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

[Hsopitalist]

Quick background: I'm an MD with 25 years of experience. I was never into math as a youngster so didn't so well. As I've gotten older (I'm 52) I really want to dig into it.

I have been doing the courses on EDX, starting from college algebra and now in precalculus. I am learning quickly but I have noticed that I tend to make EVERY mistake at least once. My girlfriend points out that I sometimes work 90 hours a week and do this when I'm tired but sometimes that's not the case.

Is the fact that I make so many mistakes this early on an indication that I should stay away from the higher things? I have read before that if you struggle through basic calculus you probably shouldn't be a math major because it doesn't get easier. I wouldn't necessarily say I am struggling but it does get frustrating when I realize the simple things I screw up on.

Any thoughts?

 

[symbolipoint]

Is the fact that I make so many mistakes this early on an indication that I should stay away from the higher things?

No.

You work as an M.D. for several hours (is that 90?) per week and you are reviewing Pre-Calculus, which is a hard course. You should learn as you go, to make fewer mistakes, and need to check your work to find those mistakes, which again helps you to figure what kinds of mistakes you may make.

What really makes progressing to "higher Mathematics" a difficulty to achieve, is the need to do your job as a medical doctor. What would happen if you interrupt that work to spend several months learning Mathematics in order to get into or "through" Calculus courses? Do you then suffer skill and knowledge deterioration for your medicine work?

 

[Hsopitalist]

Thanks for the reply S.

Yes, that's 90. But sometimes it's zero depending on how I schedule things. I have a lot of flexibility.

With the various online courses available I don't see that I will ever need to interrupt my job to focus solely on learning. I have really enjoyed what I have been learning so far and do want to continue.

 

[Orodruin]

With the various online courses available I don't see that I will ever need to interrupt my job to focus solely on learning.

I think what @symbolipoint means to say is that learning these things is typically considered a full time job in itself and even then it takes years.

Otherwise I agree with him. We all make mistakes when learning (in particular when tired from other things). What is more important is if we learn from our mistakes.

 

[Hsopitalist]

I am definitely learning where I make mistakes! It is frustrating to have so many errors but interestingly pleasant when I discover where I went wrong.

I'm spending average about 15 hours/week now since February. It seems to have displaced crosswords puzzles and reading as a hobby.

Thanks for the responses, I appreciate it.

 

[The Bill]

I have to agree that no, it isn't a bad sign. My degree is in mathematics, and I also made just about every type of mistake along the way. Some of the misconceptions I used to have are really embarrassing.

I had to work through it all, but I eventually I was able to learn enough to understand current research in the areas I'm interested in. And yeah, that took years to do.

From what you described, I don't see anything that should discourage you.

 

[Hsopitalist]

The Bill,
thanks for the perspective. So I'm gathering that what I'm going through is the norm. All these replies are helping my confidence.

 

[bhobba]

I already have a degree in math and do exactly the same thing - its normal. Forget it - you will get better. Get onto calculus as fast as you can then Boaz:
https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20

You just need basic calculus - Boaz is pretty complete.

Remember - take your time - its not a race.

After that get some exposure to more 'pure' math. The best I have come across for that is is Hubbard:
http://matrixeditions.com/5thUnifiedApproach.html
Bottom line is you are doing just fine. Keep it up and over time you will surprise yourself at what you have learned and can do.

Also remember math is not really about doing long calculations without error or proving tough theorems. Although important, what it's really about is concepts.

Thanks
Bill

 

[Hsopitalist]

Bill,
Quick follow-up. I finished the precalculus course and am using your advice to "get on to calculus as soon as you can" now I'm doing a minimum of 10 basic problems per day. Still enjoying it.

Sean

 

[StatGuy2000]

To the OP:

I did my undergraduate in math (and a masters in statistics) and have also made more than my share of mistakes. I think it's perfectly normal for people to make mistakes while they are learning any subject -- the key is to learn from those mistakes and build on your knowledge.

So I think you are doing more than fine.

BTW, I know that you have been a practicing physician for the past 25 years. As a statistician working in the health care and pharma sectors for almost 20 years, I'm well aware of the connections between mathematics and medicine (e.g. epidemiology, biostatistics). Are you possibly thinking of expanding your knowledge in this direction as well?

 

[berkeman]

I'm spending average about 15 hours/week now since February. It seems to have displaced crosswords puzzles and reading as a hobby.

Sounds like a good substitute! As others have said, don't worry about the mistakes, as long as you are learning from them.

One piece of advice from me -- I'd recommend trying to mix in as many practical problems as you can. Just working math problems in a vacuum can be good practice, but working real-world word problems is much more interesting for me. That may mean studying a bit of physics or engineering at the same time you are studying the math behind those disciplines.

Also, in case you haven't already learned this, in real-world word problems, it's a big help to carry along the units of each quantity (variables, constants, etc.) to help to avoid making mistakes and to be sure you are calculating the right thing. We have an Insights article that will help to describe what I'm talking about:

https://www.physicsforums.com/insights/make-units-work/

Have fun doc!

 

[berkeman]

BTW, if you haven't already done so, check out the Math Challenge threads that are posted by @fresh_42 -- they include a section for High School level math, which sounds appropriate for your level of learning right now:

https://www.physicsforums.com/threads/math-challenge-february-2020.983823/

 

[Hsopitalist]

To the OP:

I did my undergraduate in math (and a masters in statistics) and have also made more than my share of mistakes. I think it's perfectly normal for people to make mistakes while they are learning any subject -- the key is to learn from those mistakes and build on your knowledge.

So I think you are doing more than fine.

BTW, I know that you have been a practicing physician for the past 25 years. As a statistician working in the health care and pharma sectors for almost 20 years, I'm well aware of the connections between mathematics and medicine (e.g. epidemiology, biostatistics). Are you possibly thinking of expanding your knowledge in this direction as well?

StatGuy2000

It's not my intention to apply this new knowledge to any field of medicine, I'm exploring just for exploration's sake. Having said that, I'm always open to new approaches to old problems so who knows?

 

[Hsopitalist]

Sounds like a good substitute! As others have said, don't worry about the mistakes, as long as you are learning from them.

One piece of advice from me -- I'd recommend trying to mix in as many practical problems as you can. Just working math problems in a vacuum can be good practice, but working real-world word problems is much more interesting for me. That may mean studying a bit of physics or engineering at the same time you are studying the math behind those disciplines.

Also, in case you haven't already learned this, in real-world word problems, it's a big help to carry along the units of each quantity (variables, constants, etc.) to help to avoid making mistakes and to be sure you are calculating the right thing. We have an Insights article that will help to describe what I'm talking about:

https://www.physicsforums.com/insights/make-units-work/

Have fun doc!

berkeman

Dimensional analysis is one of the only things I remember from high school. It has carried me a LONG way.

My father has a PhD in mech engineering and we discuss real world problems every now and then (stuff he has worked on). I like the idea of learning about electromagnetics and of course understanding QM is off in the distance. Anything you would suggest as a starting point?

 

[Hsopitalist]

BTW, if you haven't already done so, check out the Math Challenge threads that are posted by @fresh_42 -- they include a section for High School level math, which sounds appropriate for your level of learning right now:

https://www.physicsforums.com/threads/math-challenge-february-2020.983823/

View attachment 257602

Thank you for this suggestion!

 

[Hsopitalist]

Berkemen,

Can you suggest some physics books that use calculus? I had two non-calculus semesters of physics back in the late 80's and want to relearn in a more math environment. "Intro" level is fine.

 

[berkeman]

Berkemen,

Can you suggest some physics books that use calculus? I had two non-calculus semesters of physics back in the late 80's and want to relearn in a more math environment. "Intro" level is fine.

Others can probably suggest some good basic physics books, but have you looked at other learning resources like good-quality videos? The Khan Academy videos have become very popular, and generally get good reviews.

I mostly learn new stuff out of textbooks as well right now, but given your limited time for studying, you might find instructive videos to be a good first step (and then look for textbooks to use for additional in-depth exploration)...

https://www.khanacademy.org/science/physics

 

[berkeman]

Quick background: I'm an MD with 25 years of experience. I was never into math as a youngster so didn't so well. As I've gotten older (I'm 52) I really want to dig into it.

BTW, I really enjoyed the medical imaging course that I took a long while back. The math behind modern scans (CAT, NMR, PET, etc.) is fairly involved, but so practical in the end. With your background you probably would find it enjoyable. I no longer have my textbook from that course, and don't remember the author, but you could look through a few of the available books on Amazon (or at your local university library) to see if any of them interest you...

https://www.amazon.com/s?k=medical+imaging&i=stripbooks&ref=nb_sb_noss_2&tag=pfamazon01-20

 

[Mondayman]

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.

 

[Keith_McClary]

You might try some "fun" math such as from Martin Gardner.

 

[Dr_Nate]

Definitely try to have fun with the math. Sometimes ditch the textbook for a little while and play with math you've already learned. Try to make up a problem for you to solve. See what is and isn't possible.

Math is also more than just symbols. In a spreadsheet, you can play around with equations and plot them. You can also throw things into Wolfram|Alpha and see what you get.

 

[Keith_McClary]

Math with Bad Drawings has some interesting problems.

Also, Mathematical Enchantments (monthly writings in and around mathematics by James Propp) (Spoiler alert, the explanation of the $2\times n$ disk packing paradox is further down the page.).

 

[mathwonk]

Just reading the title, I assumed you would say you broke out in hives when you heard the word "isomorphism". i couldn't think of any other contra - indications.

 

[Hsopitalist]

Today is my one-year anniversary on physicsforums.com. I've made tons of progress thanks to all the help I've gotten here and for that I thank you guys. Still going strong.

 

[FactChecker]

I have really enjoyed what I have been learning so far and do want to continue.

That is all I need to hear to say that you should continue. There is nothing more difficult about calculous than about the math that you have already studied. In pure math, you will eventually encounter abstraction that might be difficult, but you might also like that.

 

[Hsopitalist]

That is all I need to hear to say that you should continue. There is nothing more difficult about calculous than about the math that you have already studied. In pure math, you will eventually encounter abstraction that might be difficult, but you might also like that.

Funny you bring that up. I'm at the tail end of Stewart's 5th chapter and it seems to be all about proofs. Not sure exactly how I'm supposed to approach that self teaching.

 

[FactChecker]

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.

 

[MidgetDwarf]

Funny you bring that up. I'm at the tail end of Stewart's 5th chapter and it seems to be all about proofs. Not sure exactly how I'm supposed to approach that self teaching.

If you are still interested in a calculus based physics. Look into Alonso And Finn: University Physics. It is a neat book that does not shy away from the calculus. Almost everything has a derivation. The series is pricey, maybe around $300 to $500, but since you are a Doctor, it won't hurt your pockets too much. You could also had it down to children/grand children.

For Calculus, I would suggest to ditch Stewart Calculus, and maybe get Moise Calculus. It is a middler ground between Spivak/Apostol/Courant and Thomas. However, the book leans more towards Courant. The author has great expository skills, and makes the proof understandable.

 

[Hsopitalist]

If you are still interested in a calculus based physics. Look into Alonso And Finn: University Physics. It is a neat book that does not shy away from the calculus. Almost everything has a derivation. The series is pricey, maybe around $300 to $500, but since you are a Doctor, it won't hurt your pockets too much. You could also had it down to children/grand children.

For Calculus, I would suggest to ditch Stewart Calculus, and maybe get Moise Calculus. It is a middler ground between Spivak/Apostol/Courant and Thomas. However, the book leans more towards Courant. The author has great expository skills, and makes the proof understandable.

Hey, thanks for the suggestion. Why the heck is Finn so expensive? Went ahead and ordered a 1966 addition of Moise.

 

[MidgetDwarf]

Hey, thanks for the suggestion. Why the heck is Finn so expensive? Went ahead and ordered a 1966 addition of Moise.

Out of print. But if you are able to read a non-English language, then its a lot cheaper. Ie., Spanish, can be had for $50 for all 3. Russian for $40., etc..

 

[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.