Switching from science PhD to math BS?

[blaughli]

Hello,

TL;DR: Could it be practical to leave a PhD in Earth science in order to earn a BS in math (starting at the upper division level) if I'm tired of having a spotty math foundation and want to be able to learn anything?

I've been on a slow, wandering path towards a vaguely defined "career in science." I loved math as a kid but got sidetracked by life in high school, then I meandered in college and got a non-STEM BA, and then later I returned to STEM in community college and ended up in a physics MS program. Through lots of hard work I did well in the MS program, but knew that I had missed lots of insights because of a shaky math foundation (namely, I was weak in linear algebra and most of the non-algorithmic parts of math). Afterwards, instead of getting a job, I applied and got into a funded PhD program in an Earth science field. My rough plan was to pick up the math I needed while working on the PhD, which I knew was important because the research used some pretty advanced mathematical tools. Long story short: between a demanding course load early in the program and intense research demands (which I often didn't meet, leading to stress and feeling forever behind), I never did take the math that I felt I needed in order to truly understand and love my research. Now I'm at a crossroads in the PhD (funding very uncertain, still at least two years of work left, still can't take ownership of project since I feel like I don't really get the math underpinning it and am therefore just applying tools, turning the crank, and "analyzing" the results) and I'm starting to feel as though what I really want to do, and may have always really wanted to do, is to pursue a pure math undergraduate education. I have never wanted to lead research or be someone who makes discoveries; I'm much more inclined to build things in clever ways with tools that I have mastered (coding especially). I always secretly saw the PhD as a means to achieve a gratifying 9-5 tech job in science rather than "industry," but now finishing it feels daunting and I still don't think I'd feel qualified (by my standards) to move into the next stages of my career. As ridiculous as it might sound to walk this far down whatever path I've been following only to start over at a place I could have been 7 years ago, it feels right in lots of ways internally. I really want to take proofs! I have wanted to take proofs for a really long time! I don't know much about analysis, but it sounds like it's pretty fundamental to a deeper understanding of math. I want to take advanced linear algebra, and along the way I could take cool and useful applied classes (stats, etc). I already love programming, and I've been falling in love with stats as I've taught it in intro science courses and used it in research. Though it may seem like a step away from science (I know that a PhD in general is often the key that opens doors to science jobs), I fear that I'd always feel like a fraud if I kept just turning cranks in whatever job I could get, if I could get any, assuming that I can even finish this slog. I also may not be so averse to working a non-science job if I felt qualified for it; knowing that I could bring something special to a job and be valued and feel ownership over my work sounds exciting and empowering. Anyway, is any of this reasonable? Working and studying part time is fine, and being free of the burden of leading independent research for which I don't feel qualified sounds so liberating. Could my proposed "switch" be a practical move? I feel as though I can learn anything if my imagination is empowered with the right tools, and so I'm stuck feeling like I need to go back and study pure math before doing any more applied work. This is about a long term vision.

Thanks for reading, hopefully this is a useful post.

 

[Office_Shredder]

Do you want to learn math and then go back to finish the PhD you are doing, or do you just want to quit the PhD?

 

[jedishrfu]

The PhD will go farther in your career than switching over to get a BS in Math. Its almost always best to stay the course than to jump ship and try something new especially with only 2 years left.

With respect to your math deficiencies, have you looked at any of the online options like Khan Academy or MathIs Power4U.com for basic college math? Both have extensive free videos on many levels of math from 9th grade HS to 1st/2nd year college.

Or MIT Online or Coursera for more advanced courses.

Most of the math needed by a Physics BS as an example:
- Calculus 1,2,3
- Linear Algebra
- DIfferential Equations
- Statistics

Later of course, some more advanced stuff like:
- Partial Differential Equations and Boundary Value Problems
- Advanced Calculus
- Abstract Algebra

 

[jedishrfu]

Forgot to mention the 3Blue1Brown Youtube math channel. They have a couple of sequences on the Essence of Calculus and Linear Algebra that bring out key concepts many students miss when taking those courses.

 

[CrysPhys]

OP: If you were to drop your PhD and get a BS Math, then what? Have you thought that through?

 

[Vanadium 50]

I really want to take proofs!

You're 36 years old. You really shouldn't use non-words like "wanna". Especially when discussing careers.

I think you have several things twisted up: the courses you take, the degree you are attempting, and your future career prospects. While not unrelated, they are different things. If you want to take a class on proofs, you don't need to change your degree or career plans. You can just take a class.

Since we're talking careers, I think you should look at your resume and ask what message it sends. As I understand it, you got a degree in music. Then took some CC sources. Then started a physics MS. Then switched to Earth science. Now will be potentially switching to math. Will a potential employer think "broad interests"? Or "can't make up his mind?" or even "perpetual student". You might want to think about it.