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What would you do if you wanted to learn physics and chemistry properly?


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9 hours ago, lewelma said:

  I use it to understand how industrial processes work - so how the aluminum smelter works and why it uses one third of ALL of NZ's power. 

Is it because you need to heat it up to separate the aluminum that melts from the rocks that don't?  

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DD was in TTU-K12 (formerly TTUISD) and is a graduate of Texas Tech University High School.  Physics was THE most expensive course she took during her 7 school years there (Middle School and High School) because it required not one Lab Kit, but two Lab Kits.

I believe one thing a Physics student can do is to do ALL of the experiments.  See what happens. Did that work out the way you thought it would or did something else happen?  What happens if you change this to that?  The experiments can be fun.

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On 3/2/2021 at 3:23 PM, Not_a_Number said:

Yeah, see, this is good stuff 😛 . I need to know stuff like that. 

I'm really mostly looking for expert opinions on HOW to learn these effectively.

 

Snip

 

I don't happen to know the most efficient path for physics and chemistry learning, and I'm hoping to hear from more experts. 

I'm not sure that effective and efficient necessary go hand in hand.

I don't come at this from a math fluent background, but I have found that science understanding isn't a straight path, but one in which I scaffold in different areas at different rates.

@regentrudeused to suggest the Knight Jones physics books. I used them with my kids and thought they had a good mix of explanation, math, and application. There are associated workbooks that direct the student through more opportunities to draw diagrams and explain what is happening. 

 

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Just now, Sebastian (a lady) said:

I'm not sure that effective and efficient necessary go hand in hand.

Hmmm, let's just say the most efficient way to learn it effectively. I know a lot about that in math, because that's my area of expertise. I know next to nothing in the sciences. 

 

Just now, Sebastian (a lady) said:

I don't come at this from a math fluent background, but I have found that science understanding isn't a straight path, but one in which I scaffold in different areas at different rates.

@regentrudeused to suggest the Knight Jones physics books. I used them with my kids and thought they had a good mix of explanation, math, and application. There are associated workbooks that direct the student through more opportunities to draw diagrams and explain what is happening. 

Cool, thanks! I'll have to take a look when I start thinking about this seriously. 

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2 minutes ago, Sebastian (a lady) said:

I'm not sure that effective and efficient necessary go hand in hand.

I don't come at this from a math fluent background, but I have found that science understanding isn't a straight path, but one in which I scaffold in different areas at different rates.

@regentrudeused to suggest the Knight Jones physics books. I used them with my kids and thought they had a good mix of explanation, math, and application. There are associated workbooks that direct the student through more opportunities to draw diagrams and explain what is happening. 

 

I also found this companion book useful for seeing where students typically had misconceptions and how to clarify those areas. 

https://www.amazon.com/Five-Easy-Lessons-Strategies-Successful/dp/0805387021/ref=mp_s_a_1_21?dchild=1&keywords=randall+knight+physics&qid=1614871158&sprefix=randahl+knight&sr=8-21

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2 hours ago, Sebastian (a lady) said:

 

@regentrudeused to suggest the Knight Jones physics books. I used them with my kids and thought they had a good mix of explanation, math, and application. There are associated workbooks that direct the student through more opportunities to draw diagrams and explain what is happening. 

Knight Jones Field is good for intro physics. It does not prepare student sufficiently for upper level courses since it is not calculus based.
Not sure how far OP wants to go with physics.

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6 hours ago, Lanny said:

I believe one thing a Physics student can do is to do ALL of the experiments.  See what happens. Did that work out the way you thought it would or did something else happen?  What happens if you change this to that?  The experiments can be fun.

That's a very inefficient way to learn physics, and you can do hat only for very basic levels (sine you would not have the equipment to do any experiments for modern physics). Yes, great if you can spend infinite amount of time. But there is no reason to reinvent the wheel - scientists have done these experiments for us before and have developed theories. So, let's cut to the chase and study the theories. 

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8 minutes ago, regentrude said:

Knight Jones Field is good for intro physics. It does not prepare student sufficiently for upper level courses since it is not calculus based.
Not sure how far OP wants to go with physics.

I don’t know how far, but farther than intro level. I expect my kiddo to take serious science and would like to get ahead of her.

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I used Resnick and Halliday's physics book when I was in college. I still have it and use it to teach physics to my son. There are a lot of older threads where @regentrude and @Arcadiahave mentioned the resources that they have used and recommend. I have a few of those books as well and use them to pull out problems for reviews and test.

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4 minutes ago, Not_a_Number said:

I don’t know how far, but farther than intro level. I expect my kiddo to take serious science and would like to get ahead of her.

"serious science" for high school would be intro level: in physics, the equivalent of two semesters calc based intro physics (mech + e&m) for a strong student. Only the exceptional physics interested student would progress beyond that into Modern Physics, and virtually nobody would make it to upper level courses beyond that

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1 minute ago, regentrude said:

"serious science" for high school would be intro level: in physics, the equivalent of two semesters calc based intro physics (mech + e&m) for a strong student. Only the exceptional physics interested student would progress beyond that into Modern Physics, and virtually nobody would make it to upper level courses beyond that

I have a very accelerated and mathy kid.

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2 minutes ago, mathnerd said:

I used Resnick and Halliday's physics books when I was in college. I still have it and use it to teach physics to my son. There are a lot of older threads where @regentrude and @Arcadiahave mentioned the resources that they have used and recommend. I have a few of those books as well and use them to pull out problems for reviews and test.

For intro physics mech/e&m, I recommend Halliday. Good book. Other good option is Giancoli.
Young&Freedman has the cleanest notation and is consistent between 1-d and 2-d kinematics notation, which is one of the reasons I choose that for the classes I teach.

Stay away from the Open Source University Physics!!! Too many errors. Horrible book.

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4 minutes ago, Not_a_Number said:

I have a very accelerated and mathy kid.

I can believe that. Had two of those myself.
Are you anticipating your highschooler to cover the material of the first two years of university physics a physics major takes - or the content of the junior & senior level courses for physics majors?

ETA: My extremely mathy and advanced DD took the intro sequence of calc based physics (mech + e&m) and a semester of modern physics, all at a 4 year STEM uni, while in highschool. 

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Just now, regentrude said:

I can believe that. Had two of those myself.
Are you anticipating your highschooler to cover the material of the first two years of university physics a physics major takes - or the content of the junior & senior level courses for physics majors?

No idea. I don’t have any expectations. Probably the first two years would be enough?

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2 minutes ago, regentrude said:

ETA: My extremely mathy and advanced DD took the intro sequence of calc based physics (mech + e&m) and a semester of modern physics, all at a 4 year STEM uni, while in highschool. 

Yes, that seems like an extremely likely route. But wouldn't I need MORE than that to really assist her with that? Like, I can teach math well because I've taken a lot more math than the basics. 

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On 3/2/2021 at 11:33 AM, LadyLemon said:

Wanting to learn science from a book with out the hands on makes it harder.

I completely disagree with this--and I have a degree in biochemistry and worked as a scientist in a lab for 10 years.  

Lab work, hands on work, whatever you want to call it, is the LEAST important part of learning to think scientifically.  First you need a vast body of knowledge--which is going to come from books mostly--but that isn't sufficient.  You also need to work with the material--mentally--and that is where doing problems comes in.  Then you need to apply your knowledge to the world outside the books--like lewelma talks about upthread.  But this doesn't need to happen in a lab because what happens in the lab isn't really science.  In fact I would say this is even more true for the sciences like physics and chemistry where real world observations are just the tip of the iceberg when it comes to what is really going on.  Understanding the more descriptive sciences, such as field biology or geology, is aided by actually seeing the things being studied.

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On 3/3/2021 at 2:01 AM, Dicentra said:

I think, though, that it would be helpful for you to have someone guide you through the book and give you all the extra details and connections that the book may gloss over. 🙂  At the risk of promoting my own courses here (which I do try very hard not to do - I try to keep it to asking folks about things like split streams or course labeling issues, etc.), you might want to take a look at my parent-graded version of Honors Chem.  You'd have access to all my pre-recorded video lectures, assignments, test, and exams (along with worked answer keys) for 1 year.  You could use all of that material to help to guide you through the Chang textbook.

I've been meaning to tag you on this thread and totally spaced on your username! So thank you for chiming in. 

I'm no good at all with listening to lectures, whether pre-recorded or not. I just don't enjoy it and don't learn well that way. Do you think that's a better guide than trying to make one's way through a book? 

I have to say that I've found interactive learning the best thing, too... I'm just not sure I'd get that from lectures. 

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@Dicentra: I'm going to quote you from the other thread: 

 

"If 50.0g of hydrogen reacts with 40.0g of oxygen, what mass of water can be produced?

Without knowledge of moles, stoichiometry, limiting reactants, common diatomic elements, and combination reactions, there is no way this problem can be solved.  I can often tell an “intuition” type of student because they will tell me 90.0g of water can be produced – seems logical. 😉 There is no way that this problem can be "intuited" without knowledge of the chemistry concepts involved."

 

That's not the kind of intuition I mean. I mean internalizing the models well enough that they become intuitive. I don't mean "using your intuition from the rest of your life to figure it out." 

One can learn a LOT of formulas without internalizing any mental models at all. I know this from years of teaching math and having had this outcome. That's what I worry about: not forming a useful model no matter how many problems I work.

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On 3/2/2021 at 10:54 AM, Not_a_Number said:

Right. I’m just trying to get a recommendation for a good program. I’ve seen far too many calculus students put in the hours without much progress. Basically, I need some expert guidance.

@mathnerd for me it is not so much a good program or good books but the discussions. I used to sleep during lectures and are only awake during tutorials and labs because there are lots of discussions and clarifying of ideas and concepts there. My husband (electrical engineering) doesn’t remember much chemistry so chemistry discussions is usually among my kids and sometimes I join in. For physics and math, everyone who is free kind of join in. These are not structured discussions like tutorials, but discussions of whatever comes to mind. 

 

9 minutes ago, Not_a_Number said:

No idea. I don’t have any expectations. Probably the first two years would be enough?

 

8 minutes ago, Not_a_Number said:

Yes, that seems like an extremely likely route. But wouldn't I need MORE than that to really assist her with that? Like, I can teach math well because I've taken a lot more math than the basics. 

@8filltheheart One of her sons did his physics at university level while in high school. 
I exceeded my parents ability quite early. I think the most useful student survival skill for me and my kids was to know when and how to get help. I can’t be a subject matter “expert” in everything that my kids are good at, and I don’t wish to be. 

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3 minutes ago, Arcadia said:

@mathnerd for me it is not so much a good program or good books but the discussions. I used to sleep during lectures and are only awake during tutorials and labs because there are lots of discussions and clarifying of ideas and concepts there. My husband (electrical engineering) doesn’t remember much chemistry so chemistry discussions is usually among my kids and sometimes I join in. For physics and math, everyone who is free kind of join in. These are not structured discussions like tutorials, but discussions of whatever comes to mind.
 

I agree. I can’t learn through lectures. Most people have trouble with that. But... then what? 
 

3 minutes ago, Arcadia said:

@8filltheheart One of her sons did his physics at university level while in high school. 
I exceeded my parents ability quite early. I think the most useful student survival skill for me and my kids was to know when and how to get help. I can’t be a subject matter “expert” in everything that my kids are good at, and I don’t wish to be. 

No, obviously one can’t be an expert in everything, but I do think my kids benefit from the things I AM an expert at. 

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28 minutes ago, Not_a_Number said:

Yes, that seems like an extremely likely route. But wouldn't I need MORE than that to really assist her with that? Like, I can teach math well because I've taken a lot more math than the basics. 

To do Modern physics well, yes, I'd want the instructor to have taken quantum mechanics, and some atomic or particle physics.

For mech and e&m, a background in classical mechanics (like Taylor) and theoretical e&m (like Griffith) would be preferable, but you can probably teach it if you just mastered Young&Freedman

ETA: even though I was perfectly capable of teaching her physics, we opted to have DD take those courses at a university (where she was volunteering in the tutoring center for engineering physics, at age 15). You don't need to teach everything yourself.

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28 minutes ago, Not_a_Number said:

I'm no good at all with listening to lectures, whether pre-recorded or not. I just don't enjoy it and don't learn well that way. Do you think that's a better guide than trying to make one's way through a book? 

I have to say that I've found interactive learning the best thing, too... I'm just not sure I'd get that from lectures. 

The benefit of lectures in addition to a textbook is that you have an instructor who emphasizes what is important, summarizes the info, addresses common misconceptions. 
Textbooks are huge, and it is not feasible or necessary for a student to learn every detail that is in the book. The instructor's guidance makes the process more efficient.
To get the maximum benefit of lectures, one would have at least skimmed the textbook sections beforehand, take notes during lecture, work through every example alongside the instructor, and then go back, review the notes while working on problems. If you're interested on physics lectures, send me a pm.

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26 minutes ago, Not_a_Number said:

Yes, that seems like an extremely likely route. But wouldn't I need MORE than that to really assist her with that? Like, I can teach math well because I've taken a lot more math than the basics. 

For an elementary school aged child such as yours, a good place to start would be the Conceptual Physics book (Hewitt) as a spine. With discussions and experiments thrown in, it should have enough material to last you a couple of years. You can make this work because you will be teaching it and pacing it to customize it for your student.

For your own learning, you could pick up any of the calculus based physics books recommended on this forum and get a head start.

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2 minutes ago, Not_a_Number said:

I agree. I can’t learn through lectures. Most people have trouble with that. But... then what? 

For me it is read and then discuss with someone or tutor someone. When I had to explain in different ways to someone with only pen and paper, I really have to think hard. 
 

There are lots of things that DS16 was interested in while he was 8. Over the years he has expanded and changed his interest. I am just saying that if I were to learn everything he is interested in to the point of being able to assist with university level classes (to be ahead of him), I would burn out mentally. 

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11 minutes ago, Arcadia said:

For me it is read and then discuss with someone or tutor someone. When I had to explain in different ways to someone with only pen and paper, I really have to think hard. 

This. Every teacher knows that to thoroughly understand something, they have to teach it.

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My older ds is mathy like your daughter and is a physics major at university. At 8 he read The Way Things Work, cover to cover, over the period of 6 months and really internalized the content. 30 minutes every morning laying in my bed while I was making breakfast and getting ready for the day. He didn't zip through it, but made sure that every single idea was clear to him. I think that this kind of work with concepts first can really aid a student in understanding when you throw the math on top. 

I will also add, that my son is the top student in all his physics classes because of his math and problem solving background. He only took algebra based physics in high school with a very large conceptual component. 

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7 minutes ago, lewelma said:

My older ds is mathy like your daughter and is a physics major at university. At 8 he read The Way Things Work, cover to cover, over the period of 6 months and really internalized the content. 30 minutes every morning laying in my bed while I was making breakfast and getting ready for the day. He didn't zip through it, but made sure that every single idea was clear to him. I think that this kind of work with concepts first can really aid a student in understanding when you throw the math on top. 

I will also add, that my son is the top student in all his physics classes because of his math and problem solving background. He only took algebra based physics in high school with a very large conceptual component. 

I’ve got the problem solving down, lol. I’m very good at that. 

Why algebra-based and not calculus-based?

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On 3/2/2021 at 11:33 AM, LadyLemon said:

A bad view view here on chemistry and a real intuition for chemistry. I don't know if real intuition is a thing in chemistry, yes we learn the rules and how to use them.

There is such a thing as developing an intuition for chemistry.  I know this because I was able to do it for organic chemistry.  It comes from understanding the concepts and applying them to a ton of problems while at the same time always thinking about how things are working (as opposed to memorizing and cranking it out).

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1 hour ago, Not_a_Number said:

I’ve got the problem solving down, lol. I’m very good at that. 

Why algebra-based and not calculus-based?

He wanted to start physics at 12, but hadn't taken calculus. So regentrude recommend Knight's College Physics, which he quite liked. But it is a very fat book, so he got throught it all in about three years.  Then it was time to do chem and bio. What was nice is that by going slowly, it sank in. I think the biggest problem kids have with high school survey classes is that they go so fast that you learn it for the test/exam and then don't hit it again because you don't continue on in the same science. You switch to one of the other big three and then learn super fast again. 

My point was not to suggest algebra based physics is a better path, more to tell you that my kid gets the top grade in all his physics classes (like 97% on his last test when the mean and median were around 63%) even though he did not take calculus based physics in high school. Basically by going slowly he developed the intuition you are looking for. And then because he has the math and problem solving, all his classes are easy. 

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2 minutes ago, EKS said:

There is such a thing as developing an intuition for chemistry.  I know this because I was able to do it for organic chemistry.  It comes from understanding the concepts and applying them to a ton of problems while at the same time always thinking about how things are working (as opposed to memorizing and cranking it out).

Any suggestions for me?

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1 hour ago, lewelma said:

I will also add, that my son is the top student in all his physics classes because of his math and problem solving background. He only took algebra based physics in high school with a very large conceptual component. 

That’s hopeful for me, at least, since my background is very similar.

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2 hours ago, Arcadia said:

@8filltheheart One of her sons did his physics at university level while in high school. 
I exceeded my parents ability quite early. I think the most useful student survival skill for me and my kids was to know when and how to get help. I can’t be a subject matter “expert” in everything that my kids are good at, and I don’t wish to be. 

 

2 hours ago, Not_a_Number said:

No, obviously one can’t be an expert in everything, but I do think my kids benefit from the things I AM an expert at. 

If your dd is ready to handle the physics, she will be better off taking the courses at a 4 yr university than anything you can offer at home, even if you have taught yourself to expert.   By DEing, ds had access to labs (he took cal physics and modern at a U and I cannot fathom attempting to replicate the lab experience he had there at home), built rapport with his professors, got a summer internship in a lab while in high school, had a prof want to take him to Kit Peak for some sort of collaboration meeting (the U wouldn't let him go bc he was only 16), etc.  He was surrounded by professionals who fed his enthusiasm.  Some things are better pursued at the level they are meant to be taken in the environment that fosters the greatest opportunities for learning mastery.

FWIW, ds has an excellent sense of physics and during middle school and early high school he achieved it through watching untold number of hours of Great Course lectures (we own every single physics and astronomy lecture series they produced up to the time he graduated from high school) and reading books like Kip Thorne's Black Holes and Time Warps.   But he is not your typical kid, either.  He truly loves physics with a passion.  He took 2 physics classes beyond modern (physical and intermediate mechanics IIRC) and started with electromagnetic wave theory his freshman yr.  

Learning for you own edification and desire.....go for it and enjoy.  But, thank heavens we don't need to be experts for our kids to achieve their potential!!!!  I hate chem and stink at physics and have kids who have excelled in both!!)

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2 minutes ago, Not_a_Number said:

Any suggestions for me?

Did you read my post on the bottomed of page 1? Because I have as discussing intuition between chem nd physics. 

I will also say that I developed intuition on organic also. Much easier than in other areas if chem. And I agree with EKS, once you put the content to memory, you just need to do tons of complex problems to develop intuition. I see it kind of like the drill required to be able to speak a foreign language. You may know all the vocab and the grammar, but you can't speak it fluently until you practice a lot. 

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Just now, lewelma said:

Did you read my post on the bottomed of page 1? Because I have as discussing intuition between chem nd physics. 

I will also say that I developed intuition on organic also. Much easier than in other areas if chem. And I agree with EKS, once you put the content to memory, you just need to do tons of complex problems to develop intuition. I see it kind of like the drill required to be able to speak a foreign language. You may know all the vocab and the grammar, but you can't speak it fluently until you practice a lot. 

See, I don’t think one even needs grammar to speak a language, lol. But that’s off-topic.

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1 minute ago, lewelma said:

Did you read my post on the bottomed of page 1? Because I have as discussing intuition between chem nd physics. 

I should go back and read again 🙂 . But honestly, I’d like practical suggestions for what to DO. I don’t think I’ll have any sense about the intuitions until I have some.

 

1 minute ago, lewelma said:

I will also say that I developed intuition on organic also. Much easier than in other areas if chem. And I agree with EKS, once you put the content to memory, you just need to do tons of complex problems to develop intuition. I see it kind of like the drill required to be able to speak a foreign language. You may know all the vocab and the grammar, but you can't speak it fluently until you practice a lot. 

Hmmm. Interesting. 

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On 3/3/2021 at 2:18 PM, lewelma said:

But these things are not *intuition*. I wonder if intuition is about things you can see and experience, and we don't see and experience chemistry, only the macro scale outcome of the reactions.

I don’t think we’re using this word in the same way. I have deep intuitions about Markov chains, and we don’t experience those day to day. But I’ve studied them and gotten a feel for them.

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1 minute ago, Not_a_Number said:

See, I don’t think one even needs grammar to speak a language, lol. But that’s off-topic.

Haha. Fine. But you have to practice. 

A long time ago I read about how subjects are split into four types of learning. Analytical (math, physics), interpretative (english, media studies), synthesis (chemistry and bio), production (music and foreign language). Clearly, there is overlap. I think you will find physics very straight forward to learn because of your background in analytical learning. But chemistry is a very different kind of learning. 

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3 minutes ago, Not_a_Number said:

 🙂I’d like practical suggestions for what to DO. 

Well, my approach has been to read textbooks, do problems, think about how the problems generalizes, memorize the things that must be put to memory, review regularly, look everywhere I can to use this knowledge in real life, and do this process over many years so I don't forget what I have learned. 

So basically you need a book, time, and motivation. 

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6 minutes ago, lewelma said:

Haha. Fine. But you have to practice. 

A long time ago I read about how subjects are split into four types of learning. Analytical (math, physics), interpretative (english, media studies), synthesis (chemistry and bio), production (music and foreign language). Clearly, there is overlap. I think you will find physics very straight forward to learn because of your background in analytical learning. But chemistry is a very different kind of learning. 

Why the bolded? Only because it's taught a certain way in schools. Chemistry is really nothing but applied physics. 
The reason we perceive it as different is that we are taught at a level that is below actual understanding, so there's a lot of fudging and rules that aren't actually rules and such.

Edited by regentrude
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7 minutes ago, regentrude said:

Why the bolded? Only because it's taught a certain way in schools. Chemistry is really nothing by applied physics. 

Yes and no. Clearly, the further in you get, the more they converge, but when you first start learning them they are very different styles of learning. When I'm studying organic chemistry, I'm putting all the reactions to memory, and then I'm solving synthesis problems. When I'm studying EM, Im doing math problems. I also agree with Dicentra that there is a LOT you have to take on faith in chemistry especially in the beginning. You can't learn it linearly. What you need to know now, you won't learn til later. Nothing makes sense until you go down a bunny trail only to find you can't understand the bunny trail anyway, so you just have to memorize it. In addition the process/reactions of chemistry do not link to the macro observations like it does in physics. The two subjects require just very different learning styles.

Edited by lewelma
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10 minutes ago, lewelma said:

Yes and no. Clearly, the further in you get, the more they converge, but when you first start learning them they are very different styles of learning. When I'm studying organic chemistry, I'm putting all the reactions to memory, and then I'm solving synthesis problems. When I'm studying EM, Im doing math problems. I also agree with Dicentra that there is a LOT you have to take on faith in chemistry especially in the beginning. You can't learn it linearly. What you need to know now, you won't learn til later. Nothing makes sense until you go down a bunny trail only to find you can't understand the bunny trail anyway, so you just have to memorize it. In addition the process/reactions of chemistry do not link to the macro observations like it does in physics. The two subjects require just very different learning styles.

most of the interesting physics does not allow macro observation; that is possible pretty much only in mechanics. We don't see electric and magnetic fields, and come quantum physics, nothing can be "seen" anymore. 
One could just wait with chemistry and treat it as what it is: an application of quantum physics plus thermodynamics 🙂 Which means, quantum physics and thermo must be understood first. We're kind of doing chemistry backwards, by starting from all the empirical stuff. 

(I think @Dicentra and I had several discussions about that 🙂

Edited by regentrude
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2 minutes ago, Not_a_Number said:

Why do you HAVE to learn it like that?

because in order to have a truly systematic study of chemistry, you would have to have oodles and oodles of physics first. It's taught this way because the students do not have a quantum mechanics and thermodynamics background

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4 minutes ago, regentrude said:

because in order to have a truly systematic study of chemistry, you would have to have oodles and oodles of physics first. It's taught this way because the students do not have a quantum mechanics and thermodynamics background

Well... would it them make sense to do that first? I'm not a high school student, thankfully. And I retain things I understand much better (like most people, I would say.) 

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7 minutes ago, Not_a_Number said:

Well... would it them make sense to do that first? I'm not a high school student, thankfully. And I retain things I understand much better (like most people, I would say.) 

if you want to first complete the physics a physics major needs for their degree, just so that you them have a better understanding of chemistry....

In our program, intro to quantum and thermo are senior year courses. 

Edited by regentrude
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1 minute ago, regentrude said:

if you want to first complete the physics a physics major needs for their degree, just so that you them have a better understanding of chemistry....

Hey, why not? 😛 Sounds like fun. I got through more than a math major does for a US degree in 3 years way back when. 

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2 minutes ago, regentrude said:

In our program, intro to quantum and thermo are senior year courses. 

Serious question: how many of the freshman and sophomore are "general" classes? I went to school in Canada, and we basically had NO requirements that made us well-rounded. I just jumped into the math and did that 😛 . I got to what would be a graduate course in the US pretty quick. 

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