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Maths Presentation Tips: Video

  • Tips
    • Focus on what's interesting and don't try to present everything
    • Establish the background as well as notation at the beginning
    • Provide sufficient visual aid
    • Think about the storyline more carefully!
  • Note
    • No universal characteristic for audience, some prefers visual aid and others might not

Maths Research Tips for UG/PG: Video

  • Find Starting point: Go over textbooks or some papers to find the initial question / toy example
    • Play with it with some numerical example or rather more ambigious question(eg, "What if OOOO?")
      • Ex: Pattern of Prime in Reciprocal form
  • Literature Review to figure out what's been done and what might be interesting to drill down more ** At this point, no one knows what's going to be the right direction! Just list the init directions and explore them individually! ** One criterion to see what's interesting is Applicability to other domains
  • Communicate with other ppl by sharing your findings and see how ppl react: Writing / Quick talk / Presentation etc
  • Write up a paper to approach the broad audience

Maths Study Tips(From MATH 113 Berkeley)

  • It is essential to thoroughly learn the definitions of the concepts we will be studying. You don't have to memorize the exact wording given in class or in the book, but you do need to remember all the little clauses and conditions. If you don't know exactly what a UFD is, then you have no hope of proving that something is or is not a UFD. In addition, learning a definition means not just being able to recite the definition from memory, but also having an intuitive idea of what the definition means, knowing some examples and non-examples, and having some practical skill in working with the definition in mathematical arguments.
  • In the same way it is necessary to learn the statements of the theorems that we will be proving.
  • It is not necessary to memorize the proofs of theorems. However the more proofs you understand, the better your command of the material will be. When you study a proof, a useful aid to memory and understanding is to try to summarize the key ideas of the proof in a sentence or two. If you can't do this, then you probably don't yet really understand the proof. (When I was a student I had a deck of index cards; on each card I wrote the statement of a theorem on one side and a summary of the proof on the other side. Very useful!)
  • The material in a course is cumulative and gets somewhat harder as it goes along, so it is essential that you do not fall behind.
  • If you want to really understand the material, the key is to ask your own questions. Can I find a good example of this? Is that hypothesis in that theorem really necessary? What happens if I drop it? Can I find a different proof using this other strategy? Does that other theorem have a generalization to the noncommutative case? Does this property imply that property, and if not, can I find a counterexample? Why is that condition in that definition there? What if I change it this way? This reminds me of something I saw in linear algebra; is there a direct connection?
  • If you get stuck on any of the above, you are welcome to come to office hours. Your faculty is probably happy to discuss with you. BUT, usually, the more thought you have put in beforehand, the more productive the discussion is likely to be.