Should I Become a Mathematician?

[arshavin]

You could have just applied to a better uni- USYD, Melbourne, ANU are all fine(I go to UNSW and find the courses quite decent). University admission requirements in Australia are almost nonexistent(high school curriculum is a joke) and you could go anywhere you like.

 

[majesticman]

I had a similar quandary as well...i was planning for a Phd in Applied Mathematics ...i am from australia and currently doing a double degree involving electrical engineering and Commerce (majoring in mathematical econometrics)...from Monash Univ in melbourne

The things i needed clarification on were if i would be better advised spending a semester here doing "pure math (like advanced algebra and stuff)" units or should i apply straight after i finish my course. And are people doing straight maths majors preferred over people who come from my sort of background

 

[PhysicalAnomaly]

I did get into Melbourne but turned it down at the last minute. At the time, I was actually more interested in engineering. The melbourne model offers little flexibility and Monash is apparently better for engineering. I had other reasons as well but those are some. If I were at Melbourne, my interest in maths might never have been rekindled. Not to mention that I've been told by people who've been to both (transferred from one to the other after half of their degree) that Melbourne does have a little more pressure involved but in terms of course content, style and quality, they are quite similar. I could transfer but the difference between universities isn't big enough to justify it. You're right in saying that the high school curriculum is a joke but I would go further and say that before you reach at least honours and graduate stuff, it's quite a joke too. Compare with the stronger US and UK universities and you'll see what I mean.

I've gotten used to the standard actually. I compensate by doing a lot of self-study and I plan to take directed study units later on.

My big question now is: how will spending 2 extra years getting an engineering/science double degree affect me and will it be worth it? Would the engineering qualification and knowledge help me in any way if I decide to do a PhD in mathematics (or physics)? Or would a 2 year head start be much more advantageous?

 

[||spoon||]

I'm no expert by any means, but I have been having similar thoughts regarding engineering and physics, so i know what you mean.

If you want to go into engineering, but enjoy maths too much to give it up, perhaps there is a concurrent diploma of maths you could enrol in, might be worth looking at.

If you want to do maths i don't really see how engineering would help. Maybe someone else has actual experience or other ideas though.

-Spoon

 

[mathwonk]

i suspect engineers have experience reasoning about real phenomena, and are not as subject to the falsity that math is completely abstract. it could help them to deal with math research as something you can actually get your hands on. i believe the great topologist raoul bott, recently deceased, had been an engineer before his career as a mathematician.

 

[mathwonk]

a quote from bott:

"We had a lab where we tried to make very primitive things,
such as a microphone. We enjoyed creating
sparks, and we wanted to know how gadgets
work. So I think this was closest to what really
makes a mathematician—someone who likes to
get at the root of things."

interview by Allyn Jackson, senior writer and deputy editor of
the Notices. Her e-mail address is axj@ams.org.

 

[PhysicalAnomaly]

Strange how one semester can change one's goals. While it's true that I started the double degree with engineering as the first priority and with the science just because I didn't have the heart to leave it behind, the situation is now reversed. I'm very keen on science (maths and physics) and just clinging on to engineering because I'm reluctant to give it up.

As an aside, the physics, chemistry and some maths classes and exams are actually more difficult and challenging than the engineering ones. Science has the longest hours too. I would have thought that it'd be the other way round.

Looking at Bott's wiki, I would say that I'm thoroughly impressed. He went from completely applied stuff to the most abstract maths in a heartbeat. It seems studying engineering alongsides maths won't be a waste.

 

[zoner7]

It makes sense that if you want a PHD in math, you should study math. Engineering and mathematics are two different fields for a reason. Now, if you are worrying about marketability, I doubt that a lot of the theory math will do you any good, and this pure math is primarily what you will be learning as you work towards your PHD. Ultimately, the further you delve into a single field, the further they diverge from one another. Sooner or later the overlapping material between the two fields will be nil.

The world is all about specialization today. You are supposed to be good at one thing; this is what makes you marketable. If two Clearly, if two fields augment one another, you will be more marketable. But a PHD in mathematics and engineering stray quite a bit from one another after a while.

 

[PhysicalAnomaly]

A very good point. I guess the problem is that I don't really know for SURE that a PhD in pure maths is what I want. What if I change my mind or find that maths research isn't what I felt it would be? But solving for maximum flexibility means that compared to someone who's spent all that time on maths alone, I will be shockingly behind.

 

[samspotting]

How much overlap is there between pure math and cs?

 

[Werg22]

^^^
From what I can tell, the areas of mathematics with the most relevance to CS have to do with discrete math, number theory, graph theory, etc. I'm not sure if logic is usually included in the pure math spectrum, but it constitutes the mathematical foundation of most of CS.

 

[||spoon||]

A very good point. I guess the problem is that I don't really know for SURE that a PhD in pure maths is what I want. What if I change my mind or find that maths research isn't what I felt it would be? But solving for maximum flexibility means that compared to someone who's spent all that time on maths alone, I will be shockingly behind.

I know that at melbourne uni you can do a degree with a major in maths, but then do an extended masters in engineering. All up it still takes 6 years but you would be able to major in maths first, decide afterwards whether you wish to continue with maths and do grad study in that field. If you have a change of heart decide maths isn't for you, you still have the engineering option open.

Perhaps there is a similar option where you are currently?

-spoon

 

[mathwonk]

obama's win tuesday reminded me of the circumstances surrounding some of my low grades in school. as a senior in college i skipped hour exams to march with martin luther king jr. sometimes there are things that rate higher in priority than studying. you can always learn what a holomorphic function is, but cannot always march to help change history.

 

[majesticman]

The employmentability (is that a word?) of an engineering degree is what keeps me in this course because i can't be sure as to weather applied math research will be the "thing" for me...

am i coreect in assuming that a math phd takes 5 years??..with the first 2 years usually involving grad classses to pass the qualifying tests and then the next 2-3 aimed at math research?

 

[PhysicalAnomaly]

I believe the word you are looking for is 'employability'. XD

In a similar situation to me, eh? Except that in my case, I'm afraid that I might actually find that I prefer engineering later on.

I did consider that option, spoon. But the way that the melbourne model is put together just means that your science degree major has to be a major in engineering systems for you to be able to do that masters in engineering. Completely defeats the purpose.

 

[majesticman]

Yeah i agreee about the melbourne model...it just seems to be just giving the same courses over an elongated period of time...

I am not saying i don't enjoy engineering and econometrics ...i really like it...but i think i am ever going to pursure a Phd it would have to be in maths as that what i seem to prefer..as it is both of these fields rely heavily on maths of some form or the other...

I am more interested in applications of mathematics rather than a "pure" component <i know that sometimes these lines are blurred> that's why i am continuing with my present course over a math major in science..
What about you?

 

[PhysicalAnomaly]

I'm in a double degree - one engineering degree and one science with a major in maths and a major in physics. It's 6 years long with an honours in each though.

 

[||spoon||]

I believe the word you are looking for is 'employability'. XD

In a similar situation to me, eh? Except that in my case, I'm afraid that I might actually find that I prefer engineering later on.

I did consider that option, spoon. But the way that the melbourne model is put together just means that your science degree major has to be a major in engineering systems for you to be able to do that masters in engineering. Completely defeats the purpose.

actually that's incorrect.

You can go into the elongated masters of engineering with ANY major, doesn't even have to be in science.

I know this sounds odd, it did to me as well so i asked a course advisor and its true. I was having the same trouble as you but with mathematical physics/physics major rather than maths major. I.e I love physics but not certain wether to major in it for a few reasons including employment and not knowing enough about research to know if I would like it.

When I heard about this aspect of the masters of engineering I couldn't believe it, so went and asked, turned out to be true, solved all (well most) of my problems. My plan now is to major in physics or mathematical physics whilst leaving open engineering in case I don't like research or whatever.

-Spoon

 

[majesticman]

If what spoons says it's right then it's amazing that someone can be awarded an engineering degree after any sort of major especially if that has nothing to do with engineering or science. I suppose you do pay a time penalty

@physicalanomaly

i thought an engineering/science science allowed for only 1 major in science...what are the extra requirements for a honors program...I almost enrolled in that degree program but at the last minute changed my mind to do a Engineering/Commerce degree.

 

[Proton Soup]

engineering is practically a math minor. and even as an EE student, i had to take a lot of other coursework not directly related to EE. not only art, language and social science, but civil, mechanical, and materials engineering courses to make us more 'well rounded'. so a huge amount of your degree is spent doing 'other'.

within EE, you have a lot of diverse coursework that isn't too related: controls, electromagnetics, electronics, digital, power and machinery... a huge amount of your degree-specific work is spent getting a broad base.

when you get to the graduate level, a lot of it is just pure math, applied. maybe a course or two of undergradute work would get you up to speed. the bigger issue may be learning to think the way engineers do. I'm not sure it'd be appropriate for someone with a degree in english lit. it would have to be very elongated. like a couple of years extra.

 

[PhysicalAnomaly]

It allows for two majors. Engineering comes with an honours (assuming you do well). A science honours just needs a distinction average in your major I think. Which university do you go to, majestic?

That's EE though which is well-known for it's mathematical load. I think chemical eng maths is just lots of PDE's and ODE's. Which is probably not very relevant when it comes to pure maths.

 

[||spoon||]

I thought honours took extra time...?

 

[PhysicalAnomaly]

Engineering is a four year course and you get an honours if you do well. The fourth year is mostly research and capstone units anyway. For arts and science degrees, you have to tack on the fourth year for an honours. The double degree is 5 years long and tacking on a science honours for a double honours makes it 6 years. Which is a very long time to stay in undergrad. :(

 

[majesticman]

I did'nt know you could get and honors in engineering just by doing well (how well are we talking??..80+ avg.?) ...i thought it was a extra year of something like that...i am EE major in engineering and i can vouch for the fact that they have a lot of maths in EE

i was thinking abt just doing some of the unit that people do as math major sequence to get more exposure...

@physical
i am at Monash doing Engg/Comm...don't worry i will stay an undergrad for 5.5 yrs so i know what your are going through...the most annoying thing is to see people doing single degrees move onto a job or whatever...

 

[JG89]

Here's another free linear algebra book:

Introduction and table of contents:

http://www.math.brown.edu/~treil/papers/LADW/LADW_intro.pdf


Text of the book:

http://www.math.brown.edu/~treil/papers/LADW/LADW.pdf


I got it from this website: http://www.math.brown.edu/~treil/papers/LADW/LADW.html

 

[samspotting]

An engineer would not find it very hard to go into applied math, but I don't think engineers do anything in the way of pure math.

 

[Proton Soup]

yeah, it's hard to find motivation in pure math

 

[samspotting]

Funny, for me its the other way around :p

 

[Ivalice]

Sorry to bother anyone, and it's entirely possible that this question has been asked in one of the other 120 posts, but I was looking at a biography of Ramanujan, which said that one book he worked from was George Shoobridge Carr's book "Synopsis of Pure and Applied Mathematics" (1886). Apparently this contains loads of formulas and theorems but without proper or complete proofs. I tried to locate a copy but the only ones I could find were more than £80 or were in University libraries for reference only. Can anyone point me to an online copy of it, or to another work in a similar style, as I would be interested in having a go at proving at least the first few ... Thanks in advance

 

[samspotting]

http://books.google.ca/books?hl=en&...=X&oi=book_result&resnum=1&ct=result#PPA14,M1

Is this what you are looking for? It doesn't look that friendly...

 

[Vid]

Dover will be reprinting Paul Cohen's classic text on set theory next month..

https://www.amazon.com/dp/0486469212/?tag=pfamazon01-20

Personally can't wait for this. I'll probably preorder it sometime this month.

 

[samspotting]

How does that compare to the book I was going to read, naive set theory.

 

[mathwonk]

the way "naive" compares to "sophisticated".

halmos's book is an introduction to the language of sets intended for the beginner. I read some of it in high school and liked it.

I believe cohen's 1966 book is the revised notes from his harvard graduate course (math 280) in about 1964-5, introducing his latest ideas ("forcing") that solved the famous continuum hypothesis, probably mentioned in halmos's book as a major unsolved problem.

Cantor proved that the set of real numbers has a larger cardinality, or size, than the set of integers, and conjectured that every subset of the reals has the same cardinality as one or the other of these two sets. Cohen proved that this question cannot be decided.

both books are good, one is beginning, one is advanced. you might reasonably get both.

 

[Ivalice]

Thanks samspotter, just what I was after. Yeah, you're right it does look a bit intimidating

 

[arshavin]

Quick Question-

Is it essential to have a network of math friends/teachers as a student?

I just finished 2nd year of undergraduate math and I've pretty much been on my own so far.