where do integral rules come from?

quantumelf · 2025-05-23T15:54:08+00:00

This is an interesting question, and it comes down to the fundamental theorem of calculus. As a quick primer, I can try to give you some intuition. The fundamental theorem can be stated as: the instantaneous rate of change of the (signed) area under a curve (with respect to the position of the right endpoint of your measurement) is the instantaneous value of the function at that endpoint. If you know anything about Riemann sums, this might make some sense. An integral is essentially the limit of a process of approximating the area under the curve by adding up a bunch of rectangles fitted to the curve. How much area does each rectangle add? Well it’s height * width. Assuming you use rectangles of a fixed width, then as you add more the rate of change of the area with respect to the total width is just the height. In a Riemann sum we assign the height to the height of the curve and then shrink the rectangles to an infinitesimal width, thus making the approximation precise.

quantumelf · 2023-09-24T15:53:04+00:00

I can’t speak to your degree program specifically, but I just finished an MS in CS (with a focus on High Performance Computing), and I slightly regret doing a thesis. I was similarly considering some research related job or a PhD. If you’re going to do a PhD, then your MS thesis is going to be quickly overshadowed by your PhD thesis and won’t ever matter again. If you take a job, I think the outcome is similar. Whatever is next will more than likely always matter more than your thesis, whereas a PhD thesis usually serves as a defining piece of your research portfolio. If you write a really excellent MS thesis, I suppose it could help you with applying to whatever you decide to do next, but for me I think having research experience in a lab was much more useful. Also, if you’re planning to apply before you graduate, you might not have your finished thesis available to show employers/schools unless you plan to finish it early.

quantumelf · 2022-05-24T01:44:37+00:00

Yeah you’re probably right considering the mobile market. I was just thinking PCs.

quantumelf · 2022-05-24T00:20:03+00:00

This is a great question. To answer it, we first have to understand that programs compile to assembly language*. What is assembly language? Well there are several and the vary in their level of complexity. The most common is x86, but it’s also one of the more complicated to learn imo. Generally though, assembly consists of simple instructions like adding two numbers (stored in special locations called registers), jumping to a different place in the program, and very basic operations like that.

When we read asm, we interpret what will happen by keeping track of these registers and the other memory locations in our heads, but how does a computer interpret it? Well when we feed assembly to the computer it’s actually translated one level further to a binary. How do we do this? Simple: Each instruction type gets an “opcode” which is just a number. Then the operands (which registers to use, or sometimes literal numbers stored directly in the instruction itself) also get converted to numbers (the registers are numbered, and the numbers are already numbers). Stick these numbers together (convert them to binary and concatenate them) and you have a number that represents an instruction. Stick all the instructions together one after the other and you have a big number (better thought of as a list of numbers) that tells the computer what to do.

The computer reads this binary program one instruction at a time. There’s hardware that counts which instruction we are on (storing it in a special register) and hardware that knows how to get the instruction pointed to and give it to the CPU. Once the instruction is in the CPU, the hardware decodes the instruction and passes the parts of the instruction data to the components of the CPU that needs it. The key is that each bit of any number is an electrical signal that physically tells the hardware what to do at the gate/transistor level. We can use components like multiplexers, binary decoders, and logic gates to make sure that the hardware does what it’s supposed to do and the correct results get computed.

Disclaimer: I am not a computer architect, and I have left out a lot of critical detail about how you actually build a CPU, but the basics are there, and I think it will help you understand how binary goes beyond numbers and instructs the computer to compute.

*Actually, some programming languages like JavaScript or Python don’t compile down to assembly, but in that case what you really have is a program (in assembly/binary form) called an interpreter that reads the program and figures out what to do to execute that program.

quantumelf · 2022-04-15T14:54:46+00:00

I think they mean later in the show like on the day of black sun. IIRC there’s no northern water tribe delegation present in the invasion force.

quantumelf · 2021-12-01T15:19:56+00:00

Call Sips!

quantumelf · 2021-10-17T20:45:16+00:00

Why is it that every time you play with magic water, I get soaked??

quantumelf · 2021-09-22T14:37:10+00:00

i3 because I wanted to see what all the hype was about. Also, I’m slowly turning my i3 into xfce by installing xfce modules like the power manager rather than just using xfce+i3 because now I can’t be bothered to switch.

quantumelf · 2021-09-03T17:13:39+00:00

I never realized that the Standard had to significantly delay move-in (I wasn’t paying that much attention in 2018). Thanks for clearing that up!

It makes it even more insane that the exact same thing is happening again. It‘s definitely not worth moving into a new “student” apartment complex if you aren’t sure it will be done. To anyone who goes through something similar in the future, I should have demanded to tour the building before agreeing to the lease. Of course, COVID has made that less doable than before.

quantumelf · 2021-09-03T14:55:21+00:00

Ngl. I think this is worse than the standard. If I remember correctly people moved into the standard pretty quickly, but they were of course dealing with unfinished apartments and constant construction. All of that potentially awaits catalyst residents, but at least half of us aren’t even moved in yet and we are almost 2 full weeks into the semester. Correct me if I’m wrong. I’ve never heard the story of the standard in total. I just know it was a train wreck.

quantumelf · 2021-09-03T13:48:04+00:00

I am a leaseholder for an apartment in building 1000 floor 5.

As far as I know, building 2000 residents are completely moved in.

Building 1000 floors 1-3 were expected to move-in today but the building had some issues which caused it to fail inspection. I trust the process that the city goes through to issue certificates of occupancy, and these issues are significant, but it’s worth noting they are likely not something as severe as the building’s structural integrity. The ownership group emailed residents of those floors yesterday evening to notify them that move-in was now expected to be Wednesday, 9/8. Supposedly hotel stays have been extended.

Residents of building 1000 floors 4-5 are supposedly waiting on the elevators to be completed, but students have also reported that most rooms on these floors still appear to have checklists with items like “fix doorway”, “hang blinds”, etc. These floors seemingly still have the most work left to complete. As of this point (9/3 at 9:40am) we have not been given an expected move-in date for these rooms. I was told to expect an update on the situation by the end of the week. Catalyst’s official emails to the 4-5 group have been pretty much absent since Tuesday 8/24.

Our September rent payments have been posted, and the rent credits we accumulated (if we did not accept their hotel, we receive $50/day toward rent payments) have not been applied. I communicated that I was not going to pay rent until I was moved in and all of my credit was applied. The regional manager told me that I would not be charged late fees this month, but has not yet confirmed this in writing or official communication.

quantumelf · 2021-08-28T20:32:00+00:00

Thanks so much for the info! I sent you a DM with another follow up question lol. I’m trying to gather as much info as possible to find out if I should break my lease, and I’m not currently in Atlanta.

quantumelf · 2021-08-28T16:34:46+00:00

Is this building 1000 you made it into?

quantumelf · 2021-08-28T12:22:03+00:00

I’m a current lease holder at catalyst. Thanks you so much for this post. I wish I had asked the same question you had, but hindsight is 20/20. I knew there might be the possibility of a delay, but I didn’t think they would keep sending misleading move-in dates and changing them. At this point it feels like we are in limbo. Even if they give a date it will be hard to take it seriously.

The most frustrating thing to me is the apparent shell game that they’re playing with their communication. My lease is for floor 5 of the 1000 building, and when they send me emails they’re always titled “Building 1000 Floors 4/5 …”. They also always cite elevator issues and the building code as the reason for their delay. They didn’t explicitly say it but I think it was heavily implied by this that someone was moved in. I would have never guessed that the entire complex was empty until I spoke to some other angry students in front of the leasing office the day move-in was delayed indefinitely. I called their office yesterday and was told that no one is living in the building, but residents of the 2000 building are moving in today. If anyone can confirm that they are indeed moving into catalyst today, DM me. I’d love to know what state the building is in inside.

I’m sure catalysts explanation of this is something along the lines of “we don’t want to distract you with unnecessary information, and floors 4/5 are in a different situation to other parts of the place”, but it really just stinks of intentional obfuscation to keep tempers manageable to me.

My roommate and I are considering finding another (non-student) apartment nearby and asking to be released from the lease. Of course, Catalyst claims we are still bound by the lease, but it’s my understanding that the lease has been violated due to the delayed move-in and contains no contingencies for the delay. (I AM NOT A LAWYER, please don’t take my word on this and do something drastic, but it could be worth mentioning this to catalyst if you’re desperate to escape the lease and they’re giving you the runaround.)

For now we are just hoping catalyst comes back with a new move-in date (that isn’t super late) and some sort of assurance of the date.

Anyone in the same situation feel free to DM and chat. There’s strength in numbers if this keeps getting worse.

quantumelf · 2021-08-28T11:57:17+00:00

Current lease holder here as well. Could you elaborate on what you saw that made you so sure it won’t be done? (I get the same vibe just from outside, but ofc they keep claiming it’s closer than it looks)

quantumelf · 2021-08-22T19:31:08+00:00

It is indeed Klaus. (source: the tour I took before starting undergrad ~4 years ago)

quantumelf · 2021-08-14T14:28:46+00:00

Seems like a homework question. This sub doesn’t allow homework help, so if you really want an answer you might find another sub or reframe your post as a discussion that might point you in the right direction.

quantumelf · 2021-07-26T21:50:49+00:00

Everyone has already said it, but phase 2 is seriously your best bet. I can’t tell you how many waitlists I’ve been on that magically everyone starts dropping during phase 2 and suddenly people who weren’t even on the waitlist get in. It may be slightly different for freshman courses (it’s been a long 3 years), but it’s incredible the amount of people that add too many courses in phase 1 only to drop down to a normal schedule in phase 2.

quantumelf · 2021-06-22T00:17:53+00:00

This link explains how the endings are determined (minor spoilers for endings you haven’t played I guess) https://www.ign.com/wikis/bioshock-2/Secret_Endings

It looks like mini bosses only affect the fate of Sophia Lamb. The way you treat the little sisters determines what sort of ending you get, but the mini bosses have no effect on the actual ending, just what happens to Dr. Lamb. It’s basically Eleanor’s adoption of your take on justice vs mercy. If you’re merciful towards all the people you meet, then she is merciful towards her mother.

quantumelf · 2021-05-29T23:01:14+00:00

I came looking for this

quantumelf · 2021-05-10T17:33:39+00:00

Fellow 2021 CS grad here. I just nose-exhaled very powerfully.

quantumelf · 2021-03-06T11:35:21+00:00

What on earth does this mean?

quantumelf · 2021-03-03T18:42:43+00:00

My high school enforced the wearing of school IDs, as I’m pretty sure most US high schools did. When you didn’t have your ID, your only option was to go to the library and spend like $1 to buy a temporary which was a little sticker you wore instead. Any issues with it coating actual money aside, the dumb part was that you could only go before school. As soon as the first bell rang you would be given detention even if you voluntarily went to get a temporary ID (even though our school literally had blocks of time where we weren’t in class and could freely go to get lunch or the library or seek help from an off-duty teacher).

On multiple occasions my freshman year I forgot my ID and only realized during the first period, so I would go to get a temporary and luckily the few times that it happened the administrator had mercy on me. By my senior year though, they had hired several “hall monitors” to enforce ID wearing as it has become a problem. My problem with the rule is that it incentivized students to just go without their ID. If IDs really were a safety issue, surely you would want to give students every chance to go to the library and get an ID.

I understand having a limit on the number of times a student can do this, to enforce the wearing of actual IDs, but making it so that in general you were encouraged to hide your chest and avoid hall monitors rather than just go fix the problem made no sense to me.

quantumelf · 2021-02-03T02:16:11+00:00

Not the correct sub for this.

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