How to write a good research paper and give a good research talk

Research skills

Writing papers, giving research talks, and writing research proposals are key skills, but they aren't easy. This page describes how I approach each of these three challenges, in the hope that they may be useful to you.You probably have ideas of your own. Can you share them with other readers of this page? Here's a Wiki page that anyone can edit, where you can add your comments on the presentations below, your own thoughts and suggestions, and pointers to other material you have found useful.
Here are translations of this page into

• Belorussian
• Ukranian by Android SDK .

How to give a good research talk

"How to give a good research talk", Simon Peyton Jones, John Launchbury, John Hughes, SIGPLAN Notices 28(11), Nov 1993.

• The paper: HTML [thanks to Tyler Heibeck], Postscript or PDF 
• Powerpoint slides of the talk [updated 2004]: Zipped PPT (200k) or PDF (600k).
• Video of me giving the talk at the Technical University of Vienna, October 2004. (Needs RealPlayer v10.)

Since we wrote the paper quite a few people have written with constructive comments. Nick Nethercote also has a useful 2-page guide about giving a talk.

How to write a good research paper

"How to write a good research paper", Simon Peyton Jones.I gave this talk at the Technical University of Vienna in October 2004. There isn't a paper about it, only the talk:

• Powerpoint slides of the talk: Zipped PPT (400k) or PDF (850k).
• Video of me giving the talk. (Needs RealPlayer v10.)

How to write a good research proposal

"How to write a good research proposal", Simon Peyton Jones and Alan Bundy.

• A web page giving general advice about writing research proposals.
• Powerpoint slides of a talk on the subject, given in Moscow, April 2006: Zipped PPT (115k)

Other resources

Finally, here are some pointers to other advice I have found useful, though Google will find you a lot more besides.

• The Navigators Research Book of Style is a slide deck from the Navigators research group at the University of Lisbon. It covers choosing a research topic, doing research, and writing and submitting a paper.
• Research tips (including how to do research, how to write and present a paper, how to design a poster, how to review, etc), by Sylvia Miksch
• Notes on presenting theses, edited by Aaron Sloman, gives useful guidelines and ideas for PhD students writing their thesis.
• Chris O'Leary's essays about writing an "elevator pitch". This stuff, especially the list of attributes in the "Elevator pitch 101" page, is very relevant to writing a good grant proposal.
• Guide for preparation and publication of abstracts and A scrutiny of the abstract, both by Kenneth Landes in Geological Notes. These short notes give guidance about writing the abstract of your paper. (Both require a DjVu viewer which you can get from LizardTech.)
• Norman Ramsey's notes about his class on Technical Writing.
• Mathematical Writing, by Donald E. Knuth et al. The first three sections constitute a minicourse on technical writing: only eight pages long. The time to read it will repay itself many times over.
• How to Write Mathematics, by PR Halmos.
• Gian-Carlo Rota's excellent talk Ten lessons I wish I had been taught, which, among other things, has a bit to say about giving a talk.
• David Patterson's talk How to have a bad career in research/academia has many wise things to say on a related topic.
• Mark Leone's page has a good collection of links to other resources.
• Papers about measurement:
  • Producing wrong data without doing anything obviously wrong! Mytkowicz, Diwan, Hauswirth and Sweeney, ASPLOS 2009.
  • How not to lie with statistics - the correct way to summarise benchmark results Fleming & Wallace, CACM 29(3), pp218-221, March 1986.

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Simon Peyton Jones, simonpj@microsoft.com

Bijection, injection, surjection

Các khái niệm toán học thường dùng trên tập hợp:
1. Bijection: song ánh.
2. Injection: đơn ánh.
3. Surjection: toàn ánh.

Bijection

A transformation which is one-to-one and a surjection (i.e., "onto").

Injection

Let  be a function defined on a set  and taking values in a set . Then  is said to be an injection (or injective map, or embedding) if, whenever , it must be the case that . Equivalently,  implies . In other words,  is an injection if it maps distinct objects to distinct objects. An injection is sometimes also called one-to-one.

A linear transformation is injective if the kernel of the function is zero, i.e., a function  is injective iff .

A function which is both an injection and a surjection is said to be a bijection.

In the categories of sets, groups, modules, etc., a monomorphism is the same as an injection, and is used synonymously with "injection" outside of category theory.

Surjection

Let  be a function defined on a set  and taking values in a set . Then  is said to be a surjection (or surjective map) if, for any , there exists an  for which . A surjection is sometimes referred to as being "onto."

Let the function be an operator which maps points in the domain to every point in the range and let  be a vector space with . Then atransformation  defined on  is a surjection if there is an  such that  for all .

In the categories of sets, groups, modules, etc., an epimorphism is the same as a surjection, and is used synonymously with "surjection" outside ofcategory theory.

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