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Why do so many professors just do proofs in class?

  1. Oct 3, 2007 #1
    All my classes are just profs doing proofs. Great. Too bad the tests requires us to use what we prove to calculate something.

    For example, my prof spent the first two lectures proving cross and dot product identities (the ones found on the inside covers of many math or physics books). Why? I don't know. The tests are open book and I already know the identities work because I've used them in other classes. Oh, right, and this is an E&M class, not a math class.

    WHY do these people do this? If I cared about proofs so much, I'd be a math major. Yes, I'd like to know why the hell we have Heisenberg's Uncertainty Principle, but the test (and I assume any career in the future that would use QM) would require us to use it!

    I mean, Jesus, when I was 16 and my dad explained to me why a car works, I didn't suddenly know how to drive it.

    Not to mention, proofs are just puzzles. You are given the answer and just need to work up to it.

    Is this just me? Am I just not cut out as a physicist or something? This is really bugging me.
  2. jcsd
  3. Oct 3, 2007 #2
    I had the same complaints but its how some professors like to teach if they teach at all.

    You learn what you need to pay attention to and what you can let go.

    Some people learn a lot from proofs, I don't. I apply a pattern I see in problems and that method has got me through all my math courses and physics with A's or B+'s.

    I think the only class I took where proofs came in handy was discrete math where you had to write up your own proofs through strong induction which was a treat.
  4. Oct 3, 2007 #3
    because the point of going to school is not to learn a prescription but how to solve problems. the proofs that you call puzzles are just derivations with clever tricks, which are not the same thing and surely not all the proofs you see are like this. the point of them showing you proofs is because you should know how to apply something after learning how it works. many many upper class books don't have exercise problems anyway, and definitely fewer with numerical problems.

    personally i learned how to drive a stickshift by reading up on how it worked.
  5. Oct 3, 2007 #4
    Because it's a physics class and we care about how things are derived, because ideally we like to find something unexplained and try to find ways to describe how it behaves mathematically. Just calculating stuff using an existing formula is more of an engineering thing.

    That said, I do wish they would give students a better idea on how to use it before assigning homework that assumes you know how. So I sympathize. But the above is more or less why.

    ΔxΔp >= ħ/2 is more about...telling you roughly when things will start acting odd. The actual maths can get much more involved.

    Also I notice more than a few responses have hit while I've been typing. ;)
  6. Oct 3, 2007 #5
    If you want to just apply what greater minds have come up with and not truly understand what it is you're doing you should go to a tech school. The reason professor use proofs during the lecture is so that you can understand why what you're doing works. Anyone can teach application, that's why it's generally left to TA discussion sessions/tutoring/group and self study. It's the theory that the professors should teach.

    And I bet that teaching theory is mandatory (or at least highly looked upon) for ABET accreditation, though I'm by no means certain.
  7. Oct 3, 2007 #6
    Not to let the facts get in the way of your physics snootiness, but in every non-programming EE class I've ever taken, all the professors do during class is derive and work proofs. The students are left to their own devices to master application.
  8. Oct 3, 2007 #7
    Understand proof = understanding. Plugging in numbers and using an identity = not understanding.
  9. Oct 3, 2007 #8


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    Actually, you need both. Theory without practice is roughly as bad as practice without theory.

    (I should point out that proof isn't all there is to theory)
    Last edited: Oct 4, 2007
  10. Oct 3, 2007 #9
    Less that, more of engineering being applied science. I know at least a few of our programs will allow substituting applied math courses for prereqs (and I'm sure the profs there still go through tons of proofs). The emphasis is a little different, and it should be - engineering students usually want to graduate and go get a job engineering things already, or possibly get a Master's. There are engineers in teaching and research, but fewer students have this sort of plan than say physics majors, where it's almost expected.

    What kind of programming classes are you taking that don't involve proofs? There's a reason CS started out in many places as a math department program...
  11. Oct 4, 2007 #10
    Hardly. Take the classical mechanics class I took last year. All proofs during class. The homework? "I push this top. Give me the equations of motion."

    Thanks. Now, how do I even get started?

    And I'm not even talking about numbers. I don't need numbers. I would just like an example problem to see if I even understand what's going on. I need two points to make a line. Just giving me the proof without a way of testing whether I understand it or not won't help me.

    To their credit, some of the profs put examples on their websites, however it's a lot better when I can ask questions as they go along, or better yet, have examples that don't make logical jumps and assume you know all the tricks the professor is using.

    This would be asking for too much, I understand, but what adds insult to injury is when they do show an example, but it's something so trivial I could do it in my head. Then the homework problem takes hours and hours to solve.

    It's like going from target practice straight to the front lines. =/
  12. Oct 4, 2007 #11
    Reading up on how the mechanism of a manual transmission worked, or reading up on how to operate a stick shift?
  13. Oct 4, 2007 #12

    You know what else is "fun"? Those tests where you score 50%, then end up getting a 3.5-4.0 in the class. o_O
  14. Oct 4, 2007 #13
    LOL last year in Classical Mechanics on the second exam the average was a 6 out of 25.

    I've been told by last year's class that the averages on the E&M exams are around 30%. The prof acknowledged this, but he claims he never tries to make them hard. And I can understand that making test questions is difficult, no matter the class or subject.

    QM apparently isn't any better. Looks like I have a fun quarter ahead of me.
  15. Oct 4, 2007 #14
    Assembly on 6812 micro-controllers and data structures in Java. I've never taken a CS programming course, but I'm sure they're much, much more rigorous than ours. Our programming classes are the only classes where we really just dive into the application and don't spend any time thinking about theory.
  16. Oct 4, 2007 #15
    There are many good books out there on how to solve physics problems. I'd recommend picking up a couple and looking to them when you're stuck out in the tall grass.
  17. Oct 4, 2007 #16
    I actually find more hands on, real world programming more helpful in my current job (Software Engineer) than proving this algorithm is .23 seconds faster than the previous one.

    Thats what makes co-ops/internships so much better than school. You work with real problems, not theory. I'm not saying proofs/theory won't come into play when your on your job but how often are you going to have to reinvent the wheel?

    Thats why I'm transferring to NC State, less theory, more hands on.

    Penn State was the opposite and when you go into the interview and the employer asks what types of projects you've worked on in school and all you have to say is a bunch of theory with little side projects here and there, its not very impressive.

    On the other hand, NC State has company's like IBM/SAP/CISCO/Red Hat submit real world problems they want the students to solve. Several of my friends from penn state were quite upset because after talking to the Comp Sci majors at NC State they realized they haven't been doing jack but theory/proofs but haven't gotten to solve any real world problems.

    My employers also noticed how bad some schools are dealing with this isssue. I talked to my Development manager and asked if I should switch to NC state or not, I told him how Penn State focuses mainly on theory/proofs while I noticed NC stat was more hands on learning. He highly recommended NC State because when you leave that school you'll be ready for a job at any of the company's in Research Triangle Park.

    Think how impressed the manager would be when you say, oh yah, I solved that problem you had with SNMP Traps on your z/OS mainframe, and the other kid goes, I re-wrote the bubble sort to make it a little more efficient. wee.

    I'm not saying its not any theory, there are some courses that do invovle theory/proofs but not as heavy as my last university. I like this because I don't plan on going into research and algorithm design, blah.

    But some people like that stuff so I guess its up to what you want to do with your career, research or apply what someone else has invented.

    From my co-op not one proof has helped me out in my Software Engineering job, Design patterns/OO Design helped a ton, proofs no.
    Last edited: Oct 4, 2007
  18. Oct 4, 2007 #17
    But you can see why CS programs need to have a lot of theory, right? There is a difference between a programmer and a computer scientist. Any person can read a "C++ for Dummies" textbook and learn how to program - but it's the computer scientists who push the programming field forward. The rest of the programmers just take what's given to them by the CS people.

    That said, as a graduate student in EE I see proofs all the time in my courses that are heavy on the theory, like DSP. I rarely see any proofs in my more practical classes. It's a nice mix.
  19. Oct 4, 2007 #18
    I do see your point Maxwell.

    I guess I should have majored in Software Engineering rather than Computer Science but the major isn't very well known so I thought it would be safer going with a Comp Sci degree.

    I enjoy the whole process of making software, from initial concept, to design, to implementation, to testing, to maintaining code (actually thats not so fun if you get the joy of reading code that some person who just learned to program with a "<insert language here> for Dummies book" )

    Developing new theories in CS must be over my head.
    Last edited: Oct 4, 2007
  20. Oct 4, 2007 #19


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    Often, the "proofs" are meant to demonstrate, from first physical principles, various physical relationships and implications. Usually the resulting formulas are useful and valid only in special situations, which is often forgotten or ignored by students. So, it is important to know when and why something like a certain formula is true.

    In addition, "proofs" can demonstrate some mathematical and computational techniques that one might need in doing real physics problems... techniques that one might not get in, say, a pure math course.

    So, there certainly is something [many things, in fact] to be learned from proofs.
    It may be that wall-to-wall proofs might be too much... and that some examples should be done.... However, some professors may take the view that you can do that with your own textbook outside of class.

    On an exam, it may be that it's too much to ask students to do [new] proofs in an hour, especially if students are uncomfortable with abstract thinking and prefer working with numbers.
  21. Oct 4, 2007 #20


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    One of my profs does that right now. All he does is copy it down from the textbook.

    I don't call that teaching.

    It's funny how lots of teachers complain that students have no attention span in class and such. Have they ever thought that that is just a symptom to a bigger problem? That is... they suck.
  22. Oct 4, 2007 #21
    That's definately one thing. I have the proof in my book and I can figure out the steps on my own time. I mean, I know what the answer is and if the end point is an elegant expression, then I know there will be a bunch of cancelling somewhere in there. Starting a problem, I have no idea if the outcome will be "cooked" or not.

    But my prof from last year would always look at the class, and answer questions and stuff like that. So that's a lot better than a math prof I had who would just lecture to the board.

    One day I was the only person in class (it was a small Diff EQs class) for like the first 15 minutes. Did he ask me anything about the course? Like if I'm understanding it? Or even look at me when he was lecturing on? Nope. Acted just as if the class was full.

    And his voice was so soothing, I just couldn't stay awake.
  23. Oct 4, 2007 #22


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    I'm sure we all have some stories to tell about Prof.A , and about Prof. B... etc.

    Just curious, were these at small liberal arts colleges? small state universities? research universities? ivy?

    [edit: apostrophe trouble :P ]
    Last edited: Oct 4, 2007
  24. Oct 4, 2007 #23
    Have a prof this year that frequently shows a completely different proof from the one in the book. I wish more did like this instead of just repeating material from the book - or if you're going to lecture straight out of the book, don't tell me to pay $160 for it.

    Currently at a large public research university (makes "public ivy" lists and has crazy amounts of funding, if relevant). Taken classes at ...five? different places including two community colleges, a tech school, and another public research university.

    You get good and bad pretty much everywhere. Larger institutions tend to have more around the extremes since they can retain very experienced professors but also employ grad students that have never taught a class before (some of which may not even have the best grasp of the language...hardly their fault, but sucks when they frequently try to assert something is true and say it is not true instead...). Really, a lot of your education is on your own shoulders in college. And American high schools baby their students too much, or graduate them with transcripts affirming they've mastered material they have no clue about.
  25. Oct 4, 2007 #24
    The prof from my Diff EQ class who lectured to the board was from a community college. Now I go to the University of Washington.
  26. Oct 4, 2007 #25

    Math Is Hard

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    My friend, Scot (who is a fantastic math teacher), wrote a little page for his website called "Seven Types of Math Teachers To Avoid". Number one is the "walking, talking textbook." :biggrin:
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