Pages

Monday, July 06, 2015

Adding Mathematical Rigor to Systems Research

A bright young man I know, a recent Ph.D. graduate from another university, who works in my research area of wireless networks, contacted me recently sharing with me that he had joined industry but that he was "still interested in pursuing a research career despite being in industry." He wrote to me: 
I concur with your emphasis on the importance of mathematical analysis:
  • "you must learn how to add rigor to your work through mathematical analyses for your work to be respectable for graduate-level researchers." 
I have yet to put more efforts to learn this skill. You have a unique blend of theory and systems, thus I am wondering what your take is on how to achieve this for people with mostly systems background like me?
Here I should first clarify that "systems" here refers to computer science topics such as operating systems, database systems, network systems which tend to be more software implementation and empirical evaluation oriented in general.

This was my response to him:
I think a good starting point for learning theory is learning how to mathematical model real-world problems:  
* Check out this very basic book on mathematical modeling (aimed at HS/undergrads, I believe) as a starting point. 
* One article that guided my early efforts at doing some mathematical modeling was Hal Varian's "How to Build an Economic Model in your Spare Time

* I attempted once to write a short "tutorial" on how to apply mathematical modeling to wireless sensor networks that you might find useful as a starting point in thinking about modeling: 
*    To get a bit deeper, you do need to learn to construct proofs.   Polya's "How to Solve it" .. is indeed a good starting reference. 
* I took two courses at Cornell that really taught me to prove things:
1. A course on real analysis in the math department (something like this MIT Course on Real Analysis;  a good book for it is Strichartz's "The Way of Analysis":  )
2. A course on analysis of algorithms taught by Jon Kleinberg; the notes for the class I took got turned into a great book called "Algorithm Design."  
Like with everything, the trick to learn how to do more theoretical research is to start small and practice - build some simple models or prove some simple known things first then work your way towards something more substantial... 
I then added afterwards in a follow-up note:
The other thought that occurred to me is that in my own work, often my students and I base our approach on the analysis in a similar paper. 
Reading the classic papers on analysis of CSMA, TCP fluid modeling, Network Utility Maximization, etc. can be a starting point. Ask yourself if you could modify the analysis or assumptions a little to treat a slightly different problem. This will also give you more practice in doing analytical modeling and proofs. 
Last but not the least, it could also help to collaborate and discuss with others that are more theoretically oriented to gain insights on your own problem...


14 comments:

Anonymous said...

Perfect Article. I want to say something about this topic. Thanks for sharing. Writing is never easy. It was never supposed to be. But in the recent past, students need not worry much. If you need cheap paper writing service , then sit back I explain how we can help you.

Movers and Packers in Mumbai said...

Great post! thanks for sharing with us.
Packers and Movers in Chembur
Packers and Movers in Jogeshwari
Packers and Movers in Kharghar
Packers and Movers in Dombivli

Packers and Movers in Hyderabad said...

great post thanks for sharing this wonderful post.
Movers and Packers in Kondapur
Movers and Packers in Gachibowli
Movers and Packers in Kukatpally
Movers and Packers in Chanda Nagar
Movers and Packers in Manikonda

Christopher Blevins said...

Ideal Post. I wish to state some thing relating to this AMCAS application subject. Many thanks with regard to discussing. Composing is actually in no way simple. It had been in no way said to be. However recently, college students do not need to be concerned a lot. If you want inexpensive document composing support, after that relax We clarify the way you will help you.

William Leeson said...

Thanks for your time a lot of designed for writing it relatively blog post, it was subsequently so excellent to enjoy a book and even beneficial to raise a education simply because changed you can visit here more idea http://www.personalgoalwriting.com/our-services/career-goals-essay/.

Hopper said...

Many thanks for the period lots of created for composing this fairly article, it had been consequently therefore superb to savor the guide as well aslook here for increase the training due to the fact transformed you can travel to right here much more concept.

Christopher Blevins said...

Appreciate it a whole lot a huge amount of for placing this particularly area, the item received come to be so great to learn to read this report combined with useful to make improvements to the very best practical knowledge simply click here http://www.teachingstatement.net/our-statement-of-teaching-services/primary-teaching-personal-statement-help/ intended for facts considering rested anyone.

mikon said...

There is the best or the additional form of the mathematics which can give you the nice support for your work. You can also check more info and can define the best system with the nice approach. Just get the direction and enjoy with the nice term.

mikon said...

There is the link of the adding mathematics with the help of which you can enjoy the best system here. You can find the link of http://www.statementofpurposeexamples.net/statement-of-purpose-graduate-school/ and enjoy your day with the freedom of the systems research.

James Charlie said...

Your post definitely hits the right spot. Kudos for the hard work. Your suggestion to opt for a reliable online assignment help facility is definitely a practical and feasible one in today's scenario. This is where the impeccable online assignment help service by the MyAssignmentHelpAU platform comes into the picture. If you are looking for a comprehensive assignment help facility that caters to all your writing requirements efficiently. Their assignment help service is definitely the one-stop service for you. You can easily place an order for your complicated academic assignments with the MyAssignmentHelpAU platform in three simple steps that too at highly reasonable prices.
For more info visit here: Buy Assignment Online

Diksha said...

Thanks for your time a lot of design for writing it relatively blog post.

source:https://tractorguru.in/tractor/new-holland-3037-nx

Janisthaa ivf said...

Very Interesting article and assured as well, I hope people get lots of knowledge and Your blog was good and informative, it’s very useful to us. Thanks for sharing your thoughts, keep posting! and please check out this: https://www.janisthaaivf.com/

sources: best fertility centre in Bangalore - Janisthaa IVF

Preeti Jain said...

Nice article! Thanks for sharing

Janisthaa ivf said...

Thanks for sharing your thoughts, keep posting!

best fertility centre in Bangalore - Janisthaa IVF