Am in way over my head?

[ashramsoji]

 I started my MS Stats program at George Washington University this semester. The first course is Mathematical Statistics:

 

This is the first part of a two semester course in Mathematical Statistics. Probability theory is presented as a mathematical foundation for statistical inference. Axiomatic probability is introduced then some standard discrete and continuous probability distributions are presented. Joint distributions and transformations are discussed. Probabilistic convergence concepts are introduced.

The only requirements for the course are Multivariable Calculus and Linear Algebra, both of which I recently completed (that is as far as my mathematical education goes). I am finding the course to be impossibly difficult, to the point where I am only able to answer certain problems because their solution is either available online or because I am spending hours upon hours on them. This is giving me serious concern because I am not sure I'd be able to answer most of the questions on a midterm or the final. I'm not talking about not getting an A- in the course, but really just not being able to answer more than 25% of a test.

I feel like I can follow what the professor is lecturing and what is being explained in the book, but am at a loss when it comes to applying it. It seems like most if not all of the students in the class had Math majors or minors in college, but if that is required to be successful in the program then I am not sure why I was admitted into it.

I was wondering if people have completed similar degrees or courses and could share their experience. This course is also required for the PhD students, though there are none in the class. Do most of the students just muddle along like I am, or is this something that they are not struggling with given they know so much more maths?

[bsharpe269]

My undergrad degree is in math and I took a class like this during my sophomore year, after multivar Calc and linear algebra. You can definitely handle this class. Just spend some extra time with material since people with math majors may pick up the information a bit faster.

[StatsG0d]

It's likely that you aren't alone in feeling like that. I went through a similar thing with Real Analysis. I think when you get to the more theoretical classes, it's absolutely vital to read the textbook, sometimes several times over. Each theorem that you are introduced to, read it 5-6 times over until you start to get a good grasp of it.

 

Practice makes perfect. Try looking up exams online from other schools with their solutions. Even if you aren't able to solve all of them that's ok--just keep trying to see how to use theorems.

 

On the admissions thing, I wouldn't worry about that. I don't think they would have accepted you if they felt like you didn't have the tools. I also find that in these types of classes the homework assignments are MUCH more difficult than the exams. Professors understand that you have so much more time and resources to do homework problems. Just hang in there. We've all been there.

[epimeleia_heautou]

I echo footballman2399's comment that you are not alone. Everybody tries to exude an aura of competency, even when they don't understand something, which is stigmatized in academia. This situation is unfortunate, as it (in my experience) deters people from being honest about not understanding something and pursuing the most efficient way to remedy the problem. A huge first step is to be okay with not understanding something. It's not a measure of your intelligence or of your worth as a student/academic -- different people come to understand concepts, techniques, etc. in different ways.

 

Get used to asking questions in class. Act like it's completely normal, because it is. Probably the majority of the class will have a similar question on their mind but be too afraid to ask. Now, your instructor may or may not be all that good at explaining things. That's okay. You'll get better at identifying the sorts of questions that she can answer effectively and those that she can't. You'll get better at learning things on your own. You'll get better at realizing when the approach you're trying isn't working and that it's time to try something else. (This is important. I've found that much of the time I've lost on difficult problems is from trying the same thing over and over again when it clearly isn't getting me anywhere.) Find a study partner or group that you can bounce questions or ideas off of for difficult problems. Really, if you're not a member of a study group, join one immediately. In general, become proactive about asking for help when you need it.

 

Most importantly, if you work at sticking it out, you'll learn a skill more important than any mathematical technique or theorem, and that is persistence. Learn to tell yourself that with enough time and effort and trying different things you can get through this difficult problem, instead of telling yourself that this is beyond you. You will surprise yourself.

 

See also the top comment in this reddit thread: http://www.reddit.com/r/math/comments/1sazhk/i_dont_feel_clever_enough_to_do_higher_level/.

[wine in coffee cups]

It's common for undergrad math majors interested in statistics to take a semester of probability and a semester of math stats (like bsharpe269 did), which are usually slower versions of that master's-level C&B course sequence you're in. Even though the undergrad sequence is not a formal requirement, the class you're taking is probably designed with the expectation that most people have seen the less-advanced version before. But there are probably others in the same boat as you.

It's hard to learn completely new things in a fast-moving course, but you'll start catching up as the semester goes on. There are a lot of little tricks you use over and over again. These are surprising the first few times you see them but become old hat as you get more practice. (For example: recognizing a term as proportional to the integral of a known probability density over its support, which has to integrate to one, so you just have to mess with the normalizing constant.) I hope that even if you struggle to come to solutions yourself now, you at least understand why they're right. After you see enough of them, you will be get better at generating them yourself.

I would make a regular study group with some other people in the class. It'll be good for you all to practice explaining the intuition behind how you approach various problems. Be sure to take advantage of office hours too.

[Anakin]

I would make a regular study group with some other people in the class. It'll be good for you all to practice explaining the intuition behind how you approach various problems. Be sure to take advantage of office hours too.

 

 

I'll echo this point. Study groups can be a waste of time, but they're really effective when you get into a motivated group. Since you're a grad student, almost all your peers should offer plenty of solid groups. 

 

You might consider working with a couple different groups or one spanning all skill/comfort levels. The idea is find opportunities to learn quickly from a 'super star' who just 'gets it'  AND transfer that knowledge to a struggling friend. The process of teaching a topic or working through a tough homework problem will go a lot further than just listening to someone tell you their answer. Even if the super star shares his or her answer, it is almost guaranteed that you will approach the problem slightly differently. Explaining your work or knowledge to a friend will help you identify and fill your knowledge gaps. 

 

The second point is to work as far through a problem as you can. Let the work and your stopping point guide your conversations with the professor during his/her office hours or email messages. When you meet with the prof and he/she points out an error, then ask why and explain your reasoning. Once you've worked a problem with the professor, ask for a couple of similar problems to try at home to see whether or not you've got it. If you hit the same wall, iterate. There's no shame in that. Working problems is essential to learning math. 

 

Finally, this might be too basic, but I found this video series really helpful when evaluating my own study methods. They're directed at undergrads, but apply to every level. 

 

Best of luck!