I am an undergraduate student. I have to do a research project for my homework assignment. This is my first maths research so I have no idea what topic should I select and how to start....
I want to do a research which related to Linear algebra because i have just completed this course. Can anyone suggest me the possible and interesting research topics in linear algebra?
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Below is the guideline of the research areas which given by my professor:
The areas of research must be mathematics and its applications, such as:
Thank you very much !
- Basic research: algebra, analysis, geometry, probability, statistics, etc.
- Engineering applications: computing, internet, communications, information and digital technology, etc.
- Commercial applications: economics, finance, logistics, management, decision science, operations research, transportation, etc.
- Scientific applications: medicine, physics, chemistry, biology, environment and health problems, etc.
- Innovation designs: image and visualization, games, puzzles, algorithms, etc.
ok, here are some materials regarding Hadamard matrices and their applications:
1. Hadamard conjecture : see A Survey of the Hadamard Conjecture
2. Construction of Hadamard matrices : see this for example.
3. Applications: see here for example.
Thanks very much for your help! I like the topic! But I'm still free for suggestions (I just want to have a few selcetions just in case)
But I have one more question, what makes a good mathematical research? Do I have to come up with something new, new idea, new application, etc. (which is like an invention of a small applicable step or something) by myself (i.e. I'm sort of inventing it)? Or can i just present deep information i found from researching, information about the subject? Because just googling things and putting them on paper sounds like... a very simple research, but that's what "research" gives me the impression of, although this time there seem to be an emphasis on "mathematical".
first of all, there's a book about Hadamard matrices, in case you want to do a deeper research. the book is called Hadamard Matrices and Their Applications.
i think an undergraduate advisor can explain to you what you're expected to do in your research. of course, it'd be great if you could do an original work but
i seriously doubt it that in your level they expect you to get new results. anyway, you should talk to an undergraduate advisor in your university for clarification.