Rant about University Mathematics

[Gib Z]

Hello PFers. This may be not strictly the best forum to place this thread, but I thought my audience at General Discussion wouldn't be able to discuss this as well as the Math forum. If a Mod decides its more appropriate somewhere else, feel free to move it. Anyway, After 3 and a half years hearing people talk about it here, I have finally experienced my first month of University! Many things I have hoped would be true have indeed been true: The level of freedom is quite good. Attendance is not logged strictly so I don't have to waste as much time anymore. We can eat in class. Theres many more, but I'm not ranting to talk about those.

I'm ranting because the way they are teaching irritates me. For one, I can not find it within me to learn a little bit of a topic from one book, learn another bit from a completely different author in another book, skip a few topics from the books, learn them in a jumbled order. Learn the theory from here, but do the exercises from there.

I know I sound OCD, but I think people here might understand. Never before in my life have I studied mathematics in this jumbled way. It ruins the point of a textbook, which you progress through in the order set out by the author, and whilst you do so, you learn his/her technique, writing style, methods, and you complete the journey through the subject they made for you, enabling you to come out with a well formed, logical and structured view of the topic from a certain viewpoint.

Mostly importantly to me is the ability to see the subject clearly from a certain viewpoint, as if you have some godly birds eye view, rather than be on the ground in the murkiness of jumbled learning. From the reviews on Amazon, if you want a geometric treatment of Complex Analysis, you can get Ahlfors. If you like power series better, you might get Lang. Different authors often have completely different approaches. How do they expect us to somehow understand a topic clearly when we have to struggle to link one aspects of the theory to the others?

Another thing I'm not liking in the skimpyness of the courses. Perhaps this is how it is everywhere, but pretty much every course my maths dept offers should have "A brief introductory exposition of" added to the title. Is it normal to only cover half, or even less, of the topics that a standard textbook of that subject contains? It can't be.

Obviously, much of what I have just said may sound irrational and its probably my own inadequacy that I feel confused by this common method of teaching. Can anyone else sympathize with this situation? I don't intend to stop learning everything independently in my own style, so I don't need advice on what to do really, unless you can think of something else. Is this style prevalent everywhere? Should I try to adjust? Will it be too difficult to keep up with the material if I insist learning like I do in years to come? Any thoughts, just post it ! =]

 

[Diffy]

Two comments:

1)
You should get used to using multiple authors/ books to learn from. Real world work and problems are not often solved by consulting a single source, but rather by gathering a lot of information from lots of different places. There is also no strict order to how work comes in the real world and often structure is not evident. Try not to let your personal preferences get in the way of what needs to be learned and accomplished.

2)
Its your first month. Subject matter will increase in difficulty and build upon itself. There should be courses (as an example) such as Calc 1, Calc 2, Calc 3, that get deeper into the subject. Your professors have to start somewhere to make sure everyone is on the same page before going deeper. Remember Math is an open ended subject... There is no final course in Calculus, or Algebra... Anywhere you go all courses could be considered "An introduction to"...

Cheers,

 

[elect_eng]

... Never before in my life have I studied mathematics in this jumbled way. It ruins the point of a textbook, which you progress through in the order set out by the author, and whilst you do so, you learn his/her technique, writing style, methods, and you complete the journey through the subject they made for you, enabling you to come out with a well formed, logical and structured view of the topic from a certain viewpoint.

A good teacher will have his/her own order, technique, style and methods to create a worthwile journey. These may not match well with the book, and in such cases the book is just a suppliment. I would suggest being open to the journey a good professor will take you on.

In cases where the professor is not good (which is often, unfortunately), you can learn from the class book, and other books on your own. This is how university study is. Some professors are good and some are less than good. Some professor's styles will match well with your preferences, and some will not.

The goal is to learn. One way or another, you need to figure out how to do that under any circumstances that come your way. It's not always fair, and ranting is OK as long as you do it as a method to relieve stress. Don't let imperfect situations get you down; stay positive.

 

[MathematicalPhysicist]

There is no final course in Calculus, or Algebra... Anywhere you go all courses could be considered "An introduction to"...

Cheers,

All his BSC degree could be considered "Introductory".

 

[Studiot]

You will find that courses often start out at elementary level, usually to even out the different backgrounds of students.

But they can ramp up the level very sharply and very suddenly. You have to watch out or this can catch out an unwary student.

As regards to breadth of coverage I heard a lecturer once say
You have 20 hours of lectures in this subject and 2 hours in the exam. You can only therefore reproduce 10% in the exam. The trick is to know which 10%.

Good luck in your future studies.

PS Where do they start University in March?

 

[Mentallic]

PS Where do they start University in March?

In Australia.

I agree with what you're saying Gib Z. I too have just started my first year of uni and it frustrates me to know that I couldn't answer a couple of questions in a math quiz I had recently simply because the terminology was used in some source, while the source I was using to learn from didn't have it.
My physics lecturer actually got a list of all the possible sources to learn from, and asked the students which they use. There were a total of 15 different sources (but it was the different types of learning, books is considered just 1) and I believe the lecturer's intention when asking the students to say which source they use was that they only really rely on one source.

I know the way I'll be doing it from now on though is to have my main study reference, and just skim over the badly organized lecture notes to see if everything in there isn't a surprise to me.

 

[IttyBittyBit]

In our University, most professors just picked a book and stuck to it. We had a few (very good) professors who had their own style of doing things; they basically had their own lecture notes and stuff and used the book only for exercises.

Another thing I'm not liking in the skimpyness of the courses. Perhaps this is how it is everywhere, but pretty much every course my maths dept offers should have "A brief introductory exposition of" added to the title. Is it normal to only cover half, or even less, of the topics that a standard textbook of that subject contains? It can't be.

It's completely normal. You usually just can't teach all of a textbook in a single semester. Remember, the goal of undergraduate level math is not to make you an expert, but to just equip you with the tools you need to continue learning on your own. A good professor will capitalize on this fact and use the course to improve the student's problem-solving capabilities as well as general attraction to the subject.

I'm not saying I entirely agree with this mode of teaching; for example in our complex variables course we did all the preliminary stuff and when it came to the really interesting things, like theta functions etc., the course ended. That was a real let-down.

 

[some_dude]

You have a point, I think. Splitting math up into course-sized units is silly, but needed so the university bureaucracy can stay organized. But if you even know who Lars Ahlfors is and are in your first semester of university, I'm going to assume you're very smart and like math a lot. So, keep in mind that the university has its own agenda and it's not necessarily aligned with teaching you as much math as deeply as possible. You may run into a lot of boring, tedious stuff that will make you question whether or not you even like the subject. Try not to let that discourage you, there do exist great profs and books (like the one by Ahlfors) but undergraduate math is not all sunshine and rainbows.

 

[Gib Z]

Great, many excellent replies!

Two comments:
1)
You should get used to using multiple authors/ books to learn from. Real world work and problems are not often solved by consulting a single source, but rather by gathering a lot of information from lots of different places. There is also no strict order to how work comes in the real world and often structure is not evident. Try not to let your personal preferences get in the way of what needs to be learned and accomplished.

I wasn't saying we should only consult a single viewpoint, which indeed would be silly =] I'm used to completing one textbook that has one viewpoint, then another that has another. Often I intentionally pick a shorter book and only do every second or third exercise question, because otherwise I'd never get anywhere, but I still want to go through the theory of each book one by one. Although that's a very good point, after my BSc I won't be able to source chunks of information in such nice textbooks because they probably won't exist. Something I probably should have made clearer was that I can bear with this method, I don't have some total inability to learn in this way, but it's not my preference.

2)
Its your first month. Subject matter will increase in difficulty and build upon itself. There should be courses (as an example) such as Calc 1, Calc 2, Calc 3, that get deeper into the subject. Your professors have to start somewhere to make sure everyone is on the same page before going deeper. Remember Math is an open ended subject... There is no final course in Calculus, or Algebra... Anywhere you go all courses could be considered "An introduction to"...

It's not like that here =[ We have just "Differential and Integral Calculus" in our Junior Year, and for example a standard textbook covers the Riemann definition of the Integral, whilst this course still uses a basic vague idea of "Signed Area", and then the most related thing next year is "Vector Calculus" which doesn't address the Riemann definition, perhaps because it's "past it", and then in the third year they have "Measure Theory" and skip straight to Lebesgue! And that's not even taken by many people other than pure math majors. So, for example, one could come top of the cohort with full marks in every exam after three years of mathematics, and have never learned a definition of the Integral! There are other examples =[

I'm starting to think either: The Universities really hopes the math majors will bother to learn it on their own, or that perhaps my one has this problem more pronounced than others, from the responses I'm seeing here. If the first, it should be made more explicit because so far in this month we've already been extremely wishy washy with Epsilon Delta limits, and no one has advised me to learn them properly if I want to be a math major. And if the second, nothing to do about it I suppose.

A good teacher will have his/her own order, technique, style and methods to create a worthwhile journey. These may not match well with the book, and in such cases the book is just a supplement. I would suggest being open to the journey a good professor will take you on.

That is true, but also;

In cases where the professor is not good (which is often, unfortunately), you can learn from the class book, and other books on your own. This is how university study is. Some professors are good and some are less than good. Some professor's styles will match well with your preferences, and some will not.

Indeed, my cases so far have been "not good", so I plan to learn on my own. This was my plan from the start anyway, but I didn’t realize it would have to be like that for every student.

All his BSC degree could be considered "Introductory".

Well I guess it could, but I guess I was getting at the level of depth and thoroughness they cover things, as compared to my experiences from textbooks and high school, was quite low. Although I realize now, textbooks are textbooks, and high school baby sits you and University doesn’t. I still wish they covered a few more topics with us though.

You will find that courses often start out at elementary level, usually to even out the different backgrounds of students.
But they can ramp up the level very sharply and very suddenly. You have to watch out or this can catch out an unwary student.
As regards to breadth of coverage I heard a lecturer once say
You have 20 hours of lectures in this subject and 2 hours in the exam. You can only therefore reproduce 10% in the exam. The trick is to know which 10%.

Or be able to reproduce it all! That’s what our aim should be at least.

I agree with what you're saying Gib Z. I too have just started my first year of uni and it frustrates me to know that I couldn't answer a couple of questions in a math quiz I had recently simply because the terminology was used in some source, while the source I was using to learn from didn't have it.
….
I know the way I'll be doing it from now on though is to have my main study reference, and just skim over the badly organized lecture notes to see if everything in there isn't a surprise to me.

Same here. Could you PM me which Uni you’re going to btw?

In our University, most professors just picked a book and stuck to it. We had a few (very good) professors who had their own style of doing things; they basically had their own lecture notes and stuff and used the book only for exercises.

I’ve only had 6 teachers so far, but I can only see one who has done this successfully to what I know (I don’t know the general quality of the other literature on Mathematical Logic, and his notes seem good), and another one who tried his own set of lecture notes. His notes and lectures are exactly a collection of proofs written up on the board. I’m not liking that =[

It's completely normal. You usually just can't teach all of a textbook in a single semester. Remember, the goal of undergraduate level math is not to make you an expert, but to just equip you with the tools you need to continue learning on your own. A good professor will capitalize on this fact and use the course to improve the student's problem-solving capabilities as well as general attraction to the subject.

Let’s hope I meet a couple more of the good ones then! =]

I'm not saying I entirely agree with this mode of teaching; for example in our complex variables course we did all the preliminary stuff and when it came to the really interesting things, like theta functions etc., the course ended. That was a real let-down.

Exactly, I think they try to only teach the bare essentials as the Engineers or the Physicists may not necessarily be interested. My university has its own “Math for Engineers” stream, and some Uni’s have “Math for Mathematicians” streams. I wish mine had the funding for those!

You have a point, I think. Splitting math up into course-sized units is silly, but needed so the university bureaucracy can stay organized…. keep in mind that the university has its own agenda and it's not necessarily aligned with teaching you as much math as deeply as possible… Try not to let that discourage you, there do exist great profs and books (like the one by Ahlfors) but undergraduate math is not all sunshine and rainbows.

Very clear way to view undergraduate mathematics. I will keep this in mind.
All the good responses here have fully answered all my questions, while I blew off a bit of steam as well. Unless others want to continue some sort of related discussion, we may all consider this thread closed. Thanks PF!