<p>What's the hardest part about probability theory? I'm taking a calc based stats class this coming fall and would like a heads up.</p>
<p>Figuring out which test/rules to apply to a given scenario is definitely the tricky part...</p>
<p>Which topics should I study before school starts? I have about 3 weeks. Here's the course outline:</p>
<p>The hardest part is generally the professors, from my experience. The stats class I took in undergrad was ridiculously hard; one of my friends that only got two Bs in all of undergrad got one of hers in my stats class. Most of my friends took the class a year later when someone else took it and they all considered it an easy A.</p>
<p>^that shouldn't be a problem. If I have access to the right book with hard problems, I shouldn't be caught off guard during exams. But anyways, I do have an extremely easy prof according to my school's rating system.</p>
<p>Just to let you know, the most difficult problems usually aren't ones found in books, they're the ones made up by professors. Generally textbook problems will follow some sort of basic formula for how to solve a problem. Ones created by the professor tend to make you try to understand the material in a different way than you've been thinking about it on homeworks.</p>
<p>Well, there's a solution to that also. I can get past exams from other top schools and do those instead. Or I can take a non honors class and use the book for the honors class. For example; if I take regular physics and my class uses Giancoli(a standard text), I can use Kleppner & Kolenkow( a difficult intro used for a honors class at MIT that employs brain teaser style problems); if I take a calculus that uses a cookbook like Stewart, I can use Spivak( a difficult book used for the University of Chicago honors calculus class that employs hard computational problems and proofs); or if I take a real analysis class that uses Ross, I can use Rudin( a tough book that uses very terse proofs; its usually used for honors classes.). And if push came to shove, I can look at some problems from the Putnam. There's really no way professors are smart enough to make up problems harder than these unless they're Putnam champions.</p>
<p>I don't think Spivak would be very much help in a class being taught out of Stewart.</p>
<p>The most difficult part of probability is getting an instinct for finding the right way to think about a problem. You can know all the formulas and methods, but what's really important is being able to look at a problem and figure out the best way to come up with the answer. I guess the simplest example would be recognizing when it's better to compute the probability of something NOT happening and subtracting it from 1 to come up with the probability of something happening. Homework will likely be easier because you know you're ultimately going to be using the method from the section you're covering, so it'll be good to look at things like exams where you have to figure out what to do on your own.</p>
<p>"The most difficult part of probability is getting an instinct for finding the right way to think about a problem. You can know all the formulas and methods, but what's really important is being able to look at a problem and figure out the best way to come up with the answer. I guess the simplest example would be recognizing when it's better to compute the probability of something NOT happening and subtracting it from 1 to come up with the probability of something happening. Homework will likely be easier because you know you're ultimately going to be using the method from the section you're covering, so it'll be good to look at things like exams where you have to figure out what to do on your own."</p>
<p>Yep.</p>
<p>Just a warning CoffeeBreak, some professors consider looking at old homeworks/tests from previous years or other classes as a form of cheating. Not that you're very likely to get caught, but I've had a number of classes where we're explicitly told not to use them.</p>
<p>Being solid with your calc is good, but best to be solid with your other fundamentals as well - ex: set theory and some combinatorics. Probability is a class that builds on itself, you should be able to rock the basic concepts like sigma-algebras so as you move on you don't have to go back and keep reviewing the first few weeks as you're trying to understand the more advanced stuff.</p>
<p>@RacinReaver. Thanks. I'll keep that in mind. However, I don't think that it's an explicit rule that is stated in my school's policies on cheating. So if professors don't say from the get-go, they have no right to prosecute. </p>
<p>Personally, I don't think it's cheating at all. They give easy HW and give hard tests. They want to measure your intelligence. They want things to be out of your control. That's oppression. And it's as much as cheating as using a SAT book to study for the SAT; the schools want to measure your aptitude and you're trying to somewhat circumvent that by getting similar problems. Same thing. Yes I understand that some professors use the same exams over and over, but I can just use exams at MIT or Yale. So in that case, they should say explicitly not to use past exams @ UCLA. But they don't, as you've said.</p>
<p>Try problems involving multinomial theorem ;)
Contact me for any math queries ;)</p>
<p>For a first year class if you can remember the different tests and apply them you should be alright.</p>
<p>And as far as using old hw/tests being cheating, lol. We have an entire well-known website at my school dedicated just for old homeworks, quizzes and tests.</p>
<p>It's not oppression; they want to make you try and think critically. Not every problem you'll encounter in life is going to be in a harder textbook or solved by someone else before. A technical education isn't just about learning the known techniques to solve cookie cutter problems, it's about learning methods to solve new problems that you've never seen.</p>
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A technical education isn't just about learning the known techniques to solve cookie cutter problems, it's about learning methods to solve new problems that you've never seen.
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</p>
<p>And how am I supposed to learn methods to solve problems I've never seen before if I have no problems that I've never seen before to practice on? If I am to get good at solving new problems, I'll, as you've said or at least implied, have to do past exams, or exams from other classes or top schools(after all, books are easy). But it seems like that they don't want me to do that; they don't want me practicing new problems. Like I've said, how can I do new problems if all they give me are cookie cutters? How can I learn how to swim fast if all my trainers do is make me swim slow? How can I get good at power-lifting if all I lift are light weights? People need practice.</p>