<p>this may sound like a dumb question, but what does it entail. I mean I know you have to write proofs, but are the proofs already known. Like can I cram proofs and jut write it down on my paper, or do you have to write an original proof or something.
I take it next year fall but I just wanted to get a heads up.</p>
<p>Let me tell you. I took Real Analysis this semester, and I just took the final exam this morning. Writing proofs is hard especially for engineering students (like me). In the beginning of the semester right up to the final, I did not know how to write a proof. In lectures, I would always wonder how the proof on the board actually proves something let alone knowing when the proof is finished. I was completely lost and on midterms and quizzes, I would leave the proof-based questions blank because I wouldn’t know what to word (NOT ONE WORD!). By the way, midterms/quizzes were open book/notes. The final exam was much like the midterm/quizzes in terms of the types of questions. This time I nailed it. After a whole semester of not knowing how to write a proof, I actually wrote all of them on the final. The professors don’t “teach” you how to write a proof even though my class is suppose to teach you how to read and write them. I started to learn how to read and write proofs during my final exam this morning, and I wish it had happened earlier. This is what my experience entailed.</p>
<p>To answer your second question: The proofs are not already known. Maybe you can find them on google or yahoo answers or ask people on cramster, but they rely heavily on the theorems you go through in class. You must understand the theorems very well in order to write a proof by heart. You can’t cram proofs and just write it down on paper. It’s different every time, especially when the functions change and there’s some exception you have to consider. I guess it really depends on the type of class you’re taking.</p>
<p>I hope this helps.</p>
<p>thanks, yeah that helps.
I wished it was easy as cramming but at least I know what it is now.
Congrats on nailing it, any tips would be appreciated.</p>
<p>Well, if it’s a theory class then the proofs are already known. You’re not expected to make a mathematical breakthrough while taking a test.</p>
<p>Proofs can be difficult because there are usually so many different proofs for each topic, it can be quite tedious to study/memorize all of them. The key to a lot of proofs is being able to manipulate one side of the proof to get it to look more like the other side. A lot of times this means looking at a mathematical statement and just “knowing” what it is equivalent to (or knowing “how to” make it equivalent)…aka, what the next step is.</p>
<p>Sometimes proofs get real hairy in upper division classes. If you don’t know certain rules/equivalencies than you won’t be able to adequately write the proof.</p>
<p>The key to writing good proofs is to practice, practice, practice, practice, understand it, understand it, understand it. I’ve talked to several PhD’s about it and they all say the same thing.</p>
<p>I practice proofs relentlessly for one of my classes…and I still find myself to be relatively weak at writing proofs. There always seems to be an obscure proof that appears on the test that I haven’t practiced.</p>
<p>combinatorics = nightmare</p>
<p>One thing I found that helps is to read a lot of proofs. Also, while you are reading a textbook another good exercise is to read a theorem, but not but the proof of it, and to try to come up with a proof of your own, then if you get stuck you can look at the proof in the book for hints.</p>
<p>To do well in these classes, you’ve really got to be able to understand the material (how it fits together, why objects you talk about are important in the context of the theory, etc.). You can’t get away with not understanding the theory and just being able to do example problems like you can in many other courses.</p>
<p>For one, the variety of problems you’ll solve in these classes will be much more varied, so you’d have to practice an awful lot to be able to mechanically do all of the types of problems. Also, the problems tend to draw more upon your understanding of how things are put together in the subject, so it is more difficult to be able to do the problems without understanding the theory.</p>
<p>Following the discussion of the subject in lecture or in the book is essential to understanding the theory. Being able to reproduce the arguments made in the book and/or in lecture yourself also is very important.</p>
<p>A real class will require you to come up with your own proofs. But if you’re experienced with the area, you should be able to get some insight into how the proof is going to work.</p>
<p>Anyone know if Modern Algebra has a lot of proofs?</p>
<p>It has a fair amount, but I also found in my class that there were a lot of computations as well. Things like the euclidean division algorithm in random euclidean domains. We also did a lot of stuff with vector spaces and some really advanced linear algebra, like jordan canonical form. </p>
<p>I don’t know if I’d say that we were ever asked to prove anything on our own though. The line between computation and proof seemed really blurry to me in my modern algebra class.</p>
<p>That’s interesting. I really like math, but I’m not skilled enough at proofs to derive anything harder then Laplace transforms so I don’t want to get into a class that I’ll be over my head in.</p>