How can I advance in Math?

Colleges and Universities A-Z Massachusetts Institute of Technology
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<p>I am a freshman in high school taking Geometry in ninth grade. Most people are taking geometry or algebra 1 right now and some are even taking algebra 2 because their middle school had geometry as a class in 8th grade while mine did not. One of my friends is even taking H math analysis(trig and precalc) in 9th grade because of his private middle school. I got a perfect score on the math section of the psat, and i have a 98.8 percent in geometry. I do not mean to brag but i think i should be in a more advanced class because this is not a challenge to me at all, but my counselor will not listen. My dream school is M.I.T and I am wondering what exactly i need to do in terms of math to even have a chance to attend this wonderful university. I really like math btw so this is not just about admissions :P Thank you!</p>

<p>A regular student would take:</p>

<p>9th grade: Geometry (or Algebra I)
10th grade: Honors Algebra 2 (or Geometry)
11th grade: Honors Math Analysis (or Algebra 2)
12th grade: AP Calculus BC (or Math Analysis)</p>

<p>This is my first CC post, even though i have been reading peoples posts for a couple of months now. Thanks again.</p>

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<p>Actually, I took Geometry in my senior year because I completed only one year of high school.
So you have so much time to prepare.
My advice is do what ever you like.</p>

<p>You can always self study and use wiki etc.
[YouTube</a> - Lec 1 | MIT 18.06 Linear Algebra, Spring 2005](<a href=“http://www.youtube.com/watch?v=ZK3O402wf1c&feature=SeriesPlayList&p=E7DDD91010BC51F8]YouTube”>http://www.youtube.com/watch?v=ZK3O402wf1c&feature=SeriesPlayList&p=E7DDD91010BC51F8)</p>

<p><a href=“http://www.youtube.com/watch?v=7K1sB05pE0A&feature=related[/url]”>http://www.youtube.com/watch?v=7K1sB05pE0A&feature=related&lt;/a&gt;&lt;/p&gt;

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<p>Sadly, you will get the most out of math in high school by learning on your own. Don’t let a school system shackle your learning. I was in a bit of a similar situation like you, and I know plenty of kids at MIT who felt they did not really get out anything in math in High School.</p>

<p>There are plenty of extra opportunities to learn math. At your level I would check out the 2 books “Art of Problem solving” vol. I/II. Here’s a website for people like you who are bored by HS math. [Art</a> of Problem Solving](<a href=“http://www.artofproblemsolving.com/]Art”>http://www.artofproblemsolving.com/) You can always self-study. You’ll quickly realize that that’s usually the best way to learn in HS, unless you go to a magnet. There are lots of quality books/contests out there to learn from.</p>

<p>Secondly, try to get extra opportunities over the summer: USA/Canada Mathcamp is one. Stanford EPYG school is another. Look if your local university is offering any classes. In short, learn what you like and f*** the rest.</p>

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<p>

:slight_smile:
10 char</p>

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<p>@DannyNobel,
Given your list of courses “a regular student would take,” it sounds as if you are in that “regular track.” Is it possible to move? Is there an “advanced track”? Some high schools have fairly rigid tracking, whereas others don’t. What is your school like? What does it take to move up to a more challenging class?</p>

<p>Faraday’s suggestion about AoPS is great, but it’s also a good idea to try to challenge yourself as much as you can in the context of high school. Not to get into a college, but just to ensure that you aren’t bored to death. It might be time to bring your parents/guardians into this conversation. As a parent, I would want to schedule a conversation with that school counselor, my son, and me. </p>

<p>As for MIT – it’s so competitive to get in, that you could advance in math as far as possible and still not attain admission. But it’s a great idea to try to prepare yourself really well in mathematics, because it will open doors for you elsewhere.</p>

<p>If it doesn’t work out at your school, and you stay on the “regular track” and complete BC Calc your senior year, you’ll be fine. You’ll be far more prepared if you follow Faraday’s advice and supplement this with self-study on the side. </p>

<p>Good luck!</p>

6

<p>I studied algebra using a few textbooks from the library and some ‘for dummies’ style guides. SAT math prep stuff helped too, but that was a long time ago. I can’t really remember the specifics.</p>

<p>I studied calculus with a combination of AP prep books, Stewart’s and a few miscellaneous textbooks from the library for topics that Stewart didn’t cover well. Delta-epsilon proofs, Riemann sums, sequences and series, etc. I also used a lot of the online lectures/notes/tests from MIT’s opencourseware. Those were great. There are a lot of problems that you should see being done to get a sense of efficiency and a good order in which to do steps. Stewart’s (and most other calc books) can get a bit confusing if you can’t actually see the problems being done.</p>

<p>I used a few books for linear algebra and differential equations after that. As far as introductory texts go, they all seem pretty similar. MIT’s OCW lectures are awesome, especially for linear algebra. That’s probably a ways off anyway. </p>

<p>If you’re really interested in learning more math now, that’s great. If you just want to do it so you can get a leg up in admissions or because you think you should/have to to be competitive, you don’t. And you shouldn’t.</p>

<p>If your counselor wont put you in a higher math class, there might be a reason. What were your grades in previous math classes? If they were fine (C’s or better?) you should get your parents involved and talk to the administration. A freshman I tutored this year was in a similar situation, and that got her moved up pretty quickly.</p>

7

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<p>Faraday is absolutely correct in saying that your high school track means only so much.</p>

<p>Let me emphasize something, as someone who can say he’s seen mathematics at a vast span of levels. Your focus should be less on advancing what subject matter you know and more on developing maturity of thinking. You will find that this is the most invaluable thing you can do if you want to get the most out of college. What do I mean by this? Roughly speaking, you should try to figure out why the things they spit at you are important. Too often, the curriculum is well-designed, but poorly presented. </p>

<p>I didn’t know about these, but you can try the math competitions to get you thinking about more challenging problems. But just another way to do it is to get a good book and spend time working through it on your own time and thinking about the material. And/or checking out things like the link faraday suggested. When you have to do proofs in geometry, really practice writing them out well. When you study conic sections in Algebra 2, really figure out what the things they’re teaching you are about. When you study trigonometry, try solving some problems that actually get you to use it and appreciate what trigonometry is about, rather than just learning the trig identities.</p>

<p>One of the best things you can do for yourself in high school is figure out in what context you like studying mathematics. This means that for instance, when you get a solid understanding of calculus, you should test it by trying to read a physics text with some advanced calculus. Faraday can recommend things for you – Purcell’s book on E&M might be a good place, as that’s what an honors course at my school uses. When you do calculus, also try to actually understand the proofs to the theorems you use – e.g., as some have discussed, try Apostol. I think these things might help more than learning Diff Eqs or something, unless you have a context you specifically want to use it in. Else, it might just go in one ear, out the other. Mathematics is a subject you really only learn by actively trying to think about why you’re studying it.</p>

<p>Once you develop the confidence that you can take a subject and really think about it actively, you’ll just begin to enjoy the process ever so much more.</p>

<p>Don’t do any of this for admission specifically, because odds are you will be disappointed. Do it for the soul :D</p>

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<p>The only requirement you need in terms of math to get into MIT is the ability to be able to take single-variable Calculus, since it’s a requirement to graduate. This is the same as Calc BC, so the math track you are in will not hurt you in any way (there are people here that have never seen Calculus in high school).</p>

<p>However, if math is something you’re really interested, there’s still a lot you can do to get ahead if that’s what you want to do. For getting ahead in classes, it might help your case if you took a class outside of, and did well in that class, so you’re still learning the material, and not just skipping stuff, and you can do this through camps that offer classes, or CC, or an online class. I would recommend an online class where you can go at your own pace, and I know EPGY offers them, but I’m not sure about others.</p>

<p>And the other thing you can do is what Faraday suggested, and focus more on math outside of your classes. There’s a lot of stuff out there, like the AMC series, USAMTS, ARML, HMMT, and a lot more for math contests, and Canada/USA MathCamp, PROMYS, ROSS, AwesomeMath, and more for math camps. You might also want to check if there’s a Math Circle in your area, since they can be a great way to learn and meet others in your area that are also interested in Math. And definitely check out all that’s there at Art of Problem Solving, it’s a really good resource.</p>

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<p>Just self-study BC next year. I was in your position too but just accepted it because I was nooby. You have to take initiative. Oh and make sure to get Aops as someone said up there and get a 150 AMC. ez killz.</p>

<p>If you start early you should be fine with everything.</p>

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<p>I’m not personally familiar with all the distance-learning and internet classes these days since they weren’t available when I was in school. </p>

<p>However, if you are talking about advancing in school math, the simplest solution is to take a class at the nearest community college in the summer. </p>

<p>In terms of super-advanced contest-type math, others on this thread have offered suggestions. Art of Problem Solving is a good one, as you can do it through the internet.</p>

<p>There’s a well-known math camp at Hampshire college. (I think that’s right. It’s something like that.) Check that out too.</p>

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<p>I took geometry honors and algebra 2 honors my freshman year and now I’m a sophmore taking pre-calc and I have a 100 in that class. I live in the state of florida so I was able to take algebra 2 online while taking geometry. If you feel really advance check if your state has an oline program such as florida virtual school and take math classes there. and if you live in florida the program is free and you learn everything at your own pace. They have courses all the way up to Ap calc bc.</p>

<p>forgot to mention you can still take the program even though you do not live in the state of florida but, you have to pay for it.</p>

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<p>I was in the same situation as you during high school. My junior high didn’t offer geometry to 8th graders and by the time I got to high school I was bored out of my mind. I would get perfect scores in math team, placed in top 5 in state, etc. During sophomore year (in an algebra II H course) I started skipping to sit in on a pre-calc H class. My teacher found out after a few weeks, but she understood my frustration. She cut me a deal. I didn’t have to go to her class, and if I got A’s on the two final exams for both classes, she’d sign to have me enrolled in Calc the next year. Honestly, I never opened my algebra II book again and got A’s on all 4 finals. I took calc and got a 5, and senior year self-studyed math with the math teacher ‘sponsoring’ my study.</p>

<p>I don’t think it’s an uncommon situation. I was, however, denied at MIT this year (I just learned about the AMC this year, after the testing dates passed).</p>

<p>Take things lightly, my friend. Don’t obsess about resume-stacking for the sake of it. I did it because I really do like math, and maybe something similar can transpire for you. Take the AMC, kill math SATs (I ended up with a 760 on the SAT I with one wrong because I noticed the wrong answer about 20 seconds before time), and learn to follow the course of things. The last is the hardest to learn, though, and it certainly is something that comes with time.</p>

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<p>I had a similar situation to yours freashman year, however stick to the class and get it down, but I do encourage you to study ahead on your own time. geometry does teach you to dealwith proofs, which although they seem useless will be worth your time, but standardized tests don’t test these.</p>

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<p>Simple solution: Learn math.</p>

<p>Talk to your guidance counselors beforehand, see if there’s any way to test out of classes or take the final and get credit for taking the class.</p>

<p>You’re in Geometry, so the best place for self study is definitely the [Khan</a> Academy](<a href=“http://www.khanacademy.org/]Khan”>http://www.khanacademy.org/). </p>

<p>Once you’re in calculus and above, MIT’s [Free</a> Online Course Materials | MIT OpenCourseWare](<a href=“http://ocw.mit.edu/OcwWeb/web/home/home/index.htm]Free”>http://ocw.mit.edu/OcwWeb/web/home/home/index.htm) will be more of a rigorous approach.</p>

<p>Simple Plan (adjust to your speed)
9th summer: Study Algebra 2.
10th: Precalculus and Calculus I
11th: Calculus 2 and (Differential Equations OR Linear Algebra)
12th: Whichever of Linnie Alg and DiffEq you didn’t take and whatever math classes interest you in OCW. (this is the point where most math opens up. Try some abstract algebra if you liked linnie, more DiffEq’s if that’s your thing, or whatever)</p>

<p>This is only if you are really into math though. Most people (myself included, and I got into MIT EA) will slow this down slightly so that they really learn.</p>

<p>If your school doesn’t give you credit, who cares? Ace their math classes, and then do real math at home. Take the AP Calc test in 10th grade to ‘prove’ you really learned, and then write about it in your essays.</p>

<p>One last comment: tito777, I don’t know if your geometry class was the same as mine, but do you mean those two column proofs? Not the way anyone ever does it, and any real prof will expect you to quickly unlearn that.</p>

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<p>Yeah, geometry ‘T-chart’ proofs aren’t anything like real proofs. I suppose it helps with the basic steps of logical thought involved, but other than that, they’re rather useless.</p>

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<p>The things I’ll be saying are basically repeats of what most people have been saying, especially faraday.</p>

<p>School math is often regarded as trite, repetitive and unimaginative math, where you do these drill problems from the textbook and memorize random formulas, and I agree. If you are truly interested in furthering your knowledge, there are many paths you can take. </p>

<p>MIT, I think, also looks for you interest in math outside of school, i.e. your results on math competitions like AMC, AIME, USAMO, ARML, etc. If geometry is too boring for you, then try your hand at these math competitions, because they often get more merit than getting A+s in math (I’m not saying that getting A+ is trivial). </p>

<p>For one thing, [Art</a> of Problem Solving](<a href=“http://www.artofproblemsolving.com%5DArt”>http://www.artofproblemsolving.com) is probably the best website out there for interested students in math. The teachers there write amazing textbooks that will teach you problem-solving techniques and allow you to do problems in a much more critical way. The Introduction to Geometry is one of the best ones; even after taking that course in Geometry, you will probably still learn a lot from this book. </p>

<p>There are also many opportunities in the summer like AwesomeMath, USA/Canada Mathcamp, PROMYS, Ross, just to name a few. </p>

<p>So, if you look around, you will probably find a lot of opportunities.</p>

<p>As for you courses, you’ll have to pester your counselors, I guess. It might just work; with a recommendation and some tests, I’m taking AP Calculus BC as a freshman.</p>