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If your math-nut doesn't like AoPS Number Theory...


Gil
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Glad its not just me. I thought I was crazy. We use AoPS alongside of  Zacarro books, Numberless word problems, Mathematics: A Human Endeavor and Unified Modern Mathematics, so it took a moment to pause and realize. What a minute--this is as boring as watching paint dry!

 

Intro NT is incredibly slow until the end.  We just kind of zipped through it.  Intro Counting is much more difficult from the beginning, so more enjoyable for both me and older ds.

 

Ruth in NZ

 

How close to the end until things pick up? I'm thinking maybe we should switch up the assortment and give NT a higher priority so that we can get it done?

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I don't remember, Gil.  I just remember thinking, "OMG, get to the point!"  Modular arithmatic was the main thing you learn in the book. But I do remember thinking that we could not just skip to the end, that we actually needed to do all those boring first chapters.  So we just did them really fast!

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Okay, so I just order NT to see if AoPS would be a good fit... Does anyone like it? Arg.

 

Maybe we should just return it and move on.

 

I agree the first half isn't so great.  I think the AoPS treatment of modular arithmetic is pretty good and does the job, particularly if you are prepping for AMCs.  

 

Having said that, I found a couple of number theory books at my local library which were also pretty good, so I suspect there's a lot out there if you are keen on learning about integers.  I recommend checking the Amazon reviews.  Good luck!  

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Okay, so I just order NT to see if AoPS would be a good fit... Does anyone like it? Arg.

 

Maybe we should just return it and move on.

Once it arrives, I say at least flip through it, take a close and careful look and see what you think for yourself. Try some of the different problems and see what you think for yourself.

I'm disappointed because no one told me that the NT book was "meh". We are going to pick up the pace with the book, and that will probably help off set the less-than-ideal pacing of the content itself. 

 

Like I say, we use it along with several other texts so NT isn't the only thing we are doing. I think it would go better if you high-tailed it through the book in 2-4 months instead of dawdling it out for close to 6 months the way that we have.

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So, you guys recommend doing NT before CP?

It depends on your kid.

 

For a kid that likes ciphers, NT might be too easy. Also look at the elements of math foundations

https://www.elementsofmathematics.com

 

For a kid that likes game theory, C&P might be his cup of tea

 

My oldest did both intro books over a summer since it is too hot (around 100degF) to be outdoors.

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Excuses, excuses. :D Yeah, it was horrible this summer, but my kid didn't finish both books. I can't remember what she did because we can't function in this sort of weather.

That is why we hibernate at the library. Don't want to spike my utilities bills :) Besides there is free wifi there too.

 

ETA:

He did both books a few summers ago. Last summer wasn't that hot but this kid thinks anything above 70degF is hot.

Both my kids unfortunately inherited my tendency to get heat stroke :( which means indoor sports only for summer.

Edited by Arcadia
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My oldest did both intro books over a summer since it is too hot (around 100degF) to be outdoors.

 

Yup, us too.  (minus the 100degF)  DS needed to get them done before the camp selection problems came out, so he had a chance for answering the questions on number theory and combinatorics.  We had limited time, so we just got them done.  I did them too, and found combinatorics easy chapter by chapter, but very tricky when doing problems outside of chapters where you had to pick the technique to use. 

 

We did them concurrently.  2 days one, 2 days the other.  Variety was good to help us get through the beginning of NT. We finished NT by using the diophantine chapter in the AoPS Problem Solving Book 1.  There is no intermediate NT book currently written, so ds did the class, and it was *really* hard, so don't take it as your first intermediate class!  eeeek.

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I know some that say that NT is their favorite book - but not at my home. However, I'm tutoring a girl that is really enjoying NT. It gets much better when it gets to bases and modular arithmetic.

 

"I" like Counting and Probability way better. My oldest son's favorite book was the geometry, though he likes all things math. My second son tolerates math though he does well and is finishing up the Intro books.

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That is why we hibernate at the library. Don't want to spike my utilities bills :) Besides there is free wifi there too.

 

ETA:

He did both books a few summers ago. Last summer wasn't that hot but this kid thinks anything above 70degF is hot.

Both my kids unfortunately inherited my tendency to get heat stroke :( which means indoor sports only for summer.

You need to move farther north, near the beach, where it's almost always foggy.

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So it came today, and I see what OP means. There's some good stuff in it, but if I make dd write out most of the exercises in the first few chapters, I'll have a revolt. I'm sure we'll do some of it on a white board and/ or verbally. How much of AoPS do you have your students write out?

 

 

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How much of AoPS do you have your students write out?

For NT and C&P, my kids did those as fun summmer enrichment. They show as much working as they want to show. For the prealgebra, algebra, geometry books, they need to show full working for the longer problems so that they get practice in showing their work properly so that others can understand.

 

My DS11 physical writing stamina was behind so writing out all the steps to all the problems would just give him swollen wrists. Typing the working out in Latex is less painful however I didn't want that much screen time.

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Intro NT is incredibly slow until the end. We just kind of zipped through it. Intro Counting is much more difficult from the beginning, so more enjoyable for both me and older ds.

 

Ruth in NZ

Can you give me a strategy for zipping, please? My thought was to just do it straight through between now and June, but this feels like a step back in some ways.

 

I'm going to need to throw in some algebra. The way the book is set up is how dd likes to do math- try a problem first, then learn the skill- but she already knows a lot of what's in the first couple chapters.

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DD12 really likes number theory (not so much the AoPS book - the topic). Anyone got a source for interesting number theory problems she can do for fun?

Anything to do with ciphers/cryptology was fun for my boys. You can just google ciphers or cryptology and math circles to find problems with solutions.

 

ETA:

Example http://www.cemc.uwaterloo.ca/events/mathcircles/2013-14/Winter/Senior_Cryptography_Feb4-hndt.pdf

Edited by Arcadia
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  • 2 weeks later...

Any other number theory book recommendations? I'm still on the fence. I think I'm going to return the AoPS. I can't see having a $50 book on the shelf I'm not sure about. For level, dd is partially through Jacobs Algebra.

Now that you have it, browsed through it and slept with it for a while, then I say return it. Here, at GEAR we swing between 'meh' and hate with this book. On any given day though we can all agree that we strongly dislike the book, and I'm more than a little baffled that no one else warned me of this when I asked about this exact book.

 

Just goes to show that different things work for different people. For us, AoPS is definitely a matter of one math-nuts treasure being anothers trash. Well, maybe trash is a little harsh, but I'm seriously getting annoyed with this whole AoPS thing. Maybe we waited too long to drink the Kool Aid?

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For us, AoPS is definitely a matter of one math-nuts treasure being anothers trash. Well, maybe trash is a little harsh, but I'm seriously getting annoyed with this whole AoPS thing. Maybe we waited too long to drink the Kool Aid?

One man's meat is another man's poison :lol:

 

Nobody in my family fancy Ian Stewart the mathematician even though none of us can explain why.

 

Math hasn't change for decades and generations. You might like the old Russian or German text. It is because hubby and I like old german engineering text that we took German as a 3rd language.

 

You should read about all the raves of SM, then AoPS, then BA and AoPS on these boards. It comes in waves :lol:

 

You might want to check out Spivak or Lang for calculus. Spivak is on internet archive.

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Thanks, I'll keep them in mind for the future. We stalled out in UMM a bit, so we tried switching gears to AoPS and...its a flop for us. We'll finish because they have a streak going with their completion rate of math and the boys would genuinely hate for AoPS to be the thing that ruins their streak, lol.

 

We look forward to putting this AoPS episode behind us.

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My rough understanding is that people with more sequential strengths will prefer NT while people with visual-spatial strengths will find C&P more fun.

 

My ds12 took the Intro to C&P online course last summer.  I think he really liked it but there was that little problem of actually doing all the work...I'm certain he learned things - because he knows, or is aware, of stuff he'd have no other way of knowing - but he could have gotten so much more out of it.

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My rough understanding is that people with more sequential strengths will prefer NT while people with visual-spatial strengths will find C&P more fun.

It's less the topic, and more the pacing/writing of this book. I mean for the love of God get.to.the.point already!

My ds12 took the Intro to C&P online course last summer.  I think he really liked it but there was that little problem of actually doing all the work...I'm certain he learned things - because he knows, or is aware, of stuff he'd have no other way of knowing - but he could have gotten so much more out of it.

We'll finish this book, but I'll have to seriously rethink AoPS after this, my confidence in the series based on reputation alone has been thoroughly shaken.

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We'll finish this book, but I'll have to seriously rethink AoPS after this, my confidence in the series based on reputation alone has been thoroughly shaken.

We've decided against it. Not just because of the NT book. We just are going too many other directions for the time involved. I think my dd would benefit more from being on a typical math path, but faster. She wants the tools to be able to do more science sooner. I think we'll keep with the Jacobs/ Jurgenson/ Larson, ect books, and work ahead of her so we can do it sort of flipped.

 

We used to do Fun Math Friday. I think I'll just get some of the math puzzle books on Quarks math list and let her keep working through those after she finishes her work for the week. She working some some geometry on the side, so maybe I'll start there.

Edited by elladarcy
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We'll finish this book, but I'll have to seriously rethink AoPS after this, my confidence in the series based on reputation alone has been thoroughly shaken.

 

The main books in the traditional sequence are all written by Richard Ruscyzk himself.  The others are written by different authors, so the pacing might be different. We haven't tried NT or C&P, but we do have C&P on the shelf.  We will probably do it between Algebra 1 and 2. 

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Gil, you recently described MM has "fun" on another thread. I think this is definitely the case of one man's trash... ;)

Touche. Though honestly, I meant it as a tiny bit tongue in cheek on the fun front. You all know how I love doing what works efficiently and all that jazz...

 

So true. We did the 6th grade book. It was the best option at the time. I love to tutor with it. But the whining......

I tell the boys that their whining is music to my ears. I'm the dad, not their friend and if they don't whine enough I worry that I'm not doing my job :D.

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It depends on your kid.

 

For a kid that likes ciphers, NT might be too easy. Also look at the elements of math foundations

https://www.elementsofmathematics.com

 

For a kid that likes game theory, C&P might be his cup of tea

 

My oldest did both intro books over a summer since it is too hot (around 100degF) to be outdoors.

 

While DD and I may have been exposed to both ciphers and game theory, I couldn't tell you a definition or explain which was more appealing to her or me because I couldn't come up with sample problems for either one, just a vague sense. Would you mind too much saying a little more about these two categories, what a typical problem would look like, etc.. FWIW, DD is completing PreA 2 (online class) this month. She has also done most of Jousting Armadillos and TabletClass (don't ask...).

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Would you mind too much saying a little more about these two categories, what a typical problem would look like, etc..

Alcumus has problems corresponding to both books. You can set the focus to either of the books.

 

What appeals to my kids about C&P more than NT is the psychology/applied aspect of the questions. NT is more theoretical in comparison.

 

The C&P book practice would come in useful for SAT, eventhough you can use any test prep book for the prob & stats questions instead.

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The main books in the traditional sequence are all written by Richard Ruscyzk himself. The others are written by different authors, so the pacing might be different. We haven't tried NT or C&P, but we do have C&P on the shelf. We will probably do it between Algebra 1 and 2.

Thank you, this makes sense. I was just going to order NT, but will wait a while now and reevaluate because of this thread (thanks, Gil for saving me $50!)
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Alcumus has problems corresponding to both books. You can set the focus to either of the books.

 

What appeals to my kids about C&P more than NT is the psychology/applied aspect of the questions. NT is more theoretical in comparison.

 

The C&P book practice would come in useful for SAT, eventhough you can use any test prep book for the prob & stats questions instead.

 

ok I'll look at Alcumus, didn't think about going outside of our current text/class.

 

Will it help with the ACT? (DD just took that Saturday but might take it again next year...). Did the rumored changes to the SAT relate to this area at all or was it more the verbal area?

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Will it help with the ACT? (DD just took that Saturday but might take it again next year...). Did the rumored changes to the SAT relate to this area at all or was it more the verbal area?

I'll update later on the ACT and SAT. My complex is having renovations so we have to walk to the library to escape the noise.

 

My guinea pig oldest did the ACT in October while completing geometry and intermediate algebra. He miss full score by a point which I think is a mixture of luck and practice. Did not expect him to score that well. He is the kid who can spend hours of his spare time on Alcumus though.

 

He will be the guinea pig for the new SAT in June :lol: My youngest benefit from oldest being the guinea pig.

 

ETA:

ACT does not have probs & stats.

 

ETA:

The prob & stats portion of the new SAT

https://collegereadiness.collegeboard.org/about/alignment/math/problem-solving-data-analysis

 

Edited by Arcadia
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