Programs Is this an indication that I should stay away from higher math?

[Hsopitalist]

The proofs are not what I had in mind when I mentioned abstraction. Some proofs are just one-time tricks, but others give some deeper insight into how you should think about the subject. It is hard to tell which are which. Some proofs that seem like just a one-time trick keep showing up time and again. They really are fundamental. For a math major, you should definitely get used to the epsilon-delta proofs, proof by contradiction, and proof by induction.

Gotcha, thx.

 

[Hsopitalist]

The proofs are not what I had in mind when I mentioned abstraction. Some proofs are just one-time tricks, but others give some deeper insight into how you should think about the subject. It is hard to tell which are which. Some proofs that seem like just a one-time trick keep showing up time and again. They really are fundamental. For a math major, you should definitely get used to the epsilon-delta proofs, proof by contradiction, and proof by induction.

And I'll save my question of "what did you mean, then, by an abstraction?" for this time next year...when I hope to be much further along.

 

[Hsopitalist]

And sometimes it gets so frustrating I have to walk away for awhile.

 

[grandpa2390]

Mistakes are part of learning process in math and science. It's extremely difficult to be correct 100% of the time. It's important to make note of what kind of mistakes you are making and how to learn from them.

I remember reading that Robert Oppenheimer was known by his colleagues for getting all his physics correct but getting the wrong constants in his work. Even the big names make mistakes.

I agree. In fact, my professors stressed to us, and research has only supported them ever since, that you only learn in math/science from making mistakes. The best way to learn is to try, try, and try again. And everytime you make a mistake, you learn how "not" to do it. You learn what "doesn't" make sense. etc.

edit: apparently there are a few wise guys, so I should clarify what my intention is. If you are a perfect human being who never makes a mistake, good for you. for the rest of us, when you get a math or physics problem wrong, it's ok, stick with it, don't reach for the solution manual just yet. You'll learn a whole lot more from struggling with the problem and getting it wrong a few times along the way than you will learn from the solution manual. It's ok to make mistakes. Don't fall into the intelligence trap and think that you are a failure and should give up if you don't get everything right the first time you try. Just as good struggle builds better muscle and better character, good struggle also builds better understanding as well.

 

[FactChecker]

And I'll save my question of "what did you mean, then, by an abstraction?" for this time next year...when I hope to be much further along.

You are already dealing with examples of abstraction. When you study "functions" and their properties, that is an abstraction. The function is a mathematical concept that can be used in many real-world applications. You are studying its properties that will hold for any particular application. That concept of abstraction will be carried farther as you go deeper into mathematics.

 

[PeroK]

... that you only learn in math/science from making mistakes.

That's what I've been doing wrong all these years. I must try harder to get things wrong a few times before I get them right!

 

[FactChecker]

you only learn in math/science from making mistakes. The best way to learn is to try, try, and try again. And everytime you make a mistake, you learn how "not" to do it. You learn what "doesn't" make sense. etc.

If you make a statement like this in a forum full of obsessive/compulsive people (like me), you must expect a response. ;>)
Gauss is not regarded as a genius because of the mistakes he made. There are two types of mistakes. One type is just an error in mechanical calculations. The other type is a conceptual error. I would not worry much about the calculation errors because that is just trying to compete against calculators or computers. The conceptual errors are the ones to work on. The goal is to get enough intuitive understanding of the concepts that those errors do not occur often.

 

[grandpa2390]

If you make a statement like this in a forum full of obsessive/compulsive people (like me), you must expect a response. ;>)
Gauss is not regarded as a genius because of the mistakes he made. There are two types of mistakes. One type is just an error in mechanical calculations. The other type is a conceptual error. I would not worry much about the calculation errors because that is just trying to compete against calculators or computers. The conceptual errors are the ones to work on. The goal is to get enough intuitive understanding of the concepts that those errors do not occur often.

I think you missed the point I was making. It has nothing to do with Gauss or any other great scientist.

research shows that you learn more and retain better when you endure through your struggle with the material. It's ok to make calculation and conceptual errors as long as you stick with it long enough to realize those errors. After you sat there kicking yourself for 30 minutes or 30 hours trying to figure out where you went wrong solving the problem, the Eureka moment that you earn will stay with you for a long time. AS WELL as all of the stupid conceptual and calculator errors you made on the way to it.

So the next time you are struggling with a Physics problem and start to head on over to Chegg.com, stick with it a bit longer. an answer that is given rather than earned will teach you less. I really thought that was the philosophy of the Physics Forums help section.

 

[grandpa2390]

That's what I've been doing wrong all these years. I must try harder to get things wrong a few times before I get them right!

lol, ok wise guy. if you are getting the problem right on the first time, fine. If you are getting it wrong, don't reach for the answer key, keep working at it until you get it right.

but honestly... it doesn't hurt to experiment and try other ways of solving the problem besides the one you know will work.

 

[etotheipi]

After you sat there kicking yourself for 30 minutes or 30 hours trying to figure out where you went wrong solving the problem, the Eureka moment that you earn will stay with you for a long time.

What if, after 30 hours, you realize you missed a negative sign on the second line of working...

 

[grandpa2390]

What if, after 30 hours, you realize you missed a negative sign on the second line of working...

the next time you sit down to start working out a problem, you better believe your bookkeeping will improve. You will be checking and double checking your signs. And if you still miss one, it probably won't take you 30 hours to realize it. checking your signs will be the first thing you do.

 

[FactChecker]

the next time you sit down to start working out a problem, you better believe your bookkeeping will improve. You will be checking and double checking your signs. And if you still miss one, it probably won't take you 30 hours to realize it. checking your signs will be the first thing you check.

The lesson I learned is to do any complicated calculations in computer code with many intermediate calculations. That makes it possible to see the step-by-step results and decide if they make sense.
Even then, it may still take 30 hours because the errors are so often in the part that you were the most confident of.

 

[etotheipi]

I remember one of my teachers showing me this study which claims that you are working at the correct level if you have an 85% success rate.

There is often merit to getting stuck and having to puzzle stuff out, but if you get to the point where you're just getting everything wrong, I don't think that's healthy (for motivation or general sanity). And in the case of trivial errors like sign errors, spending lots of time searching for them is a bit of a waste in my opinion. Better just to check it and move on, and avoid all of that frustration.

 

[grandpa2390]

I remember one of my teachers showing me this study which claims that you are working at the correct level if you have an 85% success rate.

There is often merit to getting stuck and having to puzzle stuff out, but if you get to the point where you're just getting everything wrong, I don't think that's healthy (for motivation or general sanity). And in the case of trivial errors like sign errors, spending lots of time searching for them is a bit of a waste in my opinion. Better just to check it and move on, and avoid all of that frustration.

I don't know. There's merit to that opinion. Spending a ton of time trying to figure out where you went wrong just to discover it was a sign error is no fun. But at the same time, the real world doesn't have answer keys and solution manuals. Learning proper bookkeeping and how to go back and find your mistakes is important.
or even learning how to recognize when you've made a mistake.

I don't know. I'm not a genius like some of the responders to my original post. For me a degree in Physics was a degree in persistence. lol. I probably would have done better to major in engineering as I originally planned. And when people ask me what I majored in, and I tell them Physics, their initial reaction is one of awe... but I quickly inform them that I'm not a genius, I just learned how to be persistent and stick with it until I got it. and that's something anyone could do. But that's just my experience, and I thought I would share it because I think someone who went through medical school could relate to the idea and be encouraged to stick with it.

 

[FactChecker]

Learning proper bookkeeping and how to go back and find your mistakes is important.
or even learning how to recognize when you've made a mistake.

This is a very good point. Checking every single thing requires a discipline which is a learned skill.

 

[etotheipi]

I don't know either. If I'm learning a new topic, it doesn't bother me immensely if I make a silly arithmetic mistake or three, so long as I can get the overarching concepts down. I would hope that these make up most of the '15%', and as that topic becomes more familiar that the frequency of these errors decreases naturally.

 

[Hsopitalist]

You are already dealing with examples of abstraction. When you study "functions" and their properties, that is an abstraction. The function is a mathematical concept that can be used in many real-world applications. You are studying its properties that will hold for any particular application. That concept of abstraction will be carried farther as you go deeper into mathematics.

Sweet.

And my copy of Moises part 1 came today! So excited

 

[grandpa2390]

Sweet.

And my copy of Moises part 1 came today! So excited

what's that?

 

[Hsopitalist]

what's that?

It's a calculus text from 1966 recommended by midget dwarf

 

[MidgetDwarf]

It's a calculus text from 1966 recommended by midget dwarf

How do you like it so far? The first section can be a bit weird for most newcomers. So maybe you do not like this section, but it gets way better. Have you arrived to the discussion of a parabola, a neat discussion of snells law, and parabolic sector? What I found very cool was the discussion of tangency in calculus.

 

[Hsopitalist]

How do you like it so far? The first section can be a bit weird for most newcomers. So maybe you do not like this section, but it gets way better. Have you arrived to the discussion of a parabola, a neat discussion of snells law, and parabolic sector? What I found very cool was the discussion of tangency in calculus.

I read through chapter one. It's different than what I'm used to but in an interesting way. Haven't gotten to the parabolas yet. I'm excited to though.

 

[Hsopitalist]

Parabolic sector. Interesting.