Should I Become a Mathematician?

[battousai]

I'm about to take an "Honors" Multivariable Calculus class this quarter, as a freshman. I took Calc BC as a senior last year. What should I be expecting?

The book that we'll be using is by Williamson and Trotter

https://www.amazon.com/dp/0130672769/?tag=pfamazon01-20

 

[Kevin_Axion]

Can someone give me a thorough explanation of the differences between applied mathematics and pure mathematics? A school I wish to attend offers two programs which can be found here: http://www.artsandscience.utoronto.ca/ofr/calendar/prg_mat.htm . I'm interested in pursuing research in fields such as neuroscience, and A.I. Which degree is the better approach?

I'm thinking the applied math degree because there are more rigorous probability and computer science courses then the pure mathematics course. For anyone who can't find the information I'll write it out:

Mathematics Specialist

First Year:
Analysis 1, Algebra 1, Algebra 2

Second Year:
Analysis II, Advanced ODE

Third and Fourth Years:

1. Intro to Topology, Groups Rings and Fields, Complex Analysis I, Real Analysis I

2. One of: PDEs; Real Analysis I (Measure Theory)/(Real Analysis I, Real Analysis II)

3. Three of: Combinatorial Methods; Intro to Mathematical Logic, Intro to Differential Geometry, ANY 400-level APM/MAT

4. 2.5 APM/MAT including at least 1.5 at the 400 level (these may include options above not already chosen)
5. Seminar in Mathematics


Applied Mathematics Specialist

First Year:
Analysis I, Algebra I, Algebra II; (Intro to Comp Programming/Intro to CS)/Accelerated Intro to CS

Second Year:
Analysis II, Advanced ODE; Intro to Scientific, Symbolic and Graphical Computation; (Probability and Statistics I, Probability and Statistics II)

Third and Fourth Years:
1. PDEs; Intro to Topology, Groups Rings and Fields, Complex Analysis I, Real Analysis I, Intro to Differential Geometry; Probability

2. At least 1.5 full courses chosen from: Intro to Graph Theory, Intro to Combinatorics, Complex Analysis II, Measure Theory/(Real Analysis II), Differential Geometry; Data Analysis, Time Series Analysis; Numerical Algebra and Optimization, Numerical Approx., Integration, and ODE, Computational PDEs, High-performance computing

3. Two courses from: Mathematical Foundations of QM, General Relativity, Fluid Mechanics, Asymptotic and Perturbation Methods, Applied Non-linear Equations, Combinatorial Methods, Mathematical Finance, Seminar in Mathematics

Thanks!
4. MAT477Y1

 

[Bourbaki1123]

If you're into A.I. you might want some more computer science and statistics (for machine learning) in there, so if you get a minor with one of those programs I would do the second one and minor in comp sci or statistics if possible. Also, you should probably take the graph theory course when you get the option.

 

[mathwonk]

i found heath's scholarly commentary on euclid somewhat tedious. i suggest beginning with the green lion edition of the elements which i think uses heath's translation but omits the extra stuff. the unaltered original is always best.

@battousal: Williamson and Trotter is a wonderful book.

 

[mathwonk]

my class notes from the 2 week epsilon camp course in Euclid's Elements for very bright 8-10 year olds are now up on my web page at UGA.

 

[weld]

How tough is competition to become a perma faculty member at a third tier uni? Are there tons of brilliant postdocs to compete with? How many, 2, 5, 10, 50? How brilliant, just good or very good?

Also, how much time in % do you estimate is spent on doing non-research as a postdoc? Such as lecturing, teaching grad studs, administration, grant writing? I imagine you get like 80% of the time to research, the rest goes to other stuff? Is math particularly different in this regard compared to other fields such as CS, theoretical physics, etc?

 

[Bourbaki1123]

How tough is competition to become a perma faculty member at a third tier uni? Are there tons of brilliant postdocs to compete with? How many, 2, 5, 10, 50? How brilliant, just good or very good?

Also, how much time in % do you estimate is spent on doing non-research as a postdoc? Such as lecturing, teaching grad studs, administration, grant writing? I imagine you get like 80% of the time to research, the rest goes to other stuff? Is math particularly different in this regard compared to other fields such as CS, theoretical physics, etc?

80% might actually be high based on what a couple of my professors have said about not having enough time to work on research. Of course one of them was dean of graduate admissions so he might have had a slightly skewed view of things.

 

[mathwonk]

if you have some ability and do your best you will ultimately be successful.

 

[Kreizhn]

Can someone give me a thorough explanation of the differences between applied mathematics and pure mathematics? A school I wish to attend offers two programs which can be found here: http://www.artsandscience.utoronto.ca/ofr/calendar/prg_mat.htm . I'm interested in pursuing research in fields such as neuroscience, and A.I. Which degree is the better approach?

I have more than a little trepidation about replying to the first part, explaining the difference between applied and pure mathematics. Indeed, almost certainly I'm going to end up stepping on somebody's toes over this.

Essentially pure mathematics is the rigorous development and exploration of mathematical topics and consequences without the worry of applications. Of course, in this sense one needs to be wary of the use of the word "application," something I believe Hardy goes to painful lengths to clarify in his Mathematician's Apology. The expectation of a high level of rigour and a motivation of abstraction are central themes.

Applied mathematics on the other hand focus on applying (surprise) mathematics to the world. Proofs and rigour can still be found, though tend to be less prevalent than in pure mathematics. At higher levels of applied maths research, pure mathematics is still used extensively. The difference is that research in pure math is to advance the mathematical field, while research in applied math is to use those tools to discover something about nature.

If neuro and/or AI are what you really want to do, then applied mathematics is probably the best route. As Bourbaki1123 mentions, comp sci would be very useful for AI, as well as studying combinatorics (of which graph theory may be taken as a subfield). For neuroscience you'll likely want computational experience, as well as extensive exposure to differential equations (ordinary, partial, stochastic, all of 'em).

I'm thinking the applied math degree because there are more rigorous probability and computer science courses then the pure mathematics course. For anyone who can't find the information I'll write it out:

Probability theory can be taught from essentially a measure theory standpoint alone, and can be abstracted as a pure math. However, sometimes learning stuff too abstractly can make it difficult to apply.

 

[Bourbaki1123]

Anyone here to answer for this? pls do it.

The answer lies in your heart.

 

[simplicity123]

What Mathematics do you need for Algebraic topology?

As I plan to focus heavily on topology and algebraic topology this year. I need to get it down as most of motivation for category theory comes from Algebraic topology. I read that group theory is the algebra used in algebraic topology. Group theory is the worst branch of Mathematics along with metric spaces.

 

[Number Nine]

What Mathematics do you need for Algebraic topology?

As I plan to focus heavily on topology and algebraic topology this year. I need to get it down as most of motivation for category theory comes from Algebraic topology. I read that group theory is the algebra used in algebraic topology. Group theory is the worst branch of Mathematics along with metric spaces.

You may not like it, but group theory is hugely, massively, unbelievably important in just about every branch of mathematics. A lot of people find algebra dry because (to use the computer parlance) it's basically the machine language of math, but even a little knowledge of algebra goes a long way.

You heard correctly about group theory and topology. To give you an example: Just like algebra talks about isomorphisms between groups and considers isomorphic groups to be "the same" in an algebraic sense, topology concerns itself with homeomorphisms between topological spaces for similar reasons. The problem is that actually determining whether different kinds of spaces are homeomorphic is difficult, so topologists look for characteristics of topological spaces that are the same for all spaces that are homeomorphic (if these qualities are different, you know that the spaces are not homeomorphic). These qualities are said to be invariant under homeomorphism (sorry if you know all of this already, by the way). Algebraic topology introduces an invariant called the fundamental group of a topological space, which turns out to be incredibly useful in classifying spaces. The theory underlying the fundamental group, obviously, involves (in a sense) attaching a group structure to space through certain methods (look up "homotopy" if you're interested), and turns out be useful in describing all manner of qualities in topology.

You may not like group theory, but if you topology (or category theory) interests you, you won't regret learning it.

 

[simplicity123]

You may not like it, but group theory is hugely, massively, unbelievably important in just about every branch of mathematics. A lot of people find algebra dry because (to use the computer parlance) it's basically the machine language of math, but even a little knowledge of algebra goes a long way.

Group theory isn't that bad. I suppose don't like number theory aspects of it, however I've gotten used to it now. Is galois theory important for algebraic topology, as after I learn't group theory I could go onto that and take a course in it alongside algebraic topology.

You heard correctly about group theory and topology. To give you an example: Just like algebra talks about isomorphisms between groups and considers isomorphic groups to be "the same" in an algebraic sense, topology concerns itself with homeomorphisms between topological spaces for similar reasons. The problem is that actually determining whether different kinds of spaces are homeomorphic is difficult, so topologists look for characteristics of topological spaces that are the same for all spaces that are homeomorphic (if these qualities are different, you know that the spaces are not homeomorphic). These qualities are said to be invariant under homeomorphism (sorry if you know all of this already, by the way). Algebraic topology introduces an invariant called the fundamental group of a topological space, which turns out to be incredibly useful in classifying spaces. The theory underlying the fundamental group, obviously, involves (in a sense) attaching a group structure to space through certain methods (look up "homotopy" if you're interested), and turns out be useful in describing all manner of qualities in topology.

I do understand what you mean. However, it's only really the number theory aspects of groups I hate, isomorphism isn't that bad. Thats why I like topology so much as you can have two objects that look totally different and they are the same topologically. I'm not going to learn Algebraic topology until after Christmas, but make sure I will look up homotopy then. Thanks for the description, even through can't understand most of it as don't know what homotopy is.

You may not like group theory, but if you topology (or category theory) interests you, you won't regret learning it.

What Maths do I need to learn to do Algebraic Geometry?

As I plan to study heavy algebra=group theory+commutative algebra+algebraic topology+lie algebra. However, wondering do you need analysis like functional analysis to do AG? As I remember reading a book and it was saying to study AG you needed to know sheaf theory, complex analysis, differential geometry.

 

[Number Nine]

What Maths do I need to learn to do Algebraic Geometry?

As I plan to study heavy algebra=group theory+commutative algebra+algebraic topology+lie algebra. However, wondering do you need analysis like functional analysis to do AG? As I remember reading a book and it was saying to study AG you needed to know sheaf theory, complex analysis, differential geometry.

Sheaf theory is huge in AG since it's used to understand schemes, which are basically what AG is all about. AG is such a massive and fundamental subject that just about anything you learn will be helpful, but I'd mainly focus on a strong background in algebra (obviously), and maybe trying to pick up a bit of a background in projective geometry (which is interesting enough on its own). If you're interested in a bit of "recreation", I recommend the book Conics and cubics: An introduction to algebraic curves. It's a very elementary text, but you probably haven't encountered the subject before and it's very relevant to algebraic geometry.

 

[mathwonk]

algebraic geometry is the study of solution sets of polynomial equations. these sets are defined algebraically, and possesses a topology and, if the coefficients are complex numbers, also a complex analytic structure. Moreover they occur naturally embedded in projective space. Thus one can use any of those points of view to study them, algebra, projective geometry, algebraic and differential topology, and complex analysis.

Sheaves are a type of coefficients for cohomology groups that were first introduced to study complex manifolds and spaces, and later applied to algebraic varieties.

In the history of algebraic geometry, the first major step far forward was taken by Riemann, who desingularized plane algebraic curves and then studied the complex manifold structure on the desingularization, as well as the possible ways to re embed that manifold back into projective space as an algebraic variety.

Since that time over 150 years ago, the tools of differential forms and homology theory have been essential to the study of algebraic varieties. Before that time, only the simplest curves such as conics could be well studied.

One can begin to study algebraic geometry without knowing all these tools, by looking at examples and seeing gradually the need for more powerful techniques. For this reason of motivation, it is thus recommended to begin with elementary objects such as plane curves, or the Riemann theory of transforming those into complex analysis as "Riemann surfaces".

Beginning books, requiring few tools, include Undergraduate algebraic geometry by Miles Reid, and Riemann surfaces and algebraic curves by Rick Miranda, as well as Basic algebraic geometry by Shafarevich.

Two useful topics often omitted from undergraduate courses in algebra and field theory are the concepts of transcendence degree and integral extensions. Tr.deg. is crucial in algebraic geometry as it plays the role of dimension, and integrality is the ring theoretic version of an algebraic extension of fields.

Studying sheaf theory before plane curves is like studying calculus before plane geometry. Of course both these phenomena do occur in our strange world. I have attached a pdf file: "naive introduction to alg geom".

 

[Bourbaki1123]

algebraic geometry is the study of solution sets of polynomial equations. these sets are defined algebraically, and possesses a topology and, if the coefficients are complex numbers, also a complex analytic structure. Moreover they occur naturally embedded in projective space. Thus one can use any of those points of view to study them, algebra, projective geometry, algebraic and differential topology, and complex analysis.

Sheaves are a type of coefficients for cohomology groups that were first introduced to study complex manifolds and spaces, and later applied to algebraic varieties.

In the history of algebraic geometry, the first major step far forward was taken by Riemann, who desingularized plane algebraic curves and then studied the complex manifold structure on the desingularization, as well as the possible ways to re embed that manifold back into projective space as an algebraic variety.

Since that time over 150 years ago, the tools of differential forms and homology theory have been essential to the study of algebraic varieties. Before that time, only the simplest curves such as conics could be well studied.

One can begin to study algebraic geometry without knowing all these tools, by looking at examples and seeing gradually the need for more powerful techniques. For this reason of motivation, it is thus recommended to begin with elementary objects such as plane curves, or the Riemann theory of transforming those into complex analysis as "Riemann surfaces".

Beginning books, requiring few tools, include Undergraduate algebraic geometry by Miles Reid, and Riemann surfaces and algebraic curves by Rick Miranda, as well as Basic algebraic geometry by Shafarevich.

Two useful topics often omitted from undergraduate courses in algebra and field theory are the concepts of transcendence degree and integral extensions. Tr.deg. is crucial in algebraic geometry as it plays the role of dimension, and integrality is the ring theoretic version of an algebraic extension of fields.

Studying sheaf theory before plane curves is like studying calculus before plane geometry. Of course both these phenomena do occur in our strange world. I have attached a pdf file: "naive introduction to alg geom".

Mathwonk, I'm sort of fishing for motivation to some extent, but I'm wondering how much time (average hours per day/number of months/years) it took for you (as best you can recall) to go from a basic level of understanding of some notions in commutative algebra (part way through Atiyah McDonald or Zariski Samuel or what have you) to a strong, or at least reasonably solid, grasp of the Grothendiek approach and the fundamental results/areas of the field.

 

[mathwonk]

my personal history is probably not relevant but may be instructive anyway.

i began as a star high school math student in the south and got a merit scholarship to harvard. as an undergrad at harvard i could not easily adjust to the need to study everyday and flunked out. i returned and worked hard at studying and attending class and made A's by memorizing proofs in advanced calculus and real analysis and got into brandeis.

I knew almost nothing of algebra, commutative or otherwise, but hung in for a while on talent and tenacity until asked to leave brandeis too.

then i taught for four years and studied differential topology and advanced calculus and returned to grad school at utah. there i studied several variable complex analysis for one year and returned to riemann surfaces the second year.

i wrote a thesis in riemann surfaces and moduli and took a job at UGA. Then I worked hard at learning as much algebraic geometry as possible. i still knew relatively little commutative algebra (and still don't).

i made a living off my grasp of mostly several complex variables, also differential topology, and algebraic topology.

after my third year I went to harvard again as a postdoc and devoted myself to every word dropping from the lips of mumford, griffiths, and hironaka.

those two years gave me a tremendous boost. then i returned to UGA and benefited enormously from collaboration withf my brilliant colleague Robert Varley.

I still hope to master commutative algebra.

 

[sentient 6]

sorry to be off topic, but I was just wondering if anybody had any book suggestions for an introduction to number theory. I have been thinking of getting G.H. Hardy's Intro, but I thought it'd be good to ask before investing.

 

[Intervenient]

I just feel like I don't have the confidence for math, statistics in particular. I'm easily intimidated.

 

[mathwonk]

did you see lonesome dove? remeber the scene where the woman with the horse farm hires the ex sherrif? she says: "so you never been nowhere but arkansas and you never handled horses. but you ain't stupid and you ain't nailed down are you?"

get the point? you are as good a man (or woman if that is the case, but i doubt it) as anyone else. believe that.

 

[Bourbaki1123]

my personal history is probably not relevant but may be instructive anyway.

i began as a star high school math student in tennessee who got a merit scholarship to harvard. as an undergrad at harvard i could not easily adjust to the need to study everyday and flunked out.\\i retiurned amnd worked hard at studying and attending class and made A's by memorizing proofs in advanced calculus and real analysis and got into brandeis.

I knew almost nothing of algebra commutative or otherwise, but hung in for a while on talent and tenacity until I was asked to leave brandeis too.

then i went to teach for four years and studied differential topology and advanced calculus and then returned to grad school at utah. there i studied several variable complex analysis for one year and returned to riemann surfaces the second year.

then i wrote a thesis in riemann surfaces and moduli and took a job at UGA. Then I worked hard at learning as much algebraic geometry s possible. i still knew relatively little commutative algebra (and still do).

i made a living off my grasp of several complex variables, differential topology, algebraic topology, homological algebra, and category theory and sheaves.

after my third year I went to harvard again as a postdoc and devoted myself to every word dropping from the lips of mumford, griffiths, and hironaka.

those two years gave me a tremendous boost. then i returned to UGA and benefited enormously from collaboration withf my brilliant colleague Robert Varley.

I still hope to master commutative algebra.

Interesting. In your experience do most algebraic geometers come from a commutative algebra background? I had always gotten the impression that this was standard but I'm generalizing from a limited pool of examples.

Also, do you know if it's reasonably common for students coming into U Georgia who want to do algebraic geometry to have already gotten through something like Eisenbud's Commutative Algebra? I ask because I'm on the third chapter now, and I plan to be reading/doing problems in Hartshorne (other than just the first few segments of the first chapter, which is where I am now) by the time I enter grad school so I want to know if this would put me in good stead.

Lastly, I would be interested in hearing your advice on the following issue of mine:

Unfortunately (or perhaps fortunately?) I have a many areas of interest;
proof theory and constructive categorical logic/ stuff in cartesian closed categories, lambda calculus stuff etc and Model theory (to a lesser extent, for sure) on top of algebraic geometry, but to further complicate this, I also am immensely interested in the philosophy and history of mathematics, evolutionary psychology, machine learning (especially reinforcement learning, also I've been reading about the application of TD reinforcement learning to hebbian learning in dopaminergic neurons), decision theory as it applied to AI, rational choice theory, foundations of statistics (I'm a Bayesian ;p), social impact of future technology a la the work of Nick Bostrom (and Oxford's FHI more broadly), neuroeconomics, metaethics, computational neuroscience (spike train statistics and neural codes seem very interesting), the cognitive science of mathematics (I'm looking for something vaguely like Rafael Nunez's work with Lakoff, but more rigorous); the list goes on and on really.

I am become the inverse of the one-dimensional math nerd, destroyer of... hurdles? More like focus/opportunity, but it doesn't fit as well in the allusion. Needless to say, I did not focus solely on math for the duration of my undergraduate career. I've got quite a bit of anxiety about having to choose what to focus in on, and I've even toyed with the idea of taking the gamble of getting a philosophy PhD for the super slim chance that I find the right connections to get a professorship somewhere that will to some extent let me learn and publish papers about the ideas that I want to learn and publish papers about. However, I've come back to reality, and know that this will almost certainly not happen.

So, I don't know, is there any sort of advice you could offer upon hearing my spiel? Will I at least still have some time to continue to study areas other than my particular focus when I'm in grad school?

 

[Number Nine]

also I've been reading about the application of TD reinforcement learning to hebbian learning in dopaminergic neurons), decision theory as it applied to AI, rational choice theory, foundations of statistics (I'm a Bayesian ;p)

We have much to discuss then. I'm rather knowledgeable about the midbrain dopamine/basal ganglia circuitry and its involvement in reinforcement learning, so feel free to send me a PM if you have any questions.

ps -- I too am a bayesian. One day we will topple the hegemony of the null hypothesis significance test.

 

[mathwonk]

bourbaki, i think you know more than the average entering student.

 

[simplicity123]

Might as well ask about Analytical number theory since got good advice about AT and AG.

But, what branches of Maths should I learn if I wanted to work on the Riemann Hypothesis?

As I know should have down, complex analysis, algebraic geometry, non commutative geometry and ofcourse number theory. But, I was reading a book and it was saying stuff like you needed to know quantum mechanics and quantum chaos. I should know basic chaos theory and I could probably get a lecturer to teach me quantum mechanics or help me with it. But, I don't want to learn Physics because Marcus Du Sautoy was saying that it could solve RH.

I read that statistical physics was being used in P versus NP.

 

[mathwonk]

the probability that you, or anyone else, like andrew wiles, will solve the riemann hypothesis, is very low. so it makes no sense to base your whole life or career on that.

just prepare for a career in number theory and hope for the best.

 

[simplicity123]

the probability that you, or anyone else, like andrew wiles, will solve the riemann hypothesis, is very low. so it makes no sense to base your whole life or career on that.

just prepare for a career in number theory and hope for the best.

I don't believe in probability. I will either prove it or not. I doubt it be luck that proves it.

Surely I should be going into analysis? Like harmonic analysis or something like that. According to a book I read the best approach to RH is from Connes and non commutative geometry. So confused as hell on what to study.

 

[weld]

And also, when researching in theoretical mathematics, since you don't have a lab, do you still have duties such as administration, grant writing, etc? Do you end up spending more time on teaching due to the absence of lab? I really would like to know this.

Also, anyone got an opinion on working as semi-perma postdoc and staff scientists? I wonder if they're worth it or not. Again I would like to know if such positions exist in theoretical mathematics. Any information on how it is to be working as a theoretical, or heck, even applied mathematician would be great. I really need to find facts on it to decide for myself if I really want to commit to it or not. I also appreciate if you can estimate how much time (In %, if possible) is spent on miscellaneous and boring things like doing paperwork and other forms of busywork. I would love to avoid that to the greatest possible degree. Does theoretical computer science really differ a lot from theoretical mathematics in these regards? What about theoretical physics?

Finally, where can I find information on becoming a logician? Is it even a field to do research in? I'm also curious as to how much time is spent on busywork and the like.

 

[mathwonk]

Van den Eynden has a nice intro to number theory.

 

[Robert1986]

So I've been reading several threads on this board with the common theme that it is almost impossible to get into academia as a Physicist. Is the outlook for mathematicians as dismal? I am graduating in May, and obviously I am looking toward my future career. From what I gather, I have three options:

1) Get a Ph.D., and attempt to get a job as a prof, somewhere, anywhere (assuming that it is as difficult to get a job for a mathematician) or do something in the private sector.

2) Get a Master's Degree and plan on teaching high school (or doing something else, but I think I could get a job teaching high school). If I do this, I think I can find some private schools that would hire me to teach while I worked toward my master's. (In my state, I could, in theory, get a job at a government school, as well.) If I do this, I think that I could have a reasonably fulfilling career. Other than time, there is really nothing that would keep me from doing research, anyway. Additionally, I could try to teach part-time at a community college.

3) I am applying to some programs that pay students to get Specialized master's degrees while teaching in a public school. If I could get into such a program the benefits are nice, and I would get about 18 hours of actual graduate-level math credit (the other being "learning to teach" classes). This would allow me to teach high school and possibly part time at a community college. The upside is that I would be allowed to teach in any government or private school and my pay would be pretty good (for a teacher.) The downside is that I would miss a lot of the graduate level math classes. So, if I get a Ph.D., what are my chances of getting a job as a prof? Is it as dismal as it is for physicists? Do you more experienced guys have any advice? What about you younger guys, you are probably facing something similar with similar alternatives, have you thought of anything else?

 

[Bourbaki1123]

I don't believe in probability. I will either prove it or not. I doubt it be luck that proves it.

Read this: http://omega.albany.edu:8008/JaynesBook.html"

It isn't good to ignore the fact that probability theory is a necessary ingredient of highly rational thought.

 

[Bourbaki1123]

So I've been reading several threads on this board with the common theme that it is almost impossible to get into academia as a Physicist. Is the outlook for mathematicians as dismal? I am graduating in May, and obviously I am looking toward my future career. From what I gather, I have three options:

1) Get a Ph.D., and attempt to get a job as a prof, somewhere, anywhere (assuming that it is as difficult to get a job for a mathematician) or do something in the private sector.

2) Get a Master's Degree and plan on teaching high school (or doing something else, but I think I could get a job teaching high school). If I do this, I think I can find some private schools that would hire me to teach while I worked toward my master's. (In my state, I could, in theory, get a job at a government school, as well.) If I do this, I think that I could have a reasonably fulfilling career. Other than time, there is really nothing that would keep me from doing research, anyway. Additionally, I could try to teach part-time at a community college.

3) I am applying to some programs that pay students to get Specialized master's degrees while teaching in a public school. If I could get into such a program the benefits are nice, and I would get about 18 hours of actual graduate-level math credit (the other being "learning to teach" classes). This would allow me to teach high school and possibly part time at a community college. The upside is that I would be allowed to teach in any government or private school and my pay would be pretty good (for a teacher.) The downside is that I would miss a lot of the graduate level math classes.


So, if I get a Ph.D., what are my chances of getting a job as a prof? Is it as dismal as it is for physicists? Do you more experienced guys have any advice? What about you younger guys, you are probably facing something similar with similar alternatives, have you thought of anything else?

A friend of mine worked for the EPA for a while and mentioned that being a statistician at the EPA is a pretty cushy job and it isn't too impossible to find an opening if you've got your PhD.

I was under the impression that I would have to sacrifice quite a bit to find a job opening in academia and that even at that it's far from a sure thing, even at more of a teaching university. That said, since I'm still young I'm convinced that I would be perfectly happy getting paid dirt so long as I can get away with doing what I love.

 

[simplicity123]

A friend of mine worked for the EPA for a while and mentioned that being a statistician at the EPA is a pretty cushy job and it isn't too impossible to find an opening if you've got your PhD.

I was under the impression that I would have to sacrifice quite a bit to find a job opening in academia and that even at that it's far from a sure thing, even at more of a teaching university. That said, since I'm still young I'm convinced that I would be perfectly happy getting paid dirt so long as I can get away with doing what I love.

Stats is different. http://gowers.wordpress.com/2011/07/26/a-message-from-our-sponsors/
If you read this you will see that funding for stats is going to increase(even through it has the biggest slice of funding already) and yet everything else is waiting to see if funding is going to increase or decrease. Postdoc funding is only going to stats. Pretty depressing read.

I think that's good. Everyone who has amazing grades will likely go into banking or finance as academics is crappy pay with no job security. Plus you need to more every two years for a long time.

 

[Bourbaki1123]

Pretty depressing read.

Unless you like stats and have an interest in artificial intelligence and rational choice theory and computational neuroscience.

ETA: Or if you don't live in the UK (I'm in the USA) then it has relatively little impact, all of it being indirect.

 

[simplicity123]

Unless you like stats and have an interest in artificial intelligence and rational choice theory and computational neuroscience.

ETA: Or if you don't live in the UK (I'm in the USA) then it has relatively little impact, all of it being indirect.

Well, logic is the least funded Maths in England, which I think will be the same in the US. Plus you are talking about computer science which isn't Maths.

I'm thinking of doing a PhD in US because I read it's easier to get funding as they need a lot of people to teach calculus and linear algebra.

I don't know through. My grades will probably be a first this year, however I read that in the US it is much better. That there is more funding and better university overall because of high fees.

 

[Bourbaki1123]

Well, logic is the least funded Maths in England, which I think will be the same in the US.

Logic is not terribly well funded, yes. It is one of the areas I would like to go into, so that is a bit unfortunate. That said, I'm also interested in cognitive science and algebraic geometry, though the latter probably doesn't bring in the most funding either (the former, I would expect to bring in much more).

Plus you are talking about computer science which isn't Maths.

It depends on what exactly you're doing.