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Master of Mathematics Studies or PhD in Physics? 
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#1
Jan3012, 11:22 PM

P: 19

Hello everyone,
I'm about to start my honours year in a science degree majoring in nanotechnology. I am pretty confident that I'm on track for first class honours and have had a few academics inviting me to come do a PhD with them once I graduate. However, in my studies I have only completed basic mathematics (i.e. first year mathematics, I'm from Australia) and I would like to expand my mathematical knowledge, since I really enjoy it. The uni I attend offers a degree whereby people who have only done first year mathematics can essentially do 2nd and 3rd year mathematics courses, which lasts 1 year. Do you think it'd be a silly idea to enrol in the mathematics course, instead of doing a PhD straight after graduation? Or should I put off doing a PhD for a year and do the mathematics course? I may not be eligible for a PhD scholarship if I complete the master of mathematics studies... Let me know what you think. 


#2
Jan3112, 12:09 AM

P: 4,573

It would be helpful to know how much mathematics you have done. If you have at least done a calculus sequence, then you will be able to jump into many mathematics courses including your standard introductory probability and statistics sequences. Also one thing that would be helpful to you, is to ask whether extra classes outside of your discipline can be taken for your PhD. They won't be counted of course in the context of your dissertation, but if it can be done, that might be something to consider finding out. Also another important thing to remember is that by doing a PhD, you are considered to be more or less an independent learner. Because of this, its expected that you have the ability to learn new things on your own in many circumstances. One final thing I want to point out, mathematics is a pursuit in itself. What I mean by that is that it can be a 'use it or lose it' kind of thing. If you want to learn mathematics properly you will have to think about it and apply it in some way on a regular basis. With science, I think statistics is a good choice because it is used frequently and understanding it properly helps make good scientific arguments as well as understanding the different caveats of how interpreting data and statistical output can be either a good thing or a bad thing. Also I am from Australia and I have seen people jump into different areas from areas that are distinct in some way from the original area. Given that you are a scientist, if you had to do the calculus sequence like many of the science undergraduates have to, you are probably in a better position than you think and if you can do a course or two during your PhD, then that will probably be enough to get you understanding this kind of thing on your own. (IMO) 


#3
Jan3112, 03:20 AM

P: 19

Yeah, I have been trying to teach myself some other topics such as vector calculus, more in depth linear algebra and I have also covered topics in other physics and chemistry classes like simple group theory and operator algebra (from quantum mechanics). I can understand them  but nowhere near as much as I would if I were to take a mathematics class on each topic. Thanks for your help, I'll look into doing a few classes while completing my PhD. That sounds like the best approach. 


#4
Jan3112, 04:13 AM

P: 4,573

Master of Mathematics Studies or PhD in Physics?
Like other fields the best way to understand something can be done from a variety of approaches. One way can be to get involved in communities that do this kind of thing. Physics Forums is one of those communities and is one of the reasons that my knowledge of such things has improved and crystalized in a way. The other is through teaching. Teaching helps understand the same content in different ways. What I have found is that usually don't learn completely new things all the time: it's more of the scenario that you see things in a different way that opens up a whole new can of worms (i.e. even more things to try and understand!). Building on the above, the other thing to do to understand things from a different perspective/viewpoint is to see different applications of the mathematics. Mathematics as you are probably aware is used in many different areas. When you are exposed to seeing it used in one way versus another, you have a good chance of extracting something out of that comparison. After a while what happens is that when you have seen things through quite a few lenses of perspective, you don't see through individual lenses but rather through something that is different, yet still allows you to see the same knowledge that you did before. Those are just some suggestions. Also with mathematics, I will give you some advice that I have learned (a lense if you will) to help you understand mathematics and one way of thinking about it. The key things are a) representation b) constraints and c) transformations. Representations are the things to describe in some kind of language what you are dealing with. Typically mathematics are used to using numbers (up to complex) and then building structures based on those. However there are structures known as sets which form the basis of foundational mathematics and if you wanted to describe say a graph, then you would do it with a set. Understanding representation will help you understand the context associated with that representation: for example most people are aware of how numbers are used and the context they are used in. In contrast graphs are a completely different kind of structure and have a different context associated with them. Different representations have different uses and thinking about all of them and seeing how they can be 'melded' and seen from a different perspective helps you see different things. For constraints, you have to realize that this is the only way a lot of mathematics and its applications gets done. If you had no constraints you would be dealing with 'everything and anything that can happen or be described' and clearly you can see that people would run into problems. So what we do is we restrict the phenomena or the state space that we are describing until we are able to make sense of it and work with it to a point where we can take the next step and decrease the constraints (make them less constrainable). What happens is that the more abstract you go, the less the constraints are and the more you are trying to describe. So the take home message is that if you are struggling with something, increase the constraints and do so until you need to, to understand that. After that you can go in the reverse direction which allows you to see things in a different way and also helps you see 'the big picture'. The final thing is transformations. The most intuitive example of a transformation is a function like f(x) = x^2. But transformations are not just functions. An approximation of a function is a special kind of transformation. Changing one random variable to another as an approximation is a transformation. Converting a function to its taylor series under different centres is a transformation. Going from one line to the next in a sequential proof is a kind of transformation. There are many kinds of transformations that have particular purposes and understanding the context of a particular kind of transformation will help you see things are done the way they are done. There is, of course, more to the subject than these things, but I think this will help you see things in a way that mathematicians see things. If you have any other questions I'll do my best to answer them. 


#5
Jan3112, 04:56 AM

P: 1,145

Having taken a masters, I would recommend going straight into a PhD! I was stuck with doing a really tedious MSc course in astrophysics. Some guys doing PhDs attended the the class, but realising how bad it was just quietly dropped out. I had to persevere because I needed to pass the exam  and I just scraped a pass, even though I was a good honours student. Real dent in my confidence!
Check the scholarship situation carefully. Doing that duff MSc meant I could only get two years more scholarship when I looked at doing a PhD  one of the main reasons I dropped out of doing the PhD... So I'd recommend going straight into a PhD. You are better off working closely with your supervisor, and picking up what you need from books on a "need to know" basis. You are in a great situation if several people are asking you to consider doing a PhD with them. Talk to them all, in detail, about what the work involves. Try and suss out if you would enjoy working with them closely for three years. 


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