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AoPS Int Number Theory supplement suggestions

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Hi,

My son will be taking Int Number Theory through AoPS in the spring.  He has taken Intro to NT and all the other Intro courses. 

One thing that will be new to my son is that there isn't Alcumus and there isn't a book.  Alcumus has been so helpful in the past.  My son really liked solving the problems and learning from the solutions when he was unable to solve the problems correctly.  He plans on re-reading the Intro NT before class starts.  I should have printed out the transcripts of the Intro to NT class, but I never saved them.

Do you have any suggestions for resources that might help study for the course?  Books, online lectures or anything you think might help?

 

Thanks

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Hi Bugfree, welcome to the board.

 

I see you have been reading all the threads about AoPS intermediate number theory.  My ds found it quite hard.  He took it as his first intermediate class, and that was possibly a mistake as it is probably the hardest of the intermediates.  Because the class is out of the mainstream USA maths sequence, there are fewer kids in it and they are at a higher (competition) level.  So what we found is that the intermediate class has less kids hanging out in chat than in Intermediate Algebra or PreCalc.  So to get through the class, my ds had to post his questions formally on the message board starting at the beginning of the week to be able to get help each day on the week's problems, as the turn around was typically 12 to 24 hours and he needed multiple hints.  Basically, he had to swallow his pride as he did not want to post under 'halp'. It was a good learning experience, and he rose to the occasion, but now in hindsight so many of the really difficult proofs seem so easy. He just did the classes out or order.

 

As for the lack of book, that was really a non-issue for my ds.  He did prep by doing the Number Theory chapters in the AoPS volume 2 competition prep book. But really that was not enough help.  The class is strongly focused in problem solving rather than new content, so it is just a matter of learning to think sideways. This takes lots of time and persistance.

 

Just to give you a feel for the level of difficulty of the class, DS is shooting for the NZ IMO team this year, and he took the Intermediate Number Theory class at age 13.  His class schedule was: age 13:  Intermediate number theory, Intermediate algebra, Intermediate counting. Age 14: Olympiad geometry, PreCalc. Age 15: Woot, self-study calc.

 

He found intermediate number theory the hardest class he took until the Woot. However, interestingly, he is one of the best at number theory in the entire NZ camp.

 

Ruth in NZ

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My son took the Int. NT class this past year (and I did it alongside him until the end when I didn't feel like keeping up with the theory).

 

My impressions:

- not having a book was not an issue for us - did no prep and had not done the Intro NT book for 2 years

- make sure you are solid on modular arithmetic before starting the class

- my son had not been exposed to the concepts yet, however it was obvious that many of the students had been exposed to much of the content therefore putting concepts together very quickly.

- there are weekly proofs which are hard if you've not had exposure to that level of proof writing (my son had done a lot of proof writing already)

- the last few weeks are harder theory

- don't worry about mastering it all

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This weekend, when (if) I see my son, who is a freshman in college and a math major, I'll ask him if he used something supplemental with AOPS Intermediate NT. I know he asked for non-AOPS book recommendations for different math topics on the AOPS forums and got some very helpful suggestions. I can't recall if it was for NT, though.

 

Mathwonk, Kathy in Richmond, Kiana and other math-savvy people might have some suggestions. They might have also responded to a similar question already. You could try searching on these boards using their names.

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Thank you so much for the suggestions.  I really appreciate it.  

The NT class starts in February and his current class ends in a couple weeks.  I looked through previous threads on Int Number Theory and bought a couple of the books that were suggested.  Between now and his Number Theory class he will watch the online lectures and read through a couple of NT books we have.  I found this online number theory class with video lectures that I am hoping will supplement the AoPS class.  The teacher seems pretty great.   https://www.udemy.com/numbertheory/learn/

 

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