Note: This is just based on my experience of degree and A-level Maths and Further Maths. At degree I studied mostly applied mathematics and statistics/probability so this is based on that.
Differential Equations
These are particularly important in applied mathematics. I don’t think I’ve taken an applied module without them. If you haven’t done them in A-level, they are covered extensively in first year.
Differentiation/Integration
Also key to applied mathematics, but also in probability and statistics. Methods are covered in first year too. Oh and in analysis too, but that tends to look at calculus in a new light.
Matrices
These are everywhere. Particularly multiplying them, taking the inverse, eigenvalues and eigenvectors (these are in everything - even statistics), Diagonalisation comes up a bit too (probability, statistics).
Vectors
Mostly the scalar product and vector product (these are everywhere). Not so much the geometry. Kinda like M2 where you have 3D motion, finding x, v and a etc. Most things become multi-dimensional as the degree progresses so just kinda know what a vector means.
Polar Co-ordinates
Loads of them in applied maths, but converting between Cartesians and Polars is probably the main thing from A-level Further Maths. I can’t really remember what is covered in FP2 but yeah. Most of the stuff at degree is new.
Exponentials/Logarithms
How could I forget these??? I’d advise being really fluent with them because you’re kind of expected to know the log rules and converting between exponentials and logarithms. You were on my course anyway. Also the graphs of them are pretty important.
Hypothesis Tests
If you’ve done S2 then lots of Statistics at degree is based around hypothesis testing. It’ll all be taught from scratch in first year but yeah. And it’s probably less confusing when you do it at degree.
Complex Numbers
Just knowing how to manipulate really. They come up every now and again. Not to the extent that they do in FP2.
Curve Sketching
Lecturers love putting this in exams because they know we hate it. I can’t remember doing a lot of it in A-level though, but yeah practise drawing trig functions and logs/exponentials and quadratics/cubics.
Trig
Mostly just being fluent with trig identities because it’s another thing you’re just expected to be able to use when needed. Cos2x is a particularly good one to know. Hyperbolic trig also comes up. But really just knowing the exponential form because lecturers seem to love putting it in questions.
Obviously it depends on what modules you take. At Notts you can take optimisation, game theory and graph theory in third year which follows on from Decision. Pure Maths is pretty much all new (I think OCR MEI FP3 has some group theory though).
The main thing is to pay attention to first year because most of it is methods and skills that will be needed in second year. I mean, some of first year you’ll never touch again in your final years but yeah, most of it is useful.
Also don’t worry if you haven’t done Further Maths. From my experience the content from Further Maths was covered at a relatively slow pace and at first you may have to work harder than people who did do FM, but you’ll catch up really quickly.
Definition of a teacher #teachersofinstagram #teachersfollowteachers #teacherquotes #iteachtoo #teachergram
Here is a picture of the nine-dot problem. The task seems simple enough: connect all nine dots with four straight lines, but, do so without lifting the pen from the paper or retracing any line. If you don’t already know the solution, give it a try – although your chances of figuring it out within a few minutes hover around 0 percent. In fact, even if I were to give you a hint like “think outside of the box,” you are unlikely to crack this deceptively (and annoyingly!) simple puzzle.
The Nine Dot problem: connect the dots by making four lines, without lifting your pencil from the paper
And yet, if we were to pass a weak electric current through your brain (specifically your anterior temporal lobe, which sits somewhere between the top of your ear and temple), your chances of solving it may increase substantially. That, at least, was the finding from a study where 40 percent of people who couldn’t initially solve this problem managed to crack it after 10 minutes of transcranial direct current stimulation (tDCS) – a technique for delivering a painlessly weak electric current to the brain through electrodes on the scalp.
How to explain this?
It is an instance of the alleged power of tDCS and similar neurostimulation techniques. These are increasingly touted as methods that can “overclock” the brain in order to boost cognition, improve our moods, make us stronger, and even alter our moral dispositions. The claims are not completely unfounded: there is evidence that some people become slightly better at holding and manipulating information in their minds after a bout of tDCS. It also appears to reduce some people’s likelihood of formulating false memories, and seems to have a lasting improvement on some people’s ability to work with numbers. It can even appear to boost creativity, enhancing the ability of some to make abstract connections between words to come up with creative analogies. But it goes further, with some evidence that it can help people control their urges as well improve their mood. And beyond these psychological effects, tDCS of the part of the brain responsible for movement seems to improve muscular endurance and reduce fatigue.
It’s an impressive arsenal of findings, and it raises the obvious question: should we all start zapping away at our brains? That certainly seems to be the conclusion reached by the growing DIY community experimenting with home-made tDCS headsets.
But, while the list of supportive studies is far longer than those linked to here, the overall state of the evidence nevertheless continues to occupy that frustrating scientific limbo of being ultimately ambiguous – especially when we take into account all those comparatively boring, non-headline grabbing studies that found no significant effect from tDCS. In fact, a meta-analysis of tDCS studies – one of those laborious studies that study the findings of other studies – found the technique had no effect at all on a wide range of cognitive abilities. Yet that review in turn has been criticized as being too conservative and potentially biased in its own analysis.
More to the point, few of these studies have yet to be replicated, and most of them rely on a handful of unrepresentative people (US undergrads) who are asked to undertake the kind of lab-controlled tasks that usually share a questionable (at best) relationship with real world activities. And as for the long-term effects of tDCS use, or even how it affects brain function exactly? It’s not clear.
Yet none of this haziness has deterred start-ups from developing a slew of commercial tDCS headsets targeting home-users. Primary among those is Foc.us, which started off with a headset that allegedly enhances gaming ability before expanding to ones that improve learning speed as well as athletic endurance. There’s also Thync, a mood-enhancing headset that’s been described as a “digital drug” that can help users “energize or relax without drinks or pills.” While not quite based on tDCS, it uses pulses of electricity to target cranial nerves just under the skin to supposedly induce various moods.
Another such start-up, Halo Neuroscience, recently introduced its own headset, which stimulates motor neurons in a way that supposedly accelerates the strength gains and skill acquisition of athletes.
The firm reports on its own unpublished “preliminary results” with elite Olympic ski jumpers showing a 31 percent improvement in their propulsion force, with significantly less wobble when airborne. Even if a far more modest result than 31 percent turned out to be true, these sorts of findings could mean that tDCS is set to become a significant performance enhancer in the sporting world. Will its use in competitive settings be considered cheating?
In academic contexts, some universities are already trying to curb the off-label use of prescription drugs to enhance academic performance, with Duke University explicitly considering such use as “cheating.” Similarly, the Electronic Sports League, which holds massive gaming tournaments with million dollar prize pools, has started randomly testing players for so-called “smart drugs” that may give e-athletes an edge over their non-doping opponents.
Would using Foc.us’s GoFlow to “learn faster” be considered a similar instance of academic dishonesty by Duke University? Or what about using Foc.us’s gaming headset in the context of shooting down virtual enemies? If these devices give any sort of a boost, it’s not clear why their use should be considered any different from drugs like Adderall or Ritalin, at least in regards to cheating.
In non-virtual sport, the World Anti-doping Agency (WADA) prohibits substances and methods when they satisfy any two of these three criteria: 1. they confer a performance enhancement; 2. they pose an actual or potential risk for athletes; and 3. they violate the “spirit of sport.”
If the preliminary findings from Halo Neuroscience on ski jumping are even remotely valid, the first criterion would certainly be met. On the other hand, it’s not yet clear if tDCS poses a noteworthy potential risk for athletes – though any such risk would almost certainly be smaller than the one involved in soaring over 100 meters through the air, as in the case of ski jumping. But does it violate the difficult to define “spirit of sport”? It’s a question that WADA may wish to avoid: to answer yes may commit it to trying to ban the unbannable. As far as we can tell, tDCS leaves no uniquely detectable impact in the brain: a ban would not be enforceable.
On the other hand, tDCS may simply be construed as not “artificial” enough to threaten our (often arbitrary) notions of fairness, whether in sports or academic settings. Unlike injecting or ingesting a synthetic drug, many may have the intuition that a weak electric current is comparatively “natural” or “clean.” For instance, even though the effects are similar, WADA currently tolerates athletes who increase their red blood cells (and therefore, presumably, their performance) by sleeping in a tent that simulates high altitude, but not those who do so by blood doping or EPO. Something about sleeping in a tent to enhance performance does not strike us as suspect in the way that drugs or blood transfusions do. Perhaps tDCS will be occupy the same corner as altitude tents: for the rule makers, both can be convenient inconsistencies in the rules, as both elude detection anyway.
An yet, while we can question the evidence for the actual efficacy of most performance enhancers currently used, tDCS in particular stands out in calling for more data. Unlike Adderall or anabolic steroids, at the moment anyone can get their hands on a tDCS headset by legally ordering one online. And even if these headsets become more closely regulated, people can still cheaply make their own using common items found at electronics stores, stimulating any part of their brain, or their children’s. Given the current hype around it, it would be good to know more about how exactly it impacts the brain — and the long term consequences.
Top Image: These are increasingly touted as methods that can “overclock” the brain in order to boost cognition, improve our moods, make us stronger, and even alter our moral dispositions. Credit: Fabrice Coffini/GettyImages
Source: Scientific American (By Hazem Zohny)
First spread for May. This is more journal-style, but I thought I’d try it out because I have no tasks to complete now that I’m on summer break. What do you guys think? 😁 . . . . . #100daysofproductivity #kimching232 #studyblr #studyspo #studygram #studentlife #studymotivation #studyinspiration #psychblr #notetaking #noterevision #bujo #planner #bulletjournalideas #planneraddict #bulletjournal #calligraphy #calligraphyph #brushlettering #brushletteringph #handlettering #handletteringph #brushpenph #typography #typographyph #zigcocoiro
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GOOD NEWS FOR #PublicSchools IN WISCONSIN - http://goo.gl/VqdsFt
The authors of the report contacted superintendents throughout #Wisconsin, to determine how the new flexibility provided by #GovScottWalker’s 2011 legislation has allowed them to alter their #Education programs for the BENEFIT OF STUDENTS, without the self-interested intrusion of organized labor #UNIONS.
“Superintendents of public schools no longer have to seek approval from public unions in order to make changes to the administration of their schools,” the report said. “They are free to adopt the best practices of teacher pay and classroom management.
“They can hire and fire teachers according to criteria other than the rigid policies from a union (#CollectiveBargaining agreement). The words ‘#Seniority’ and ‘teacher #Tenure’ can be terms of the past for many districts.”
There is now merit pay for teachers, in various forms across the state. In the old days of collective bargaining, teachers were stuck on rigid pay scales based strictly on the number of years they taught and the number of graduate credit hours they earned.
1) Have a game plan before each semester starts. Make sure that you don’t overload yourself with too many units or extracurricular activities. Do enough while still staying sane
2) Take some fun classes that had nothing to do with your major. Branching out and trying new things is always good
3) Join clubs that interest you. See what is out there
4) Go to Professor’s and TA’s office hours and come up with questions you want answered. Going to office hours will allow you to stand out from the hundreds of students they see on a daily basis
5) Let go of toxic people. If they don’t care about you now, they never will
6) Make sure to use some of your free time for yourself, whether it is by exploring the city or watching a movie on a Friday night. Always studying and isolating yourself is not healthy. Small breaks are always needed
7) Take care of yourself. Make sure to stay hydrated and eat your meals. Sometimes we forget when we are stuck in the library all day
8) If you don’t have time to hang out with friends, ask them if they wanna join you to study, even if it may be in silence. Sometimes having company while you study will motivate you more
9) Friends will always come and go. But never let go of the ones that are there for you at your worst. Some of the friendships you make in college will last a lifetime
10) Reach out to close friends or to a therapist/psychologist on campus if you are going through anything rough. A helping hand will go a long way when needed
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Chandni Langford teaches fifth grade in the Woodbury City public school system in New Jersey. When she heard that her students were nervous about an upcoming test, she devised a clever and heartfelt way to encourage them.
The pictures have since gone viral with over 18,000 shares, and hundreds of people have chimed in with messages of support. But it’s the students’ response that will leave you in tears.
It should come as no surprise that investigations have shown that many for-profits do in fact target low-income people who can’t pay. These people areoften minorities.
Steve noticed the same thing at his school: “Most of my students made minimum wage, and over half were black. Every one of my students had a loan, and it’s all they ever talked about. Some felt strong-armed into them, but some wanted them. They lived off of them. They wanted the loans as another source of income because they couldn’t make ends meet with their regular jobs. They took a few classes to keep up appearances, but I would always know why they were really there. Every college has these students, but at my college, I had several in every class I taught. I never knew what happened to them after the semester and they were 20 or 40 grand in debt. Many struggled to make ends meet, and the college offered an easy way to get loans. What did you think was going to happen?”
For-profit universities vastly prefer loans – and the long-term, interest-bearing income they generate – to straight cash payments. So much so that they often don’t take cash: “One student in particular told me that she had $20,000 from an inheritance in cash, but ran into roadblocks everywhere. My college wouldn’t accept cash, so she tried a check. They told her they couldn’t, since they had too many issues with bounced checks. She then tried paying online in full, but she was told she shouldn’t because ‘What if you decide to drop a class? Would you still want to pay for it?’ She then tried monthly payments, but she was informed she was too late to sign up. She could only take a loan.”
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