Maths for Engineering graduate studies

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Choosing between rigour-based real analysis, rigour-based complex analysis, and linear programming/optimization for graduate studies in communication systems hinges on the specific requirements of advanced courses in the field. The discussion highlights that courses in stochastic signals necessitate a solid foundation in rigour-based real analysis, ideally with knowledge of measure theory. In contrast, modern control systems demand formal training in rigour-based complex analysis. Additionally, internet communication systems emphasize the importance of linear programming and concepts common in computer science, such as graph theory and algorithm complexity. Given the diverse prerequisites, the decision should align with the intended focus within communication systems while maintaining flexibility for various areas of study. The participant's strong mathematical background, including calculus, ODEs, PDEs, and introductory complex analysis, supports the pursuit of advanced mathematical concepts, making it feasible to explore multiple options while considering the requirements of graduate courses.
hadroneater
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My to-the-point question: If I were to pick between rigour-based real analysis, rigour-based complex analysis or linear programming/optimization, which one would be the most beneficial for pursuing graduate studies in communication systems?

My mathematical background:
- All the typical EE maths (Calculus up to Vector Calc, ODEs, PDEs, Fourier analysis)
- Mathematical proofs (relearning calculus using sigmas and deltas, proofs, sets, axioms, convergence, etc)
- Intro to complex analysis (non-rigorous, mostly just calculations)
- Intro Statistics and Probability
- Applied PDEs and Numerical Analysis

I am going into my last year of Electrical Engineering and plan on pursuing graduate studies in communication systems or a related field. I have the option of taking one or two graduate courses in my last semester of study. However, professors of these courses all recommend or require certain math prerequisites. For example, a course in stochastic signals requires a working knowledge of fundamental rigour-based real analysis with recommended knowledge of measure theory. A course in modern control systems strictly imposes a formal course in rigour-based complex analysis as its requirement. Another course in internet communication systems highly recommends previous experience in linear programming and mathematics typical for a CompSci student (graph theory, algorithm complexity, etc).

From what I can gather, even though all of these courses are in the same general field, their pre-reqs are completely different. Of course, an actual graduate student will probably not tackle all of these areas of study and will only have select math pre-reqs. For me, I am not sure what I actually want to focus on and would like to keep options open.
 
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You got a lot math for an Engineering student.
 
^ Up to 3 higher-level math courses can count towards technical electives and I am also trying to do a math minor.
 
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