<p>My calculus teacher, like most other teachers, only assigns some of the problems in the book. As a student, am I expected to know everything in every chapter? Am I expected to be able to solve every single problem the book asks me?</p>
<p>I’m working towards becoming a math major, and I’m sort of worried that I don’t understand 100% of the material. I understand almost everything the teacher expects me to… but not everything the book does. </p>
<p>At what level would a student be able to fully comprehend a calculus(1-3) book? At this level how much of it should I understand?</p>
<p>You only need to understand what the teacher tells you unless you want to simply learn more or need more practice problems. Just because something is in the book does not mean that it is written in the correct way to facilitate learning or is relevant in the eyes of the department as something everyone taking the class should know.</p>
<p>YOU MUST KNOW EVERYTHING!!! EVVEERRYYTHHHIINNGGG!!
Chapter 5, problem 16B - WHAT IS THE ANSWER?!?!
Page 356 - Whats the 17th word in paragraph 5. WHAT IS IT???</p>
<p>Know it or the world will implode and everyone’s death will be YOUR fault - and you’ll have a severely long jail sentence because you killed EVERYONE!
It’ll happen, TRUST ME. Happened to someone I once knew, but now he’s in jail FOR A VERY LONG TIME!!</p>
<p>1) LOL
2) Really, you just need to know how to do problems. To do that, you need to understand the main concepts, but yeah.
3) A large part of being a math major is deriving/proving/BSing things on the tests.
4) math = proofs.</p>
<p>You must know every last thing or else you will fail and you will have to drop out of college and your parents will disown you and then you will have to flip burgers for the rest of your life.</p>
<p>If it helps, I’ve never had a class where I was able to cover everything in the textbook. I’ve never even had a textbook that was exactly the same size and scope as the curriculum. If that was ever the case, teachers would probably become obsolete. What you should understand is that the textbook is a supplement, to be used at your’s and the professor’s discretion. It contains all that information because some of the thousands of professors in the country might use different parts of it than others, but no one professor will ever use all of it. This doesn’t just go for math but for pretty much any subject.</p>
<p>I’m not discouraging you from understanding the other problems, but that is a decision that you have to make based on what you think that you will need to prepare for the final exams.</p>
<p>While people are replying sarcastically, there is something to the question. </p>
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<p>To the part in bold, I would say yes, or at least you should feel if you spent the time, you should be able to make lots of progress and talk about the problems intelligently. To the first part, no, emphatically…and the first part is what people find a little funny. Courses seldom cover the whole book, and the whole point of a course is for the instructor to highlight what’s important to you, sometimes in the book, and perhaps at times from outside, in relation to the overall subject.</p>
<p>But getting back to part in bold - as an aspiring math major, your time is well spent learning how to read math books. No specific knowledge will help you way too much, but the ability to figure out what a book is jabbering about and turn it into something intuitive is really important, and a much bigger step than the so-called jump people fuss about from computations to proof-writing. A proof really is just an explanation. The important thing is that it usually encodes information about a subtlety in structure that is interesting for whatever reason.</p>
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<p>This is oversimplified to the extreme. Some of it is right, but statement 4 is very misleading…</p>
<p>yeah proofs are just the way you communicate new ideas in math . . . its not like math majors sit down and decide to be gay about everything and get nothing done. the content is the ideas–not the proofs</p>
<p>I think it’s a legitimate question, especially since (I’m assuming) you’re a frosh.</p>
<p>From my experience, math has a HUGE disparity. A lot of math majors really suck at math (conceptually), and the ones that are good are really good. If you’re struggling with math early on, you might want to switch. There’s lots of applied math fields to consider if you like applying math to more concrete problems. </p>
<p>I switched from math–> chem –> accounting. Accounting doesn’t really deal with any interesting math, but the analysis involved can involve the same creativity, etc. Same idea with many engineering/sciences. </p>
<p>If you like math, it doesn’t mean you should major in math. Find what you like–applications might be more appropriate if you’re questioning yourself.</p>
<p>As a former math major in recovery, I can say that you don’t need to know everything, just what you’re studying at the moment. The more math you get to know, the easier it is to fill in gaps along the way (one big way gaps come up is transfer/AP credit replacing classes that aren’t complete overlaps). After completing perhaps a couple quarters of calculus beyond Calc I-II-III, the other material becomes relatively manageable.</p>