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DS was asking this morning to learn Linear Algebra (eeek!) because he thinks it will help him with his programming. He's working in AoPS Pre-Algebra right now. I don't see any easy way to accelerate him via AoPS to get to the point where he can start Linear Algebra any time soon. But then I remembered that Elements of Mathematics claims it can get kids from pre-algebra through calculus in 3 years. So I'm considering having him take a break from AoPS to do EoM.

 

I know that EoM doesn't have all their courses available yet, but for those of you who've tried them, do you really think they do a decent enough job teaching the foundational concepts that a kid who completes them will be ready to tackle Linear Algebra? DS is young enough that he can always go back to AoPS and do their intermediate courses to go more "in depth" with the concepts.

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I don't have a comment on the teaching, but we tried the first course or two way back, three years ago I think.  I'm surprised they don't have all the courses done yet; that might make me skeptical about future releases and whether it would be an efficient program for your ds's goals.

 

It sounds like he has very specific reasons in mind for learning linear algebra - might he be interested in Counting and Probability and/or Number Theory for programming purposes?  Those would be accessible to him much sooner.  Otherwise, maybe someone can suggest some sort of introduction to linear algebra that would be accessible sooner.

 

:lurk5:

 

Eta, poking around a little on google, some say that calc is not necessary to learn linear algebra, just high school algebra.  I suppose it depends on the linear algebra course.

Edited by wapiti
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Life of Fred also has a Linear Algebra book, which might be a fun introduction to read now, even if he can't do all the math yet (DD and DH bought LOF Real Analysis and Five Days this past weekend for exactly that reason).

 

I didn't realize that LoF had a Linear Algebra book, thanks for the recommendation!

 

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DS was asking this morning to learn Linear Algebra (eeek!) because he thinks it will help him with his programming. He's working in AoPS Pre-Algebra right now.

 

Its heresy, but I'd ignore him... or maybe being benignly neglectful is more the case. He probably doesn't want to learn linear algebra; He probably wants to learn to game program. This 4 part series , http://blog.wolfire.com/2009/07/linear-algebra-for-game-developers-part-1/ , is a decent intro to  vectors and translation, rotation, and maybe scaling for (high school-ish)game programmers. There are plenty of other tutorials for folks without the math. Eventually he needs beefy theoretical LA but for right now he's probably better off with something less rigorous. I would continue rigorous math in parallel to whatever hackish math he wants to learn for programming. Eventually his programming and math maturity will meet.

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He did well enough on the EoM aptitude test to be recommended and he said it was fun (he has loved AoPS/BA, Singapore IP, MEP, etc.) So I went ahead and bought him the 1st course. We'll see how he likes it and then decide about continuing on in the series vs. resuming AoPS.

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  • 1 month later...

How old is your son Crimson Wife? (I am on my phone). And since he seems to have done the course in six weeks how was the time commitment?

 

He will turn 11 later this fall. He's been spending 3.5 to 7 hours per week on it according to the most recent progress report.

 

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  • 2 weeks later...

CW..

 

DS9 (10 in December, and beginning Singapore 5 in a couple of weeks) took the assessment and it strongly suggested he enroll in the course.  But he has not completed all of elementary mathematics yet.  

 

Having taken the course, would you suggest holding off on that first course until after completing elementary math?  Or is that first course just a good supplement to add in some logic and critical thinking?  

 

DS will be doing Singapore 5 along with the remainder of Beast 4 and then Beast 5 over the next year. 

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Having taken the course, would you suggest holding off on that first course until after completing elementary math?  Or is that first course just a good supplement to add in some logic and critical thinking? 

 

A lot of the content in the first course is stuff that isn't covered in a typical K-12 math sequence. My FIL is a retired high school math teacher with a master's in math and he said that he hadn't seen the stuff DS was doing (modular arithmetic) until college.

 

Some of the topics in EMF 2-7 are covered in Singapore 5 & 6 (decimals, negative numbers, ratios & proportions, Cartesian coordinates) but tackled in a very different fashion. My DS has finished SM 5 & 6 but I still think he will get a lot out of EMF.

 

EMF reminds me a lot of CSMP and some of the units in the secondary level of MEP. Only I don't have to try to figure it out myself first :thumbup:

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Would you think EMF PLUS Singapore PLUS Beast would be too much?  

 

Another option would be to have him complete Singapore 5 this year and then while he is wrapping up Beast 5 next spring and summer, enroll him in the first EMF course.  Then, EMF plus AoPS next fall for pre-al?  Too much?  Overkill?  Or a nice assortment of different kinds of maths?  

 

I honestly was very surprised he scored as well as he did on the EMF assessment. He's always been very intuitive with math and numbers but his reading, while advanced, is not on par.  

 

EMF is brand new to me...hadn't heard of it until EIMCS was mentioned in a different thread a couple of days ago.  

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Would you think EMF PLUS Singapore PLUS Beast would be too much? 

 

Depends on the kid and how much he enjoys math. My DS did SM 4 on alternate days as BA 3. He didn't end up using any of the other BA books for a combo of reasons.

 

He stopped AoPS Pre-A when he started EMF. I suppose I could've had him do alternate days but he loves EMF so much that I'm fine with him doing it exclusively for now.

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Depends on the kid and how much he enjoys math. My DS did SM 4 on alternate days as BA 3. He didn't end up using any of the other BA books for a combo of reasons.

 

He stopped AoPS Pre-A when he started EMF. I suppose I could've had him do alternate days but he loves EMF so much that I'm fine with him doing it exclusively for now.

 

Wow! That's awesome that he enjoys it so much. :)

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DS9 (10 in December, and beginning Singapore 5 in a couple of weeks) took the assessment and it strongly suggested he enroll in the course.  But he has not completed all of elementary mathematics yet.  

  

My DS11 tried EMF at 8. I actually looked for the old thread because I forgot how old he was when we tried.

http://forums.welltrainedmind.com/topic/450604-elements-of-mathematics-foundations/

 

Did your son take the free assessment for IMACS? He might clear that too.

https://www.eimacs.com/aptitude.htm

 

Terry Kaufman called to discuss my kids IMACS aptitude test results. He is a really nice guy, not pushy and patient in explaining.

 

Wow! That's awesome that he enjoys it so much. :)

Jojomom's daughter is completing the modules

http://forums.welltrainedmind.com/topic/577499-elements-of-mathematics-foundations-for-credit/

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Arcadia, I didn't administer the iMACs because I thought that was for high school?  

 

I'm going to wait until at least the spring before starting him with EMF.  Mostly...I'm concerned about maturity.  Plus, he's already going to be loaded down pretty heavily this fall.  

 

He asks about it quite a bit though...he thinks it's all going to be games and traffic light problems, lol. 

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Arcadia, I didn't administer the iMACs because I thought that was for high school?

My Dec05 boy finished AoPS into to algebra and intro to geometry before trying the iMACS aptitude test. I don't know what is the cutoff score on the aptitude test. Mine are interested in the CS classes.

 

I'm holding back on signing up until all my kids outsource classes has started and I know how much time everything they sign up for takes.

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My Dec05 boy finished AoPS into to algebra and intro to geometry before trying the iMACS aptitude test. I don't know what is the cutoff score on the aptitude test. Mine are interested in the CS classes.

 

I'm holding back on signing up until all my kids outsource classes has started and I know how much time everything they sign up for takes.

 

 

That's pretty much about what I figured...

 

He's had some Algebraic introduction, but not enough.  It would be interesting, however, to administer the aptitude test and see just how intuitive he is.  

 

Sometimes...a lot of times, I think I underestimate him.  I specifically held him back from accelerating too far ahead of "grade level" because I had maturity concerns.  He's not typical accelerated in that he's not highly motivated.  Aside from being very bright, he's your typical 9 yr old boy that would much prefer to be outside playing than inside doing math.  

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IIRC I paid $45 for EMF 1 and ~$150 for the bundle of 2-4. So a similar price as Derek Owens and less than AoPS online.

 

Thank you, Crimson Wife. That is affordable for me. Is eIMACS more expensive because it is an interactive program?

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Is eIMACS more expensive because it is an interactive program?

EMF is self study with help available through their forum, kind of like AoPS. eIMACS might be more expensive because a tutor is assigned.

 

"What exactly does "self-study" mean?

Self-study means that an EMF student is expected to complete these courses without assistance from an instructor.

....

 

If EMF courses are self-study, what should my child do if he or she needs help understanding the material?

When students are logged into the EMF site they may access the EMF Help Forum. In this forum, EMF students may post questions to be discussed and answered by other students. Questions that cannot be answered satisfactorily by other students are filtered through to experienced instructors and mathematicians who will respond appropriately through the Help Forum. Students, however, are not given direct access to an IMACS instructor." https://www.elementsofmathematics.com

 

"Each student in our university-level courses and our AP® CS course is assigned a principal eIMACS instructor, who is available for questions through the eIMACS Message Center, by phone, or by email"https://www.eimacs.com/about.htm

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anybody can structure a course so that it uses any other course, but intrinsically, linear algebra does not use calculus at all.  linear algebra is about linear functions, while calculus is about non linear functions (much harder), and in fact is about approximating non linear functions by linear functions, so linear algebra should logically be a prerequisite for calculus, not the other way around.  In fact it is taught that way nowadays at most good schools, (like Harvard).

 

there are lots of free linear algebra books on the web, at all levels of difficulty, and essentially none of them really use calculus.  I have written three or four of them myself.  the most sophisticated math they use is usually polynomials in one variable.  Many books do not use even that.

 

let me explain briefly why calculus may come up in a linear algebra class.  An operation F is linear if  F(x+y) = F(x) + F(y) for all inputs x,y, and also F(cx) = c.F(x) for all scalars c and all inputs x.

 

In fact differentiation obeys these laws, i.e. if D is differentiation, and f and g are functions, then D(f+g) = D(f) + D(g) and D(cf) = cD(f).  So differentiation is an example of a linear operation and hence may be mentioned in a linear algebra course.  So if you learn calculus first, and linear algebra afterwards, they may point out that you could have understood calculus better by using concepts of linear algebra.  But sophisticated courses teach linear algebra first and then use it to teach calculus.

 

Because non honors courses usually teach in a historical order instead of a logical order, one often sees courses offered in the traditional but illogical ordering: calculus, differential equations, linear algebra; instead of linear algebra, calculus, differential equations.  But honors courses at top schools do it right.

 

here is the syllabus for the first half of (super honors) advanced calc at harvard:

 

http://www.math.harvard.edu/~ctm/home/text/class/harvard/55a/08/html/syl.html

 

and here is the syllabus for thje second half:

 

http://www.math.harvard.edu/~ctm/home/text/class/harvard/55b/10/html/syl.html

 

 

notice the 1st half is all algebra and the second half is all analysis (calculus).  Mind you i do not recommend taking this particular course since the emphasis at harvard seems to be on making it really hard, but that is because of the speed, not the ordering.  Take it somewhere where they use the same ordering but you go slow enough to learn it well.

 

 

here is a link to a free linear algebra book, that i have not lookd at lately but i remember as being very easy.

 

http://joshua.smcvt.edu/linearalgebra/

 

well i just looked at it and maybe it is not my best recommendation,  i prefer the book by paul shields, because it works in 2 and three dimensions and this is better for beginners than n dimensions.

 

here is shields' book:  (which i also have not looked at lately but recall from when my wife took the course from it.  shields is from stanford.)

 

https://www.amazon.com/Elementary-Linear-Algebra-Paul-Shields/dp/0879011211

Edited by mathwonk
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here is an example of linear mathematics:  suppose you can make a batch of 2 dozen cookies using 2 cups of flour, one cup of sugar, and one egg.  how much of those ingredients do you need to make 4 dozen cookies?  you guessed it: 4 cups flour, 2 cups sugar and 2 eggs.

 

but suppose that investing  $1,000 at 7% annual interest for 10 years returns $2,000 and you want to know how much it returns at 14%.  I doubt if it is $4,000, but you could check me on this.  e.g 14 times the rate, or close to 100% annual interest, would almost double yearly, so return close to 2^10 ≈ $1,000,000!  thats why people like warren buffet's 20% return.  unfortunately the price of those shares in berkshire hathaway have always been out of reach.  they went over the time i watched them from 3.000 to maybe 300,000.

 

this is non linear math.

 

on the other hand investing twice as much money at the same rate does seem to yield twice the return, i.e. it is linear in the investment amount, but not in the interest rate.

 

technically, (1+r)^10. P is linear in P but not in r.

 

of course (1+r)^n. P is not linear in n either, so tell your kids, if they can't find a better rate, then start investing earlier, to make n larger.  i.e. if it doubles after 10 years, it multiplies by 2^5 = 32 after 50 years.

Edited by mathwonk
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^^^^This is why I'll be outsourcing DS' accelerated math...lol

 

I took Calculus in college...don't remember a single bit of it.  

 

Word.

 

EMF is self study with help available through their forum, kind of like AoPS. eIMACS might be more expensive because a tutor is assigned.

 

"What exactly does "self-study" mean?

Self-study means that an EMF student is expected to complete these courses without assistance from an instructor.

....

 

If EMF courses are self-study, what should my child do if he or she needs help understanding the material?

When students are logged into the EMF site they may access the EMF Help Forum. In this forum, EMF students may post questions to be discussed and answered by other students. Questions that cannot be answered satisfactorily by other students are filtered through to experienced instructors and mathematicians who will respond appropriately through the Help Forum. Students, however, are not given direct access to an IMACS instructor." https://www.elementsofmathematics.com

 

"Each student in our university-level courses and our AP® CS course is assigned a principal eIMACS instructor, who is available for questions through the eIMACS Message Center, by phone, or by email"https://www.eimacs.com/about.htm

 

The forum is nothing like the AoPS forum.  There is help, but it takes a while.

 

 

FWIW, for people who are considering this, the difficulty seems to jump at Algebra.  HOWEVER, we have noticed that the program is definitely a work in progress and is constantly changing.  DD started this, I think 2 years ago, as her warm up "fun math."  She stalled a couple of times, when she was busy with other things and it was getting confusing.  Each time she came back to a vastly different scenario, which had clearly been tweaked and improved.  The last stall happened right before Christmas last year, when she she signed up for Mathcounts for the first time and started the first EMF Algebra class (note: her regular math was AoPS Intro to Algebra B).  It was too much, so EMF was the first thing I chucked overboard (in my opinion, it's a nice supplement, but only a nice supplement.)  She started playing around with it a bit this summer and, again, they have added a LOT of teaching content.  Nonetheless, she's pretty much lost interest.  The first few classes were fun and engaging; as time when on, the fun factor was lost.  For the money, I think AoPS is a better investment.  Just my two cents.  YMMV  :)

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