Mathematics for a high-end math student

[lewelma]

I need some advice or an honest assessment.  As many of you know my ds is an outstanding math student, and has been working in competition mathematics for 3 years.  He went to his first university class today and was *very* underwhelmed.  He has been stewing that he had missed the first week of classes because he was competing in Hong Kong, and was expecting to need to do 20-25 hours this week to catch up from last week. Um, he knows it all. There was no challenge in the lecture and there is no challenge in the assignment due on Friday.  He was like :confused1: .  DS does not see himself as brilliant, and I'm not sure I do either. He is good, but *that* good? Not so sure. Is this just par for the course in a second class in Linear Algebra?  (intro linear algebra is the prereq for this class). Is the school's student body just at a much lower level than ds (even through he is only 15 and they are 18-20)?  Is ds really that brilliant?  He certainly didn't come out on top at the IMO.  I feel really confused as to what to make of this.  

 

More importantly what we are going to do in the future. We were told by the head of the department whose daughter goes to Auckland (the flagship uni here), that he had looked at his daughter's assignments and the math classes here were of equal difficulty.  Is Auckland off the table? If so, ds will have to go outside of NZ for university, which means more research, more tests, more money, further distance.  It is kind of a big deal.

 

And more immediately, I'm seriously concerned that ds will struggle to do well in a low level class just because of boredom.  He's going to start working through all the Linear Algebra applications in his book - like facial recognition, which he was really excited about.  And I suggested that I get him Spivic or Apostle, and have him work through the theoretical side of univariate calc to prep for his next class. But what to do?  DS asked me, 'why should I go to class? I can just learn this on my own.' And he is worried about the study group that has been set up because 'no one wants someone younger to help them.'  I was so hoping that he could meet some kids there, but now he is concerned that he will come across arrogant. It just seems like a disaster, and one that will continue for the next 2 years.  Is competition math so hugely different from standard math, that my ds is doomed to boredom in every math class from now on?  I'm just feeling very confused, and would love you guys just to help me think this through.

 

Ruth in NZ

Edited July 19, 2016 by lewelma

[OneStepAtATime]

:grouphug:  :grouphug:  :grouphug:

[Brad S]

I'm not sure.  Your DS may be that bright.  I'd guess that the level of the class is too low for him -- not the course, per se, but the level of problems and challenge that they're doing.  Your DS should probably be taking classes at a challenging university.  On the other hand, it is two classes in, so things might change.  As you probably know, math classes by the same name can be tremendously different at one university vs. another. And, yes, he probably can learn the linear algebra material on his own.  

 

I'm not sure how to find the right university, but you might want to look at how their students do on the Putnam exams (at least in the US).

 

ETA: I would guess that the student body is at that much of a lower level than your DS.  The difference in a 15 year old and 18-20 year old doesn't really mean much in math, except that if they're taking the same class, the 15 year old is probably a much better mathematician.  It's not at all like literature or some other subjects where life experiences bring maturity.  As far as comparing with IMO participants, you may want to look at what universities past participants are attending or have attended; those might be some that you'd both want to consider in your pool of schools.

 

Edited July 19, 2016 by Brad S

[quark]

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Edited July 19, 2016 by quark

[lewelma]

Thanks for the ideas Brad! It will give me some places to look for future plans.

 

 Just a note, ds is not planning to leave high school for 2 more years, and there is only one university in town. 

[katilac]

Does he have a syllabus? That should help him figure out if the class is starting with review and thus will get more challenging, or if the assignments are par for the course. 

 

I definitely think I would have him go talk to the professor. He can offer some clarity on what's expected in the class, and he might have some further suggestions.

 

Do you have ACT-type scores? They don't provide the whole picture, but comparing his math scores to those at the available universities can give you some idea of where he stands. 

 

Rankings have their flaws, but this might be of help: http://www.usnews.com/education/best-global-universities/australia-new-zealand

 

I poked around a little, and it doesn't seem like Auckland even has a math major.  

[lewelma]

No syllabus that we can find.  Just a highlighted table of contents from an online book, that is highlighted in different colors. I'm guessing each color is a different week?  This second linear algebra class is still using a "elementary linear algebra" textbook, so we assumed it would get into proofs. But it looks like not really. So 2nd year course still using a 1st year book? It is a different book than the 1st year course, but that had a different prof.  DS asked if he was accidentally signed up for the 1st year course, and he is not.  So I'm not sure why the entire class seems to be review. The head of dept did say that ds's proofs for Number theory that he did at age 13 covered half of the content of the 2nd year number theory course.  DS said that now, 2 years later, and a heck of a lot of additional study in number theory, that he can't believe that a 2nd year course would teach him anything.  He only has 2 days left for add/drop because he missed the first week of class when he was at the IMO.

 

If he were to talk to the prof, what in the world would he say?  He has gotten portfolio entrance into this class so he does not even have grades from a previous university class to show for his hard work. Is he asking for extra work?  Is he asking for advice on a more advanced textbook?  What should he *want*?

 

There is more than one university in Auckland, and the University of Auckland definitely has a math major and the biggest department in the country.  Mathwonk looked at the honors theses and said that they were good, so the dept can't be all bad. But if this is the level of the courses or even a bit higher, ds is sunk!

Edited July 19, 2016 by lewelma

[regentrude]

I have read what you wrote about your son over the years. Face it already: yes, he is THAT brilliant. Anybody who competes in the IMO at 15 is THAT brilliant.

He will not find a challenge in regular university math courses, because those are geared towards students who are just normal.

The first week may start slowly, but even then, a regular college math course will not have the level of challenge he is used to. U suggest he give it another week or two and then make an appointment to talk to the professor.

 

ETA: As for the study group: he should just not mention his age and it will be fine. My DD was tutoring calc based engineering physics at the tutoring center of the university when she was 15 years old; of course she would never mention her age to the students she was working with. The students really liked her. Her age was never revealed until some tied to ask her out and it came out that she was seriously young; they backed off immediately.

Edited July 19, 2016 by regentrude

[regentrude]

Specific things he could discuss with the prof, depending on his goal for the class:

testing out of the course after self-study. That would give him credit without him having to jump through the hoops of all the minute daily assignments and attendance requirements.

more/deeper work above and beyond the scope of the course. Will not give him more credit, but  he will learn more.

 

[lewelma]

Ok, so what to do?  I thought getting university credit for 2nd-year classes would be a good idea rather than self studying.  But do I just buy him a harder book?  So have him read the same content but at a higher level?  And then what about the tests?  I am serious that I see him mucking it up because he can't even perceive of such simple problems.

 

He actually got up the gumption to ask a question at the end when the prof asked for questions.  He told me what he said, and it was really clearly laid out.  He had apparently spent time in class coming up with a conjecture and then proving it. So he simply asked if he was right.  Well, the prof went off on something he had already covered.  So ds said, yes, but I was asking about this second point.  Took the prof more than 5 minutes of staring at the board (and the kids were walking out of the class) to say, well yes you are right.  DS was horribly embarrassed, because the prof made him repeat himself 4 times. And now he said he won't be asking any more questions. Clearly, the question was way too high a level for the class. ug. 

Edited July 19, 2016 by lewelma

[lewelma]

We were posting at the same time. 

 

Well, in NZ, ds has the option of taking *only* the final exam for his entire grade.  He does not have to do the assignments if he does not want. No attendance requirements. The problem is hoofing it up to the university 3 times a week. It is going to really mess up his study schedule. I guess he could just skip the class, but then why bother to take a class?

 

As for the study group, in contrast to girls, boys get beards.  DS doesn't have even a hint of facial hair yet as he is a blondy. So it is pretty obvious.  

Edited July 19, 2016 by lewelma

[regentrude]

Ok, so what to do?  I thought getting university credit for 2nd-year classes would be a good idea rather than self studying.  But do I just buy him a harder book?  So have him read the same content but at a higher level?  And then what about the tests?  I am serious that I see him mucking it up because he can't even perceive of such simple problems.

 

He actually got up the gumption to ask a question at the end when the prof asked for questions.  He told me what he said, and it was really clearly laid out.  He had apparently spent time in class coming up with a conjecture and then proving it. So he simply asked if he was right.  Well, the prof went off on something he had already covered.  So ds said, yes, but I was asking about this second point.  Took the prof about 5 minutes of staring at the board (and the kids were walking out of the class) to say, well yes you are right.  DS was horribly embarrassed, because the prof made him repeat himself 4 times. And now he said he won't be asking any more questions.  ug. 

 

He should make an appointment to discuss with the professor what the best course of action is.

As a prof, I would prefer if a student in this situation came to me, rather than being bored in class. We would discuss what his goals with the class were and how to achieve them. We could discuss whether creating an honors version of the course would be possible and desirable, whether the student would like to self study and test out, whether there were materials I could provide so the student could learn more.

 

As for the question: the professor is in the lecture with a certain goal, is prepared for certain material, and is used to a certain set of students. If somebody comes with a thought that is completely outside of what the instructor normally experiences, it is quite normal that the prof feels caught off guard, has to clarify that he really understood what the student was getting at (again, because a similarly sounding question from most students would be on a completely different level), and may need a minute to shift gears and think. That does not mean the prof was inept - it just meant that this kind of question would be best posed after class or at office hours, and not quickly thrown in at class. That is something your DS learned now :)

 

ETA: I sometimes have students ask questions that sound impressive, reveal a knowledge of buzzwords and some half-digested reading, and are often utter nonsense. If a student in an intro lecture asked a really deep, well founded question about higher level material, I would probably ask back twice that I understand correctly what he means (because normally the question that starts like this never goes anywhere), and then may have to work out a few lines, or think a few minutes, before answering - or may have to defer the answer until I had time to think about it. It's not that I don't know the material, but I may not be able to find a good answer to a student if caught unawares.

Edited July 19, 2016 by regentrude

[lewelma]

As for the question: the professor is in the lecture with a certain goal, is prepared for certain material, and is used to a certain set of students. If somebody comes with a thought that is completely outside of what the instructor normally experiences, it is quite normal that the prof feels caught off guard, has to clarify that he really understood what the student was getting at (again, because a similarly sounding question from most students would be on a completely different level), and may need a minute to shift gears and think. That does not mean the prof was inept - it just meant that this kind of question would be best posed after class or at office hours, and not quickly thrown in at class. That is something your DS learned now :)

 

I would agree with this.  It was more ds's feeling of "oops, shouldn't have asked a question.  Next time, I'll keep my mouth shut and assume that my proof is accurate." He actually said that he brought it up in class because he thought it was a useful point that would be good for the class to realize. Clearly, he was wrong.  He has no understanding of the background of these students, and I'm guessing he won't have a clue what is an appropriate in-class question vs what should be asked after class because it is beyond the scope of the class. Perhaps all of his questions are after class questions.

[lewelma]

He should make an appointment to discuss with the professor what the best course of action is.

As a prof, I would prefer if a student in this situation came to me, rather than being bored in class. We would discuss what his goals with the class were and how to achieve them. We could discuss whether creating an honors version of the course would be possible and desirable, whether the student would like to self study and test out, whether there were materials I could provide so the student could learn more.

 

 

I was assuming, actually, that the prof would not want to see students.  I don't think there are office hours here, and there is a "class representative" who you are supposed to route all your questions through so that the prof only has to deal with one person. Should ds talk to the class representative or try to jump straight to the prof? 

 

DS's thoughts right now are to keep his head down, do the work, and self study a harder and more complete text.  But then *why* am I paying for him to take the class????  Seriously, I have better things to do with $1000!

Edited July 19, 2016 by lewelma

[lewelma]

 

ETA: I sometimes have students ask questions that sound impressive, reveal a knowledge of buzzwords and some half-digested reading, and are often utter nonsense. If a student in an intro lecture asked a really deep, well founded question about higher level material, I would probably ask back twice that I understand correctly what he means (because normally the question that starts like this never goes anywhere), and then may have to work out a few lines, or think a few minutes, before answering - or may have to defer the answer until I had time to think about it. It's not that I don't know the material, but I may not be able to find a good answer to a student if caught unawares.

 

Thanks for this detail.  I will tell ds so he has a better understanding.  This is ds's first day of his first class.  And I think he was just hoping for *more.*  (especially, because he missed the first week).

[regentrude]

I was assuming, actually, that the prof would not want to see students.  I don't think there are office hours here, and there is a "class representative" who you are supposed to route all your questions through so that the prof only has to deal with one person. Should ds talk to the class representative or try to jump straight to the prof? 

 

 

The bolded is VERY strange. Your DS  should talk to the class representative and find out whether he understands the system correctly, or he could just ask the prof after class whether he could meet with him. It makes absolutely no sense to route all questions through an intermediary, especially if these are questions of deeper mathematical nature (and not just stuff like "when is HW due"). What is the prof to do, explain the proof to the representative and have the rep pass it on to the student? That makes absolutely no sense.

 

DS's thoughts right now are to keep his head down, do the work, and self study a harder and more complete text.  But then *why* am I paying for him to take the class????  Seriously, I have better things to do with $1000!

 

That is exactly the question: what is your/his goal for this class? Is it to learn to function with the logistics of a college class? Is it to master the material? Is it to earn formal credit? It may well be that taking this class is not the best thing to accomplish the end goal.

Edited July 19, 2016 by regentrude

[regentrude]

I would agree with this.  It was more ds's feeling of "oops, shouldn't have asked a question.  Next time, I'll keep my mouth shut and assume that my proof is accurate." He actually said that he brought it up in class because he thought it was a useful point that would be good for the class to realize. Clearly, he was wrong.  He has no understanding of the background of these students, and I'm guessing he won't have a clue what is an appropriate in-class question vs what should be asked after class because it is beyond the scope of the class. Perhaps all of his questions are after class questions.

 

The bolded has me chuckle. Oh, your DS would be a dream student to a prof - in a small honors graduate class at a top tier school.

No, he should not bring something up because he thinks it would be useful for the other students to realize (unless the prof made an actual mistake; this he should politely point out!). Chances are, it will be far over the top of everybody else. Even the instructor will not bring up everything that he thinks would be useful for the class to know, because, presumably, he has an understanding what they can and cannot be expected to grasp and how deep they can be expected to think. Chances are, your DS' level of insight is so far beyond that of his class mates that his attempts to educate them are utterly futile. He should leave the educating the others to the prof and ask the questions that aid his own understanding.

 

But this, too, is a valuable learning experience. He should not assume that his fellow students live and breathe math like he does or even care about any deeper insight. Most of them will just want to pass the class.

Edited July 19, 2016 by regentrude

[lewelma]

The bolded is VERY strange. Your DS  should talk to the class representative and find out whether he understands the system correctly, or he could just ask the prof after class whether he could meet with him. It makes absolutely no sense to route all questions through an intermediary, especially if these are questions of deeper mathematical nature (and not just stuff like "when is HW due"). What is the prof to do, explain the proof to the representative and have the rep pass it on to the student? That makes absolutely no sense.

 

 

 

That is exactly the question: what is your/his goal for this class? Is it to learn to function with the logistics of a college class? Is it to master the material? Is it to earn formal credit? It may well be that taking this class is not the best thing to accomplish the end goal.

 

Well, I have no idea about the class representative.  I am new to this system.  This is what the course guide says " your class representative is available if you come across problems and for any reason the issue cannot be resolved directly with the staff.  If you would like to talk about a concern you have, please email your class rep and a meeting can be arranged."  The class rep has also organized the facebook page and the timing for the study group.  So who is "staff" ?  Is that the prof?  Why would ds have problems resolving an issue with the prof? There are no office hours listed, so does ds just e-mail the prof and ask for an appointment?  Would ds write up proofs of conjectures and then bring them to this appointment?  I just can't fathom *how* ds can up the level to *his* level.  I definitely feel out of my depth here as to how to advise him.  

 

As for goals?  I thought it would be to take the next class after finishing up the AoPS classes.  He has really blossomed with the social side of AoPS, so I thought a face to face class would be a good thing.  I also thought that earning credit for classes completed was something you just did?  How would you ever convince a university that you have completely the first 2 years of math courses on your own time?  How would this work?

[lewelma]

The bolded has me chuckle. Oh, your DS would be a dream student to a prof - in a small honors graduate class at a top tier school.

No, he should not bring something up because he thinks it would be useful for the other students to realize (unless the prof made an actual mistake; this he should politely point out!). Chances are, it will be far over the top of everybody else. Even the instructor will not bring up everything that he thinks would be useful for the class to know, because, presumably, he has an understanding what they can and cannot be expected to grasp and how deep they can be expected to think. Chances are, your DS' level of insight is so far beyond that of his class mates that his attempts to educate them are utterly futile. He should leave the educating the others to the prof and ask the questions that aid his own understanding.

 

But this, too, is a valuable learning experience. He should not assume that his fellow students live and breathe math like he does or even care about any deeper insight. Most of them will just want to pass the class.

 

Haha.  Very good distinction.  He wanted to bring up a point to educate the others (he had already proved it to himself so knew it was right).  He should focus on questions he has. I will tell him! I guess he was thinking of it as a group of people searching for understanding together rather than a top down lecture.  Perhaps this is more the way AoPS ran?  I have no idea.  

 

The problem as I see it is that he will not have any questions with the current material.  He just looked at the first homework set, and said to me "well, I'll have to write it up." No study, no reading, no figuring it out, just going through the motion of writing down the obvious to turn in the assignment.  The entire exercise will serve no purpose for him. I think he was hoping that he would have questions that a prof would answer.  If going to lecture is the same as reading the text book, ds can't figure why he should go to class.  He asked, are all math classes like this?  I could just learn any class with a book, why do people take math classes?  Yet, he *loved* every AoPS class he took.  What a let down today.  sigh

 

He actually was hoping that by jumping all the first year courses that he would get with kids who love math.  When does this happen?  3rd year courses?  In NZ, you get your degree in 3 years because there is no liberal arts year.  So if ds is to skip into 3rd year courses, he will complete the undergraduate material before finishing high school. 

Edited July 19, 2016 by lewelma

[regentrude]

Well, I have no idea about the class representative.  I am new to this system.  This is what the course guide says " your class representative is available if you come across problems and for any reason the issue cannot be resolved directly with the staff.  If you would like to talk about a concern you have, please email your class rep and a meeting can be arranged."  The class rep has also organized the facebook page and the timing for the study group.  So who is "staff" ?  Is that the prof?  Why would ds have problems resolving an issue with the prof? There are no office hours listed, so does ds just e-mail the prof and ask for an appointment?  Would ds write up proofs of conjectures and then bring them to this appointment?  I just can't fathom *how* ds can up the level to *his* level.  I definitely feel out of my depth here as to how to advise him.  

 

Oh, that means something completely different! That means if you have problems with the prof or TA, this is the chain of command to get them resolved. In the US, we are required to specify this chain of command in our syllabi so the students know to whom they can complain if there are unfair grading, lost assignments, mistake riddled lectures, inappropriate behavior and bringing it up with the instructor directly does not lead to a resolution. 

 

Wanting to discuss mathematics is not a "problem" in this sense. He should ask the prof after class when he would be available to discuss a certain point, or email him if he feels more comfortable doing that. He can write up things, or ask the prof what would be a good way to discuss this. I strongly recommend he initiate the conversation; there may be ways to get the depth he needs, and he should not stew about it and become resentful. He just needs to realize that the class is not geared towards students with his mindset, background, and abilities.

 

 

As for goals?  I thought it would be to take the next class after finishing up the AoPS classes.  He has really blossomed with the social side of AoPS, so I thought a face to face class would be a good thing.  I also thought that earning credit for classes completed was something you just did?  How would you ever convince a university that you have completely the first 2 years of math courses on your own time?  How would this work?

 

it deleted this, so I'll type again:

see the prof and ask for credit by examination. This way, credit shows up on the transcript without the student having taken the class.

I have students do that occasionally, not  very often. At our school, they get credit abut no grade if they pass but do't get an A; they get credit and an A for their transcript f they get an A in the course exam.

 

 

Edited July 19, 2016 by regentrude

[regentrude]

I guess he was thinking of it as a group of people searching for understanding together rather than a top down lecture.  Perhaps this is more the way AoPS ran?  ...

 

He actually was hoping that by jumping all the first year courses that he would get with kids who love math.  When does this happen?  3rd year courses?  

 

AoPS classes are filled with kids who are searching for understanding and who love math. that is a specially self selected bunch - because it is not required to take those classes.

During undergraduate at a not top highly selective school, I would not expect any math class to have such a demographic. There may be a few students like that, but never the majority. He may encounter that in a very good graduate school. Even a mediocre grad school will be filled with students who cannot think at his level and who just want to pass.

Edited July 19, 2016 by regentrude

[lewelma]

Oh, that means something completely different! That means if you have problems with the prof or TA, this is the chain of command to get them resolved. In the US, we are required to specify this chain of command in our syllabi so the students know to whom they can complain if there are unfair grading, lost assignments, mistake riddled lectures, inappropriate behavior and bringing it up with the instructor directly does not lead to a resolution. 

 

Wanting to discuss mathematics is not a "problem" in this sense. He should ask the prof after class when he would be available to discuss a certain point, or email him if he feels more comfortable doing that. He can write up things, or ask the prof what would be a good way to discuss this. I strongly recommend he initiate the conversation; there may be ways to get the depth he needs, and he should not stew about it and become resentful. He just needs to realize that the class is not geared towards students with his mindset, background, and abilities.

 

Well that is good to know. I think the lack of office hours is what made me think that the prof doesn't want to see students. I think it will be hard to get ds to approach the prof because he will feel that he is putting the prof out. Do professors actually want to spend time with students or are they busy people with other things to do?  I went to Duke and I *never* went to see a prof, they just seemed too aloof to me.  What is a good way to initiate this exchange?  What does ds ask for at first?  I don't think he can say "this class is too easy and I'm looking for some advanced readings."  Does he say "I have some questions about the class, is there a time we can meet?" And then when he is in private, say um, I know all this stuff already, is there additional material you can give me?  I'm kind of with ds, I would feel very much like I am imposing.  Must be some sort of cultural thing. 

[lewelma]

AoPS classes are filled with kids who are searching for understanding and who love math. that is a specially self selected bunch - because it is not required to take those classes.

During undergraduate at a not top highly selective school, I would not expect any math class to have such a demographic. There may be a few students like that, but never the majority. He may encounter that in a very good graduate school. Even a mediocre grad school will be filled with students who cannot think at his level and who just want to pass.

 

This is very discouraging.  :crying:

[lewelma]

 

 

see the prof and ask for credit by examination. This way, credit shows up on the transcript without the student having taken the class.

I have students do that occasionally, not  very often. At our school, they get credit abut no grade if they pass but do't get an A; they get credit and an A for their transcript f they get an A in the course exam.

 

Are you saying that you can get actual university credit for self study without paying the money?  

[regentrude]

Well that is good to know. I think the lack of office hours is what made me think that the prof doesn't want to see students. I think it will be hard to get ds to approach the prof because he will feel that he is putting the prof out. Do professors actually want to spend time with students or are they busy people with other things to do?  I went to Duke and I *never* went to see a prof, they just seemed too aloof to me.  What is a good way to initiate this exchange?  What does ds ask for at first?  I don't think he can say "this class is too easy and I'm looking for some advanced readings."  Does he say "I have some questions about the class, is there a time we can meet?" And then when he is in private, say um, I know all this stuff already, is there additional material you can give me?  I'm kind of with ds, I would feel very much like I am imposing.  Must be some sort of cultural thing. 

 

The prof may not have posted office hours publicly, but that does not mean he is not available for students. I don't post office hours; I post the hours during which I am available in the tutoring center.

 

I cannot speak for your particular prof. It has been my experience that professors love talking to and working with students like your DS. It will be a welcome change form the never ending dumb questions that a thorough reading of the syllabus would have answered.

Typically, profs teach because they love it to see students understand something and are happy to share their excitement of the subject.

Any of my colleagues at my department would be glad to talk with a student like your DS. I would strongly encourage him to initiate contact with the prof. As you are completely correct, he should obviously not complain that the course is too easy, but explain in private what his issue is. But he should do it!

[regentrude]

 

Are you saying that you can get actual university credit for self study without paying the money?  

 

 

yes, exactly

[regentrude]

This is very discouraging.  :crying:

 

But come to think of, it has to be like that: if your DS is in the top tiny fraction of a percentile in mathematical ability and interest (and being in the IMO team means that he is one of the top few math kids of the country), there cannot be enough students to fill a class at a regular uni. 

 

And taking uni courses at a younger age does not compensate for the fact that he thinks differently and grasps abstract concepts faster than almost anybody else.

Edited July 19, 2016 by regentrude

[lewelma]

But come to think of, it has to be like that: if your DS is in the top tiny fraction of a percentile in mathematical ability and interest (and being in the IMO team means that he is one of the top few math kids of the country), there cannot be enough students to fill a class at a regular uni. 

 

And taking uni courses at a younger age does not compensate for the fact that he thinks differently and grasps abstract concepts faster than almost anybody else.

 

I think I thought that not all kids like to do competitions so there would be other kids loving math that ds had not met. And that the first year would weed out the slower, less-interested kids. And that they would all congregate in Auckland. I thought we could make it work at Auckland, and now I am just not so sure.  This is massive.  Saying that ds *needs* to be educated out of the country. It is one thing to say overseas is a nice to have, it is another to say it just isn't going to work here.  He has already brought up this week that he is not sure he will be able to work in NZ. And as I see it, if he does not go to university here, he will not build an in-country network which basically guarantees that he will leave.  I guess I am just sad. Profoundly sad.  DH and I moved for NZ for a better life for us, and yet it won't be for our ds.  This is just huge.  There is no other way to put it.  I think the IMO last week got me thinking about his future path and the uni class this today is just the nail in the coffin. I'm sure it will take me quite some time to get my head around it.  

[Mike in SA]

Sorry for jumping in late - was having technical issues.

 

I think you've gotten some good feedback already, but to add a key point - linear algebra is one of the easiest math classes your son will ever see.  It's an easy A course for most math students, and your son is not most students.

 

I agree with the idea of speaking to the prof (and if that doesn't yield results, the dept chair).  That's the only real solution.

 

Be ready to bear with the course, because it is a gateway subject for the fun ones.  It will get harder - modern algebra and topology will be mind-opening and interesting.

[Mike in SA]

Oh, and Auckland is a fine program.  :)

[regentrude]

I think I thought that not all kids like to do competitions so there would be other kids loving math that ds had not met. And that the first year would weed out the slower, less-interested kids. And that they would all congregate in Auckland. I thought we could make it work at Auckland, and now I am just not so sure.  This is massive.  Saying that ds *needs* to be educated out of the country. It is one thing to say overseas is a nice to have, it is another to say it just isn't going to work here.  He has already brought up this week that he is not sure he will be able to work in NZ. And as I see it, if he does not go to university here, he will not build an in-country network which basically guarantees that he will leave.  I guess I am just sad. Profoundly sad.  DH and I moved for NZ for a better life for us, and yet it won't be for our ds.  This is just huge.  There is no other way to put it.  I think the IMO last week got me thinking about his future path and the uni class this today is just the nail in the coffin. I'm sure it will take me quite some time to get my head around it.  

 

:grouphug:

I understand. This is hard. I hope he can make it work, but there just may not be enough critical mass. He needs to talk to the math profs (not just this one, but also others and the chair) and find out.

Edited July 19, 2016 by regentrude

[lewelma]

You are not late to the party.  I'm actually surprised anyone is up!  Isn't it like 4am or something?

 

I've talked to ds about jumping ship and switching to multivariate calc, but he said no, that he had prepped for this class.  And he is right.  We chose this class because we got a lot of feedback from many sources that multivariate calc would be more fun and better understood with linear algebra and analysis first, so that is the plan.  DS will be very glad to hear that this is just *the* easy class, and that the others will be better. He was quite excited about the applications section in the textbook, which seemed to motivate him to finish up any part in the textbook that he had not already covered by reading/studying wikipedia.  :huh:  He also did like my idea about working through spivic or apostle univariate Calc this term, as the February-June term is when the IMO stuff kind of takes over and he won't have time to take an Analysis class AND self study theoretical calc. So better to do it now while he is taking the easy linear algebra class. I also told him that we can pound out his english papers so he doesn't have to worry about them Apr-July next year. So we can take advantage of this easy class and fill the time in other ways.  DS said it is not a huge problem to have his first university class be super easy.  I think in some ways he might have had relief mixed in with the surprise/boredom. He definitely expected it to be hard. 

 

 

Oh, and Auckland is a fine program.  :)

 

Is it?

Edited July 19, 2016 by lewelma

[regentrude]

  I'm actually surprised anyone is up!  Isn't it like 4am or something?

 

It's 11am  here in Germany ;)

[Mike in SA]

You are not late to the party.  I'm actually surprised anyone is up!  Isn't it like 4am or something?

 

I've talked to ds about jumping ship and switching to multivariate calc, but he said no, that he had prepped for this class.  And he is right.  We chose this class because we got a lot of feedback from many sources that multivariate calc would be more fun and better understood with linear algebra and analysis first, so that is the plan.  DS will be very glad to hear that this is just *the* easy class, and that the others will be better. He was quite excited about the applications section in the textbook, which seemed to motivate him to finish up any part in the textbook that he had not already covered by reading/studying wikipedia.  :huh:  He also did like my idea about working through spivic or apostle univariate Calc this term, as the February-June term is when the IMO stuff kind of takes over and he won't have time to take an Analysis class AND self study theoretical calc. So better to do it now while he is taking the easy linear algebra class. 

 

 

Linear algebra is a grin-and-bear-it course.  It's really that easy.  Discrete math will be, as well.  I assume he is taking 250?

 

As for Auckland, it does have a respected math program.  Be sure to get him involved in their specializations, though - it is a bit limited in offerings overall.

 

Long term, he will need to go elsewhere.  Maybe not as an undergrad, but eventually, he will need to.  The range of courses there is simply not sufficient unless he falls in love with one of their strengths.

 

ETA: Linear algebra is rarely taken as an only math course.  It's generally taken with second-semester calculus, or at least with multivariate.  It isn't necessary for the ordinary calculus sequence.

Edited July 19, 2016 by Mike in SA

[lewelma]

Linear algebra is a grin-and-bear-it course.  It's really that easy.  Discrete math will be, as well.  I assume he is taking 250?

 

As for Auckland, it does have a respected math program.  Be sure to get him involved in their specializations, though - it is a bit limited in offerings overall.

 

Long term, he will need to go elsewhere.  Maybe not as an undergrad, but eventually, he will need to.  The range of courses there is simply not sufficient unless he falls in love with one of their strengths.

 

 

This is the kind of specific opinions I need.  Thanks.

 

I'm off to bed....

[lewelma]

Regentrude, thanks for taking the time to answer all my questions!! :001_wub:

[regentrude]

Regentrude, thanks for taking the time to answer all my questions!! 

 

You're welcome. I know how frustrating it must be to find a way for a highly gifted student.

[LisaKinVA]

This gave me much to think about (for dd -- not anything to add, other than yes, your child is simply that brilliant!).

 

My dd is not a math competition girl -- and is not nearly at the level of your son (she's 14 1/2).  She's ready for calculus as a freshman -- which puts her well ahead of the curve for top math students in the US (and this is even doing two Algebra courses, two Algebra 2 courses, and now 2 precalculus courses).  Most university math programs we've found, she will most likely complete more than half of the university credits required for the major before graduating high school -- and your son far surpasses her.  

 

[LisaKinVA]

This gave me much to think about (for dd -- not anything to add, other than yes, your child is simply that brilliant!).

 

My dd is not a math competition girl -- and is not nearly at the level of your son (she's 14 1/2).  She's ready for calculus as a freshman -- which puts her well ahead of the curve for top math students in the US (and this is even doing two Algebra courses, two Algebra 2 courses, and now 2 precalculus courses).  Most university math programs we've found, she will most likely complete more than half of the university credits required for the major before graduating high school -- and your son far surpasses her.  

 

[Mike in SA]

This is the kind of specific opinions I need.  Thanks.

 

I'm off to bed....

 

No problem.  I'm about to head to work.  :)

 

Something to consider for mathematics programs, in general: there's not much difference between undergraduate programs.  They are almost the same - the only real differences among the majority of schools is the number of course offerings.  Otherwise, content is roughly equivalent:

 

Calculus

Multivariate Calculus

Discrete Math

Linear Algebra

Differential Equations (2 semesters)

Probabiliity

Mathematical Statistics

Real Analysis (2 semesters) - sometimes one is called "Advanced Calculus"

Algebra (2 semesters)

Topology (2 semesters)

Complex Analysis

 

Sometimes probability and statistics are combined into a lighter overview; sometimes a student only needs four of the last 7 (from real analysis on); sometimes discrete math is not required, and so on.

 

There are only a handful of elite math programs that exceed this, among them Cambridge, Oxford, MIT, Princeton, Cornell, Chicago, Texas, Berkeley, Stanford, Duke, Harvard, ETH Zurich...  You get the idea.

 

For the most part, a mathematics student should be preparing for graduate school, which is where there starts to be better separation among schools.  Until then, it really doesn't matter all that much which school you choose.  Going overseas isn't going to create a magical difference in quality of mathematical instruction at the undergrad level.  The subjects simply don't differ all that much - it's all old hat content.

[Brad S]

...

 

Something to consider for mathematics programs, in general: there's not much difference between undergraduate programs.  They are almost the same - the only real differences among the majority of schools is the number of course offerings.  Otherwise, content is roughly equivalent:

 

...

 

 

There are only a handful of elite math programs that exceed this, among them Cambridge, Oxford, MIT, Princeton, Cornell, Chicago, Texas, Berkeley, Stanford, Duke, Harvard, ETH Zurich...  You get the idea.

 

For the most part, a mathematics student should be preparing for graduate school, which is where there starts to be better separation among schools.  Until then, it really doesn't matter all that much which school you choose.  Going overseas isn't going to create a magical difference in quality of mathematical instruction at the undergrad level.  The subjects simply don't differ all that much - it's all old hat content.

 

While the course titles and core content may be the same, the level of depth isn't always: think AoPS vs a typical class at lower levels, and the same thing can happen at the university level.  Mike's list of programs may do this more consistently over the generations, but there are other places where you can delve into math at a much deeper level than the basic programs.  You should definitely not just expect it; you need to look into it first. 

 

I agree with the earlier posts that many of the students are likely not nearly at your son's level of interest or ability, but I think that a lot of the math profs are likely to have interests similar to your DS's.  That's why they became math professors.  The key is whether they'll engage with your son.  While some may be aloof and not want to meet students, others will, especially if it's to discuss higher level, challenging problems. 

 

Ruth, it might still be possible for your son to make it work in NZ, with possibly a year or two somewhere else.  But I agree with other posts that it's not realistic to expect that a program will be appropriate just because it's at a university.

 

[cjzimmer1]

We were posting at the same time. 

 

Well, in NZ, ds has the option of taking *only* the final exam for his entire grade.  He does not have to do the assignments if he does not want. No attendance requirements. The problem is hoofing it up to the university 3 times a week. It is going to really mess up his study schedule. I guess he could just skip the class, but then why bother to take a class?

 

As for the study group, in contrast to girls, boys get beards.  DS doesn't have even a hint of facial hair yet as he is a blondy. So it is pretty obvious.  

 

A few thoughts but no real suggestions.

 

My DS is pretty advanced as well (took AP Calc BC as a freshman) took more advanced classes with a private tutor.  We talked to quite a few schools about math progression and with the exception of one small school(which was far more flexible on many counts than any other place we talked to although they didn't have as many truly advanced classes to offer but if it had worked would have been a great jumping off place), everyone said he would have to start at Calc 3 and take those classes.  There were no test out options nor would they let him take a final to "prove" he knew the material.  So DS knows he is going to have to sit through some mind numbing classes but the only conselation is that he knows they will ensure he keeps a good grade point average.  So if they will allow him to just take the final and you are sure he a has full understanding of the topic than by all means go that route.  I can understand the "why take the class" but consider it a hoop to jump through because most people really don't understand how kids can be that accelerated and need some kind of documentation.

 

As far as his level compared to others.  Yes he really is that far ahead of others.  When you live with it every day it's pretty easy to assume your kid is closer to average than brilliant because that's just "normal" to you.  So not only is he ahead of these other kids, clearly he is an intuitive learner.  So material that might take a full lecture or a week to get through for everyone else will only take him a few minutes to grasp.  Not only does he grasp the complexity better he also gets it faster.  It's like a double whammy.  But unless you find someone who really "gets" your DS and his abilities, he will probably end up jumping through those hoops to prove what he knows before he can get access to the classes that will truly interest and challenge him.

[vonfirmath]

ETA: As for the study group: he should just not mention his age and it will be fine. My DD was tutoring calc based engineering physics at the tutoring center of the university when she was 15 years old; of course she would never mention her age to the students she was working with. The students really liked her. Her age was never revealed until some tied to ask her out and it came out that she was seriously young; they backed off immediately.

 

This was my husband's experience as a young college student. (He went into college at 14 or 15.) Everyone seemed to assume he was older. He even had girls flirting with him and trying to get him to ask them out -- until he mentioned his age.  But he studied with them and even tutored in math sometimes and all was good.

 

 

[Mike in SA]

While the course titles and core content may be the same, the level of depth isn't always: think AoPS vs a typical class at lower levels, and the same thing can happen at the university level. Mike's list of programs may do this more consistently over the generations, but there are other places where you can delve into math at a much deeper level than the basic programs. You should definitely not just expect it; you need to look into it first.

 

Having taught at an elite and DW at both a Russian uni and a directional, I honestly don't see that significant of a difference in the preparation afforded an undergrad. The grad school will typically compensate as needed.

 

I would, of course, advise against a small school with limited offerings if the grad school objective is an elite.

 

The texts are largely comparable except at an elite (where they WILL differ). We compare those regularly in the course of work. The mathematical foundations simply haven't changed much recently.

[quark]

.

Edited July 19, 2016 by quark

[8filltheheart]

Ds used to sit in class proving everything to himself while other instruction was going on.  He also got to know his professors and they would lend him all sorts of personal books and spend time talking to him about things outside of class that interested him.

[quark]

.

Edited July 19, 2016 by quark

[Arcadia]

He actually was hoping that by jumping all the first year courses that he would get with kids who love math. When does this happen? 3rd year courses? In NZ, you get your degree in 3 years because there is no liberal arts year.

Is there a 4th year honours or just straight to masters? For my alma mater, even the BSc Math honors candidates may not like math but be there for the pay difference. The honors degree pays more than just bachelors. At the MSc and PhD level is when you get a higher concentration of math enthusiast. So something to think about if you are still considering the exchange program there. Computational physics had the highest math cutoff requirements in Science Faculty at my time, same as for Engineering Faculty and higher than math majors. Friends and relatives has similar undergrad experience at the universities in Australia.

 

I know I freaked even the guys classmates out when I asked questions in math class especially for proofs because they told me. My alma mater's system was easy, just email the lecturer for a time slot to meet.

[Kathy in Richmond]

Ruth, I'm sorry for your son's initial experiences in his university class, but I'm certainly not surprised. The vast majority of college linear algebra classes are taught at a pretty easy level. Most of the students have not had prior exposure to proofs, so the class usually concentrates on matrix calculations...boring!

 

It was not any different for my kids here, to be honest. I never pursued dual enrollment for them locally, because they would have had similar problems after doing lots of AoPS, math competitions at high levels, and summer math camps. We just self studied at home using texts and some MIT OCW. For the most part, they were able to do so independently. They still enjoyed interaction with other math loving kids, so they continued AoPS courses when they could (and of course math teams and summer camps,too).

 

When ds got to MIT, he was allowed to enroll in any math class that he saw fit. They trust kids there. My dd at Stanford took the 51H honors sequence. It re-does multivariable calc, linear algebra, and diff equtions in a much more theoretical way. Definitely not like most classes...no numbers or matrix calculations there, just theory & proof. Stuff I didn't see for the most part till grad school.  Even I lucked into a great math sequence at U Rochester way back when. It used Apostol's two classic volumes & was a real treat.

 

I can suggest some other ways to learn linear algebra if he decides to drop the class, or if he just wants to supplement:

 

Gilbert Strang's Linear Algebra on MIT OCW Scholar

 

Linear Algebra Done Right (pdf) by Sheldon Axler. Solutions. I used this with dd in high school.

 

Tom Apostol Vol 2. What ds used in high school & I used in college.

 

Here's a peek at the Stanford math classes I mentioned above: Honors math 51H; math 52H

Lots of former math olympiad kids, math camp kids, etc, end up in this sequence and find it to be an OK fit (too hard if anything).

 

In the meantime, hugs to you both while you work out a solution for the next few years... :grouphug:

 

ETA: Dd found that most intro classes outside of the 50H series started out relatively easy, including regular linear algebra, real analysis, etc. Profs in those classes couldn't assume that their students had been exposed beforehand to proof methods, so they started out by covering the basics. They did ramp up as the year progressed, though, so there's always hope. :)

Edited July 19, 2016 by Kathy in Richmond

[Mike in SA]

Ds used to sit in class proving everything to himself while other instruction was going on. He also got to know his professors and they would lend him all sorts of personal books and spend time talking to him about things outside of class that interested him.

Um, that was me back in the day, too. I built a large library of unused publisher samples of textbooks...