Mathematics Levels 57: Fill & Download for Free

I am a mathematician (but I studied physics as an undergrad and hence I know a bit about both fields). These facts are probably not that surprising, but here they are anyway:Most (if not all) of us suck at arithmetic. There is a (probably apocryphal) story of a famous mathematician who when asked an example of a prime number said 57. Most of us can barely add to save our lives (especially while splitting restaurant bills). So we all hate the term "Do the math." (Simply because "mathematician" is not equal to "calculator".) This brings me to the next point.Even strongly mathematical fields like physics or engineering rarely touch (except in high-energy physics) research-level mathematics. In fact most people (even if they do a masters in physics or computer science) stop at early twentieth century mathematics. So as a consequence, we are universally asked "Really? What research can one do in mathematics any more?"We are paid in universities to teach. In fact, most of us never produce anything applicable or useful in our lives and some of us take pride in it. All this "mathematics is very useful everywhere" stuff is not applicable to research in pure mathematics. Our aim is not to produce something that can be applied. (Think of poetry for instance.) However....Mathematics is strongly inter-connected. So strongly that a tool (Ricci flow) that is developed solely to solve a pure mathematics problem (The Poincare conjecture) is used in Robotics. I used to think that Tropical geometry is divorced from "mathematical reality”. But apparently, it was applied by an economist recently to the banks in UK! This is the reason we believe that even if applied mathematics is the only thing that can make a difference to a lay-person, one shouldn't ever get "rid" of even obscure branches of pure mathematics.As for physics, most physicists don't actually study buzzwords like the Big Bang, Quantum Field theory, General Relativity, or String theory. It is perfectly reasonable for some physicists to never know these things in their lives.

Oh boy…..Calm down..you still have close to one yr..One thing I can help you with is that without any second thought - complete your ncert mathematics three times till the time of preboards .Then during preboards, work with 10yrs solved papers.Believe me, this will surely fetch you 90+ marks.Maine yahi nahi kiya tha isliye mere number bhi Dekh Skte ho (57/100)One of my friend adopted this strategy and got 95/100 in 2018 paper.Bhai mujhpe bharosa karke itna kr lena.Failures often give the best advice.Believe me..All the best.

Currently, the Voyager is transiting at an outward velocity of 57 km/sec relative to the Sun.It is losing energy, bit by bit to the Sun’s (and the Solar System’s) continuous retarding pull, but since the probe had already attained escape velocity, we will never be able to cancel out its forward velocity and reverse its direction.The probe is currently transiting the ‘Heliosheath’ — the region where the particle flux flowing outward from the Sun encounters the hyper-diffuse interstellar medium creating a ‘bow-shock’ somewhat similar to the kind made by the prow of a speedboat:The Voyager I is currently one hundred and forty one times the distance of the Earth from the Sun or 141 A.U.The residual power left on the on-board RTG can maintain transmitter power and run attitude gyros until about 2025.What then?The Oort cloud is still a ways, nearest estimate being at 50000 A.U. Assuming no major events overtaking our intrepid little space probe, Voyager I is not expected to be near much of anything for another three centuries.After that the probe will go into orbit around the Galactic center, with no scheduled encounters with anything until about 40000 years, when it passes within 1.6 Light Years of a star named Gliese 445. At that range, Gliese will just be another star in the night sky, not that Voyager could see it; all of its electronics and the RTGs are long dead, hovering near the equilibrium interstellar temperature (about 3 Kelvin).Voyager I has been steadily losing speed (although it will never quite reach zero velocity w.r.t our Sun) there might be some level of erosion and pitting on the surface caused by a constant bombardment of interstellar cosmic rays and dust. The Voyager record, if exposed to interstellar space, might get completely erased, although that is an ill-informed guess on my part.A billion years from now? There is no way of telling. There are fundamental physical and mathematical ‘effects’ that prevent us from making even a rough estimate of how the probe’s trajectory will alter over such timescales. The Solar System has multiple, tiny incremental and chaotic variables that prevent us from seeing ‘forward’ beyond a given time period. This is known as Lyapunov time. For the Solar System, Lyapunov time is 5 million years. Wild, wild guess? The Voyager I keeps orbiting the center of the Milky Way.A trillion years from now? Well according to existing models, star formation has ended and the Universe is now much, much darker in the visible spectrum. Any event, no matter how improbable, becomes a certainty with enough time. The possibility that the Voyager I will escape major misfortune until then is slim indeed.??????????