Curriculum question

J

jpanknin

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Hi everyone. I could use thoughts on how to proceed here. I'm self-learning and am trying to figure out the best curriculum. I work with a bunch of engineering PhD's (applied math, computer science, physics, operations research, statistics, etc. ) and am trying to get myself up to a decent level of math so that I can communicate effectively. It's been 20 years since college and though I took most of the classes below back then I've forgotten most of it. My plan is to go through trig, precalculus, calculus, linear algebra, statistics and then figure out what's next after that. I'm using Mckeague's trig book (8E - almost done with it), Stewart's precalc (7E) and calculus (8E) books, and Strang's Intro to Linear Algebra (5E) book. I'm doing every section in each book and 99% of the problems in each section, so if I do one section per day I can finish in around 10 months. My goal is not just to get familiar, but develop a really strong foundational understanding that I can build on. We do a lot of AI, machine learning, deep learning, data science, etc. which is very math heavy, so I need to be able to understand these at an intuitive level. Thus, the "Dummies" collection wasn't sufficient.

My questions are: 1) is this a good approach given the balance of time and how well I need to know the material and 2) how important is the precalc (cutting out precalc would save about 3 months) or should I move straight into the calculus book after trig (I'm good at most of the precal stuff, though it's been a long while since I've covered it and certainly didn't learn it intuitively back then, and some of the precal material is also covered again in the calculus book, so I don't want to spend time covering the same topic twice). I'm fine spending the time if I need to, but don't want to spend time on something redundantly.

Any thoughts and suggestions are appreciated.

JP
 
One does not need a PhD to communicate in the material you mentioned although it would help with calculus and linear algebra--not that you said that you need a PhD.

It seems that you want to learn it well so I do advise you to study Pre Calculus. There is going to be lots of repeated material within ALL the subjects you listed so just don't read the repeated sections more than once but I would advise you to look at the problems at the end of those sections. As far as doing every problem that may not be a great idea. If 10 problems are exactly the same is it really worth doing all 10 problems?

Learning one section per day and doing 99% of the math problems at the end of the section is not going to be bad at the beginning but at some point you will have to give some problems some deep thought. Any given problem could take you a bit of time to figure out.
 
Jomo said:
One does not need a PhD to communicate in the material you mentioned although it would help with calculus and linear algebra--not that you said that you need a PhD.

It seems that you want to learn it well so I do advise you to study Pre Calculus. There is going to be lots of repeated material within ALL the subjects you listed so just don't read the repeated sections more than once but I would advise you to look at the problems at the end of those sections. As far as doing every problem that may not be a great idea. If 10 problems are exactly the same is it really worth doing all 10 problems?

Learning one section per day and doing 99% of the math problems at the end of the section is not going to be bad at the beginning but at some point you will have to give some problems some deep thought. Any given problem could take you a bit of time to figure out.
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You MAY simplify your life a little by a slightly different approach. Rather than doing 99% of the problems in the section, LOOK at 100% of them and make a choice on each one. If it looks easy, skip it. If you do not see IMMEDIATELY how to solve it, stop and work on that one. You have to be terribly honest with yourself. It doesn't work for everyone, even if the one is terribly honest.

I'm a little afraid of the assignment of 1 section per day. If that's TOO SLOW, it may lead to boredom or laziness. If, on some days, you're feeling good and you just tackled a short section, then maybe do a second or a third. Don't limit yourself with your goals. Goals should stretch, not limit.
 
Thanks @Jomo and @tkhunny. You both have good points. I started with a goal of two per day, but I often find that one section per day is too fast given the time I need to spend digging into the concepts and understanding them intuitively (on top of other work obligations). Yet it also feels like progress is coming very slowly with only one per day. Thus the balance I'm trying to strike. I appreciate the thoughts and suggestions.
 
tkhunny said:
You MAY simplify your life a little by a slightly different approach. Rather than doing 99% of the problems in the section, LOOK at 100% of them and make a choice on each one. If it looks easy, skip it. If you do not see IMMEDIATELY how to solve it, stop and work on that one. You have to be terribly honest with yourself. It doesn't work for everyone, even if the one is terribly honest.

I'm a little afraid of the assignment of 1 section per day. If that's TOO SLOW, it may lead to boredom or laziness. If, on some days, you're feeling good and you just tackled a short section, then maybe do a second or a third. Don't limit yourself with your goals. Goals should stretch, not limit.
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If I am doing a self-study math - after MASTERING all (with pencil paper & 100%) the example problems - I tackle the problems assigned at the end of the chapter. I do not "do" 100% of those problems. If there are say 25 problems, I pick to do 1, 5, 10, 15, 20 & 25. After doing those if I "do not feel comfortable" - I do 2, 6, 11, 16, 21 & 24.

This strategy worked well for me, my children and the students I tutored. The main-stay of this strategy is to MASTER all the example problems (100%) in the textbook.
 
I surely disagree with Subhotosh's last post. It may be that you only know how to do 1, 5, 10, 15, 0 and 25 but no other problems. As tkhunny suggested, look at ALL the problems and if there is any doubt at all as how to do it, then do it.
 
Jomo said:
I surely disagree with Subhotosh's last post. It may be that you only know how to do 1, 5, 10, 15, 0 and 25 but no other problems. As tkhunny suggested, look at ALL the problems and if there is any doubt at all as how to do it, then do it.
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That will be highly unlikely - specially if they know how to do the #0 problem......
 
Subhotosh Khan said:
That will be highly unlikely - specially if know how to do the #0 problem......
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At least I do not think that 1 is on the 5 times table.

Yes, it is highly unlikely but can sometimes be truer than other times. Why not be sure you can do all of them.

When I was an instructor I gave very unstructured homework assignments. I told my (mature college) students to do enough problems at the end of the sections so that you know how to do all of them. For some students it might have been 3 or 4 problems and for others it may have been every problem in the textbook plus some more from another book. I firmly believe that students do not work at the same pace and I saw first hand as a student that structured homework assignment did not always work. Sometimes there were not enough problems for some students and sometimes I could not do many of the problems that were not assigned. Possibly in high school this would not have gone over well but my students respected me and knew that I had their best interest at heart. I had to go over many more 'homework' problems in class but that was fine.
 
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