Deniseibase Posted April 12, 2011 Share Posted April 12, 2011 My daughter is on track to finish calculus well before the end of high school. She wants to study math in college, so obviously we want four years of math in high school, if not more. What do you do beyond calculus? I know there are a lot of possibilities ranging from Calculus II to number theory to probability and statistics and what not, and I figure she'll have her own opinion on it based on what in particular she is thinking about for college by that point. But as an English major mom I would love to get some ideas of what the possibilities are, especially as far as what texts you would suggest - thanks so very much! Quote Link to comment Share on other sites More sharing options...
In The Great White North Posted April 12, 2011 Share Posted April 12, 2011 I let ds go to the local high school for a class called Math Modeling. It was project-based, computer modeling and he loved it. It did use a bit of differential equations, but otherwise was actually little math. (He's majoring in computer science, not math.) If your dd wants to major in math, I would definitely lean towards doing all the AoPS extraneous books. Quote Link to comment Share on other sites More sharing options...
KAR120C Posted April 12, 2011 Share Posted April 12, 2011 My daughter is on track to finish calculus well before the end of high school. She wants to study math in college, so obviously we want four years of math in high school, if not more. What do you do beyond calculus? I know there are a lot of possibilities ranging from Calculus II to number theory to probability and statistics and what not, and I figure she'll have her own opinion on it based on what in particular she is thinking about for college by that point. But as an English major mom I would love to get some ideas of what the possibilities are, especially as far as what texts you would suggest - thanks so very much! There is a lot you can do between algebra and calculus -- number theory, counting & probability, more problem solving -- and they have what amounts to three algebras (1 & 2 in their Introduction book and 3 in the Intermediate book, although it's not unheard of to finish 1 & 2 in a single year) plus precalculus... so there's plenty to keep a kid busy and beef up the usual sequence. AP Statistics (not offered at AoPS) is also completely accessible before calculus. For a future math major, I think I'd probably try to get to as many of those topics as possible before calculus, rather than waiting until after. I personally don't like to interrupt the precalculus-calculus 1-calculus 2-calculus 3 sequence, so once you start on that I'd recommend continuing straight through to the third (college) semester of calculus. And if it's available to you, I would be more inclined to go with a local college so you can have all three semesters from the same source (and not worry that one picks up somewhere other than where the previous left off). I haven't yet reconciled that with my liking for AoPS... if DS is young he might do AoPS Calculus first and then pick up a university sequence (twice certainly would have done me some good...) or we might find that it's overkill. After calculus... I think Art of Problem Solving has a group theory class, but I might just see what the available local or online universities can offer. Quote Link to comment Share on other sites More sharing options...
MomsintheGarden Posted April 12, 2011 Share Posted April 12, 2011 My dd only got through Calc II and took the BC exam. My next student will probably get through Calc II before his senior year, and I'm planning to have him do Calc III (Multivariable Calc). We do Chalkdust here, and I found DVD instruction with (mostly) Dana Mosely from CD for Calc I-III, so all I need to do is buy the Multivariable book + SM. If he finishes Calc III, I will have him do Linear Algebra and possibly Statistics. AP Stats is a good course, but it will not get you stats credit for a math major because is not calc-based physics. If you need more ideas, I'm sure Kathy in Richmond can give you some. Her daughter did math beyond Calc in high school. She's now a math major at Stanford.:001_smile: HTH, GardenMom Quote Link to comment Share on other sites More sharing options...
LoriM Posted April 12, 2011 Share Posted April 12, 2011 My daughter pushed to Calculus at 15, then actually went back to College Algebra-PreCalculus-Calculus I-Statistics at the local community college while she was 16-17 yo, then started Calc II at 18 (and a freshman) at the university. I found it a good fit for her to skill-and-drill the algebra skills (which, by the way, enabled her to graduate summa cum laude in mathematics) at the pace of a college class before pushing her forward to the harder concepts of Calc II. I agree that there is plenty of math to do prior to the Calculus sequence, and I think it's pretty important to be a master of numbers and algebraic manipulation before diving off into the advanced concepts of university mathematics. Many students work too few problems to be masters. Quote Link to comment Share on other sites More sharing options...
mom31257 Posted April 12, 2011 Share Posted April 12, 2011 Life of Fred has college level books, Statistics and Linear Algebra. I have a math degree and Linear Algebra was my favorite class in college. Statistics is defintely a useful math in many fields of study. Quote Link to comment Share on other sites More sharing options...
regentrude Posted April 12, 2011 Share Posted April 12, 2011 We are not there yet, but after calculus 1 comes calculus 2 and then calc 3 (multivariable). Both are five hour classes at the university requiring ten hours out-of-class work, so each could be a year long high school course if taken independently at a more moderate pace. After that, differential equations would be next. If my mathy kids feel no desire to continue the straight sequence, we can branch out doing number theory, probability, special topics in geometry, fractals and chaos. The AoPS books are great. Quote Link to comment Share on other sites More sharing options...
SunD Posted April 12, 2011 Share Posted April 12, 2011 We're definitely not there yet, but in addition to what's been mentioned, my high school also offered Discrete Mathematics, Differential Equations, Vector Calculus, Topology, and Chaos Theory. I also seem to remember Set Theory or something like that, but I don't see it in their offerings anymore. Quote Link to comment Share on other sites More sharing options...
eumyang Posted April 12, 2011 Share Posted April 12, 2011 I was a math major in college, and the following is a list of the core (lower division) math courses that all math majors had to take: Calculus I Calculus II Multivariable Calculus Linear Algebra Differential Equations Discrete Mathematics Probability & Statistics The question to the OP is, however, how much of Calculus will her dd "finish"? Will she get through single-variable calculus (Calculus I & II), or will she finish Multivariable Calculus (aka Calculus III) as well? Whatever she has completed, she can go through the rest of list, at whatever pace works for her. 69 Quote Link to comment Share on other sites More sharing options...
Carol in Cal. Posted April 12, 2011 Share Posted April 12, 2011 The calculus track continues with differential equations and linear algebra. However, there are 'breadth' math studies that are also really helpful down the road--statistics, statistical experimental design, programming logic, etc. Quote Link to comment Share on other sites More sharing options...
StephanieZ Posted April 12, 2011 Share Posted April 12, 2011 We'll do Calculus. Then we'll do Statistics (way easier, BTW). I will mix in some AoPS books, etc as we go along. Kids will still likely be 'done' before end of high school unless they fall in love with AoPS or math in general and so we add MORE of the 'extras'. If the kid loves math and is not done with homeschool and is done with what I can provide, they can take courses at the local uni or online. . . otherwise, they can take the last year or two of high school to focus on other interests. (Once they've gotten great scores on Calc AP and/or established thier competecny via uni. courses.) Quote Link to comment Share on other sites More sharing options...
Belacqua Posted April 12, 2011 Share Posted April 12, 2011 After single variable, my kid used MIT Opencourseware for multivariable and then linear algebra. We're looking at differential equations next, followed by discrete mathematics. I agree with Great White North that the AoPS courses and books are excellent, as well (hardly an unpopular opinion around these parts :)). Even if your daughter isn't interested in math competitions, the Math Olympiad training course from AoPS introduces all manner of nifty topics, some of which might spur an interest in deeper study. Quote Link to comment Share on other sites More sharing options...
jennynd Posted April 12, 2011 Share Posted April 12, 2011 Multivariable Calculus Linear Algebra Differential Equations (Ordinary DE/Partial DE) Discrete Mathematics ) those are very key if u are interested in engineering also Quote Link to comment Share on other sites More sharing options...
Deniseibase Posted April 13, 2011 Author Share Posted April 13, 2011 Wow, thanks so much for all the ideas! As an English major who BARELY finished Algebra II (and that 25 years ago and promptly forgotten ;-), I had no IDEA all these options were available! It looks like I will definitely have to look into The Art of Problem Solving - we had looked at it previously, but she's not interested in contests & I didn't really realize it was for more than that. Quote Link to comment Share on other sites More sharing options...
Julie in MN Posted April 13, 2011 Share Posted April 13, 2011 My oldest did calculus I in public school 11th, then calculus I at community college for 12th, then calculus I and forward with his degree program. That was his choice, and he felt he learned more along the way. Julie Quote Link to comment Share on other sites More sharing options...
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