lewelma Posted January 17, 2015 Share Posted January 17, 2015 The Squad training looks to be about 10 to 15 hours per week for the first half of the year. Because of this, there will not be time for the original plan: Original math plan: First half of year: AoPS precalc + self study of basic Calc1 Second half of the year: Calc2 at the university + AoPS WOOT To do this in addition to the squad training and his other work is unrealistic, so I am trying to come up with plan B. I've been looking at the university booklet and when different courses are offered, and this is what I think might work. But I really don't know what I am talking about, so I need some advice!!! Plan B First half of 2015: AoPS precalc + squad training Second half of 2015: Linear Algebra at university (200 level) + AoPS WOOT (he can't take calc2 because he won't have time to study calc 1 beforehand) First half of 2016: Discrete mathematics at university (200 level) + self study Calc 1 (I would assume that the discrete maths would help with the IMO in 2016) Second half of 2016: Calc 2 (100 level) or if he can self study calc2 also, he can take multivariate in this term instead. ++++ So my questions: 1) I think that the prof we talked to said that AoPS precalc would act as the 'algebra' prereq for linear algebra. Do I have this right? Here is the linear algebra description: "fields, vector spaces, linear transformations, eigenvectors, spectral decomposition, quadratic forms." It uses Elementary Linear Algebra by Anton as its text. It has a prereq of 'algebra', a 100 level class which is described as: "introduction to linear algebra, including matrices and vectors, complex numbers, eigenvectors, and algebraic structures" with A first Course in Linear Algebra by Easdown as its text . I want to make sure he is prepared for this class if it is his first university class. 2) Would linear algebra and discrete math help with the IMO in 2016. or just discrete math? 3) Is there a reason that he should take calculus before these other 2 classes? Because calc 2 and multivariate are both only offered in term 2. So there will be a major delay if we have to wait until July 2016 to take Calc2 or multivariate before these other classes. One alternative is to skip any university classes this year (2015), and do the AoPS programming classes instead. There is only a 3 month gap between AoPS precalc and the WOOT so not a huge down time without people and camaraderie. Typically there is a programming course offered then. So please, all you lovely people, advise us what would be the best option. Thanks heaps! Ruth in NZ Quote Link to comment Share on other sites More sharing options...
1053 Posted January 17, 2015 Share Posted January 17, 2015 . Quote Link to comment Share on other sites More sharing options...
lewelma Posted January 17, 2015 Author Share Posted January 17, 2015 Ok, so no linear algebra on the IMO. The main problem we have is his need for mathematicians in his life. Online is fine, but we are running out of AoPS courses. So this is why we are looking at the university. I thought that if I could get a class for him July to November that would also be helpful to the competitions, this would be the best of both worlds. But there is just not much available that seems appropriate. In the July to Nov term they offer: Calc2 Multivariate Calc Linear Algebra Everything else is either for engineers, or 100 level that he is placing out of, or 300 level. So maybe it would be better to just do an AoPS programming course at that time. He could then spend those months self-studying Calc. Quote Link to comment Share on other sites More sharing options...
Mike in SA Posted January 17, 2015 Share Posted January 17, 2015 I don't remember the content of Anton's book, but some college linear algebra courses require some basic calculus -- not much, but a bit. Discrete math is fairly foundational, and an excellent step forward for both competition and further study. Some universities have a second semester of it, or advanced number theory. Either of those would be worth a venture if the prereqs were met. Plus, discrete math is imminently accessible to anyone who has completed the AoPS sequence (particularly counting & probability). Although I normally wouldn't recommend it, pretty soon, you will need to get through Calc 1 & 2 to open the doors to bigger and better things. MIT-OCW has a number of excellent, powerful offerings that rely on a strong calculus foundation. This is simply due to presentation method -- much of the later content is relevant to competition. For the time being, why not take a semester to give extra time to prep? If that isn't an option, discrete math could be a self-study option, as could advanced geometry or number theory. Quote Link to comment Share on other sites More sharing options...
kiana Posted January 17, 2015 Share Posted January 17, 2015 He would be fine with Anton's linear algebra with the AOPS precalc. Anton actually starts with the very basics so while I would expect the university to omit or breeze through those chapters, he can page back to review if anything is unfamiliar. Anton *does* have a very few problems where calculus is required but they are clearly marked. I would double-check by e-mailing back to whomever you spoke to. I would also recommend that he fill any available extra time with slowly beginning his self-study of calc. The reason is because to get access to the awesome pure mathematics classes in the 300-level that I think will be totally up his alley, he's going to need the foundations course in the second year, which requires calculus. Another alternative could be: Term 1: AOPS precalc + squad training. Term 2: self-study calc 1 + aops WOOT. Term 1: self-study calc 2 + discrete math at university Term 2: multivariable, linear, or both, depending on how discrete math went. The advantage of this plan is that if he gets too busy to finish self-studying calc 1 + 2, he should at least make it through calc 1, and then in the second year's term 2 he could take calc 2. Quote Link to comment Share on other sites More sharing options...
Kathy in Richmond Posted January 17, 2015 Share Posted January 17, 2015 The Squad training looks to be about 10 to 15 hours per week for the first half of the year. Because of this, there will not be time for the original plan: Original math plan: First half of year: AoPS precalc + self study of basic Calc1 Second half of the year: Calc2 at the university + AoPS WOOT To do this in addition to the squad training and his other work is unrealistic, so I am trying to come up with plan B. I've been looking at the university booklet and when different courses are offered, and this is what I think might work. But I really don't know what I am talking about, so I need some advice!!! Plan B First half of 2015: AoPS precalc + squad training Second half of 2015: Linear Algebra at university (200 level) + AoPS WOOT (he can't take calc2 because he won't have time to study calc 1 beforehand) First half of 2016: Discrete mathematics at university (200 level) + self study Calc 1 (I would assume that the discrete maths would help with the IMO in 2016) Second half of 2016: Calc 2 (100 level) or if he can self study calc2 also, he can take multivariate in this term instead. ++++ So my questions: 1) I think that the prof we talked to said that AoPS precalc would act as the 'algebra' prereq for linear algebra. Do I have this right? Here is the linear algebra description: "fields, vector spaces, linear transformations, eigenvectors, spectral decomposition, quadratic forms." It uses Elementary Linear Algebra by Anton as its text. It has a prereq of 'algebra', a 100 level class which is described as: "introduction to linear algebra, including matrices and vectors, complex numbers, eigenvectors, and algebraic structures" with A first Course in Linear Algebra by Easdown as its text . I want to make sure he is prepared for this class if it is his first university class. 2) Would linear algebra and discrete math help with the IMO in 2016. or just discrete math? 3) Is there a reason that he should take calculus before these other 2 classes? Because calc 2 and multivariate are both only offered in term 2. So there will be a major delay if we have to wait until July 2016 to take Calc2 or multivariate before these other classes. One alternative is to skip any university classes this year (2015), and do the AoPS programming classes instead. There is only a 3 month gap between AoPS precalc and the WOOT so not a huge down time without people and camaraderie. Typically there is a programming course offered then. So please, all you lovely people, advise us what would be the best option. Thanks heaps! Ruth in NZ I would postpone calculus altogether for now. Maybe something like: 1st half of 2015: AoPS precalc + Squad training 2nd half of 2015: AoPS programming class + WOOT Your Plan B 2016 plans look great for now. When my son made MOSP & had additional at-home required work (extremely time-consuming problem sets which they would be called on to present during the first days of camp + APMO,etc), I dropped all unnecessary 'mom' math work for that time period. Squad training will give him essentially the same stuff as WOOT and AoPS Olympiad Geometry. No way would I have him working through all three of those, or even two. AoPS precalculus contains an introduction to linear algebra, as much as he needs for now. A course in discrete math would be more valuable for olympiads. You can safely save the uni linear algebra for the future, sometime before leaving high school. Calculus is NOT a prerequisite for either discrete math or linear algebra. Learning programming is always a good idea. The AoPS classes are very mathematically based. My MOSPer loved that kind of computer science. I'd have your son dip his toes into it now, just in case it turns out to be an area of interest! As always, good luck! I'm so excited for y'all! Quote Link to comment Share on other sites More sharing options...
lewelma Posted January 17, 2015 Author Share Posted January 17, 2015 Thanks guys! I think the best plan is to self study calc1 and 2 and jump to multivariate in 2016. He really likes the AoPS book and I think he wants to work through it instead of the highschool NCEA books or Anton. I could also get him the Spivik book to play with. I'll ask him if he wants to consider the AoPS programming course, sometimes they don't dovetail well which is the problem we are having with Oly Geo and Precalc as they run concurrently for 3 weeks. And looking at what I have below, might be better to wait on programming just from an overbooking point of view. But I'll ask him, because he does love AoPS classes! So basically what Kiana suggested: Term 1 AoPS precalc + squad training Term 2 WOOT + AoPS Calc self study (he doesn't want to do the class as it will destroy his summer, so he would work July to Dec) Term 1 squad training again (pretty likely) + University Discrete math class - prof said that ds has already covered about half of the class with the intermediate AoPS material, so this could be a good first class even though it is at 200 level. Term 2 Multivariate Calc at university (or Calc 2 if he doesn't get through enough material) When my son made MOSP & had additional at-home required work (extremely time-consuming problem sets which they would be called on to present during the first days of camp + APMO,etc), I dropped all unnecessary 'mom' math work for that time period. Squad training will give him essentially the same stuff as WOOT and AoPS Olympiad Geometry. No way would I have him working through all three of those, or even two. Well he will have 3 weeks of Oly Geo, Precalc, and squad training all running concurrently. :huh: We are kind of stuck with that now. I'm guessing he won't do *anything* else expect maybe the violin. Not sure you saw the additional comments I made in the other thread: x-post Ok, here is the schedule. He has to take the BMO2 (British MO, 4 hours), the AMO (Australian MO, 8 hours over 2 days), and the APMO (Asia Pacific MO, 4 hours). In addition, every 3 weeks he has a problem set to turn in that looks like it will take 30-40 hours as it has 8 proofs to write. They will give feedback on all of these exams and problems; and how he performs in the next 3 months will determine if he is on the team or not. The first big problem, he will have AoPS Olympaid geometry and AoPS PreCalc running concurrently for 3 weeks and at the exact same time of day starting on 26 Jan. This will overlap with the first problem set which is due on 8 Feb. He also has to raise $2000 travelling expenses! Although we can pay, we are going to try to get him to raise the money. Will start another thread on this issue. The next problem: we have already settled on dates to visit American and have organised with all our relatives, and the dates *exactly* overlap with the IMO in Thailand. Sigh. We don't think he will get in, but perhaps we can get some travel insurance for cancellation of his ticket?!??! Don't know. Finally, we have a serious problem with this year's (2015) math plans of doing AoPS PreCalc, Calc1 (self studied), Calc2 at university, and the AoPS WOOT and doing this in addition to the Squad training. Will start another thread on this too. As far as I am concerned, it is a disaster, and things will have to change. I am feeling very :confused1: and :hurray: and :willy_nilly: . This was very unexpected. Quote Link to comment Share on other sites More sharing options...
Kathy in Richmond Posted January 17, 2015 Share Posted January 17, 2015 Term 1 AoPS precalc + squad training Term 2 WOOT + AoPS Calc self study (he doesn't want to do the class as it will destroy his summer, so he would work July to Dec) Term 1 squad training again (pretty likely) + University Discrete math class - prof said that ds has already covered about half of the class with the intermediate AoPS material, so this could be a good first class even though it is at 200 level. Term 2 Multivariate Calc at university (or Calc 2 if he doesn't get through enough material) Well he will have 3 weeks of Oly Geo, Precalc, and squad training all running concurrently. :huh: We are kind of stuck with that now. I'm guessing he won't do *anything* else expect maybe the violin. Not sure you saw the additional comments I made in the other thread: x-post Ok, here is the schedule. He has to take the BMO2 (British MO, 4 hours), the AMO (Australian MO, 8 hours over 2 days), and the APMO (Asia Pacific MO, 4 hours). In addition, every 3 weeks he has a problem set to turn in that looks like it will take 30-40 hours as it has 8 proofs to write. They will give feedback on all of these exams and problems; and how he performs in the next 3 months will determine if he is on the team or not. The first big problem, he will have AoPS Olympaid geometry and AoPS PreCalc running concurrently for 3 weeks and at the exact same time of day starting on 26 Jan. This will overlap with the first problem set which is due on 8 Feb. The new schedule looks good to me. Self studying calculus could certainly work in Term 2 along with WOOT. In fact, I like that a lot, especially using the AoPS textbook. I think it'd be a great fit. No, I hadn't seen your other post about the schedule details. Concerning those 3 weeks of overlap, I'd certainly drop all other work!! That's going to be intense, especially Olymp Geom at the same time as squad training. Precalc should be OK I would think. Quote Link to comment Share on other sites More sharing options...
lewelma Posted January 17, 2015 Author Share Posted January 17, 2015 Concerning those 3 weeks of overlap, I'd certainly drop all other work!! That's going to be intense, My parents were planning on arriving a week earlier and being in the middle of his double class. We asked them to shift later by a week and now I am very very glad we did! Glad you think the new plan will work. I'm very sorry right now that I spent $180 on Anton! Also, all my physics plans are now out the window. Back to the drawing board :auto: Quote Link to comment Share on other sites More sharing options...
kiana Posted January 17, 2015 Share Posted January 17, 2015 Well, the good news is that Anton appears to be their textbook for multivariable as well, so it's not a complete loss, just postponed :D Quote Link to comment Share on other sites More sharing options...
lewelma Posted January 17, 2015 Author Share Posted January 17, 2015 Well, the good news is that Anton appears to be their textbook for multivariable as well, so it's not a complete loss, just postponed :D Yes, they use it for multivariate too. But have you seen the book?!?! :eek: I think it would be my worst hell. I can see why ds wants to use the AoPS one. Also, I found Anton in the public library the other day which made me feel even more :banghead: about spending the $$. Quote Link to comment Share on other sites More sharing options...
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