I am entering my 4th year undergraduate BS math program next month. I am certain I will want to do a PhD program eventually but I am not sure if I should do a MA before it.  I have decent undergraduate non-math grades(8.8~) and pretty good math grades (9.8~). I also have done quite a few graduate courses(most of them self study) in various topics: Algebraic number theory, Algebraic topology(homotopy, homology, cohomology under a professor), Lie groups, Galois theory(introductory), Model theory(under a professor), Universal Algebra(under a prof), Set theory(under a professor) and Functional Analysis.  I also expect close to full on my gre subject test(from mock tests).  I am not sure how much value this adds and/or how to present it properly but this is all I have to show for my undergraduate years. Under these circumstances, what would the chances of acceptance into a very good PhD program be? I would like apply to an algebraic number theory/logic oriented program(like Berkley and UCLA). Also, what is the best way to make them aware of my self study? Do I mention it in my statement or should I ask my professors to mention it for me?  What are the benefits of doing a MA before PhD or vice versa?   Edit: In response to one of the comments, my career goals are to eventually get a research position in math(maybe academia, maybe elsewhere but definitely pure math oriented research).
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I've been considering applying to graduate school of some form or another in Mathematics. During my undergraduate years, I did decently on my undergraduate coursework (mostly A-s, some As, a B) but not stellar, and it wasn't until I started taking graduate courses as a senior that I started buckling down and getting solid As or higher. I also had no research experience at this time.  I eventually want to apply to a Ph. D program in pure mathematics. Since I didn't really click until later in undergraduate years, so I was considering applying to 2-year masters programs in mathematics, and then based on my performance there, decide whether I'm fit to work towards a Ph. D.      My question is, what are the advantages and disadvantages to completing a master's program before applying to a separate Ph. D program?   I know masters degrees are sometimes considered terminal degrees. Would doing well in masters coursework be advantageous in applying to Ph. D programs later on as opposed to immediately after undergrad years? Does strong performance as a masters student make one a more attractive candidate, or do programs have less interest in applicants who already have a masters? Is it wiser to apply for a Ph. D directly? I'm sorry if this question is considered too much of a soft question. Thank you.
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I've taken up self-study of math. (How smart can that be?) I've just about finished a course in real analysis which spent a lot of time on metric spaces and some time revisiting calculus.  I was thinking of trying abstract algebra. I would appreciate any book recommendations.  Thanks in advance.  Andrew
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Suppose you do bad in undergraduate school in say computer science. But you do very well in a masters program in computer science. If you want to apply to a PhD program in computer science, will the masters degree grades offset the undergraduate degree grades?
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I'm interested in cutting edge string theory studied by research physicist. I'm wonder what  mathematics is needed and how far am I in terms of mathematics background needed and how much more mathematics do I need in order to study it properly and reach my goal. My mathematics level is at calculus/Linear algebra.
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When applying for PhD programs (or  or ) that require only a statement of purpose and , I was advised to first check if some faculty members (or is one good enough?) in the university have the same research interests as I do. I remember reading or hearing something like, it may be helpful to read up on the research that those faculty members have done and possibly contact some of those faculty members, and then incorporate the reading and contacting in the statement of purpose.   So what could I ask those faculty members? What I think:      Hello Prof/Dr ___ .I'm interested in applying in your univ and am interested in X. Can I ask more about what you research? This is my  (I'm from blah blah blah. I have a master's, but it's in applied not pure math. I've done some self-study blah blah blah). Do you think I am a good fit for the university? Would you consider taking me on as a PhD student? Do you think I am better suited for MS/MPhil than a PhD?    And then how do I incorporate the e-mails in my statement of purpose?
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I have been taking Abstract Algebra graduate classes, and we will begin studying Galois theory.  However, since it is a graduate-level course, the teacher has assumed everyone already had taken undergrauate-level algebra. Problem is, I come from an Engineering background, which did not have it.  Needless to say, I am a bit lost on what I need to know. The teacher will do a brief revision on fields, but I do not even know much about rings (I am fairly comfortable with groups though, since we studied it).  So, long story short, my question is: What do I absolutely must know about rings and fields to understand Galois theory?  I would also appreciate any references that may help. I have been reading Artin's Algebra, and Goodman's Algebra: Abstract and Concrete for now.    And, just to clarify, I do intend to learn more about Algebra later on. It is just that I need to keep up with the lectures, so I must learn the necessary things in a really short time.
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I'm currently a junior in mathematics at UIUC. I have been doing pretty well in my math courses (mostly A and A+). I will be completing a graduate course in topology, a second course in abstract algebra, and a complex analysis course before I graduate.  I feel that I can work hard to maintain good grades in my math courses, but my non-math courses are not that good (some B and C's).    Do graduate schools care more about my math courses grades more or my general GPA more?  Will poorer marks in non-math courses hurt my chances of getting into good grad schools?
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I've always had an interest in electrical engineering (actually all engineering in general) and I've decided that I'd like to pursue a graduate degree.  I guess I'm wondering if I should really try to do this or just keep it as a fun hobby I spend all my free time doing.  So, the question is,  how does one change fields between undergrad and grad school?  A specific example follows, but please provide answers that address a more general case, so that your answers will be helpful to other people with the same general question.  I already have a BS and MS in chemistry with a minor in applied math.I published three papers during my MS, one first author in the top journal in my specialty and two as coauthor in an average and a so-so journal.  I hope those will count for something.  I finished my BS with around 3.1 and my MS with a 3.9 gpa.  I'm sure that my MS advisor would write me a great letter.  My GRE scores are too old to count so I'd have to retake it or try and get a pass on it since I already have a graduate degree.  Since finishing school I've been working for 4 years as a chemist.  I can get great recommendations from my supervisor who is a PhD chemist.      I've been working for a while to cover some of the things I would have learned in a BSEE to try and make up for my lack of one.  I worked through some texts on analog/digital design, lots and lots of programming, built a balancing robot that got a bit of internet attention, and I'm currently working on an autonomous robotics project that's looking really good so far.  After that I have more project ideas than I have time or money for.    I want to apply for PhD programs (specifically in controls/robotics) but I'm worried that my application will get tossed right away because I don't have a BSEE.  Maybe I should just apply to MS programs?
35066
I have recently passed my qualifiers and research proposal. My research is in computational mechanics. I had two courses (continuum mechanics and finite element method) as part of my research related courses. I will be using the concepts learnt in the courses in my research, though my research will be more applied than theoretical, so will involve utilizing a commercially available software and develop few additional routines for it.  Now, I scored B+ in both the courses (the minimum grade required for being eligible for qualifying exams was a B-). I struggled through few concepts but fared fairly well in the qualifiers and answered most of the questions asked by the committee.  However, I am concerned that my average grades might be an indicator that I might not be fit for the field I have chosen to build a career in. Now, I am confident that I will manage to adequately complete my PhD thesis and publish papers as required.   But, I am worried that academia is going to be a closed door for me. Eventually, if I get tenure track position after my PhD, I will have to teach these subjects (There's no teaching assistantship opportunities in my department for me), and how will I be able to teach something in which I fared poorly? Also, I will have to do theoretical research work after my phd, and I will not fare well in that. What should I do?
15870
I was reading the following article by Mathew Might.  I saw the following the paragraph  What doesn't matter GPA? I don't care if it's 2.0 or 4.0. I won't even look at it. The school you went to? I'll judge you the same whether you went to Nowhere State U or a top-ten school. Transcripts? Never seen one. GREs? Irrelevant. Where you work/worked? Unless it's a research lab, it's not important. I don't think these items have much predictive capacity as to whether or not someone can complete a Ph.D.  Is Mathew Might telling the truth? For me it's very hard believe that GPA, GRE scores and undergraduate school don't matter. I used to think that they play an extremely important role in grad school admission.
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I'm an engineering undergraduate, and my university doesn't require me to take any math courses past the standard calculus sequence and differential equations. The field I am interested in entering in grad school is slightly math-intensive, to the point that it requires more math than what I have taken. At this time, I have two years left to graduate, and I'll be taking about 17-18 hours each semester until then, so it would be very difficult me to tack on an extra math course. I was considering simply officially auditing one, so that it appears on my transcript and so that I at least have some exposure to the subject.   My question is: will this have any positive benefits while I'm applying to graduate school? Or would the admissions committee assume that I didn't learn as much as someone who actually took the course, and take it with a grain of salt that I know the material?  On a related note: what about if the course I audited was on directly in my major? Would that be beneficial (if it were, say, a graduate-level course)?
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Dear Academic SE advisers,  I am a college sophomore in US with double majors in mathematics and microbiology. My algorithmic biology research got me passionate about the number theory and analysis, and I have been pursuing a mathematics major starting on this Spring semester. I have been independently self-studying the number theory textbooks written by Niven/Zuckerman/Montgomery, Apostol, and Ireland/Rosen on this semester. As this semester progressed, I discovered that I am more interested in the pure mathematics than applied aspects (computational biology, cryptography, etc.). I want to pursue a career as analytic number theorist and prove the Collatz conjecture and Erdos-Straus conjecture.   I have been thinking about doing the number-theory research on my university (research university; huge mathematics department). I have been self-studying the NT by myself and also regularly attending the professional and graduate seminars on number theory but I did not do any pure mathematics research as an undergraduate. Should I visit NT professors in my university and ask them about if I can do undergraduate research under them? If research is not possible (perhaps due to my lacking maturity), should I request of doing independent reading under them and later proceed with the research? How should I ask them? What should I address? If even independent reading is not desirable to them, what should I ask to them or do in my own?   As for my mathematical background, I have been taking Calculus II (computational) and discrete mathematics. I will be taking calculus III (vector calc.) on Summer, followed by Analysis I, Probability, Theoretical Linear Algebra on Fall 2015. As for my self-studying on this semester, I have been studying NT textbooks (mentioned above), proof methodologies, and basic linear algebra.   Thank you very much for your time, and I look forward to your advice!  Sincerely,  PK
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I  am a PhD student in Mathematics. I have found one advisor in my local University who does not know my research field at all, but  has allowed me to choose my own problems and solve them independently. Initially, I was quite happy as I didn't need to switch places (which I don't want at all). The problem started when my advisor could not assist me in solving the problems I chose. It even happened that I chose a problem to work on and when I told him about it, he said that's an excellent problem and I should solve it.Later on after meeting another professor  in this field he told me that it has been solved long before and hence I had no point working on that again. He does listen to me when I say something about the problems but fails to give me any critical feedback in my topic. I searched the web but there are so many directions of the topic I am working on, I am feeling puzzled which way to go. Moreover there is no research group existing in this field in my local University with whom I can discuss or get some inputs abut my problems. I am unable to answer the following questions of mine which is affecting my research considerably:  1.Has my decision to stay in my hometown and not go to reputed institutes and talking to experienced professors backfired on me? How can I come out of this situation? 2.Is  PhD done in this way only without any help from anyone ?At least my advisor says so.  Any comments/advice will be helpful.
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This is in reference to my question: .  I was told in the answer of the above linked question that chances of landing a job as an assistant professor in Mathematics are quite slim. Very few people will actually get a permanent position in academia.  An article of 2014 shows only 0.5-3% of PhD graduates will actually get a job as an Assistant Professor.  But I have two questions:        Why do so many people still apply for a PhD in some reputed institutes in India even knowing the harsh reality? I found there are 1500 applications for four PhD scholarship positions.          One answer says that people move to industry, but I still don’t understand how after doing a PhD in suppose differential geometry or algebraic geometry one can do a job in industry if he/she gets no position as an assistant professor.   Will one be satisfied to do some managerial work in some Consultancy firm after doing a PhD in Mathematics?      Are people jobless after a PhD?   Completion of a PhD requires so much effort. So why is there no value after doing it?      NOTE:  In the most up-voted answer below it has been said that many who enroll for  a PhD don't even wish to pursue an academic career.  I have been asking my seniors who are currently pursuing a PhD or are in the verge of completing their degree or who have completed it. They said that they all want to be Professors in some Universities and want to be involved in research because that is the dream job for them.  I am obviously talking about PhD in Mathematics
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Are students with masters degree allowed to enter a masters program in the same area at a good university?  Is second masters a good option for a better research experience and improving your CV before applying to a PhD in top programs? I am specifically interested in US universities and computer science.
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I am a PhD student (mid stage) and my work includes the use of mathematics. I try to learn as much as possible. I am facing a problem: I spent enough time on the mathematics required for my research, and according to my research supervisor I am good at understanding proofs, theorems, etc. at an intuitive level, but in writing I still have some work to do. Many times I try to write things and, although I think I am not that so bad, there is still a problem to be resolved.  Question: Is writing in research so very important? I have seen some research papers of some star people whose writing does seems to be very impressive to me (although I may be wrong).  Edit: Please note that I don't consider myself a star: that's why I am asking this question. I am trying my best to improve my writing skills and it has improved to some extent, but to me it appears that I may not get that much better at writing. Let me tell you a story: once during my PhD I worked with a professor other than my supervisor, and then we got some result so he ask me to write a paper. I took 4-5 days write a paper 8-9 pages long, then he told me that I wrote in a cryptic manner. (This happened in my first year.)
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If I do a non-thesis MS program in statistics, will I be eligible for an admission in to a PhD program in Statistics later in my life? The MS program I am looking into is a non-thesis program but I still have to complete a research project requirement (which involves oral presentation as well as some form of a written report) towards the end of the program...I am still not sure if it can lead to a PhD program though.  Thanks!