Real analysis and Integration course for EE
Hi,
I'm an undergraduate 4th year Electronics engineering student. So far I have taken courses from various fields of microelectronics and telecommunications. This year, I've decided to direct my career more to telecommunications (might be a field like wireless communications, digital image processing, etc). Basically, I will need a lot of mathematics and algorithmic knowledge to pursue a graduate study in one of these fields, which I am gradually trying to acquire in the last year of my bachelors. For this matter, I would like to find out whether learning Real Analysis would do any help in my graduate studies in these fields. Obviously, there is a lot of math involved in electronics (esp. telecommunications), but so far as I know, the essential parts of the required math are Linear Algebra and Probability&Statistics. Also, I have never taken a real analysis course so far, yet I have quite good knowledge of calculus. This semester, a course on "Integration" is offered at my university, however I am not sure whether I can take it before taking an introductory level real analysis course, also I am not sure it would be in any relation with my further studies. I wonder what other would think about this. The integration course basically introduces the Lebesgue integral and relies on many concepts from real analysis. Can I do a few weeks of selfstudy to acquire the sufficient background for this course without going into a rigorous, lengthy study of real analysis? Or should I take a real analysis course first before an integration course? Morever, would any of these be useful for a telecommunications oriented career of an electronics engineer? Sorry for the confusing style of question, but I could not find a better way to formulate it. Thanks a lot. 
Re: Real analysis and Integration course for EE
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My first instinct is no, it won't really be directly useful to EE. I am a phys/math major now and I am in real analysis. So far there is basically zero relevance to anything outside of pure math, and consists of proving theorems and relations. Taking real analysis will improve your understanding of calculus, but an applied mathematics course would probably be much more useful to you than analysis 
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The biggest relevance I see to the OP is in the study of Fourier series and Fourier transforms. If you want to understand these things fundamentally, then Lebesgue integration is a necessary prereq. If you just want to use these things without caring about rigour, then don't take the course. 
Re: Real analysis and Integration course for EE
From personal experience. Will you use it on a regular basis? No. Can you do without it? Yes. Will the knowledge give you a deeper understanding of the tools that you use. Definitely. For me, an understanding of pure math makes me a better thinker even though I'm concerned with finding solutions to physical problems. I don't need to do the proof but I am better if I can understand it when I need to. I know why we use a tool and when it is applicable. It makes me a better problem solver, able to think in ways that I would not otherwise.
If you are in a typical undergrad engineering curriculum you've probably had calculus, ode's, and linear algebra and you would probably have a hard time just writing an acceptable proof that y=x is continuous. Take undergrad real analysis or linear algebra and see what it's about. It's probably very different than you think. Or get a couple of easy reading books and spend your own time on it just to get the feel. I don't know where you are, but in the US taking a class in integration theory without any background in analysis is a sure way to fail a class. 
Re: Real analysis and Integration course for EE
Yes, a course on real analysis will help with graduate studies in communications. I work with quite a few folk with PhDs in comms; most if not all of them took undergrad real analysis. Some of them took several such classes  I know folks who did indeed take courses on integration theory, although they were graduate courses.
Some anecdotes: We have a younger guy at work take a first year graduate comms class to improve his understanding of his work: he really strugled this past semester since he hadn't taken real analysis. The professor essentially assumed that you had, and the regular full time students knew that analysis was an "unofficial" prereq. I work with another fellow who TAd information theory and said that the class had a bimodal grade distribution: the upper group all had taken real analysis, and the lower group had not. Information theory is part of comms, and it is a highly mathematical subject. Having said that, I am sure that it is just fine to wait until until grad school to jump into it. If I were you and had time for more math, I would speak with a) the comms profs in your department and get their advice, and b) talk to the math department and see what their recommendation is in terms of what courses you are ready to tackle. I am not a comms person, and never took real analysis. I must say that as a practicing research engineer my less than stellar math background occasionally is a problem. I did teach myself "baby" intro undergrad analysis (book by Lay) and more theoretical linear algebra (Axler) which has at least helped me read the more theoretical engineering journal articles without my eyes glazing over quite as quickly. Good luck! jason 
Re: Real analysis and Integration course for EE
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