<p>Okay so at my school you have to take Algebra 1 as a freshman (its a public school and this is a way the government grades the school). This year, as a sophomore, I am taking Algebra 2 (weighted) and Geometry. I realized I really like math, and if I want to go somewhere like Harvard I def. need to step up my game. Anyway here is my dilemma for which I need advice on, Im going to take College Algebra and Trigonometry this summer (and get college credit for both). So when I go back for my junior year I can take dual credit courses. I plan to take Analytic Geometry and Calculus 1 for the first semester and then for the second semester I plan to double up on math courses and take Analytic Geometry and Calculus 2 and Linear Algebra. During that summer (between junior and senior year) I plan to take Analytic Geometry and Calculus 3. So for my senior year I could take Vector Calculus and Differential Equations 1.<br>
Some other courses I could take are Modern Algebra, Probability and Statistics 1, Linear Algebra and Matricies, Advanced Calculus 1, Graph Theory, and Enumerative Combinatorics.
***Oh yeah, my school doesnt have any AP or honors courses so Im taking DC.</p>
<p>If you’ve only taken Algebra I or 2 so far, that’s not enough for you to recognize whether or not you really like math.</p>
<p>Nor is it enough to see whether you can handle two higher level math classes at the same time. Calculus 2 and Linear Algebra at the same time may be a bit much, and you’re not leaving yourself time to absorb and understand what you’re learning if you’re going to take more classes over the summer. You don’t have to have all those math classes to get into Harvard, and if you bite off more than you can chew, you won’t do well in them. </p>
<p>Taking both Algebra 2 and Geometry this year, you are in position to take Trig and then Calculus. If you take Calculus your senior year, you will be in the same position as the multitudes of students who take AP Calculus during senior year - not at any particular disadvantage when applying to Harvard or any other college.</p>
<p>And you don’t need to be taking Diffy-Q as a high school student to get into a top school, even as a prospective math major.</p>
<p>There is no rush to squeeze in so many college math courses during high school. If you have the mindset that you must take these courses to get into Harvard, you’ll probably end up frustrated with math. </p>
<p>If you’re interested in the problem solving aspects of math, check out the Art of Problem Solving books. If you’re more interested in figuring out why everything works the way it does, I recommend reading about proofs from a book like Velleman’s How to Prove It.</p>
<p>The benefit of reading as opposed to taking college classes is that you can do everything at your own pace and jump around to whatever seems interesting. From my experience with admissions, Harvard doesn’t care if you took a course in Calculus 3, but they do care if you’re interested in math, however that interest manifests itself.</p>
<p>First, I’d like to point out that your interests may change over time. A lot of supposed math majors start out taking a bunch of math classes in college only to find out they weren’t prepared for the rigor of the courses (ie math 55a-b). I’m assuming you wish to be a math major since you proposed taking modern algebra and combo. </p>
<p>Regarding your courses, the plan you have is fine. Though, if you find yourself mindlessly plugging in formulas (ie Euler’s formula or integration by parts) and getting 100% in your classes doing so, you may wish to try truly understanding every formula. For example, most people just plug in numbers to the Pythagorean Formula: a^2 + b^2 = c^2. Do you actually understand it or do you just plug in numbers? Most people (engineering majors) plug in numbers. Others (math majors) try to prove it in numerous ways. </p>
<p>Also,
as ^ says,
[Art</a> of Problem Solving (AoPS)](<a href=“http://www.artofproblemsolving.com/]Art”>http://www.artofproblemsolving.com/)</p>
<p>and</p>
<p>[The</a> Art of Problem Solving, Vol. 1: The Basics: Sandor Lehoczky, Richard Rusczyk: 9780977304561: Amazon.com: Books](<a href=“http://www.amazon.com/The-Art-Problem-Solving-Vol/dp/0977304566/ref=sr_1_1?ie=UTF8&qid=1356144662&sr=8-1&keywords=the+art+of+problem+solving]The”>http://www.amazon.com/The-Art-Problem-Solving-Vol/dp/0977304566/ref=sr_1_1?ie=UTF8&qid=1356144662&sr=8-1&keywords=the+art+of+problem+solving)</p>
<p>and when you feel comfortable enough with math:</p>
<p>[Chicago</a> undergraduate mathematics bibliography](<a href=“http://www.ocf.berkeley.edu/~abhishek/chicmath.htm]Chicago”>Chicago undergraduate mathematics bibliography).</p>
<p>Also, check out Terence Tao’s blog:</p>
<p>[There?s</a> more to mathematics than rigour and proofs What’s new](<a href=“http://terrytao.■■■■■■■■■■■■■/career-advice/there’s-more-to-mathematics-than-rigour-and-proofs/]There?s”>http://terrytao.■■■■■■■■■■■■■/career-advice/there’s-more-to-mathematics-than-rigour-and-proofs/)</p>
<p>The first two will concern you. Everything up til the end of differential equations (non-rigorous of course) will fall under the “fuzzy-hand waving” category. Most people do not ever make it or choose to make it past this stage. </p>
<p>If you do decide to go through with math and choose to involve yourself in more rigorous math than competition math, I have written up a rough plan of a schedule that starts summer of your junior year (assuming you obtain enough mathematical maturity). It can be found in this post:</p>
<p><a href=“http://talk.collegeconfidential.com/15129101-post4.html[/url]”>http://talk.collegeconfidential.com/15129101-post4.html</a></p>
<p>Lastly, don’t view yourself as a failure if you don’t end up at Harvard. If you do, good for you. If not, there are plenty of math programs (ie SUNY, UCLA, University of Wisconsin, etc) with great programs that will prepare you for graduate study (I mean what else are you going to do with pure math?).</p>