When did you first encounter "proof based" mathematics?by Best Pokemon Tags: calc, higher level, methods, proof, proof difficult 

#19
Nov812, 10:22 AM

C. Spirit
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#20
Nov812, 10:44 AM

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I also learned my first proofs in high school, first geometrical like proving that two triangles were congruent, but i think my first "serious" proof was that sqrt(2) is irrational.
I agree that many theoretical math proofs are rather useless for physics and you simply don't have the time to learn the same background for all the math you use as a mathematics student does. But i believe one of the basic things about becoming a physicist and a scientist in general is being critical and question everything. And it's definately useful to know were basic math as l'hôpital's rule or the chain rule come from, knowing why this stuff works so why you can appy it. 



#21
Nov812, 03:45 PM

P: 54

Well, I don't find proofs useless... I believe that the things you learn in physics make a lot more sense if you know proof based math. For example, take Laplace's equation, I'm sure that the first method that comes to your mind is separation of variables, but why can you make the assumption that the solution is a product with the variables separated? How do you know it will work? A lot of physicists just scratch their heads and say "well who cares! it works!", but if you knew the math, you'd know that it has to do with the symmetries of the Laplacian, the method actually makes sense! Maybe proofs are useless when calculating stuff, but they make things a lot clearer (at least for me)... 



#22
Nov812, 03:45 PM

P: 164

I've read that there is a way of doing the standard school geometry problems WITHOUT the standard proof method. To make it more intuitive for kids and stop them hating maths.
Anybody know anything about this? 



#23
Nov812, 04:01 PM

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#24
Nov812, 04:18 PM

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While I agree that high school geometry classes have a lot of problems and could be improved a lot, I don't think proofs is something we want to eliminate. What should be eliminated are stupid things like twocolumn proofs and memorizing definitions of obvious and useless terms (seriously: high school geometry books seem to get high from defining useless terms that nobody really cares about). Furthermore, geometry is a field with a very rich history. But this rarely gets told in the classroom. One can use geometry to make a link to so many exciting subjects: for example, when I was in geometry, we learned as an axiom that through every point there exists a unique line parallel to a given line. I find it a shame that they didn't pick up a sphere and show that this wasn't true there. They also could have made connections to modern physics and they could have told us that our space is not euclidean. All of these things would make geometry class so much more exciting. But no: my entire geometry class was just a collection of dry facts nobody really cared about. 



#25
Nov812, 04:55 PM

P: 164

http://www.amazon.com/Proofswithout.../dp/0883857006 "Proofs without Words: Exercises in Visual Thinking (Classroom Resource"Materials) " I have education & math degrees & some kids are visual learners. I've marked many high school math papers where kids "just dont get it", and the job of educators is top help the worst as well as best students. If alternative strategies are needed then so be it. 



#26
Nov812, 07:32 PM

P: 81

Like others, my first experience with proofbased mathematics was a geometry course during my freshman year of high school. I wasn't very good at it then, because I didn't put a lot of effort into learning the material needed to formulate a proof.




#27
Nov812, 07:36 PM

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#28
Nov912, 08:42 AM

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First year at university now, the whole 1st semester is full of proofs in both real analysis and linear algebra. Quite different from high school  the only proofs I remember from there are things like "square root of 2 is an irrational number."
Surprisingly, I find the real analysis proofs easier compared to the linear algebra ones, unlike most of the other students  while the the proofs in linear algebra are simple and obvious, the technical part of writing them down with all the various indexes makes it very confusing... It's weird to me that writing down some linear algebra proof can be so long and tedious, when the "idea" behind the proof is so straight forward. Might be because of the more "systematic" nature of the subject? I don't know. 



#29
Nov912, 12:37 PM

P: 201

I first encountered proofs in Grade 11 (I am Canadian and unsure of what this translates to in terms of a US equivalence). The only proofs we did were basic trigonometric proofs.
However, when I entered my first of university I was overwhelmed with the number of proofs in my firstyear calculus class. I felt as if I "understood" the proofs (in that I could read one and understand what was happening and was able to follow the logic) but I was unable to prove things myself. The class assumed you were already familiar with proofs and I did poorly in it. Since then the math classes I have taken have been at an applied level as opposed to a theoretical level for the most part. I feel as if most high schools do a poor job of preparing students for rigourous proof based mathematics. 



#30
Nov912, 12:55 PM

P: 828

This thread is interesting to me. I am a US student and I've lived here my whole life. I took Calc. I, II, and III as well as linear algebra before encountering what I would consider a real "proofbased" class. Sure, there were proofs mentioned in the calc classes and we did some "baby proofs" in linear algebra (prove this thing isn't or is a subspace, etc). My first real proofbased class was probably the second semester of my second year in college.
I find it interesting that people do proofs in high school (though, I wouldn't call most geometry classes 'proofbased') or as freshmen in college. Those of you who have done that, are you in school in the US? or somewhere else? 



#31
Nov912, 03:05 PM

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#32
Nov912, 03:18 PM

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#33
Nov912, 03:58 PM

P: 11

I think it's a bit of a tradition really. The attitude of all the professors (not just the analysis professors) is basically "analysis and linear algebra are basic subjects of higher math, upon which advanced math is based, and as such they should be taught as early as possible." 



#34
Nov912, 04:00 PM

P: 45





#35
Nov912, 04:00 PM

P: 45

The last two years in high school I learned topics such as algebra, functions, advanced trigonometry and trigonometric identities, vectors, calculus, sequences, series, approximations, counting (permutations and combinations), matrices and complex numbers. In most of these we had to do proofs. The main proof methods we used were direct proof, proof by contradiction and proof by induction.




#36
Nov912, 06:14 PM

P: 5

I first encountered "proofbased mathematics" in high school in a Geometry class. The work could have been more engaging, although, and I think this would have been good for me and the other students too. I plan on learning more math with you all and on this forum. Best Pokemon, your second to last post doesn't seem appropriate but perhaps I have misunderstood your writing.



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