Other Should I Become a Mathematician?

[mathwonk]

what do you think of the book suggestions in the first 5 pages of this thread?

here are some remarks i wrote to guide pre phd quals students in algebra:

http://www.math.uga.edu/graduate/AlgebraPhDqualremarks.html

in general, the best books are by the most famous mathematicians, gauss, euclid, archimedes, courant, hartshorne, cartan, artin, jacobson, van der waerden, hilbert, milnor, thurston, riemann.

 

[sandy.bridge]

@ Mathwonk

I'll be taking my first Linear Algebra course next term. Is there any way for you to relate the difficulty of such a course, relative to Calc I, II, III, IV (differentiation, integrals, vector calculus, PDE, etc)? I'm merely taking the course for because it interests me, however, this will be my 7th course for that term.

Here's the outline of the material covered: Vector spaces, matrices and determinants, linear transformations, sets of linear equations, convex sets and n-dimensional geometry, characteristic value problems and quadratic forms.

 

[Number Nine]

@ Mathwonk

I'll be taking my first Linear Algebra course next term. Is there any way for you to relate the difficulty of such a course, relative to Calc I, II, III, IV (differentiation, integrals, vector calculus, PDE, etc)? I'm merely taking the course for because it interests me, however, this will be my 7th course for that term.

Here's the outline of the material covered: Vector spaces, matrices and determinants, linear transformations, sets of linear equations, convex sets and n-dimensional geometry, characteristic value problems and quadratic forms.

Linear algebra is a very nice bridge towards more theoretically oriented mathematics; you'll find it very different than any math you've done so far. The material will be considerably more conceptual than your calculus course (i.e. it becomes very important to understand the "big picture", and you'll spend a bit less time dealing with equations), and this might end up being your first exposure to proofs. That said, if you managed to get through vector calculus (a nightmare for many people), you should have no trouble with linear algebra if you put in the time.

If you want a taste of what you're in for, watch a few of the prophet Gilbert Strang's lectures on the subject...
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/

 

[Dembadon]

@ Mathwonk

I'll be taking my first Linear Algebra course next term. Is there any way for you to relate the difficulty of such a course, relative to Calc I, II, III, IV (differentiation, integrals, vector calculus, PDE, etc)? I'm merely taking the course for because it interests me, however, this will be my 7th course for that term.

Here's the outline of the material covered: Vector spaces, matrices and determinants, linear transformations, sets of linear equations, convex sets and n-dimensional geometry, characteristic value problems and quadratic forms.

The following link contains one of the best free books I've come across for linear algebra:

http://joshua.smcvt.edu/linearalgebra/

Down towards the bottom of the page, you'll see a link for the pdf of the book and its solution manual. I highly recommend it for a first course.

 

[qspeechc]

what do you think of the book suggestions in the first 5 pages of this thread?

I know about the beginning of this thread, but you have made many other recommendations, I believe.

here re some remarks i wrote to guide pre phd quals students in algebra:

http://www.math.uga.edu/graduate/AlgebraPhDqualremarks.html

i general, the best books are by the most famous mathematicians, gauss, euclid, archimedes, courant, hartshorne, cartan, artin, jacobson, van der waerden, hilbert, milnor, thurston, riemann.

Thanks for the link, and the recommendations.

 

[sandy.bridge]

The following link contains one of the best free books I've come across for linear algebra:

http://joshua.smcvt.edu/linearalgebra/

Down towards the bottom of the page, you'll see a link for the pdf of the book and its solution manual. I highly recommend it for a first course.

Thanks for the link.

Linear algebra is a very nice bridge towards more theoretically oriented mathematics; you'll find it very different than any math you've done so far. The material will be considerably more conceptual than your calculus course (i.e. it becomes very important to understand the "big picture", and you'll spend a bit less time dealing with equations), and this might end up being your first exposure to proofs. That said, if you managed to get through vector calculus (a nightmare for many people), you should have no trouble with linear algebra if you put in the time.

If you want a taste of what you're in for, watch a few of the prophet Gilbert Strang's lectures on the subject...
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/

Awesome. I prefer the more 'theoretical' classes anyways.

 

[mathwonk]

for some reason, linear algebra is considered more advanced than calculus when the opposite seems more correct to me. if you look over the book by jim hefferon linked above, you will see how elementary all the ideas are in it. just adding and multiplying by scalars, and occasionally taking a square root. there are no limits, no complicated definitions such as riemann sums, which occur in calculus. actually linear algebra is prerequisite to calculus. not the other way round. the only reason it is taught in the opposite order in some schools, most schools, is that science courses want students to see calculus early, so it is taught in a mindless computational way. that is very hard to understand, hard partly because the students do not yet have linear algebra.

so if you have survived several quarters of calculus, i assume you will have little trouble with linear algebra.

having said this, it is true that if you have only had very computational courses in calculus, with no proofs or reasoning, courses which were never even offered in the good old days, you may be shocked at the level of abstraction in a theoretical linear algebra class.

When i was in high school in the 1950's, we still learned euclidean geometry with proofs, so this abstraction was not so new to us. indeed my freshman college calculus course also had proofs, so to me linear algebra was relatively easy except when it hit jordan canonical form, which can be made to look hard. your course description however does not even mention covering jordan form, and i think hefferon's book does not either.

as mentioned often, there are at least 3 or 4 linear algebra course notes for free on my website you might look at.

 

[sandy.bridge]

Interesting. I hope a 7 course load isn't too overwhelming.

 

[Number Nine]

Interesting. I hope a 7 course load isn't too overwhelming.

Which courses?

 

[sandy.bridge]

EE 212 Passive AC circuits, EE 214 System Modeling and Network Analysis, EE 216 Probablitly Statistics and Numerical Methods, EE 232 Digital Electronics, EE 292 Electrical Engineering Laboratory I (an entire class dedicated to lab work), Math 224 Calculus IV for Engineers, Math 226 Linear Algebra...

Lol, looks fun. Furthermore, I had a meeting with my department head and got approval to execute a dual degree in EE and Physics. I'm so happy. I was worried that the Engineering department was going to be annoying regarding me lengthening the program. I'm wanting to take 3 courses from each department each term, until I am fully finished.

 

[Sankaku]

...does not even mention covering jordan form, and i think hefferon's book does not either.

Chapter 5, Section 4
Page 379

Just to make sure no-one misses it.

 

[mathwonk]

thank you for that correction. i wonder if i was familiar with an older shorter version of hefferon's book, but anyway jordan forms are certainly in this one. note it seems to be dated 2011.

to learn that topic however, it is necessary to read all of chapter 5, and the key section is the section on nilpotence. he puts it all together in the section titled jordan form, but the main work had been done earlier. see especially the concept of a string basis.

to see the difference in pace between hefferon's book and my little primer of linear algebra, note that I cover jordan form from scratch in the first 10 pages compared to his almost 400 pages. Then I go on to cover also rational canonical forms in the last 4 pages, which I do think he omits to mention.

the difference is that jordan form only works when the minimal polynomial has all its roots in the given field, while rational canonical form always works under any circumstances.

 

[Dougggggg]

Does anyone know where I can find a good list of graduate schools for math outside of the US?

 

[bpatrick]

I just thought I would chip in with a little bit of my journey to become a mathematician.

I was always rather talented with mathematics, but I was more gifted when it came to music. In grade school, I performed well enough on the IOWA (or whatever that test was way back that we took at public school in the north east) to be sent up two grades in math. This resulted in me starting algebra I in 6th grade, algebra 2 in 7th, geometry in 8th, trig/precalc in 9th, and then calculus in 10th grade (which was all that my school district offered), so I had no formal mathematics during my junior and senior years of high school.

During those two years, I managed to flip through a linear algebra book and a differential equations text that my father had from when he was in college. I was very active in music and made it all the way to play 2nd trumpet in the state orchestra and 1st cornet in the state band my senior year.

Even though I had gotten a perfect 1600 on my SAT (during the late 90s before they changed it or whatever), I decided against going to an Ivy league, and my father was a little against me going exclusively to a music conservatory (which I wanted to do) because he saw my gift for mathematics and science going to waste if I attended a conservatory.

I ended up going to a medium sized (5000ish undergrad) private university that happened to have a great trumpet professor, a great orchestra, and a solid science school. While I was at university, I majored in musicology (basically music history and theory) and managed about 1/3 of my coursework to be a very broad training in the sciences. I suppose I was technically a "pre-med music major". I took 4 semesters of biology, 5 semesters of chemistry, 5 semesters of physics, and pieced in a few math courses (via placement exam I exempted myself from calc 1, 2, and intro differential equations) including: multivariable calc, complex analysis, and a year long course in bifurcations and dynamics.

As far as grad school, I went to a music conservatory for a masters degree in trumpet performance, but having no job prospects and large amounts of debt after my degree, I decided to review a little and take the MCAT so I could actually have a fighting chance of making money during a career, always with the hope of being able to eventually settle down into a career in neurology and play in a semi-professional symphony, or at least a dinner theater or something.

After my first year of medical school, my grandfather and father both passed away (heart disease and cancer) within a very short period of one another. Due to financial and estate matters, I had to take a leave of absence from school to work and take care of things in general.

When I attempted to return to school, I found that I was being declined for every med school loan I applied for (not having my father, who had perfect credit as a cosigner). Needless to say, I tried my best for months to try to come up with a way to finance the rest of medical school, but without any family (or close friends who might have been able) at all at this point to help out, it seemed that fate didn't want me becoming a neurologist.

Since mid-late 2000s I've been trying to get by via freelance music gigs and have been bouncing between cities and in and out of homelessness and employment. Given the almost double digit unemployment rate in the US now, it's not terribly surprising that somebody like me (very little formal employment history, sometimes no legal address, being "overqualified" because I have a masters degree, and no "useful" trade skills) is having trouble finding work. I've gotten a few temp jobs over the past few years, but none have even had the possibility of getting me a permanent employment.

Back in 2009, I met my current fiancee who was a sophomore in college (we're 6 years apart ... it's not that creepy, haha). I've been working odd jobs, getting gigs here and there, and making ends meet for us. I've also been fortunate enough to be able to audit quite a few mathematics and physics courses from her school (for free). I've sat in on two semesters of electromagnetic field theory, a semester (so far) of quantum mechanics, real analysis, algebra, differential geometry, and topology (still this semester).

She's graduating this spring (currently #1 in her class, woot, so proud!) and is applying for PhD programs in I/O Psychology.

My/our plan is for me to work part-time and audit / enroll in a graduate level class or two each semester during her first year (wherever we end up ... we'll know in Feb/April 2012). My plan is to pass all of the PhD qualifiers that the school administers during the following summer and then put in my formal application for PhD candidacy after I pass all of them.

I'm taking the Math subject GRE this April and am already quite confident. I took the general GRE test this past August when it was only $80 (due to the format change) and my "estimated score range" that is given at the end of the test was 750-800 on both the verbal and the quantitative ... so we'll see on Nov. 1st how I actually did with the new scoring system.

I know my current strategy is a bit unorthodox, but so is the path I had to take to get here. I really think I've found my calling in mathematics (even though it's taken me over a decade to get here). If anybody has some advice for me or my "auditing for a year + destroying the qualifiers" strategy of obtaining PhD candidacy ... I'd love to hear any thoughts.

Well, I hope it was somehow entertaining to read this. There are myriad ways of achieving any of your goals. I'm just one of many strange stories out there of how people have gotten to wherever they're headed.

 

[mathwonk]

i'm sorry you were denied your shot at medical school, but you seem fine with it, so i am delighted we have your talent back in pure math. you will be very successful in my opinion. good luck to you and your fiance'e.

 

[synkk]

I just thought I would chip in with a little bit of my journey to become a mathematician.

I was always rather talented with mathematics, but I was more gifted when it came to music. In grade school, I performed well enough on the IOWA (or whatever that test was way back that we took at public school in the north east) to be sent up two grades in math. This resulted in me starting algebra I in 6th grade, algebra 2 in 7th, geometry in 8th, trig/precalc in 9th, and then calculus in 10th grade (which was all that my school district offered), so I had no formal mathematics during my junior and senior years of high school.

During those two years, I managed to flip through a linear algebra book and a differential equations text that my father had from when he was in college. I was very active in music and made it all the way to play 2nd trumpet in the state orchestra and 1st cornet in the state band my senior year.

Even though I had gotten a perfect 1600 on my SAT (during the late 90s before they changed it or whatever), I decided against going to an Ivy league, and my father was a little against me going exclusively to a music conservatory (which I wanted to do) because he saw my gift for mathematics and science going to waste if I attended a conservatory.

I ended up going to a medium sized (5000ish undergrad) private university that happened to have a great trumpet professor, a great orchestra, and a solid science school. While I was at university, I majored in musicology (basically music history and theory) and managed about 1/3 of my coursework to be a very broad training in the sciences. I suppose I was technically a "pre-med music major". I took 4 semesters of biology, 5 semesters of chemistry, 5 semesters of physics, and pieced in a few math courses (via placement exam I exempted myself from calc 1, 2, and intro differential equations) including: multivariable calc, complex analysis, and a year long course in bifurcations and dynamics.

As far as grad school, I went to a music conservatory for a masters degree in trumpet performance, but having no job prospects and large amounts of debt after my degree, I decided to review a little and take the MCAT so I could actually have a fighting chance of making money during a career, always with the hope of being able to eventually settle down into a career in neurology and play in a semi-professional symphony, or at least a dinner theater or something.

After my first year of medical school, my grandfather and father both passed away (heart disease and cancer) within a very short period of one another. Due to financial and estate matters, I had to take a leave of absence from school to work and take care of things in general.

When I attempted to return to school, I found that I was being declined for every med school loan I applied for (not having my father, who had perfect credit as a cosigner). Needless to say, I tried my best for months to try to come up with a way to finance the rest of medical school, but without any family (or close friends who might have been able) at all at this point to help out, it seemed that fate didn't want me becoming a neurologist.

Since mid-late 2000s I've been trying to get by via freelance music gigs and have been bouncing between cities and in and out of homelessness and employment. Given the almost double digit unemployment rate in the US now, it's not terribly surprising that somebody like me (very little formal employment history, sometimes no legal address, being "overqualified" because I have a masters degree, and no "useful" trade skills) is having trouble finding work. I've gotten a few temp jobs over the past few years, but none have even had the possibility of getting me a permanent employment.

Back in 2009, I met my current fiancee who was a sophomore in college (we're 6 years apart ... it's not that creepy, haha). I've been working odd jobs, getting gigs here and there, and making ends meet for us. I've also been fortunate enough to be able to audit quite a few mathematics and physics courses from her school (for free). I've sat in on two semesters of electromagnetic field theory, a semester (so far) of quantum mechanics, real analysis, algebra, differential geometry, and topology (still this semester).

She's graduating this spring (currently #1 in her class, woot, so proud!) and is applying for PhD programs in I/O Psychology.

My/our plan is for me to work part-time and audit / enroll in a graduate level class or two each semester during her first year (wherever we end up ... we'll know in Feb/April 2012). My plan is to pass all of the PhD qualifiers that the school administers during the following summer and then put in my formal application for PhD candidacy after I pass all of them.

I'm taking the Math subject GRE this April and am already quite confident. I took the general GRE test this past August when it was only $80 (due to the format change) and my "estimated score range" that is given at the end of the test was 750-800 on both the verbal and the quantitative ... so we'll see on Nov. 1st how I actually did with the new scoring system.

I know my current strategy is a bit unorthodox, but so is the path I had to take to get here. I really think I've found my calling in mathematics (even though it's taken me over a decade to get here). If anybody has some advice for me or my "auditing for a year + destroying the qualifiers" strategy of obtaining PhD candidacy ... I'd love to hear any thoughts.

Well, I hope it was somehow entertaining to read this. There are myriad ways of achieving any of your goals. I'm just one of many strange stories out there of how people have gotten to wherever they're headed.

Best of luck to you, how old are you may i ask?

 

[bpatrick]

@ mathwonk Thanks, the math community in general seems intensely welcoming. Almost every professor that I've sat in on their class has been very obliging and encouraging, which is understandable considering their love of the subject. I'm glad that (at least I think) I've finally found my niche even though it has taken me quite a while to get there. It amuses me to think that some day (although it's unlikely), I could be one of those half-page biographies that are scattered throughout many pure math texts and make you think, wow, that person had to have been quite a character. I often read them, amused at how extraordinary their stories are, whether they be about how the mathematician was a child prodigy, killed in a duel, published while working as patent clerk, resigned as a math professor to become a philosopher instead, or hundreds of other amazing stories.

@ synkk Thanks for the vote of luck ... and I'm 27, so I have a few years on the young whipper snappers who are 21-22 and heading straight into grad school after their bachelors, but I'd like to hear any of them play Petrushka like I can, hah.

 

[lisab]

Well, I hope it was somehow entertaining to read this. There are myriad ways of achieving any of your goals. I'm just one of many strange stories out there of how people have gotten to wherever they're headed.

What an interesting path you're taking through life! I found your story entertaining and inspiring -- thank you for writing it .

 

[deckoff9]

@bpatrick: That sounds like a super interesting life story. I am in a similar situation. I am 27 years old and applying to grad school this winter. Spent 4 years as a pro poker player after my undergrad, but I'm not engaged and I have my parents' help so I am thankful for both ;)

You plan sounds pretty good, though I warn you against getting too cocky. I hope you listen, because I'm pretty sure I wouldn't have listened to myself even as recently as a year ago when I decided to start taking classes again. I was pretty good at math as a kid too. Skipped some grades, did well in city competitions, 800 SAT math/750-800 range on the GRE I just took. None of that is honestly very impressive compared to even the mediocre students in better math undergrad programs.


Did you take the tests for the classes that you sat in on and do well? If so nice job, and it may be possible to ask for letters for recommendations from those professors. If not I'd be a bit more worried about getting recommendations. Graduate level math is a good deal harder than undergraduate math, and graduate students are a LOT smarter and harder working than undergrad students. If you don't do well in those classes and don't have recommendations lined up it's going to be hard to guarantee you do well enough to get said letters. Doing well on qualifying exams I don't think is enough to make up for bad letters.

It may be worthwhile just to take undergrad classes and get good grades in them and be on the safer side, if your fiancee is going to a better science program. Again I'm not sure if you took the tests for the classes you sat in on. If you did and did really well and already got recs, then yeah go for it. But if you're just going to take 3 graduate classes and is expecting to do well enough to get those letters from those professors, I highly highly recommend a backup plan.

Also, not to repeatedly try to rain on your parade, but I wouldn't feel so confident about the GRE subject test unless you've literally taken a practice version (a recent one since the recent ones are a lot harder) and done really well. I'm auditing classes at UCSD now (ranked around 15 in America) and none of the 4 TA's who divulged their score to me got above 80 percentile. That test is serious business.

 

[bpatrick]

@deckoff9 Thanks for the words of advice, anything and everything is welcome at this point. Coming from the music background where I'm used to 50-100+ trumpeters (most with equally impressive degrees and pedigree) showing up to an audition, playing behind a screen (so the judging committee can't weigh any factors except sound), and only one guy winning the gig ... the thought of simply performing perfectly on PhD qualifying exams (that many programs report having less than an 80% first-time pass rate for students already admitted into programs) seemed like a sound way to propitiate the department.

You asked how I've done with the courses so far. Well, from 6+ years ago when I was an undergrad, my average in the three "graduate level" courses I took was a 4.0. Out of the "graduate level" classes I've audited here, I was only allowed to take the final in two of them, but I received a perfect final exam on both. This semester I'm not being allowed to participate in Quantum, just sit there and listen, whereas Topology has a weekly quiz which I am taking along with the class. The prof knows where I stand with my background and obviously where I stand compared to the rest of my class. The course is set up as the first 13 weeks being fundamentals then the final two weeks being student taught (MWF class and 6 students in the class including myself) so we each have to choose an "application topic" to lecture during one of the final lecture periods, which the prof is welcoming me to participate in.

I actually have been a little worried about getting the 3-4 required letters that most departments want. I haven't kept in touch at all with any profs from undergrad (6-10 years ago) and I highly doubt any letters noting my performance while earning my masters in music will be worth anything. So far I have one very strong letter from the Algebra prof I audited from and got one of two perfect scores on the final. I'm hoping to continue developing my relationship with my current Topology professor to the point where I can get a strong endorsement from her as well. As for the 3rd (and possibly 4th) letters, I was hoping I could get one from a prof I take a grad level course with when I get to whatever institution Debra and I will be at next year, and then maybe even use a former professor (and my adviser) from med school ... even though it's not a related field, I have kept in touch with him and he will gladly give me a sound recommendation that, if nothing else, relays that I am capable of excelling in the first year medical school curriculum (which may mean something to a math department, maybe not too, no clue to be honest, but I figured it would be better than a tepid recommendation from a math professor who does not know me as well).

As for the GRE, you could be right that I'm overconfident. I've taken 4 practice tests so far and found them all to be pretty easy other than working out time management issues. I found an old test (from 1990s), a newer test (from 2007 maybe?), took the first test from the REA "Best Test Prep" book, and the one from Princeton Review book. The old one and the Princeton Review one were very easy and I estimate the real thing will be a great deal more difficult, but the other two seemed to be more on par and what I'm expecting to encounter in 6 months.

I did about 1 month of studying for the MCAT after not having any science classes for about 3 years and then ended up getting a 43Q on it, which was well above the average of any ivy league medical school I looked at and I had no trouble getting into any of the medical programs I applied to. From the way it sounds though, the math GRE is significantly harder, which is good to have many warnings from people this far in advance. I'm really hoping to get at least above 90% of other takers on the thing when I take it in April, but again, not sure how realistic that is since I'm still trying to fill in a gap or two in subject matter tested that I wasn't exposed to yet (numerical analysis and statistics).

 

[deckoff9]

@bpatrick: Looks like you have a pretty good have on your shoulders. You sound pretty well prepared so good luck to you. FWIW, a 90% is ridiculously high for an American grad student. If you can get that I think everyone here will be extremely impressed.

One thing I would consider is trying to get into a REU if you have time. I'm not sure how realistic it is for students auditing the class, since they might give priority to people who are actually attending the school, but it never hurts to ask.

 

[zoxee]

So i have pretty much terrible GCSEs compared to most people (Bs/Cs), i messed around a lot after my GCSE's and finally fixed up around 18, now I'm in my second year of a levels (A2) studying A level maths, chemistry, economics, AS Further maths. I achieved AAAA in Maths chem and economics and biology (AS) but dropped biology. Now your probably wondering why i didn't take further maths from the start if i had the intention of studying maths, well i did try to but the college didn't allow me to as my GCSE maths grade is a B (this was 2 years ago...) and they thought i wasn't capable enough, but i think i am, and they now think i am so they're allowing me to take it to AS. Looking around forums, reading about mathematicians etc it seems like they all had perfect grades in mathematics, and everyone has A2 further maths, and I'm just here with my AS (predicted A and A* in regular mathematics).

So with all my qualifications, the lack of further maths at A2 would i really be capable for a mathematics degree at a good university (i'm hoping to go around top 10 for maths UK, top 50-100 world (hopefully))? I really do love mathematics, the only reason i got a B at gcse is mainly because i didn't do anything at all, and have stepped up my game at a levels, but every other good mathematicians was good throughout their life, and i just feel like a failure and not capable at a good university (I want to go to kings/nottingham/york).

Let me know what you think... thanks.

 

[mathwonk]

I know my thread is too long to easily search but if you find my story somewhere you will learn that i had a checkered career, being required to leave college with about a C-/D average as a sophomore, being let go from grad school with only a masters after 5 years, then finally getting back into grad school in my 30's, and being given a maximum of 3 years to finish and being told that was "slow". But I worked consistently very hard roughly from age 29-42, the thing that had been missing earlier, and had a satisfying career which just ended in retirement in 2010. I was even treated to a birthday bash in 2007 for helping younger people get established.

http://alpha.math.uga.edu/~valery/c...95S60SJW*MTY1Njk4Njg4NS4zLjAuMTY1Njk4NjkwNi4wso even late bloomers and people with flaws can have fun in this game too, with persistence and luck and friends. You can too.

Practically, go talk to some mathematicians at those schools you want to attend and get their advice. if you know something and can do something they may notice it by speaking to you, and then they may be able to help you. That's what I did.

 

[dkotschessaa]

I know my thread is too long to easily search but if you find my story somewhere you will learn that i had a checkered career, being required to leave college with about a C-/D average as a sophomore, being let go from grad school with only a masters after 5 years, then finally getting back into grad school at age 32, and being given a maximum of 3 years to finish and being told that was "slow". But I worked consistently very hard roughly from age 29-42, the thing that had been missing earlier, and had a satisfying career which just ended in retirement in 2010. I was even treated to a birthday bash in 2007 for helping younger people get established.

check out: http://www.math.uga.edu/~valery/conf07/conf07.html


so even late bloomers and people with flaws can have fun in this game too, with persistence and luck and friends. You can too.

Practically, go talk to some mathematicians at those schools you want to attend and get their advice. if you know something and can do something they may notice it by speaking to you, and then they may be able to help you. That's what I did.

Well, perhaps there is some hope for a 35 year old Undergrad.

 

[wisvuze]

I know my thread is too long to easily search but if you find my story somewhere you will learn that i had a checkered career, being required to leave college with about a C-/D average as a sophomore, being let go from grad school with only a masters after 5 years, then finally getting back into grad school at age 32, and being given a maximum of 3 years to finish and being told that was "slow". But I worked consistently very hard roughly from age 29-42, the thing that had been missing earlier, and had a satisfying career which just ended in retirement in 2010. I was even treated to a birthday bash in 2007 for helping younger people get established.

check out: http://www.math.uga.edu/~valery/conf07/conf07.html


so even late bloomers and people with flaws can have fun in this game too, with persistence and luck and friends. You can too.

Practically, go talk to some mathematicians at those schools you want to attend and get their advice. if you know something and can do something they may notice it by speaking to you, and then they may be able to help you. That's what I did.

hello mathwonk, I recall seeing your story somewhere and it's a really nice down-to-earth inspirational one. How did you pull through and keep going with math with your head up? If I were in that position, I would feel extremely discouraged ( to the point of rethinking life choices.. et c) . Was it a situational life problem? Or was it more because you were a little slower at "fitting in" with being a student ( work ethic, concentration abilities .. et c)?
thanks

 

[headworld93]

'm an economist (in embryo) but maths is a passion 've nursed since i was a kid i love economics and would desire to venture into econometrics. I would love to meet great mathematicians to tutor me and make me a better mathematician

 

[mathwonk]

I wasn't consistently devoted to doing math, I just went through a lot of changes and wound up lucky. I remember one day at the meat market, reading a newspaper about the 25th anniversary or so of the atom bomb. I had been there a couple years and at least 2 of about 20 guys had died, homicides, and I was getting a little wiser. I missed doing science, and felt that I was in the wrong place. I started looking for a job and found a teaching job, the first step back.

Then I taught for 4 years, got married and had a child, and was facing dismissal for not having a PhD, even though all agreed I was well qualified in terms of knowledge, indeed more so than most others. So i was forced to go back to school, and then things got slowly better.

I found it very embarrassing on behalf of academia that I could hold a meat lugging job by bringing the meat off the truck competently, but no matter how well I did my teaching job I could not hold it without a degree. No matter how smart or well qualified you are, in academics it helps to have a union card to get a job. (The meat lugging job was non union.)

 

[Sina]

So i have pretty much terrible GCSEs compared to most people (Bs/Cs), i messed around a lot after my GCSE's and finally fixed up around 18, now I'm in my second year of a levels (A2) studying A level maths, chemistry, economics, AS Further maths. I achieved AAAA in Maths chem and economics and biology (AS) but dropped biology. Now your probably wondering why i didn't take further maths from the start if i had the intention of studying maths, well i did try to but the college didn't allow me to as my GCSE maths grade is a B (this was 2 years ago...) and they thought i wasn't capable enough, but i think i am, and they now think i am so they're allowing me to take it to AS. Looking around forums, reading about mathematicians etc it seems like they all had perfect grades in mathematics, and everyone has A2 further maths, and I'm just here with my AS (predicted A and A* in regular mathematics).

So with all my qualifications, the lack of further maths at A2 would i really be capable for a mathematics degree at a good university (i'm hoping to go around top 10 for maths UK, top 50-100 world (hopefully))? I really do love mathematics, the only reason i got a B at gcse is mainly because i didn't do anything at all, and have stepped up my game at a levels, but every other good mathematicians was good throughout their life, and i just feel like a failure and not capable at a good university (I want to go to kings/nottingham/york).

Let me know what you think... thanks.

You are right about the fact that having bad grades in undergraduates mostly effects your chances of getting into graduate schools (but since your chance is not zero, you may always increase as much as possible by applying to many places and personally contacting academicians etc). However if you are doing a PhD a good advisior may be as important as a good school. If you are not like a top notch student then it will be ofcourse very hard to get to schools like cambridge. However the schools you have listed here, if you display sufficient interest and motivation (in your CVs or in interviews) then with some luck too you should have a considerable chance of getting. But ofcourse earning a PhD acceptance is quite depends on luck. I have seen perfect students with perfect CVs not getting acceptance from any good school. In the end it seems like a bit chaotic process and having personal contacts in schools seems to help alot.


As for being capable or not. I was a genetician in BS and starting taking serious math courses only in my final two years. If you pick a topic, let's says differential geometry, then it won't take you more than a few years to learn first the prerequisies (in my case real analysis and point set topology) and then get the basics of topic (smooth manifolds and riemannian geometry) to move to more advanced topics (principal bundles, inf. dimensional dif geo etc). It is almost true to say that to do mathematics, mathematical maturity (that is understanding how to think and learn like a mathematician) is the most important thing. At this part I was very lucky to have some teachers that communicated this idea to me very clearly and again lucky because they were also interested in geometry, analysis and topology :) So basic level courses should help you with this. What you really need is motivation and a subject, I think. Not having an undergraduate in mathematics, I was also weak in topics such as Complex Analysis and Functional Analysis. But they were not urgent prerequisites to learning differential geometry. I am learning them slowly as I go by and more fastly when I have free time to study.

 

[Sina]

published while working as patent clerk.

wasnt that a physics story :p

 

[mathwonk]

We get a lot of questions from people wanting to know their chances of admission to a top school when they themselves do not have top records. This makes little sense. This may stem from a misguided belief that even weak students from good schools find success because of the reputation of the school. In the end, and usually sooner, you will rise or fall based on your own reputation.

Assuming admissions offices do their job well you will not get undeserved admission, and it is even better for you if you do not get it. All you need and should expect is admission to a school that is commensurate with your background and demonstrated ability. Once you get that, your job is to excel where you find yourself. Then you may start the slow and gradual climb back up to higher level places.

Indeed being a good student at a lower level school will gain you more (i.e. academic awards, financial support, intellectual advice, future placement), from professors there and better treatment than if you were an "also ran" or worse at a more competitive place. The journey forward always begins wherever you are now.

My own story may be of limited value, especially if told too often, but I have this same experience. Early in my career I was accepted to less famous schools based on a spotty record with some good aspects, bounced eventually out of those and worked my way back through hard effort through a variety of sources and less famous jobs to get back eventually to being at least a visitor at Harvard, my dream place. While there, I met professors who had known me earlier but did not now recognize me.

When I recalled our earlier association, one famous mathematician actually apologized for not admitting me earlier to Columbia grad school when I had applied. I was very surprised by this as it seemed to me he had made the right decision at the time. Without the work habits I had acquired over the intervening years I think it unlikely I would have succeeded there. But association with good schools is very seductive. Another professor quizzing me on my background learned I had gone to Harvard as an undergraduate, and just assumed that experience 15-20 years earlier explained my current success.

Neither ones presence at a top school, nor any magic spark in ones makeup, can predict success. Only hard work, consistently applied leads to that. Just watch the work habits of the smartest person you know. Yes he/she will learn faster than you and I will, but they do hit the books/study hard when the time comes for it. They do not take anything for granted. As someone told me long ago, when I was beginning to turn things around, "if you stop working, things will stop happening".

 

[n_student]

Hey, I have been a long time lurker on these forums and finally got enough courage to ask a burning question that has been in the back of my mind a long time.

How much of being a good mathematician comes from being taught and learning at a young age as compared to talent and hard work?

I ask because I am a freshman at a top university who is interested in pure math. I have had no training in proofs. Some of my classmates in pure math are far ahead of me and I don't know if I can possibly catch up. I have talked to a graduate student in pure math who said: “people who are successful in pure math are taught from a very young age and blaze through their undergraduate. It is nearly impossible to go into academic-math starting in university.”

I really like math and am considering it as my major but I don't want to walk into a dead end.
That said, I am really devoted and am an incredibly hard worker ounce I follow a path.

Is it possible for a person like me who, is starting pure math in their undergraduate to make a meaningful contribution to academia and get a professorship?

 

[nickadams]

I was wondering the same thing as n student, except i am even worse off than him because I did not pay attention in my math classes all throughout high school so I basically have zero math knowledge at this point. I don't see how it would be possible for me to catch up to those who have been working hard at math since they were in 8th or 9th grade (or maybe even earlier. yikes). :/

 

[Sina]

Well you can always catch up during your free time such as summer holidays, given that learning the basic topics usually proceeds much faster once you get used to the topic. I was pretty much the same situation when I decided to do physics (till then as I stated some many times, I was a genetician). Took me some years to catch up but you can. That is what really being an academician is all about anyway; studying something else in your free time besides the regular courses. If you are feeling an urge to read and learn about a topic of your choice
then in my opinion you are pretty ready for doing a Ph.D provided that you can find an advisor that also works on that topic.

While catching up though, try to keep your grades as high as possible. Alas when you apply for a Ph.D they won't really know that you were studying math in your own free time, or you were doing projects (since a great many of them do not give results in undergraduate). They moslty care about your shiny grades as the sign for your capacity to work*. So if in future you want to get to a good school for PhD, alas you will have to do that catching up all the while keeping your other grades very high. So don't let go of your other courses (even if you don't really like them).

*: though it is usually true that high grades mean high capacity for work, low grades by no means signifies low capacity for work. but schools don't like taking risks and do not really believe in the idea that the more the variation the greater the chances for something unusual to come out (evolutionary perspective). So given that there are enough applicants with 4.0 grades and good reccomendations they will take them all and probably won't care about the others :) That is why if you have average to high grades (but not very high) you should also apply for as many as about 15 universites of various levels (to be realistic do not apply to cambridge, stanford etc that will only make you lose money).

 

[n_student]

Well you can always catch up during your free time such as summer holidays, given that learning the basic topics usually proceeds much faster once you get used to the topic. I was pretty much the same situation when I decided to do physics (till then as I stated some many times, I was a genetician). Took me some years to catch up but you can. That is what really being an academician is all about anyway; studying something else in your free time besides the regular courses. If you are feeling an urge to read and learn about a topic of your choice
then in my opinion you are pretty ready for doing a Ph.D provided that you can find an advisor that also works on that topic.

While catching up though, try to keep your grades as high as possible. Alas when you apply for a Ph.D they won't really know that you were studying math in your own free time, or you were doing projects (since a great many of them do not give results in undergraduate). They moslty care about your shiny grades as the sign for your capacity to work (though it is usually true that high grades mean high capacity for work, low grades by no means signifies low capacity for work). So if in future you want to get to a good school for PhD, alas you will have to do that catching up all the while keeping your other grades very high. So don't let go of your other courses (even if you don't really like them).

Thanks for the advice, my grades are quite good so far and I don't plan on letting them drop. I am curious though on how much top grades factor into getting accepted. Like how much your chances fluctuate on getting into a good grad school if you have a 3.5GPA vs a 3.9 GPA?

Some disciplines though are more forgiving for late starts than others, and I hope to know which math falls into. Writing, engineering and computer science are areas where experience and hardwork are big factors in determining your outcome in the field (at least from what I have heard :P). Chess on the other hand is impossible to contribute to the field unless you started at a young age.

 

[Sina]

Alot changes from 3.5 to 3.9 however with 3.5 you have a fair change of getting into good schools provided you make many applications (one examples would be Duke applied).

If by contribution you mean making a ground shaking discovery, well than it is true that such people show mathematical talent at an early age, especially for pure math. But for applied math in fields such as mathematical biology (but not mathematical physics you also have a good chance of doing good things provided that you are a good mathematician have sound knowledge of the part of biological field you are working on.

But if by contribution you mean working on problems that seem interesting to you and get some satisfactory and some times important results on them, then there are many examples where late comers could do that. There are for instance quite a number of examples of that around me.

ps: By the way I am only a student currently doing PhD so you may want to consult more experienced&older users for the contributions part :)

 

[Nano-Passion]

If by contribution you mean making a ground shaking discovery, well than it is true that such people show mathematical talent at an early age, especially for pure math.

I wonder if this case is always true?

 

[deckoff9]

People who tell you you can't do something are always just hating. With this as with everything else you won't know till you try. FWIW I bet 90% of graduate students never see a proof until college sophmore year, not that that really even matters.

 

[mathwonk]

I think I answered this in the post just before you asked it nstudent.

 

[Sina]

I wonder if this case is always true?

I wouldn't claim to know the definite answer to this question as I am only a graduate student and have much to see yet. But as far as what I h ave seen it is statistically true :)

 

[n_student]

I think I answered this in the post just before you asked it nstudent.

I was really hoping you could answer my question, being an experienced professor. I will try and make it more clear this time.

I am curious about the level of ability that can be attained, which is different than the ability to get into top schools.

The math graduate student I talked to was very depressed. Even getting into a top 20 school and being top in his class he was still lamenting that he was light years behind the students who started when they were kids and wished he went into another subject he liked: physics- where he could make a contribution.

Now I definitely do not want to be make a critical decision based on a grad students word. I came here to cross check my sources , hopefully from people with experience in academia.

I know that you had a roundabout way getting a PHD, but to my understanding you had an incredibly good start when you were young.
How much of a persons potential is tied to starting math early?
Do you know others who started proof based math in university and were able to succeed?

Hopefully my question is more precise this time!

 

[U.Renko]

The math graduate student I talked to was very depressed.

Well, that explains a lot.

Honestly: When seeking advice or when you need to make decisions, avoid talking to depressed people.

 

[Mépris]

I was really hoping you could answer my question, being an experienced professor. I will try and make it more clear this time.

I am curious about the level of ability that can be attained, which is different than the ability to get into top schools.

The math graduate student I talked to was very depressed. Even getting into a top 20 school and being top in his class he was still lamenting that he was light years behind the students who started when they were kids and wished he went into another subject he liked: physics- where he could make a contribution.

Now I definitely do not want to be make a critical decision based on a grad students word. I came here to cross check my sources , hopefully from people with experience in academia.

I know that you had a roundabout way getting a PHD, but to my understanding you had an incredibly good start when you were young.
How much of a persons potential is tied to starting math early?
Do you know others who started proof based math in university and were able to succeed?

Hopefully my question is more precise this time!

If you were to read back through this thread, I'm certain you'd find that he mentioned that his math background was somewhat limited when entering college.

That was quite a few years ago and I can only guess but I doubt there were too many Terry Taos then either...

 

[bpatrick]

I am curious about the level of ability that can be attained, which is different than the ability to get into top schools.

...

How much of a persons potential is tied to starting math early?
Do you know others who started proof based math in university and were able to succeed?

A book everybody should read who is having questions about early career in mathematics is:

A Mathematician's Survival Guide: Graduate School and Early Career Development by Steven G. Krantz.

It answers so many questions and has given me much inspiration considering my university education was Musicology and pre-medical, with my graduate education being Trumpet performance ... I didn't see a formal proof until JUNIOR year of college ... aka when I was 20.

If I felt I was in some way inferior to somebody who had blazed through undergrad math and passed the PhD qualifiers when they were 20, I'd have second doubts too, but age has nothing to do with your ability to succeed as a mathematician. Most of the professors I have studied under (a few who were PhD'd by ivy league programs and have wonderful careers) have said that work ethic and the ability to endure failure are much better traits to have than early prodigy status.

As far as I'm concerned, everybody is more or less on equal standing when they get to the point where they can pass all their quals. Some will do it at age 20, some at age 30, and yeah that may make the 30 year old significantly less likely to win the Fields medal (me included), but whatever, I'd rather take the Nobel prize money ... which has no age limit.



Good luck with whatever you chose. That book is more than worth the read. You can probably find it somewhere online without too much trouble ... djvu versions are out there and quite easy to find for free.

p.s. an afterthought I had ... statistically, there may be a correlation between age of getting to the level when you are able to do original research and how "fruitful" your career is. However, I would imagine this is more due to the fact that the "prodigy" may be more socially inept due to discrimination at points in their life, combined with being pushed by guardians and advisers to the point of not having a "normal" social life, hence increasing their mathematical productivity ... like I'm probably not going to ever be a famous award winning mathematician / biophysicist, but I would argue that is because I will spend a large portion of my time with my fiancee (and eventually children) and catching a game plus a few drinks with friends rather than pushing myself totally in applied mathematics. Will I have a productive and fruitful career, sure, but I still think that has much less to do with age, but rather to level of devotion to the field.

 

[Stylish]

Hey n_student. Like you, when I was a freshman I also had no experience with things like proofs. In fact, I had never had any experience with proofs until an analysis/introduction to proofs class in my junior year. Needless to say, I had a lot of trouble with even the simplest of proofs at first.

It was also at this point though that I realized math is what I wanted to do; I originally chose it as a major because I (thought) I was good at it. I spent a lot of time studying for that class, and by the end of it I had more than caught up with my peers.

I didn't just learn how to do proofs though. I realized that hard work and dedication can go a long way, and not just in mathematics. I think you are at a huge advantage because you've already stated that you are "really devoted" and an "incredibly hard worker". Now I am having to spend my time going over all of my earlier courses because I didn't bother trying to truly understand the material, but if you start studying now I'm sure you'll be just fine.

 

[eliya]

I think people shouldn't judge themselves just by statuses. That is, you can't think you're not a good mathematician because you didn't get your PhD from a top 10 school, and aren't teaching in a top 10 school.
I think that mathematicians are people who like doing math, not people who like staring at their diploma that has some big name school on it. If you like doing math then it doesn't matter when you started, where, or how big of a contribution you'll make. What matters is whether or not you like doing math or not.
Yeah, there are benefits for studying at a highly ranked school, or for teaching at one, but remember the following:
If you're in a big department, then it is very likely that there will be a lot of visitors who will give talks in your school. There are also many different mathematicians in your department, and I'm sure they're all very smart and that they are all people you can learn from. Also, sometimes you can be at a school that isn't ranked very high, but is close to other great schools, so you can always make a small trip for a seminar or a talk. For instance, you can go to Brandeis, which has a smaller math department, but be very close (geographically) to MIT and Harvard. Same thing with universities in Chicago and NYC; they're all close to other universities.

Lastly, I think that the math you do in high school requires different thinking than math you do at the university level. I think that people are capable of both kinds of thinking. Being bad at high school math doesn't mean you can't do well in higher level math. Just work hard at your classes, and make sure you really understand the material. Don't think about status. It doesn't really matter in the end.

P.S. Before anyone criticizes me. I'm not saying that highly ranked schools are ******** or that they're unnecessary. I just think people can do well in math at other places.

 

[mathwonk]

Did you know the Fields medalist Hironaka was at Brandeis before he was at Harvard?

 

[Nano-Passion]

Did you know the Fields medalist Hironaka was at Brandeis before he was at Harvard?

According to wikipedia it was kyoto university not Brandeis.

http://en.wikipedia.org/wiki/Hironaka

The university seems to be a very solid one too.
http://en.wikipedia.org/wiki/Kyoto_University

 

[mathwonk]

i didn't know where he got his BA, I meant he was on the Brandeis faculty before he went to the faculty at Harvard. As I recall, he went from the faculty at Brandeis to that at Columbia and then to Harvard. I was trying to illustrate the fact that many less famous schools have outstanding faculties. Hironaka also lived in Kyoto when the ICM was held there in about 1992, and I believe he was also on the faculty there at RIMS.

 

[AcidRainLiTE]

Hi Everyone,

I want to apply to graduate school this year for a PhD (or possibly masters, but with the eventual goal of a PhD) in math. As an undergrad, I did a double major in math and physics with physics being my primary major.

My application is strong, with the exception of my Math Subject GRE scores. I did really poorly on them (43rd percentile or 620 out of 900), mainly because I didn't study correctly. Other than that, I have straight A's or A- in all of my math and physics courses and have good scores on the general GRE (94 percentile in verbal, 91 percentile in quantitative). I also am sure my professors will give me strong recommendations.

My questions is, will my bad Subject GRE scores destroy my chances at getting into grad school this year? I know I could take them again, study properly, and do much better, but that would mean I would have to wait to apply until next year. I would really like to go this year. I graduated in 2010 with my BS, have been working since then, but am ready to go back to school and would like to do so without working another year in the corporate world. What do you think? What are my chances of getting in?

 

[homeomorphic]

Hi Everyone,

I want to apply to graduate school this year for a PhD (or possibly masters, but with the eventual goal of a PhD) in math. As an undergrad, I did a double major in math and physics with physics being my primary major.

My application is strong, with the exception of my Math Subject GRE scores. I did really poorly on them (43rd percentile or 620 out of 900), mainly because I didn't study correctly. Other than that, I have straight A's or A- in all of my math and physics courses and have good scores on the general GRE (94 percentile in verbal, 91 percentile in quantitative). I also am sure my professors will give me strong recommendations.

My questions is, will my bad Subject GRE scores destroy my chances at getting into grad school this year? I know I could take them again, study properly, and do much better, but that would mean I would have to wait to apply until next year. I would really like to go this year. I graduated in 2010 with my BS, have been working since then, but am ready to go back to school and would like to do so without working another year in the corporate world. What do you think? What are my chances of getting in?

Get in where? I don't think it's that important that you have to get into the top schools. You might not get into Princeton or Harvard, but that's not the end of the world. Assuming you aren't broke, you should just apply and see what happens. You won't lose anything except a modest amount of time and money. You can always try again later. If you don't insist on going to one of the very top places, I don't think you'll have any trouble. Just apply to a whole bunch of places. Like 8 places, let's say.