This is definitely field-specific and also depends on where you're seeking employment. A number of TT jobs I applied for this year asked for a teaching portfolio, evidence of teaching excellence or effectiveness, or copies of teaching evaluations along with my application, before or after a phone interview, and prior to a campus interview. While it may not help a great deal, it can definitely hurt an applicant, especially if the evals you get aren't very good and there are other applicants with better evals you're being compared to.
As for actual advice, I'll start with the following:
- Figure out what resources are available to you as a TA or instructor in your department, in your college, and through the university's teaching center. And then take advantage of them. My PhD university's teaching center flat-out told me that I was one of three grad students from my department (90 grad students) they had ever met with or assisted. Now part of this was due to my department's culture where consulting the teaching center was seen as an admission of failure but that's BS and you should ignore that if people are saying it.
- When in doubt, consult the internet. By which I mean, if you have to create a syllabus, google around to see syllabi others have created for that course or a similar course. If you're looking for appropriate wording for a policy, again you can consult the internet (though you may want to consult your peers and department first because some stuff is university-specific and/or university mandated). Looking for an assignment idea? Google it. Sample rubric? Google for one. There's really no reason to reinvent the wheel.
- Accept that it will take you a while to gain your footing in the classroom. Be willing to change midway through the term and to do different things for different sections because not all students are the same.
- Take advantage of any courses/workshops/tutorials that will help you become a better teacher. Again, the teaching center will probably offer workshops or brownbags. These are awesome as a grad student because most of the attendees will be TT faculty so you can see what they're struggling with or what they're doing that works and use it in your teaching. Doing that early on will make you more effective in the long run, leading to better evals.
- Devise and administer a midterm evaluation of your students that's for you. Take their feedback seriously and incorporate it into the course. It almost always leads to improved semester evals, even if you don't change very much.
- Have someone else (an experienced teacher) observe your teaching. It will be painful and awkward and difficult. But, it will help you improve. It will also give you more material for your future teaching portfolio.
- Take the time to identify excellent teachers on campus (whether or not they're in your field) and observe them. You may need to ask them first, of course. If you're having trouble finding someone, ask the teaching center. Watching other people who are awesome, especially those who do it in totally different ways (like observing a lecture for 400 students vs a seminar for 30 students), will help you understand the variety of what works and identify some techniques that will work for you.
- Oh, and take the time to learn your students' names whenever possible. They appreciate it.
Okay, that was a lot of advice and probably more than you can do all in one semester. But, I hope it helps someone!
If you want to get the coursework done, I remember hearing that some institutions offer certificate courses in Maths at the University level in India. I guess they might be ISI's or IMSc or IITs IISc IISER's or alike. This is especially useful if you would like to work in mathematical bio. You can also enquire at the HBCSE or TIFR.
LSE offers a 1yr distance diploma in maths too.
I think if you can get university level credit in calculus etc. courses from some MOOC, which could be accepted by your target schools, will be a great option.
As someone trying to figure out rotations as well, I highly recommend that you try to contact PIs and their lab members. You don't need to set up all of your rotations before coming to graduate school but it's fairly common for incoming students to have their first one set up. Realistically, all basic research can be made translational (since that's how many many labs get more grants). For example, people might think work on insects is irrelevant to humans but that is completely untrue. Also, if you have PI's available that are getting CNS publications, then I don't know why you are hating on your school. It is an immense achievement even at top tier schools to get a CNS publication. These faculty members getting the publications will usually have the most funding and will be able to do the top notch research that you need to get your own CNS publications.
Finally, to figure out how much prospective PIs expect from their graduate students and postdocs, ask to speak to some of them. While there are some PIs that just want their graduate students/postdocs to always be "busy," there are others where they are able to motivate their lab members to do so on their own. Ideally, you want to get to the point where you are working long hours because you want to.
Personally, I found this article very inspiring and recommend that you have a read too: https://www.statnews.com/2015/11/06/hollywood-inspired-scientist-rewrite-code-life/
Hi! Being graduated from one of the universities in London as an Indian, I can tell that you have ample opportunities there ( I guess, quite comparable to Boston). Also, the British masters courses have different structure than those in the US. If you feel prepared to jump into thesis within an year and want to follow a fast track to PhD, then King's course is a valid option. As PlanB has said, go for the place that best prepares you for your intended PhD coursework, network and research experience wise.