Probability from EE or Pure Math department? EE major

[DrummingAtom]

This probably (60%?) seems like a strange question but I have the option of taking probability from either the EE or pure math department and want to know how each will deal with the subject. Here's the course descriptions:

EE - Introduction to Probability Theory. Covers the fundamentals of probability theory, and treats the random variables and random processes of greatest importance in electrical engineering. Provides a foundation for study of communication theory, control theory, reliability theory, optics, and portfolio analysis.

Pure Math - Introduction to Probability Theory. Studies axioms, combinatorial
analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chain.

They both use the same book, A First Course in Probability, Sheldon Ross 8th Ed. From the course notes they seem to dwell on different chapters like the course descriptions show. Any suggestions?

Thanks.

P.S. - Both the professors that are teaching the pure math course are nonlinear partial differential equations researchers. The EE professor is a communication theory researcher.

 

[charlesjeon]

What is your major?

Communications Theory is somewhat signal processing + probability. In the intro level, prob theory will be very similar. The pure math course might introduce you to measure theory while the engineering course will not.

 

[sweetpotato]

Ask other students from the EE department. I was in the same situation at my school, and turns out that the EE probability class covered more material and was harder than the math probability class. This was because the EE one had to cover certain topics/standards set by ABET, while the math one didn't. In addition the professor teaching the EE one was much more rigorous than the prof teaching the math one.

 

[DrummingAtom]

What is your major?

Communications Theory is somewhat signal processing + probability. In the intro level, prob theory will be very similar. The pure math course might introduce you to measure theory while the engineering course will not.

I'm an EE major but have the option to take either. I've never taken a pure math (or probability) course but I'm intrigued by the idea because I do like math a lot. I want my mind blown by some cool concepts.

 

[DrummingAtom]

Ask other students from the EE department. I was in the same situation at my school, and turns out that the EE probability class covered more material and was harder than the math probability class. This was because the EE one had to cover certain topics/standards set by ABET, while the math one didn't. In addition the professor teaching the EE one was much more rigorous than the prof teaching the math one.

At my school, I've heard that the pure math one is easier than the EE in terms of workload but I haven't heard anything about the actual material. I'm just curious if a pure math course dwells concepts more because from the engineering courses I've taken so far they've just thrown equations at us.

 

[waht]

The main focus of study in an EE statistics class are random variables. The book by Yates and Goodman is commonly used in many universities:

https://www.amazon.com/dp/0471272140/?tag=pfamazon01-20

Also, in an introductory EE statistics class, the professor will likely assign a MATLAB project, or might cover the basics of information theory, which is a big plus.

 

[cmos]

I would definitely try to get the opinions of other students, but most of the time, the engineering math course will give you a good feeling of why you're learning what you're learning while the mathematics math course will leave you guessing what all of the effort was good for.

Not to be taken too seriously, but also not to be forgotten, I'll leave you with this quote from Carver Mead:

Most of us took mathematics courses from mathematicians—Bad Idea!
Mathematicians see mathematics as an area of study in its own right. The rest of us use mathematics as a precise language for expressing relationships among quantities in the real world, and as a tool for deriving quantitative conclusions from these relationships. For that purpose, mathematics courses, as they are taught today, are seldom helpful and are often downright destructive.

 

[chiro]

Hey DrummingAtom.

The advice for picking the course would IMO be based on the diversity of examples and areas being looked at as well as the relevance for you personally.

Looking at the description it seems the EE offering would probably be a better course because of the above, but this may not be the case.

My justification for the above is that probability is a very applied subject and unless probability is put into context of an applied situation, it is nothing more than a formalism that is not used. Statistics for this matter is in the same boat.

If the mathematical department offering provides good diversity of examples like the EE but also mentions some theoretical results that are able to be put in an applied perspective, then my preference if it were up to me, would change.

The thing is that once you really get what's going on, you'll be able to look at a problem in most fields and understand how to apply these concepts to that field to solve some problem which I'm sure you are aware of being an engineer in training.

I would only offer one caveat to the above suggestion for taking the EE course: in a good solid mathematical offering, you will understand not only the how but the why and I'm afraid if you try and extrapolate your experience in an EE course using certain techniques without understanding them in depth to a different problem or domain, then you might end up doing the wrong analysis and tests which will give you numbers in the forms of probabilities or test statistics that are utterly useless.

For this reason it is important to know the assumptions behind particular kinds of analyses if you ever have to do something like write a technical report using statistical analysis or if you have to analyze a situation that you are unfamiliar with either statistically or even in terms of the actual domain itself.

So if you do the EE course, just take a little bit of time out to see what the actual assumptions are and keep that in the back of your mind when it comes to doing the examples so that you know when something doesn't work and shouldn't be used vs where something does work and should be used.

Good luck with your course.

 

[DrummingAtom]

So if you do the EE course, just take a little bit of time out to see what the actual assumptions are and keep that in the back of your mind when it comes to doing the examples so that you know when something doesn't work and shouldn't be used vs where something does work and should be used.

Hey chrio, thanks for the reply, that's some good advice.

I've noticed that I usually have to take a lot of time (much more than others) to understand the concepts of the math from these engineering courses. It's very frustrating to me how math is taught in an engineering course which is why I'm seriously considering taking the pure math one. I looked at the previous math course exams and they have about half of applied and half of proofs which I think is enough to make me take it.

Just out of curiosity, have you taken a pure math probability course? If so, did they focus on concepts and give math some motivation? I think I need something like this for my sanity in this program.

 

[chiro]

Just out of curiosity, have you taken a pure math probability course? If so, did they focus on concepts and give math some motivation? I think I need something like this for my sanity in this program.

At the end of year when I graduate (fingers crossed!) I will have one major in statistics and the other in mathematics. At the end of the degree I will have done 8 courses in statistics that are 2nd year and 3rd year subjects.

I haven't taken what you call a pure probability course. This course basically is a course from a measure-theoretic point of view and concerns things like assessing convergence which while is useful in many contexts, is not anywhere used in comparison to your standard applied probability and statistics applications concerning the 'intuitive' probability (continuous and discrete distributions that are easy to describe and easy to use with normal integration and normal summation calculations).

The initial probability course I took was for the most part application driven which in hindsight was the right approach. There were some proofs but most of these had to do with going from assumption to final result which helped actually understand not only the how but the why: I imagine it's similar to what is done in physics and possibly engineering but I don't know for sure.

So basically we looked at the results, understood what they meant in terms of how, when and why they are used and then worked on problems.

The thing is however you don't want to let these things distract you too much from your engineering: it's important you know when to use them, but statisticians are the ones producing the methods and proving that they say what they should do and as long as you are aware of this and factor it in, that should be enough.

It's the same sort of analogy of using the rules like the chain rule and product rule for derivatives as well substitution theorem for calculus: There is no point for an engineer to go any deeper than is necessary, but they do have to know when not to use them when it's dangerous or simply flat out wrong.

 

[RoshanBBQ]

This probably (60%?) seems like a strange question but I have the option of taking probability from either the EE or pure math department and want to know how each will deal with the subject. Here's the course descriptions:

EE - Introduction to Probability Theory. Covers the fundamentals of probability theory, and treats the random variables and random processes of greatest importance in electrical engineering. Provides a foundation for study of communication theory, control theory, reliability theory, optics, and portfolio analysis.

Pure Math - Introduction to Probability Theory. Studies axioms, combinatorial
analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chain.

They both use the same book, A First Course in Probability, Sheldon Ross 8th Ed. From the course notes they seem to dwell on different chapters like the course descriptions show. Any suggestions?

Thanks.

P.S. - Both the professors that are teaching the pure math course are nonlinear partial differential equations researchers. The EE professor is a communication theory researcher.

If the descriptions are any indicator, the EE will teach the same stuff as the MATH except it will include a survey of random processes on top of random variables. I would personally avoid taking an introduction to probability that has random processes in it.

 

[Chunkysalsa]

If its taught by the EE department then I would take that one. Especially since there are many topics in EE that are heavy on statistics (i.e. communications) so it would nice to see that connection as you are learning the stats.

I took a stats class for engineers that was taught by the math department that was completely useless. I felt like I needed to learn some of the mathematical reasoning to everything we were studying rather than looking up some values in a table. I'm taking the prob/stat class that math/stat majors have to take over the summer since I'm also a math major. Hopefully they will teach it with a more mathematical focus so I can understand it better.