<p>I plan on majoring in math, and in order to prepare for taking college level classes I bought a calc text book and started self studying some more stuff on my own. I seem to be able to do problems in the text book, but I don't feel like I actually understand the concepts. I feel more like I'm just looking at examples and memorizing the steps for how to solve problems, rather than learning the actual concepts. I'm beginning to wonder if math isn't the right thing for me. I have read explanations of concepts multiple times, but still don't feel very confident. What should I do? Is this an early sign that I should try something else? Am I just an over-eager/crazy frosh to be?</p>
<p>You should strive to understand that concepts and more importantly go over the proofs, step by step. Most Math major classes deal with areas of mathematics that are far away from Calculus and rely on analysis of proofs. </p>
<p>Maybe try a different textbook or use the MIT OCW lectures to help.</p>
<p>hey broken_symlink,</p>
<p>Being able to do the problems is already a good step since you don't have a teacher and I can't ask questions. I bet most kids in your class aren't even reading the textbook the summer before.</p>
<p>I agree.</p>
<p>Since you are already taking the initiative to prepare before college, you should be fine in the university. Professors and TAs should take the time to clear up any foreign concepts during the class and if not, you can go to office hours.</p>
<p>If you want more preparation, I highly suggest the MIT OCW lectures.</p>
<p>Free</a> Online MIT Course Materials | Mathematics | MIT OpenCourseWare</p>
<p>I'll take a look at OCW. I also recently ordered a copy of What is Mathematics by Richard Courant. Hopefully it will help.</p>
<p>If you could gain the knowledge you'd get in college by just reading textbooks on your own, without paying college tuition, wouldn't everyone just do that instead? ;) The importance of a degree notwithstanding, colleges were made for teaching you stuff. I wouldn't sweat it quite yet! The fact that you can tackle the problems at all is pretty darned good.</p>
<p>As far as I can tell, there are no actual Calculus I lectures on OCW unless you mean just the typed lecture notes for single variable calculus. Anyway, it is a great resource, but with how MIT condenses traditional Calculus 1 and 2 into one course and the fact that most MIT students already have some background in basic calculus it may come off as a bit terse and in general not the best way to introduce OP to Calculus (I have used materials from a few courses on OCW but not for my intro calculus courses so I may be wrong.)</p>
<p>There is no shortage of resources on Calculus around the web including proofs and communities to help with your questions, here are a couple pages that may prove beneficial:</p>
<p>video lectures, (take note this is Calc 1 and 2 condensed to one term)
Banner</a>, A.: The Calculus Lifesaver: All the Tools You Need to Excel at Calculus.</p>
<p>This professor's page has literally a textbook worth of notes for Calculus I that may be beneficial:
Pauls</a> Online Math Notes</p>
<p>Don't sweat it now; when you're at college you will have an actual professor in person/TA/friends in the same course and tutoring will be available in which Calculus is a very popular offering. Just reading a textbook by yourself is not always the most effective way of learning especially since you may just now be getting used to scientific texts/proofs and the notation used.</p>
<p>Another thing I found is that I tend to avoid complicated trig stuff. I don't know any trig identities, and I learned about radians in precalc, but I don't really remember any of it, because it was about 2 years ago. I don't find doing trig stuff in calculus very intuitive. It seems intuitive in geometry, but when it comes to calc it feels like plain old memorizing stuff. I'm hoping Courant's book can help me in this area.</p>
<p>Brush up on your trig, it will pop up when you least expect it.</p>
<p><em>shudders at Taylor series</em></p>
<p>Hahaha, yeah it's true. I used to panic when I saw trig come up in calculus. Like nshah9617 mentioned, it comes up often when it's least expected in all your calculus courses. Getting comfortable with trig will come up handy.</p>
<p>Courant's book is amazing!!! I have only read up to the first exercise in chapter 1, but its such a mind expanding experience. I don't know if this book will actually help me with trig though.</p>