mean?

You don’t sound stupid! They can be pretty confusing at first, and I’m sure you’re not they only one that doesn’t fully understand them (myself included) so let’s learn how to draw Feynman diagrams!

You do not need to know any fancy-schmancy math or physics to do this!

I know a lot of people are intimidated by physics: don’t be! Today there will be no equations, just non-threatening squiggly lines. Even school children can learn how to draw Feynman diagrams. Particle physics: fun for the whole family.

For now, think of this as a game. You’ll need a piece of paper and a pen/pencil. The rules are as follows (read these carefully):

1. You can draw two kinds of lines, a straight line with an arrow or a wiggly line:

You can draw these pointing in any direction.

2. You may only connect these lines if you have two lines with arrows meeting a single wiggly line.

Note that the orientation of the arrows is important! You must have exactly one arrow going into the vertex and exactly one arrow coming out.

3. Your diagram should only contain connected pieces. That is every line must connect to at least one vertex. There shouldn’t be any disconnected part of the diagram.

In the image above, the diagram on the left is allowed while the one on the right is not since the top and bottom parts don’t connect.

4. What’s really important are the endpoints of each line, so we can get rid of excess curves. You should treat each line as a shoelace and pull each line taut to make them nice and neat. They should be as straight as possible. (But the wiggly line stays wiggly!)

That’s it! Those are the rules of the game. Any diagram you can draw that passes these rules is a valid Feynman diagram. We will call this game QED. Take some time now to draw a few diagrams. Beware of a few common pitfalls of diagrams that do not work (can you see why?):

After a while, you might notice a few patterns emerging. For example, you could count the number of external lines (one free end) versus the number of internal lines (both ends attached to a vertex).

How are the number of external lines related to the number of internal lines and vertices?

If I tell you the number of external lines with arrows point inward, can you tell me the number of external lines with arrows pointing outward? Does a similar relation hole for the number of external wiggly lines?

If you keep following the arrowed lines, is it possible to end on some internal vertex?

Did you consider diagrams that contain closed loops? If not, do your answers to the above two questions change?

I won’t answer these questions for you, at least not in this post. Take some time to really play with these diagrams. There’s a lot of intuition you can develop with this “QED” game. After a while, you’ll have a pleasantly silly-looking piece of paper and you’ll be ready to move on to the next discussion:

What does it all mean?

Now we get to some physics. Each line in rule (1) is called a particle. (Aha!) The vertex in rule (2) is called an interaction. The rules above are an outline for a theory of particles and their interactions. We called it QED, which is short for quantum electrodynamics. The lines with arrows are matter particles (“fermions”). The wiggly line is a force particle (“boson”) which, in this case, mediates electromagnetic interactions: it is the photon.

The diagrams tell a story about how a set of particles interact. We read the diagrams from left to right, so if you have up-and-down lines you should shift them a little so they slant in either direction. This left-to-right reading is important since it determines our interpretation of the diagrams. Matter particles with arrows pointing from left to right are electrons. Matter particles with arrows pointing in the other direction are positrons (antimatter!). In fact, you can think about the arrow as pointing in the direction of the flow of electric charge. As a summary, we our particle content is:

(e+ is a positron, e- is an electron, and the gamma is a photon… think of a gamma ray.)

From this we can make a few important remarks:

The interaction with a photon shown above secretly includes information about the conservation of electric charge: for every arrow coming in, there must be an arrow coming out.

But wait: we can also rotate the interaction so that it tells a different story. Here are a few examples of the different ways one can interpret the single interaction (reading from left to right):

These are to be interpreted as: (1) an electron emits a photon and keeps going, (2) a positron absorbs a photon and keeps going, (3) an electron and positron annihilate into a photon, (4) a photon spontaneously “pair produces” an electron and positron.

On the left side of a diagram we have “incoming particles,” these are the particles that are about to crash into each other to do something interesting. For example, at the LHC these ‘incoming particles’ are the quarks and gluons that live inside the accelerated protons. On the right side of a diagram we have “outgoing particles,” these are the things which are detected after an interesting interaction.

For the theory above, we can imagine an electron/positron collider like the the old LEP and SLAC facilities. In these experiments an electron and positron collide and the resulting outgoing particles are detected. In our simple QED theory, what kinds of “experimental signatures” (outgoing particle configurations) could they measure? (e.g. is it possible to have a signature of a single electron with two positrons? Are there constraints on how many photons come out?)

So we see that the external lines correspond to incoming or outgoing particles. What about the internal lines? These represent virtual particles that are never directly observed. They are created quantum mechanically and disappear quantum mechanically, serving only the purpose of allowing a given set of interactions to occur to allow the incoming particles to turn into the outgoing particles. We’ll have a lot to say about these guys in future posts. Here’s an example where we have a virtual photon mediating the interaction between an electron and a positron.

In the first diagram the electron and positron annihilate into a photon which then produces another electron-positron pair. In the second diagram an electron tosses a photon to a nearby positron (without ever touching the positron). This all meshes with the idea that force particles are just weird quantum objects which mediate forces. However, our theory treats force and matter particles on equal footing. We could draw diagrams where there are photons in the external state and electrons are virtual:

This is a process where light (the photon) and an electron bounce off each other and is called Compton scattering. Note, by the way, that I didn’t bother to slant the vertical virtual particle in the second diagram. This is because it doesn’t matter whether we interpret it as a virtual electron or a virtual positron: we can either say (1) that the electron emits a photon and then scatters off of the incoming photon, or (2) we can say that the incoming photon pair produced with the resulting positron annihilating with the electron to form an outgoing photon:

Anyway, this is the basic idea of Feynman diagrams. They allow us to write down what interactions are possible. However, you will eventually discover that there is a much more mathematical interpretation of these diagrams that produces the mathematical expressions that predict the probability of these interactions to occur, and so there is actually some rather complicated mathematics “under the hood.” But just like a work of art, it’s perfectly acceptable to appreciate these diagrams at face value as diagrams of particle interactions.  Let me close with a quick “frequently asked questions”:

What is the significance of the x and y axes?These are really spacetime diagrams that outline the “trajectory” of particles. By reading these diagrams from left to right, we interpret the x axis as time. You can think of each vertical slice as a moment in time. The y axis is roughly the space direction.

So are you telling me that the particles travel in straight lines?No, but it’s easy to mistakenly believe this if you take the diagrams too seriously. The path that particles take through actual space is determined not only by the interactions (which are captured by Feynman diagrams), but the kinematics (which is not). For example, one would still have to impose things like momentum and energy conservation. The point of the Feynman diagram is to understand the interactions along a particle’s path, not the actual trajectory of the particle in space.

Does this mean that positrons are just electrons moving backwards in time?In the early days of quantum electrodynamics this seemed to be an idea that people liked to say once in a while because it sounds neat. Diagrammatically (and in some sense mathematically) one can take this interpretation, but it doesn’t really buy you anything. Among other more technical reasons, this viewpoint is rather counterproductive because the mathematical framework of quantum field theory is built upon the idea of causality.

What does it mean that a set of incoming particles and outgoing particles can have multiple diagrams?In the examples above of two-to-two scattering I showed two different diagrams that take the in-state and produce the required out-state. In fact, there are an infinite set of such diagrams. (Can you draw a few more?) Quantum mechanically, one has to sum over all the different ways to get from the in state to the out state. This should sound familiar: it’s just the usual sum over paths in the double slit experiment that we discussed before. We’ll have plenty more to say about this, but the idea is that one has to add the mathematical expressions associated with each diagram just like we had to sum numbers associated with each path in the double slit experiment.

What is the significance of rules 3 and 4?Rule 3 says that we’re only going to care about one particular chain of interactions. We don’t care about additional particles which don’t interact or additional independent chains of interactions. Rule 4 just makes the diagrams easier to read. Occasionally we’ll have to draw curvy lines or even lines that “slide under” other lines.

Where do the rules come from?The rules that we gave above (called Feynman rules) are essentially the definition of a theory of particle physics. More completely, the rules should also include a few numbers associated with the parameters of the theory (e.g. the masses of the particles, how strongly they couple), but we won’t worry about these. Graduate students in particle physics spent much of their first year learning how to carefully extract the diagrammatic rules from mathematical expressions (and then how to use the diagrams to do more math), but the physical content of the theory is most intuitively understood by looking at the diagrams directly and ignoring the math. If you’re really curious, the expression from which one obtains the rules looks something like this (from TD Gutierrez), though that’s a deliberately “scary-looking” formulation.

You’ll develop more intuition about these diagrams and eventually get to some LHC physics, but hopefully this will get the ball rolling for you.

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There is no end to my biology notes… But hey, being an artist helps.

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Best study tip EVER!

Not only will you find problems using this trick. You’ll find a tonne-load of notes, exam questions WITH answer keys, and even lecture notes in pdf format and powerpoint presentations!

It’s a great idea to use the resources you find this way to study AHEAD, even during the summer holidays. This will ensure your college success! Remember: stay on top of your game!

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“I hear and I forget. I see and I remember. I do and I understand.”          – Confucius 

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first notes of school year, first notes for physics, and first breakdown ft. honors pre-calculus … starting junior year strong⛈

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Literally do your work as soon as you know it exists. If you get homework, do it during your free or when you get home or on the train if you really want to, on the day you get it. Just got set an assignment? Get the draft done that weekend. It doesn’t have to be amazing and absolutely ready to send in, it just needs to exist. Just got sent an email? Reply when you see it. If you’re not sure how to response to it, write Dear (), leave a gap and then write Regards () and keep that in your drafts. Set a reminder on your computer or write the reminder on a sticky note that you’ve got that sitting in your drafts and you need to send it off in the next 24 hours. Need to clean your room? Don’t spend time thinking or planning how you’re going to clean it or how you’re going to change up the space in the process, just pick stuff up and put it where it should be until everything’s in order. Done. Seriously dude, when a task arises as an issue, tackle it as soon as you realise it exists. Remember, it doesn’t need to be amazing it just needs to be done. So, when the due date of the task creeps closer, you can go back, work with what you have and make it the quality you want it to be. 

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Fractures:

Depression: Broken bone portion pressed inward; skull fractures.

Comminuted: Bone breaks into many fragments; common in the elderly.

Simple/Closed: Clean break, bone doesn’t penetrate skin.

Compression: Crushed bone; spinal fractures.

Compound/Open: Bone penetrates skin.

Greenstick: Bone breaks incompletely; common in children.

Impacted: Broken bone ends forced into each other; results of blocking a fall.

Pathological: Results of disease and degeneration of bone tissue.

Spiral: Ragged break as a result of twisting forces; common sports injury.

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tips for organizing quals notes/general studying tips...I'm taking them at the end of the Spring semester eep!

i sure do have some! context: i’m an english lit phd, at an R1 institution, & my quals involved 

3 reading lists (for major, minor, & research fields) totaling about 300 items

a written portfolio (3 sample syllabi, a publishable article, dissertation prospectus)

& a 3-hour oral exam (30-min presentation, 2.5 hours of questions from reading list & portfolio) conducted by a 5-person faculty committee (3 direct advisors, one for each field, & 2 additional examiners).

i took mine 6 months early, so i only had about 6 months to prep instead of the usual 10 months to a year.

>> advice on reading for your quals, under the cut.

Keep reading

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one of my favourite quotes by frank ocean!

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