Mathematics as a Career Path

Mathematics as a career choice has been picking up among the students of India since the last couple of years. But sadly, very few students are aware fully of the scope they have to study in India. Most go for the local colleges and Universities in their neighbourhood. In this article we shall discuss the avenues that are open to students after they pass their 12th class in India.

India has a rich tradition in math since time immemorial, and this has led to the establishments of various centres of learning in math and related sciences. In the present day too, there are various institutes offering math education and research of world repute in India. Typically the road to an education in math starts after passing the 12th class in India. A student then has the opportunity to either opt for a BSc degree or an Integrated MSc degree or a BS degree or an Integrated MS degree.

The two best places in India offering a Bachelor’s degree in math are the Indian Statistical Institute (ISI), Bangalore and the Chennai Mathematical Institute (CMI), Chennai. ISI offers a B.Math degree, and admissions are held after a tough screening test in various centres of India held in late May each year followed by a personal interview at Bangalore. CMI offers a BSc degree in Mathematics and Computer Science and another in Mathematics and Physics, admissions to which is through a written test held in various centres of India in late May each year, which may be followed up by an interview later. Both ISI and CMI also admit students who have qualified in the Indian National Mathematical Olympiad (INMO). For ISI they also have to attend an interview in Bengaluru. For ISI the interview takes place at Bengaluru. Added to that CMI also admits students who have qualified in the Indian National Olympiad in Informatics (INOI) and Indian National Physics Olympiad (INPhO). The INMO is held every year on the first Sunday of February. But to appear in the INMO, one has to pass the Regional Mathematical Olympiad (RMO) which is held in various centres throughout India in December every year. Similarly to appear in INPhO one has to pass National Standard Exam in Physics(NSEP) and for INOI one has to pass either of Zonal Computing Olympiad(ZCO) or Zonal Informatics Olympiad(ZIO).

A student can also opt for a BS degree in math, which is a 4 year course. At present the two best places in India for a BS degree are the Indian Institute of Technology (IIT), Kanpur and the Indian Institute of Science (IISc), Bangalore. IIT admits students via the JEE Advanced held every year in April-May. While IISc admits students via the JEE Mains, JEE Advanced and Kishore Vaigyanik Protsahan Yojana (KVPY). The KVPY is held every year in November for students in classes 11th, 12th and UG 1st year.

A student can also opt for an integrated BS-MS dual degree course in math offered at the Indian Institutes of Science and Education Research(IISERs) which is a 5 year course. The IISERs are located in Pune, Mohali, Kolkata, Bhopal and Trivandrum. The IISERs admit students via KVPY, JEE Advanced. One may also apply via marks in board exams and then writing the IISER entrance exam which is held in mid July in the five IISERs. The marks in board exams depends on the INSPIRE cutoff for the respective boards.

After the BSc/BMath/BS degrees a student has the opportunity to get an MSc or an MS degree from the many places in India and abroad. They can also apply for an Integrated MSc-PhD degree offered at some places in India. Ideally the best places in India for a Masters degree in math are mentioned below:

• CMI, through admission test held in late May
• ISI, Kolkata or Bengaluru through admission test held in late May

For Integrated MSc-PhD programmes the best places are:

• Tata Institute of Fundamental Research (TIFR), Mumbai and Bangalore admits through a written test held in May and followed by an interview
• IISc, Joint Admission Test for M.Sc. (JAM) followed by an interview at IISc
• The Institute of Mathematical Sciences (IMSc), Chennai admits through the National Board of Higher Mathematics (NBHM) exam followed by an interview
• Harish Chandra Research Institute (HRI), Allahabad admits through the NBHM exam followed by an interview
• IISERs (Pune, Mohali, Trivandrum, Bhopal, Kolkata) also has a good Integrated MS-PhD course and they admit students either via their own exams or NBHM

If a student wants to opt for an Integrated MSc in math then the best place in India is the University of Hyderabad, which admits students through a written test held in early June. Various other central universities also have the Integrated programme, amongst them the best curriculum after the University of Hyderabad is at the Pondicherry University and Tezpur University. In recent years, many new Central Universities have also started this course.

A student can also opt for an Integrated MS degree offered at present by the IISERs, and also at the National Institute of Science Education and Research (NISER) at Bhubaneswar and Centre for Basic Sciences (CBS) at Mumbai. The IISERs admits students via JEE Advanced, KVPY and through board exam performances. While NISER and CBS admits students through the National Entrance Screening Test (NEST) held every year in early June.

After a Masters degree, a student can pursue a PhD. The best places in India to get a PhD in math are TIFR, IMSc and HRI. Normally these institutes (except TIFR which has its own exam) accept students who have cleared either NBHM or the CSIR JRF exam followed by an interview. Students who have been awarded INSPIRE Fellowships by the Department of Science and Technology (DST), GoI may also be called for interviews at these institutes. Apart from these, CMI, ISI, IISc, IISERs and NISER also has a very highly ranked PhD programme.

Students studying at all the above institutes are paid fellowships of Rs.5000 for the Bachelors students, Rs.5000-Rs.7000 to the Masters Students by the DST and around Rs.12000-Rs.18000 for the PhD students. In CMI PhD students are paid Rs. 26000-28000 for PhD and Rs. 9000 for M.Sc. But recent hike in fellowship for PhD students mean that they might be paid as high as Rs. 26000 in the coming session onwards.

In this article we have only focused on the best institutes in India. There are many other quite good places to study mathematics. Among them mention may be made of the Institute of Mathematics and Applications (IMA) at Bhubaneswar and the University of Delhi.

Things that made Jobs a great CEO.

These are the things that made Jobs a great CEO:

1. A Vision.

Jobs had always been a visionary first and then CEO. He had the vision of delivering cool to the people and make them feel more and do more by themselves. That vision was his fuel. That's what drove him forward. It was his vision that made him see things that others had missed.

2. The Ability to Learn.

Jobs always had the desire to learn about things that got his interest on the go. For that, he learned to change the three basic things one needs to in order to learn the true nature, the true design of everything. Those three things were understanding, attitude and behaviour. Jobs knew this very well that design is all about how it works rather than about how it looks.

3. The Ability to Lead.

As we all know it, Jobs always wanted to be important and that's what drove him forward to learn the principles of leadership. Jobs had learned to acquire the ability to convince almost anyone.

4. The Ability to Recruit.

Jobs found this part to be the most challenging thing to do. In his early days, he wasn't that good with this skill and he faced many difficulties because of that and even got fired from his own company. But that didn't stop him there. It only took him forward to start two more successful companies but this time, in a wiser and better way.

5. The Ability to Improvise.

The ability to improvise and to learn go hand in hand. Steve knew it well that mistakes are something that no one should be afraid of. He knew that mistakes only make a man more experienced. And the better the experience, the better is the judgment.

6. The Ability to Manage.

Steve always kept on learning to be a good manager. He always kept track of time and the market. He always knew what the people needed and he was always after delivering it to them. For him, details mattered a lot and it was worth waiting to get them right. And he would always deliver the thing that the people actually wanted even if it cost more than the other products in the market.

7. The Ability to Present.

Steve's Presentation Skills are always appreciated by everyone. Presentation was something that Steve focused a lot upon. He always used to present it like a magician pulling out a rabbit out of his hat. He always made people wonder what his next venture was. Plus, he knew the magic trick behind bringing the hidden smiles on their faces.

Physics - Nuclear Physics Fundamentals and Application

What is the net charge of our universe?

It's a very good question.

Most people imagine that the universe is overall neutral.

There would be a problem if the universe is finite (compact) with a net charge, since electric field lines would wind around the universe forever if the photon is truly massless. But the universe need not be finite - it seems that it is quite close to being flat, and may be infinite, too.

But a charged universe has been proposed on more than one occasion. An early attempt was made, I think by Herman Bondi, to explain the expansion of the universe by means of electrostatic repulsion.

He suggested this might be caused by a tiny difference in the charge on the electron and the proton, and then worked out some of the consequences, which others have followed up on.

Within a very short time, however, the charge difference between electron and proton was constrained to be extremely small by improved direct experiments of the Millikan oil drop type. The current limit on this charge difference is

Δqe−p<∼10−21e,

which is sufficient to rule it out as a cause of the expansion of the universe.

There are other limits on similar charge differences between other particle species coming from experiment and astronomical observations, and any charge on the photon is very tightly constrained to be zero. For certain kinds of dark matter there are also very tight constraints on any charge that it may carry.

But baryon number is also shown by direct constraints to be conserved in all observed particle interactions.

And yet, by all observational evidence from cosmic rays, there is no sign of any large concentration of antimatter in the universe. So it appears that either the universe started  with an excess of baryons, or that something in the basic interactions occurring in the early universe must have violated baryon number conservation.

There are actually imaginable mechanisms, even within the standard model of particle physics, to violate baryon number conservation. However none of these standard model mechanisms would seem to be sufficient to produce the observed matter-antimatter asymmetry in the best available models of the early universe. So something beyond the standard model would seem to be required.

So one may well question whether charge conservation might be violated, too. Possibly charge might have escaped into extra dimensions, if such exist,  or there might be some other charge violating interaction that was active in the early universe.

It turns out that, if the distribution of the net charge were uniform and homogeneous, and if one models the universe as a medium with infinite conductivity, which seems as if it should be a reasonable assumption at most times during the hot Big Bang evolution, then there would be no detectible electric fields. 

However there could be a magnetic field due to the motion of the net charge in a universe which is expanding. This field in turn would have created vorticity in the matter, and this vorticity, it turns out is sufficient to create anisotropy in the cosmic microwave background radiation.

This argument places a very strong cosmological constraint on any possible net charge of the universe. The excess charge per baryon would be bounded by

qe−p<10−26e.

http://arxiv.org/pdf/hep-ph/0310...

The constraint would be weaker for a non-uniform magnetic field, but still quite strong, and comparable with the best terrestrial bounds on the electron proton charge difference.

However this argument is quite obviously pretty strongly model dependent - one might very possibly be able to avoid it if one tried a non-standard cosmology of some stripe: but then other constraints naturally come into play of course.

The direct effects of the net charge on photons and other particles travelling through the universe, it turns out, would be expected to be quite small as long as the charge is small. The presence of the net charge will result in Compton scattering of photons, but this is a very small cross-section.

There would be some index of refraction, too, for the space between the galaxies due to the presence of the charge, if it is taken to be uniformly distributed as some sort of gas of charged particles. But on the basis of calculations of the plasma frequency for a given charge density this could be made quite small, except for very low frequencies. 

If one assumed say, that the net charge was carried by a uniform gas of protons, there would very likely be observable effects on the spectrum of high energy cosmic rays. The interactions of protons have fairly large cross-sections by comparison with the electromagnetic interactions.

Does the Big Bang Theory conflict with the First Law of Thermodynamics?

It is possible that the total energy of the universe is zero.  That's because in addition to mass energy and energy of motion, there is an enormous gravitational binding energy. So the actual energy of the universe is zero, and there is no problem with the conservation of energy; it is zero, and it always has been.

Zero?  Yes, it is possible.  Potential energy is difficult to notice unless you try to move to a very different location.  

I say "possible" because if you do a classical calculation for the total energy, and assume that the mass density is at the "critical" value (just enough to give us a large scale Euclidean geometry), then the negative binding energy exactly cancels the positive mass and expansion energy. But it is not obvious that the zero calculation is still valid using general relativity; there is dispute over whether a calculation of total energy makes sense, when there is nothing outside to reference, and now we would have to include in the dark energy, and that has no classical analog.  

But this zero energy solution is my favorite way to think about it.

Why does the observable universe have this shape of two cones, when it's actually the same everywhere?

The answers so far talk about light cones, but I suspect you mean this type of image (from SDSS).

Each of the points in this picture is a galaxy and we are located at the center. The reason for the two blank cones is just that it's hard to map those areas - our Milky Way galaxy gets in the way!

So it's not that there's nothing there, it's just that it's a lot easier to see distant galaxies that are away from the plane of our galaxy, so that's where we tend to focus.

What existed before the Big Bang?

The big bang, as we commonly term the colossal expansion of the universe, was, to say it simply, the beginning of everything. Including Space and Time. The notion ofbefore and after is relevant only with reference to a given time. But when there is notime, no events taking place, how can you say anything occurred before something else did? 
The big bang is considered as the absolute beginning of the observable universe.

According to modern physics, even nothingness, or absolute vacuum has energy. That means, even nothing has something. So we cannot even say that there was nothing before the big bang! It was the origin of everything, including nothing...