BS/MS Math Degree and Grad School

[Geust]

I'll be starting The latter half of my math degree this upcoming Fall term, and while checking some prerequisites for my degree, I realized that I can turn my BS into a BS/MS by adding one more year and a few graduate courses.

Now, I've been a bit confused about PhD programs and their preferences for non-graduate students taking graduate courses. So my question is, would grad school prefer the BS/MS over the BS? Is an MS necessary for grad school? With the BS/MS I will be taking grad level analysis and algebra after taking modern analysis and modern algebra, both of which are one semester courses. If I stuck with the BS route, I'd only take modern analysis and modern algebra; is this enough for grad school?

 

[Geust]

Do grad schools prefer students who come in with an MS?
The MS would include two semesters of intro analysis and two of algebra and one semester of real analysis.

 

[Geust]

Bump, input is appreciated, even if it's anything about a mathematics masters and/or PhD.

 

[bhobba]

Where are you? That's a big factor.

In Australia, and some other countries such as England based on the British system, to do a PhD you need to do either an honors year or a Masters. However if you do an honors year you have to get a first class or high second class degree. If you do a masters that's not required - but of course if you just scrape through you probably won't find admission easy.

I was in the same boat - my professors wanted me to go on and do a PhD but advised not to do an honors year but a Masters instead - that way you don't have push yourself to get high honors. I decided to go to work instead so it didn't matter.

If you are in the US you can do a Phd straight after your degree. However I personally wouldn't do that - I would deepen my knowledge first with a Masters. Phd's are hard - no need to not make it as easy on yourself as possible. My understanding is, in the US, with a Masters it will reduce the time of your Phd but I am no expert in the US system so don't hold me to it.

Thanks
Bill

 

[Geust]

I'm in the US.

I don't think there's need for an honors year over here.
But it would make sense that a master's would shorten the length of your PhD, if you take classes pertinent to your PhD.

Also, there's an option for an "honors thesis" for a bachelor's degree at my uni which gives you the designation of "Honors in Mathematics" at graduation. You can also take 6 credits of graduate level courses to get this distinction.

But yeah, I hope someone from the US can confirm the master's reducing the length of one's PhD.
Thanks for your input.

 

[bhobba]

Also, there's an option for an "honors thesis" for a bachelor's degree at my uni which gives you the designation of "Honors in Mathematics" at graduation.

One thing I can confirm, whether it's done in your Bachelor's, or in a Masters, is a research thesis is ALWAYS looked on favorably for admission to a PhD regardless of where you want to do that PhD. This is the reason countries like Australia require it - the Honors year and all but a few coursework Masters have a significant research component - they want to see proof of your aptitude for it before admission. And besides wouldn't you really feel more comfortable haveing a bit of research experience under your belt before undertaking the major amount of research for a PhD?

For example check out:
http://www.math.illinois.edu/GraduateProgram/GraduateGuide.pdf
'For Ph.D. degree candidates, what is most desirable is some experience beyond coursework such as can be found in undergraduate seminars, summer REU programs, summer intern programs, or undergraduate thesis work'

Thanks
Bill

 

[Geust]

I actually was planning to do an honors thesis for the precise reason you mentioned, to have the experience of mathematical research before graduate school. I was also planning to do one summer of a REU program. On top of that, I was planning to attend as many seminars as possible since I feel that I'd find them interesting.

Now on a tangentially related note, what analysis classes are included in a math sequence in Australia? At my college, one would take a one semester modern analysis class first (at this point your bachelor's requirement for analysis has been fulfilled); this course uses a book like Spivaks. Then, there are two semesters of "introductory analysis," a graduate level sequence that would use a text like Principles of Math. Analysis by Rudin. After this, one can take real analysis.

When people talk about undergrad analysis requirements, they never mention the modern analysis course. So, I was wondering: is there such a course commonly found in Australian colleges? Is it just advanced calculus? The reason I'm asking is because I'm deciding on whether or not I should skip it; I've been studying through analysis on my own with Rudin and supplements, and I was wondering if it's a critical course.

 

[Mmm_Pasta]

A PhD in the U.S. is roughly 5-6 years. The first two years is spent taking coursework that is equivalent to a master's. The rest of the time is spent on research.

 

[Geust]

Alright, so the BS/MS should save me one year, assuming it covers the courses necessary for my PhD and the credits for my MS are accepted by the PhD program I choose.

Would a PhD program prefer that I take the courses beforehand? Or is it necessary that I take them in the program?

 

[bhobba]

Now on a tangentially related note, what analysis classes are included in a math sequence in Australia?

Oh - this is a touchy one.

First I personally do not think you can call yourself a mathematician unless you have done at least real analysis, colloquially called doing your epsilonics.

In Australia while at high school you generally do the equivalent of US Calculus 1, you do US Calculus 2 first semester university. When I did it second semester, after Calculus 2, you did real analysis (like it or not - no escaping) then Mulitivariable Calculus first semester second year. Third year you could do more advanced analysis in the form of a course offered to both graduate and undergraduate students - Analysis A and B - they were basically on Lebesgue integration, Hilbert spaces and applications. I did Analysis B - they excused me from Analysis A because I was considered a good student (translation - willing to work) and studied it during the semester break by myself. My school was good like that. I did mathematical economics which you are supposed to have done introductory macro and micro economics but waived it if I did some reading in the break. It was a cool subject - I was the only student. Analysis B was cool as well - there were 3 of us.

People however loathed it - they were always complaining - why do I have to study this yucky useless stuff and the place I went to (QUT in Australia) succumbed and removed it. Now what you do first and second semester first year is a combination calculus 2, with an introduction to differential equations, linear algebra and mulivariable calculus thrown in. You complete the studies of those area's second year, but it allows you to do subjects like Statistical and Mathematical Modelling that require a smattering of knowledge of those areas second year before the detailed study - normally you would need to wait until third year to do it. And analysis had been combined into one subject done only at graduate level - although good students can partition to take it undergrad.

To me this is deplorable and a shameful dumbing down of the curriculum. But these days universities are responsive to students demands - students wanted the back of it and the university obliged.

Thanks
Bill

 

[bhobba]

A PhD in the U.S. is roughly 5-6 years. The first two years is spent taking coursework that is equivalent to a master's. The rest of the time is spent on research.

That is different to Australia - its entirely research based and takes three years - but from what I hear virtually no one does it that fast - 4 years is more common. I suspect this is the reason for the higher entry requirements and why I think with a Masters you may be able to shorten it in the US.

Thanks
Bill

 

[Geust]

Alright, so it seems to me that my plan to take intro analysis by skipping modern analysis would be analogous to your original curriculum for third year students considering that I am a junior myself, which further encourages my decision.

But I also wonder-- what did you work in such that they allowed to to waive certain classes? Were you also a good student in other regards which, coupled with willingness to work, allowed you to skip a few steps?

 

[bhobba]

But I also wonder-- what did you work in such that they allowed to to waive certain classes? Were you also a good student in other regards which, coupled with willingness to work, allowed you to skip a few steps?

I was a straight honors student. I don't know what its like in the US but here in Australia you can take a subject either by having done the pre-requisites or have the permission of the instructor. That permission was generally given for good students without the pre-requisites if you did some pre-reading.

The reason I was a straight honors student is I worked my butt off. That's one way to do it. There were other students that nearly got straight honors and had a much more relaxed attitude. They were the ones I envied - it came so natural to them.

Thanks
Bill

 

[Geust]

That does remind me, the courses can be taken either after prerequisites or "with permission of instructor." This would pose a problem for me since I am new to the university, and have not seen or met with any potential professors.

Also, what do you mean that you were a straight honors student? Was it a title given for good grades?

 

[bhobba]

Also, what do you mean that you were a straight honors student? Was it a title given for good grades?

Back when I did it, those many moons ago, you had 5 grades - fail, pass conceded, pass, credit and honor. When I said I was a straight honor student I got nothing but honors. By a nearly straight honors student it is meant one that gets mostly honors with a few credits scattered about. Either type of student is considered good, and are generally taken under the wing by professors who will do stuff like waive pre-requisites and allow you to work with them final year on research.

Now its a bit different - you have 7 grades given as 1 - 7 - 1 and 2 are a fail, 3 a pass conceded, 4 - pass, 5 - credit, 6 - a distinction and 7 - high distinction. From what I can gather getting consistently a high distinction is very rare these days - not like in my time when a few students got all or mostly honors. The other thing I have been told that changed is the ability to ask questions that extend the coursework on exams. This makes it much harder as well. Before they never did that - it was simply similar questions to what you did in the tutorials and class. From what I can gather the reason for that is you generally extended it in assignments but too many people simply copied off others so to see if students could do it they did it on exams. I am not in favor of that because an exam is an artificial situation and what you are doing is testing if people can think under exam conditions - not if they know the material. But still you need to see somehow if they can extend it so I guess its all they could really do. Bottom line - its now a LOT harder to do really well than when I did it.

I believe the US is a bit different again - you have 1-4 grades - I think a 2 would be a pass - a 3 a credit and a 4 an honor. I don't know if they have this idea of extending people during exams or not.

Thanks
Bill

 

[Geust]

Ah, I see. Actually, in the US the grades are either F, D, C, B, or A, where F and D are fail, C is just passing, B is passing, and A is passing with higher marks. So you were practically a straight A student.

And I am not sure if they extend coursework on exams, although I'm leaning towards the idea that they do not.

Another question: when did you take algebra? I'm planning to take it after analysis, but it seems to come before it in come colleges, and after in others. In my opinion, it seems tougher than analysis.

 

[bhobba]

Another question: when did you take algebra? I'm planning to take it after analysis, but it seems to come before it in come colleges, and after in others. In my opinion, it seems tougher than analysis.

What algebra do you mean? I did modern algebra (introduction to groups, rings etc) and linear algebra first year, applied linear algebra second year. They had an advanced algebra subject but I didn't take it. I did do some research work with one of the lecturers on computer error correcting codes that had some more advanced algebraic stuff to do with irreducible polynomials but don't ask me anything about it now - forget all of it.

Thanks
Bill

 

[Geust]

That's what I meant, modern algebra and graduate algebra found after it.
But I'll probably end up worrying about graduate algebra near the end of my BS/MS-- for now, I'll work on intro analysis and real analysis.

Thanks for all your input thus far!