American Mathematical Society texts

[Teachin'Mine]

An old thread turned up, and it in Karin had mentioned that there are texts available from the American Mathematical Society. Has anyone used them?

 

I went to the site and found this one http://www.ams.org/bookstore-getitem/item=mcl-6 which looks interesting. Honestly, some of it also looks like a foreign language to me. :lol:

 

If any mathy moms wouldn't mind taking a look, I'd love to hear feedback on how this could fit into the high school math progression. Dd is doing Calculus I and probably II this year with Saxon. After that, she'll probably take cc courses. But I'd love for her to get more of the why behind the math she's learned. I'm wondering if this text, or some other one, would offer that. I was also assuming that she'd get this in college courses, but with all the comments on the level of cc courses, I'm not so sure anymore. :tongue_smilie:

 

Regarding the book above, where would it fit in the calculus sequence? Would it be detrimental to skip a semester of calculus to fit in something different? What about statistics? Wouldn't that be good to have or would it be better not to interrupt the sequence? I'm assuming that she'll need to repeat these calculus courses in whatever college she attends as I keep reading that the rigor of these course is far different from the cc classes.

[kiana]

I haven't *used* that book and can't find reviews. However:

 

From reading the table of contents, it looks like it should definitely follow at least calculus 1. It is a total digression, however -- it is a topic that is, as they said, popular in competitions but not really used for classroom math.

 

As to "How does it fit into the calculus sequence?" -- well, the short answer is that "It doesn't." It's an interesting topic, but you won't see equations of that type until later, and you won't see them identified as such until later still. I don't honestly know if she'd be able to go directly into it without some experience in problem-solving.

 

What is she planning on majoring in? Does she have any idea yet or is the idea just to increase mathematical literacy and increase knowledge of "why" things work as opposed to "how"? And why this book in particular?

[Teachin'Mine]

Thank you for your reply Kiana. You asked good questions. I'll answer them in your quote. :)

 

I haven't *used* that book and can't find reviews. However:

 

From reading the table of contents, it looks like it should definitely follow at least calculus 1. It is a total digression, however -- it is a topic that is, as they said, popular in competitions but not really used for classroom math.

 

See this is part of why I'm asking about the why and trying to tie in problem solving as well. She's never been involved in competitions, but the students who have are the same ones she'll be in class with in college. I'm wondering if the lack of competition type math will put her at a disadvantage.

As to "How does it fit into the calculus sequence?" -- well, the short answer is that "It doesn't." It's an interesting topic, but you won't see equations of that type until later, and you won't see them identified as such until later still. I don't honestly know if she'd be able to go directly into it without some experience in problem-solving.

 

She doesn't have experience in problem solving - other than minimal SAT prep work before the test. I looked at the first lesson, and it seems that a lot of information wasn't included - I'm guessing it's assumed that the student would have already known what I perceive as "missing". I haven't shown it to my dd yet to know if she'd be able to follow it or not. I just know that she hasn't worked with one of the symbols yet, but she's only about a third of the way through her calculus text.

What is she planning on majoring in? Does she have any idea yet or is the idea just to increase mathematical literacy and increase knowledge of "why" things work as opposed to "how"? And why this book in particular?

 

She's planning on majoring in math. More specific than that, she doesn't know at this point. Honestly, the interest in the "why" is coming from me. A few years ago she had no interest in knowing why, but now she's more open to learning why. I'm not sure that she'd want to take a side trip, so to speak, to do that though. She's enjoying calculus and wants to keep forging ahead in that. I was reading a thread from Feb that Creekland had brought back to life, and in it Karin had mentioned these texts. I went to the site, and found this title to be interesting. I'm open to any book suggestions. Honestly, I'd love something that doesn't take a huge amount of time, and assumes that the math has already been learned, and then just goes from there to explain why it works. Kwim? But in addition to that, I'd like something that teaches how to solve a problem. Any problem really. How to analyze the information given and how to work with that to come up with a plan for arriving at the solution. I know this would need to have problems which need to be worked, but again, ideally it wouldn't be hugely time consuming as she's got a very full schedule. :tongue_smilie:

 

Any thoughts?

[8filltheheart]

I know nothing about anything, so take this w/ a grain of salt, but perhaps you should look at the AoPS books. There are plenty of challenging problems to solve in the cal book. ;)

[Teachin'Mine]

I know nothing about anything, so take this w/ a grain of salt, but perhaps you should look at the AoPS books. There are plenty of challenging problems to solve in the cal book. ;)

 

I'll bet there are. :) But for the problem solving, I'm really looking for work in areas other than calculus. She's getting plenty of a challenge in learning calculus on her own from the text. ;)

[kiana]

I'll bet there are. :) But for the problem solving' date=' I'm really looking for work in areas other than calculus. She's getting plenty of a challenge in learning calculus on her own from the text. ;)[/quote']

 

I would seriously look into the problem-solving books (not the curriculum, the problem-solving vol 1 and 2) from the AOPS people as an introduction. They include a wide variety of subjects and reteach them. They were also originally written for people who'd learned math elsewhere and needed a problem-solving supplement. If she (thus far) has not wanted to know why but just how, university math will probably be awfully difficult for her and I would start at the beginning for encouragement.

 

The AMS books are good too but I think you will find more support via the online forums for the AOPS books.

[Teachin'Mine]

I would seriously look into the problem-solving books (not the curriculum, the problem-solving vol 1 and 2) from the AOPS people as an introduction. They include a wide variety of subjects and reteach them. They were also originally written for people who'd learned math elsewhere and needed a problem-solving supplement. If she (thus far) has not wanted to know why but just how, university math will probably be awfully difficult for her and I would start at the beginning for encouragement.

 

The AMS books are good too but I think you will find more support via the online forums for the AOPS books.

 

Honestly, I never learned the why of math in school and it didn't affect my ability to do well in Calculus I and II in college. I'm not familiar with a wide variety of math books, but I don't think most, there are some exceptions which have been mentioned here on the boards, really teach the whys - they focus more on the how. She was doing algebra when she was 11yo, so I don't think it's unusual at that age to not be concerned with the why of it all - especially when it's not taught in the text. :) I do agree that the whys are important for math beyond the usual in college. That's why I'm interested in seeing what's out there now.

 

Those AoPS problem solving books keep coming up as a recommendation. I always like to flip through a book before purchasing as it's an easy way to see if it's what you're looking for, but I haven't had the opportunity to do that with these yet. Are these set up differently from the regular AoPS texts? From what I've heard here, in those books they give the student the problem and then they try to figure it out on their own, and then read the solution. Is this the same? Or do they teach how to approach various problems and then give ones to work on? Do you know of any site which allows a look inside the book? I've searched for this in the past, but didn't find any.

 

I agree that I want to start with simpler problems so she can concentrate on learning how to go about solving them the quickest way rather than working calculus problems beyond what she's already learned. :tongue_smilie: She's had no problem applying the math she's learned to physics and chemistry, so it's not that she can't apply the math, and she does well on the standardized tests. What I'm looking for is more how do you approach the problems that require you to look at the problem in a whole different light - like brainteasers I suppose, or like the problem solving skills needed for the AMC.

[kiana]

Honestly' date=' I never learned the why of math in school and it didn't affect my ability to do well in Calculus I and II in college. I'm not familiar with a wide variety of math books, but I don't think most, there are some exceptions which have been mentioned here on the boards, really teach the whys - they focus more on the how. She was doing algebra when she was 11yo, so I don't think it's unusual at that age to not be concerned with the why of it all - especially when it's not taught in the text. :) I do agree that the whys are important for math beyond the usual in college. That's why I'm interested in seeing what's out there now.[/quote']

 

Sorry if my comment came across as snarky, it wasn't intended that way. Many young students are far more interested in how and some never become interested in why.

 

What I meant was that if she's going to major in math, she's going to need to learn how to think mathematically. Learning the whys rather than just the hows is part of that. It's better for it to be a gradual exposure than to just be tossed into it as a young math major.

 

You may have not been explicitly taught the whys, but (for example) learning when to integrate and when to differentiate in a word problem is part of the 'whys' that I was meaning. Many calculus students struggle with this -- if you give them a function, and TELL them to maximize it along a specific interval, they can do just fine, but if you give them a word problem and tell them to maximize (e.g. the area of a window, especially an oddly shaped one) it is far more difficult. This applies to the general population of calculus students. If you did well, it is likely that you intuited this without being taught.

[Teachin'Mine]

Oh no! The limitations of the written word strike again! :tongue_smilie: I never thought you were being snarky at all! I was just saying that the whys weren't taught when I was in school either. As for why I got through calculus okay probably had more to do with the class taken. I wasn't at a top math/engineering school and only took those two classes to satisfy the requirement for my non-math major. I don't remember real world problems being included at all. :tongue_smilie: It's actually been through homeschooling my daughter that I've put a lot of things together in math that I never had before - and I'm just referring to simple elementary math as it's been years since I've taught her.

 

I absolutely agree that the whys are important! :)

 

I don't know why I hadn't found these excerpts from the Volume 1 book before, but I found this:

 

http://www.artofproblemsolving.com/Store/products/ps-aops1/exc1.pdf

 

In skimming through it, it doesn't seem to me that the whys are explained here either. But then again the focus of the book is on problem solving, and it does seem like it would work well for that. :) I may have to put this on the Christmas list.

 

Any suggestions for what would explain the whys? Or will the AoPS book address that sufficiently?

 

Thank you!!! :)

[Sebastian (a lady)]

I'm also not an elite math person. But AoPS also has some books designed for math competition. Maybe these would help with the problem solving, without being all about calculus.

 

ETA: In the wiki section of AoPS, there are also years worth of AMC tests (8/10/12) with solutions. She might also enjoy working through problems on Alcumus. (Heck, I get a charge out of doing those problems.)

Edited November 18, 2011 by Sebastian (a lady)

[Sebastian (a lady)]

My understanding is that some of the why of the math is taught through discovery method. As an example, the algebra book starts with the properties of addition and multiplication, not because that's what always comes in the first lesson, but because those properties are the engine that make the next lessons go (problems involving negative and fractional exponents, for example).

 

You might want to flip through the excerpts for the other books, including the number theory and probability books.

 

Another book I really like is Calculus Made Easy by Silvanus Thompson. It is old enough that there are free digital versions online. There is also a new edition that was revised by Martin Gardener. I really wish I'd had this text when I was struggling through college calc and the calc based physics and engineering courses I had to take.

[Teachin'Mine]

I'm also not an elite math person. But AoPS also has some books designed for math competition. Maybe these would help with the problem solving, without being all about calculus.

 

ETA: In the wiki section of AoPS, there are also years worth of AMC tests (8/10/12) with solutions. She might also enjoy working through problems on Alcumus. (Heck, I get a charge out of doing those problems.)

 

Yes thank you. That's the one Kiana had suggested as well, and I think we'll give it a try. :)

 

I've checked out the AMC tests and they didn't look so bad until someone posted about the test questions this year! It looked exceptionally challenging. :tongue_smilie: These are the kinds of problems that I picture math geeks doing just for fun. :lol:

[Emerald Stoker]

nm

[Teachin'Mine]

Hi, Teachin'Mine,

 

Let me preface this by saying I don't belong in this thread!

 

But I have been having fun the last week or so poking around on this site that Ray suggested over on one of the other boards (Logic? Accelerated? one of those two): http://www.jamestanton.com/ .

 

He is brilliant at explaining the whys, I think; he's got books for sale on Lulu (with lots of samples) and his own youtube channel--I'm not sure if the math goes up far enough for what you are seeking (the books he's done so far seem to stop at calculus BC and probability/statistics, but others are in preparation, he says). He has a PhD in math from Princeton, so they're math books by a mathematician, like the AoPS books.

 

I don't have any idea whether that helps, but I live in hope!

 

Best,

HG

 

Yes! You do belong in this thread. Thank you!

 

I've been looking through some of what's available on his site, and the books look great! I'm thinking that the Solve It might work well and some of the others look interesting too. I'm not looking for anything beyond what he's already got available. :)

 

Thank you for mentioning this!

[Teachin'Mine]

My understanding is that some of the why of the math is taught through discovery method. As an example, the algebra book starts with the properties of addition and multiplication, not because that's what always comes in the first lesson, but because those properties are the engine that make the next lessons go (problems involving negative and fractional exponents, for example).

 

You might want to flip through the excerpts for the other books, including the number theory and probability books.

 

Another book I really like is Calculus Made Easy by Silvanus Thompson. It is old enough that there are free digital versions online. There is also a new edition that was revised by Martin Gardener. I really wish I'd had this text when I was struggling through college calc and the calc based physics and engineering courses I had to take.

 

Thank you! Since we posted about the same time, I had missed this post. :tongue_smilie: The calculus book looks great!!!

 

I have a feeling that I worded something wrong in my original post as every seems to say that they shouldn't be posting here. :001_huh: I appreciate all the replies and great info. :001_smile:

[Kathy in Richmond]

I saw your post when I was running out the door this morning and finally came back to it tonight (on vacation visiting my kids this week - got to meet one of the WTM boardies today while the kids were busy :D)

 

I was going to recommend that you look at the AoPS texts (esp the classic problem solving volumes and the number theory or counting and probability), but everyone else already beat me to it. She'd find appropriate challenges & complete solutions. They are meant for bright math-lovers and they're all about why math works and not at all about rote learning. I'd especially think that a course such as number theory would provide a good glimpse into non-calculus-based math, how mathematicians think and prove things, etc.

 

In any case, I'd advise you to avoid the AMS book about functional equations at the present. AoPS has a chapter on them if I remember correctly, and it's the material that's appropriate for her level. If she's truly interested in reading about a broad range of math, you might take a peek at the MAA (Math Association of America) bookstore online instead. They have publications aimed more at interested young people than the AMS.

 

The AMC 8/10/12 contests are a rich source of mathematical ideas and problem-solving. They're much more tough than they seem at first glance! The MAA publishes First Steps for Math Olympians, which she might like. It includes problems from past AMC's, and it's organized topically like a textbook & has complete solutions included.

 

Another book I recommend to all aspiring math majors is the classic How to Solve It by Polya.

Edited November 19, 2011 by Kathy in Richmond

[Teachin'Mine]

I saw your post when I was running out the door this morning and finally came back to it tonight (on vacation visiting my kids this week - got to meet one of the WTM boardies today while the kids were busy :D)

 

Kathy, welcome back from vacation. :001_smile:

 

I was going to recommend that you look at the AoPS texts (esp the classic problem solving volumes and the number theory or counting and probability), but everyone else already beat me to it. She'd find appropriate challenges & complete solutions. They are meant for bright math-lovers and they're all about why math works and not at all about rote learning. I'd especially think that a course such as number theory would provide a good glimpse into non-calculus-based math, how mathematicians think and prove things, etc.

 

Thank you for the suggestions. Would the number theory be a full year course or a semester? Where should we fit it into the calculus progression? When we get the problem solving books, should she just work on that on her own, or would it be appropriate to give credit for the work?

 

In any case, I'd advise you to avoid the AMS book about functional equations at the present. AoPS has a chapter on them if I remember correctly, and it's the material that's appropriate for her level. If she's truly interested in reading about a broad range of math, you might take a peek at the MAA (Math Association of America) bookstore online instead. They have publications aimed more at interested young people than the AMS.

 

Thank you!

 

The AMC 8/10/12 contests are a rich source of mathematical ideas and problem-solving. They're much more tough than they seem at first glance! The MAA publishes First Steps for Math Olympians, which she might like. It includes problems from past AMC's, and it's organized topically like a textbook & has complete solutions included.

 

I think I had looked at the AMC 10 in the past and it didn't look too bad, but this 2011 test, think it was the 12, looked incredibly challenging. I couldn't get the link to work - is this it? http://www.amazon.com/First-Steps-Math-Olympians-Competitions/dp/088385824X I'll add it to my "wish list".

 

Another book I recommend to all aspiring math majors is the classic How to Solve It by Polya.

 

On the wish list too. This sounds great as it sounds like it will introduce her to the way mathematicians approach math. This is the kind of thinking I'm hoping for her to get a start on. :)

 

Do you have any suggestions on how the next couple of years should look for her math courses? She's working on Saxon Calculus - the 2nd edition which includes I and II. She's about a third of a way through the 148 lessons. In the fall, she could take a cc class. I was thinking that it would be best to begin with Calculus II so she can get used to learning math in a lecture setting with familiar material. She would rather not repeat anything. She'll take a placement test with the math department, so she won't take anything she's not prepared for, but I'd love to have your input on advice. Where would number theory fit in? Should she plan to take statistics in cc?

 

As you can tell, I'm really fuzzy about what direction she should take. I'm also trying to take into account that the advice here generally is to repeat calculus from Calculus I in university as the rigor, or emphasis, or teaching style, will be very different. I'm wondering if it's better for her to keep going with the calculus courses, as she'd like to do, or if the time would be better spent on problem solving, taking the AMC tests, and similar pursuits? Or would colleges look at this as having been ahead in math and then dropping it, so to speak. :tongue_smilie:

 

Don't feel that you have to answer this right away as I'm sure you're probably quite busy settling back in at home, and none of these decisions need to be made immediately. :) Thank you for all your great input on these boards!

[Kathy in Richmond]

Teachin'Mine - Sorry that I'm so slow in replying. I'd just started my trip in my previous post & got home the night before Thanksgiving. Just getting caught up now!

 

I would count the AoPS number theory and counting & probability texts as 1/2 credit each. They will take about one semester to complete self-studying at home. If you take the online version of the course (and granted it moves really fast), it lasts for 12 weeks. I also counted those online classes as 1/2 credit each on my kids' transcripts. The AoPS problem solving books could also be done for credit. I used volume two as half of my daughter's precalculus class, & so she earned 1/2 credit for working through it.

 

Where do these classes belong in the traditional math class progression? Well, they don't, because they're different from the math that leads to calculus. My kids began & enjoyed number theory and counting/probability after they'd finished algebra 1 and geometry. You could start at any time after that, too. We always did problem-solving math in tandem with our 'regular' math (from algebra 1 onward), so it was an extra math, not a substitute for another course. They earned credit for problem-solving math if they took a formal prob-solving course online from AoPS (or the one time when my dd used AoPS Vol 2 as part of precalc), but mostly they did that stuff w/o credit.

Do you have any suggestions on how the next couple of years should look for her math courses? She's working on Saxon Calculus - the 2nd edition which includes I and II. She's about a third of a way through the 148 lessons. In the fall' date=' she could take a cc class. I was thinking that it would be best to begin with Calculus II so she can get used to learning math in a lecture setting with familiar material. She would rather not repeat anything. She'll take a placement test with the math department, so she won't take anything she's not prepared for, but I'd love to have your input on advice. Where would number theory fit in? Should she plan to take statistics in cc? [/quote']

 

If she's finishing calculus in the tenth grade, then she's on the same track that my two were on. Some ideas for the next two years:

 

The usual suspects: multivariable calculus, linear algebra, differential equations. These could be taken at your cc or through an online provider like EPGY. EPGY offers several university level math classes (even more beyond those I listed). It works best for kids who like to self-teach, and since you've described your daughter that way in your posts, I think that she may like it. We found their course materials to be very nice mix of textbook and interactive tutorials on the computer. Homework sets were challenging but reasonable, with a written midterm and final (if I remember correctly). EPGY doesn't always work so well if the student needs lots of support, because then it's dependent on the quality of the assigned tutor (a mixed bag). They're pricey but quite generous with financial aid if that's a factor. You just have to call them up and ask about how to apply for it.

 

Statistics: I'd tend to prefer the AP class over the cc class here. It's well designed for high schoolers, and she has the prerequisites already. It can be self-studied (my son did) or taken through PA Homeschoolers (like my daughter) - highly recommended as a terrific interactive online course that colleges will respect.

Computer Science: If your daughter intends to go to a highly selective school in math or another STEM area, she'd do well to have some programming experience under her belt before she goes. Both the PA Homeschooler AP Comp Sci Java class or AoPS online Python class are great choices (and I'm sure there are many more out there). Again, she already has the needed prerequisites for these.

Non-calculus track math: This includes number theory, counting and probability, abstract algebra, etc. AoPS, EPGY, or even MIT OpenCourseware would give her some alternatives. AoPS has a new group theory course (prereq=basic number theory,, combinatorics, and complex numbers). Here's an MIT OCW class that my son recommends for advanced high school kids to get them interested in discrete math.

 

Any potential math major would be well-advised to sample some on this off-the-beaten track math. As a math professor in my former life, I saw lots of kids come in thinking they'd be math majors, only to be disappointed upon finding out that university mathematics is a different beast from the alg-geom-trig-calculus stuff of their high school days. There's lots of proofs, lots of abstractions, and not so many numbers and calculations (and if that's what they truly liked about math, then they usually ended up in some sort of engineering or applied science instead).

 

For example, here's a link to the syllabus for the honors math major track for the first ten weeks of freshman year at my daughter's university. You don't see many numbers or even many calculations. It was highly abstract and proof based.

Problem-solving or contest math: Self-studying with the books we've already mentioned is great, or you could sign her up for one of AoPS' many contest math prep classes. She doesn't even have to take the contests themselves; what she'd learn in the classes would be more than worthwhile. This is also a nice option for a kid who wants to sample different areas like number theory before committing to just one. For example, my dd took their AMC-12 prep class. Over 12 weeks the course covered ideas from advanced algebra, number theory, functions, combinatorics, inequalities, statistics, sequences/series, complex numbers, trig problems, and lots of advanced geometry - a smorgasbord of math.

 

You won't run out of math!:D Honestly, the problem we had was that there wasn't enough time to do everything that we wanted to do before she left for university...

 

I'm also trying to take into account that the advice here generally is to repeat calculus from Calculus I in university as the rigor' date=' or emphasis, or teaching style, will be very different. I'm wondering if it's better for her to keep going with the calculus courses, as she'd like to do, or if the time would be better spent on problem solving, taking the AMC tests, and similar pursuits? Or would colleges look at this as having been ahead in math and then dropping it, so to speak. :tongue_smilie:

[/quote']

 

My best advice is to start out by trying some problem-solving math (like AMCs) AND also to try a different kind of math like number theory, where she'd get a flavor of how mathematicians think deeply about simple ideas and gain some practice in proofs. Both are equally valuable experiences for a girl like your daughter.

 

Then decide whether she likes that better, or whether she'd like to pursue advanced calculus, diff equations, etc.

 

Or, if she's like my dd, that she wants to do all of the above.:tongue_smilie:

 

As for repeating classes in college, my advice is "it depends." My kids would have died if they'd had to repeat calculus, and neither did. My son even challenged his way out of multivariable calc, which he'd self-studied at home. He was mad that they made him take Differential equations over at the university, but it worked out well because the professor, in spite of using the same textbook he'd self-studied at home, injected a LOT of extra theory into the class. My daughter repeated multivariable calc at university, but it was the class I linked to above. It was a whole different beast than the partial derivatives and multiple integrals we'd done at home.

[Teachin'Mine]

Teachin'Mine - Sorry that I'm so slow in replying. I'd just started my trip in my previous post & got home the night before Thanksgiving. Just getting caught up now!

 

No problem at all - welcome back! :) Thank you so much for taking the time to write out all this great information. It's going to take me a bit of time to look through everything and undoubtedly come up with more questions. The link to your daughter's class looks like a foreign language! Thank you for explaining how different university math is from high school math.

 

I would count the AoPS number theory and counting & probability texts as 1/2 credit each. They will take about one semester to complete self-studying at home. If you take the online version of the course (and granted it moves really fast), it lasts for 12 weeks. I also counted those online classes as 1/2 credit each on my kids' transcripts. The AoPS problem solving books could also be done for credit. I used volume two as half of my daughter's precalculus class, & so she earned 1/2 credit for working through it.

 

Where do these classes belong in the traditional math class progression? Well, they don't, because they're different from the math that leads to calculus. My kids began & enjoyed number theory and counting/probability after they'd finished algebra 1 and geometry. You could start at any time after that, too. We always did problem-solving math in tandem with our 'regular' math (from algebra 1 onward), so it was an extra math, not a substitute for another course. They earned credit for problem-solving math if they took a formal prob-solving course online from AoPS (or the one time when my dd used AoPS Vol 2 as part of precalc), but mostly they did that stuff w/o credit.

 

If she's finishing calculus in the tenth grade, then she's on the same track that my two were on. Some ideas for the next two years:

 

The usual suspects: multivariable calculus, linear algebra, differential equations. These could be taken at your cc or through an online provider like EPGY. EPGY offers several university level math classes (even more beyond those I listed). It works best for kids who like to self-teach, and since you've described your daughter that way in your posts, I think that she may like it. We found their course materials to be very nice mix of textbook and interactive tutorials on the computer. Homework sets were challenging but reasonable, with a written midterm and final (if I remember correctly). EPGY doesn't always work so well if the student needs lots of support, because then it's dependent on the quality of the assigned tutor (a mixed bag). They're pricey but quite generous with financial aid if that's a factor. You just have to call them up and ask about how to apply for it.

 

Statistics: I'd tend to prefer the AP class over the cc class here. It's well designed for high schoolers, and she has the prerequisites already. It can be self-studied (my son did) or taken through PA Homeschoolers (like my daughter) - highly recommended as a terrific interactive online course that colleges will respect.

Computer Science: If your daughter intends to go to a highly selective school in math or another STEM area, she'd do well to have some programming experience under her belt before she goes. Both the PA Homeschooler AP Comp Sci Java class or AoPS online Python class are great choices (and I'm sure there are many more out there). Again, she already has the needed prerequisites for these.

Non-calculus track math: This includes number theory, counting and probability, abstract algebra, etc. AoPS, EPGY, or even MIT OpenCourseware would give her some alternatives. AoPS has a new group theory course (prereq=basic number theory,, combinatorics, and complex numbers). Here's an MIT OCW class that my son recommends for advanced high school kids to get them interested in discrete math.

 

This looks good!

 

Any potential math major would be well-advised to sample some on this off-the-beaten track math. As a math professor in my former life, I saw lots of kids come in thinking they'd be math majors, only to be disappointed upon finding out that university mathematics is a different beast from the alg-geom-trig-calculus stuff of their high school days. There's lots of proofs, lots of abstractions, and not so many numbers and calculations (and if that's what they truly liked about math, then they usually ended up in some sort of engineering or applied science instead).

 

Yes this is what I've been wondering about. It would help to know which way she intends to go as it will make finding the right college a bit easier.

 

For example, here's a link to the syllabus for the honors math major track for the first ten weeks of freshman year at my daughter's university. You don't see many numbers or even many calculations. It was highly abstract and proof based.

Problem-solving or contest math: Self-studying with the books we've already mentioned is great, or you could sign her up for one of AoPS' many contest math prep classes. She doesn't even have to take the contests themselves; what she'd learn in the classes would be more than worthwhile. This is also a nice option for a kid who wants to sample different areas like number theory before committing to just one. For example, my dd took their AMC-12 prep class. Over 12 weeks the course covered ideas from advanced algebra, number theory, functions, combinatorics, inequalities, statistics, sequences/series, complex numbers, trig problems, and lots of advanced geometry - a smorgasbord of math.

 

You won't run out of math!:D Honestly, the problem we had was that there wasn't enough time to do everything that we wanted to do before she left for university...

 

I can see that there's lots of choices - thank you!

 

My best advice is to start out by trying some problem-solving math (like AMCs) AND also to try a different kind of math like number theory, where she'd get a flavor of how mathematicians think deeply about simple ideas and gain some practice in proofs. Both are equally valuable experiences for a girl like your daughter.

 

Then decide whether she likes that better, or whether she'd like to pursue advanced calculus, diff equations, etc.

 

Or, if she's like my dd, that she wants to do all of the above.:tongue_smilie:

 

As for repeating classes in college, my advice is "it depends." My kids would have died if they'd had to repeat calculus, and neither did. My son even challenged his way out of multivariable calc, which he'd self-studied at home. He was mad that they made him take Differential equations over at the university, but it worked out well because the professor, in spite of using the same textbook he'd self-studied at home, injected a LOT of extra theory into the class. My daughter repeated multivariable calc at university, but it was the class I linked to above. It was a whole different beast than the partial derivatives and multiple integrals we'd done at home.

 

Thank you Kathy!!!