How can a freshmen/sophomore get an idea of what upper division math is like?

<p>I read a lot that upper division math classes are much different from lower division. I was wondering if anyone had any tips for a student still taking calculus, as to how they could get an impression of whether they will like upper division math or not. </p>

<p>Is discrete math at all helpful as an introduction?</p>

<p>I like math, but am only on Calculus 1 and have no idea if I would hate or love upper division math... but finding out earlier rather than later would make my college plans a lot easier! Thank you for any opinions!</p>

<p>Why don’t you pick up an introductory analysis book such as Intro to Real Analysis by Bartle? I’m sure with some googling you’d be able to find an old copy. or one by Michael Spivak.</p>

<p>I took a course in logic/set theory/intro to proofs before I took what I consider upper-division classes. If you’re a pure math major, I can only tell you that the pure math classes I’ve taken were in real analysis, algebra, and complex analysis. I was applied. Would I consider the course useful for real analysis? no. it was somewhat useful for abstract algebra, but i feel like you could get by without it. </p>

<p>you can definitely get an idea of real analysis from a harvey mudd lecture series on real analysis that’s on youtube. i watched every video when i took it.</p>

<p>is it harder? depends on the person. personally, i feel like pre-calculus was my hardest class i ever took compared to the rest of the classes i had in my math degree. if you like proofs, you should do well. </p>

<p>Thanks CalDud! When I’ve tried to open up a book, I’ve been overwhelmed by my lack of knowledge - And ended up thinking that I’d have to complete a lot more math to even understand enough of what the professor or book is saying to have any idea! But that’s a lame excuse. I’ll give the lectures a try. </p>

<p>(please excuse the run-on sentence)</p>

<p>Ah, I usually feel that way when I glance through the book without reading it. However, I feel like there’s nothing really to teach other than basic proof techniques ( which you can learn of quickly). It just goes into way more depth and you should really read the fine print, know your definitions, since you truly need to know what something means instead of the simple application of a theorem or formula. </p>

<p>I was massively confused for the first couple weeks, but you get over it. Just make sure you can choose the best teachers possible for learning. Otherwise, I feel like you will become discouraged rather quickly. I had a friend who was retaking Real Analysis a second time who happened to be in my class (that’s how we became friends) and his first teacher shouted at him during office hours that he shouldn’t be a math major. Dude is graduating this fall. I usually chose the hard professors but the ones that were also pretty good/great at teaching the material. Gotta have a balance if you can get one. I would definitely say it is a weeder course. 75% of the class was failing by the end (even with a curve applied). He failed half. The second part half also failed. But he was a good teacher! Someone I know who failed it with an F wound up getting a B+ with someone else with minimal effort. Your education is what you make of it.</p>

<p>At some schools, discrete math courses include an introduction to proof techniques that will be commonly used in more advanced math courses.</p>

<p><a href=“Basic Analysis: Introduction to Real Analysis”>http://www.jirka.org/ra/&lt;/a&gt; is a free textbook on real analysis, a proof-oriented upper division math course.</p>

<p>A non-free classic textbook on the subject is Walter Rudin’s Principles of Mathematical Analysis. You may want to take a look at it in the library.</p>