Brad S Posted June 12, 2015 Share Posted June 12, 2015 DS was in bricks and mortar "high school math 2 (honors)" this past year, as of tomorrow, he's back to homeschooling and decided to use Art of Problem Solving for math. Even though his next scheduled class in school would be precalculus, I bought him the AoPS Intermediate Algebra book since AoPS is a more challenging text. Do you have any recommendations for transitioning to AoPS? I'd like it to be a successful transition. DS will be starting it in the next couple of days. We haven't completed any AoPS books so far, although we also have the Introduction to Counting and Probability book, and our plan is to alternate it with Intermediate Algebra whenever DS wants a change of pace for a day or a week. Thanks! P.S. DS had a pretty strong algebra 1 background, then used Jacobs Geometry, and last year pretty much covered through algebra 2 and some miscellaneous topics at a level above an average public school honors level, although apparently lots of volume but not problems anywhere near AoPS level. Thanks for any recommendations on starting with AoPS! Quote Link to comment Share on other sites More sharing options...
Kathy in Richmond Posted June 12, 2015 Share Posted June 12, 2015 Sounds like your son is starting in the right place with the Intermediate Alg book, & I like your idea to alternate with the Intro C&P text for variety. My only advice is to take your time. The first few chapters may be a bit of alg 2 review, but it will quickly move on to new material. There's a balance in using AoPS. You can't really schedule their higher level texts like you could with something like Jacobs. Sometimes it's OK to take a whole week to get through an end of chapter challenger set. On the other hand, you don't want him to get too hung up on any one problem to the point that he's staring at it too long without making any progress. When that happens (& it will with the challengers at times!) it's perfectly OK to either mark those problems to revisit at a later date or even to read through the solution. The Intermediate Algebra text and also the Precalculus text are my favorites. So much good stuff! Btw, Int Alg contains the advanced algebra portion of a typical precalculus courses, in addition to many algebra topics not addressed in standard texts. Precalculus contains trig + complex analysis + an intro to linear algebra and vectors. Most of all, have fun! 2 Quote Link to comment Share on other sites More sharing options...
Arcadia Posted June 12, 2015 Share Posted June 12, 2015 If your kid get stuck and don't want parents to help, you can ask him to hit the forums. You need an account to post but you can read without account. http://www.artofproblemsolving.com/community My boys have their own Alcumus accounts and they like reading the public forums and their class forums. Did you buy the solution manual? My oldest sometimes solve the questions in a different way from the book but it's nice for me to have the solutions manual as a quick check. 1 Quote Link to comment Share on other sites More sharing options...
Brad S Posted June 13, 2015 Author Share Posted June 13, 2015 Sounds like your son is starting in the right place with the Intermediate Alg book, & I like your idea to alternate with the Intro C&P text for variety. My only advice is to take your time. The first few chapters may be a bit of alg 2 review, but it will quickly move on to new material. There's a balance in using AoPS. You can't really schedule their higher level texts like you could with something like Jacobs. Sometimes it's OK to take a whole week to get through an end of chapter challenger set. On the other hand, you don't want him to get too hung up on any one problem to the point that he's staring at it too long without making any progress. When that happens (& it will with the challengers at times!) it's perfectly OK to either mark those problems to revisit at a later date or even to read through the solution. The Intermediate Algebra text and also the Precalculus text are my favorites. So much good stuff! Btw, Int Alg contains the advanced algebra portion of a typical precalculus courses, in addition to many algebra topics not addressed in standard texts. Precalculus contains trig + complex analysis + an intro to linear algebra and vectors. Most of all, have fun! Thanks, these are really helpful points, both with some specifics and the general comments!! We'll be sure to take "our" time, esp. starting in June -- actually, I think DS will do this mostly himself; although I'm trained as a mathematician, DS likes to be independent. Arcadia's recommendation to sign up for the AoPS forums is a good one. DS will probably resist that too at first, but I'll probably just sit down with him and get him started; I think he'll eventually go there. It's great to get that feedback on the end of chapter challenger problems sometimes taking some time. We might have wondered if DS wasn't getting the material. He'll probably be happy to know it's "OK" when we get there. In school they went through more material but with less depth than we did at home prior to this past year, so AoPS will be quite a change. I'm also happy to know that Int Algebra and Precalculus were your favorites. I was regretting that perhaps we missed a better one in Intro to Algebra but now feel better about this...also love your "Have fun" comment. For DS, I hope he gets off to a good start. Thanks again! If your kid get stuck and don't want parents to help, you can ask him to hit the forums. You need an account to post but you can read without account. http://www.artofproblemsolving.com/community My boys have their own Alcumus accounts and they like reading the public forums and their class forums. Did you buy the solution manual? My oldest sometimes solve the questions in a different way from the book but it's nice for me to have the solutions manual as a quick check. Yes, we have the solutions manuals for Int Algebra and Intro to C&P. Thanks for the forums recommendation. I think DS will be reluctant to get started, but I think it will be useful both to answer questions and see what types of questions others have. Thanks!! Does anyone else have any suggestions as we start off with AoPS Intermediate Algebra? Thanks! Quote Link to comment Share on other sites More sharing options...
daijobu Posted June 24, 2015 Share Posted June 24, 2015 Please keep us informed of his progress. We're a little bogged down in the polynomials chapters right now. It's at a level far, far beyond what I did in high school. I may take the advice of someone else here, and skip the remaining polynomials chapters (except Vieta's formulas) and move on. But I only have the summer left before dd starts regular school, so I want to make sure she has some experience with sigma notation and she understands the logarithmic identities. (Aren't there only 5 of them?) Quote Link to comment Share on other sites More sharing options...
daijobu Posted June 24, 2015 Share Posted June 24, 2015 The Intermediate Algebra text and also the Precalculus text are my favorites. So much good stuff! Do you have any words of inspiration for getting through the polynomials chapters? We're getting so bogged down and I'm seriously considering just moving past them, so we can get to the more basic stuff she'll need for school in the fall. Quote Link to comment Share on other sites More sharing options...
Pegs Posted June 24, 2015 Share Posted June 24, 2015 I spent some time on Alcumus before starting on the AoPS books, and found it to be a wonderful introduction to problem solving math, rather than the *apply this algorithm to these expressions* math I was used to. I honestly felt like I grew myself some more brain, working through such clever problems. 1 Quote Link to comment Share on other sites More sharing options...
Arcadia Posted June 24, 2015 Share Posted June 24, 2015 We're a little bogged down in the polynomials chapters right now.Chapter 6 to 9? Which sections are you stuck on? I can ask my kid how he thinks through those. He finds Vieta formulas convenient. He likes logarithms because of radioactive decay so it neatly tied in with his science. What is on the summary on page 451 is useful. ETA: He also finds the AIME past year solutions useful after he tried the questions. 1 Quote Link to comment Share on other sites More sharing options...
Kathy in Richmond Posted June 24, 2015 Share Posted June 24, 2015 Do you have any words of inspiration for getting through the polynomials chapters? We're getting so bogged down and I'm seriously considering just moving past them, so we can get to the more basic stuff she'll need for school in the fall. What is she taking in the fall that she needs to get ready for? Those chapters on polynomials in AoPS Intermediate Alg are pretty intense! I usually recommend concentrating on these sections for a first pass through: Ch 6: all Ch 7.1 - 7.5 Ch 8 omit Ch 9.1 - 9.2 She could always come back & do more later if interested and/or if pursuing AMC contests at higher levels like AIME or USAMO. The topics I make sure that my students know are polynomial division (including synthetic division), Vieta's formulas, the Factor & Remainder theorems, the Fundamental Theorem of Algebra, The Rational Root theorem, finding upper & lower bounds on roots, & Descarte's Rule of Signs. They're all covered in the sections I listed with the exception of Descarte's Rule, which is discussed in the "Extra!" box on page 260. Have you considered using a different text just for these topics? I'd also recommend (1) the polynomial chapter in the original AoPS Problem Solving vol 2 for a more concise approach, or (2) one of the old Dolciani Structure & Method Alg & Trig text (my 1992 copy has a chapter titled Polynomial Equations that goes over all of the above in a more straightforward fashion), or (3) Schaum's Outline of College Algebra (chapter on Theory of Equations). This was some of the more mind-twisting math stuff that I learned in high school math. My teacher, Mr. Grimm, didn't use a single textbook for precalculus, but he taught polynomial theory from that chapter in Schaum's Outline. I loved the stuff, but it took a while before I really grasped it all. I definitely sympathize! :001_smile: 2 Quote Link to comment Share on other sites More sharing options...
daijobu Posted June 24, 2015 Share Posted June 24, 2015 What is she taking in the fall that she needs to get ready for? Those chapters on polynomials in AoPS Intermediate Alg are pretty intense! I usually recommend concentrating on these sections for a first pass through: Ch 6: all Ch 7.1 - 7.5 Ch 8 omit Ch 9.1 - 9.2 She could always come back & do more later if interested and/or if pursuing AMC contests at higher levels like AIME or USAMO. The topics I make sure that my students know are polynomial division (including synthetic division), Vieta's formulas, the Factor & Remainder theorems, the Fundamental Theorem of Algebra, The Rational Root theorem, finding upper & lower bounds on roots, & Descarte's Rule of Signs. They're all covered in the sections I listed with the exception of Descarte's Rule, which is discussed in the "Extra!" box on page 260. Have you considered using a different text just for these topics? I'd also recommend (1) the polynomial chapter in the original AoPS Problem Solving vol 2 for a more concise approach, or (2) one of the old Dolciani Structure & Method Alg & Trig text (my 1992 copy has a chapter titled Polynomial Equations that goes over all of the above in a more straightforward fashion), or (3) Schaum's Outline of College Algebra (chapter on Theory of Equations). This was some of the more mind-twisting math stuff that I learned in high school math. My teacher, Mr. Grimm, didn't use a single textbook for precalculus, but he taught polynomial theory from that chapter in Schaum's Outline. I loved the stuff, but it took a while before I really grasped it all. I definitely sympathize! :001_smile: What is she taking in the fall that she needs to get ready for? It's a class called...wait for it...Math 2! I have no idea what it is either, but we figure it must have geometry as a prereq. In an email, the school recommended that the students be familiar with sigma notation, and I thought that would be an easy summer topic. And I thought logarithmic id's would be easy to knock off as well. If we have more time this summer, I'd also like to hit piecewise defined functions, only because I thought that was fun in high school. (Can't forget the hiccup function: f(x) = 1 if x is an integer,and f(x)=0 if it isn't!) Have you considered using a different text just for these topics? I'd also recommend(1) the polynomial chapter in the original AoPS Problem Solving vol 2 for a more concise approach, or You know, I do have volume 2 lying around; thank you for the recommendation. I'll open it up and take a look. 1 Quote Link to comment Share on other sites More sharing options...
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