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This is a bit like following a game of chess by checking to see that each move was legal or like running the spell checker on an essay. At this point you should feel confident talking about the paper with colleagues thinking critically about the results and being able to compare the work to other research in the field if you have read other papers.
Then read the outline section titles to get an idea of its structure.
How to read math papers. In doing my close reading of the particular thing I want I often take notes. Depending on the results of my reading the thing I set out to read I might go on to read other parts of the paper. But I generally dont.
If Im reading a paper without a specific goal I generally start at the beginning and read the introduction. Ideally this contains the statements of the main results but if it doesnt I skim the paper. This guide lists selected major resources that you can use to start researching your topic in Mathematics some links to articles and webpages that may help you as read scientific papers.
PhD Mathematics University of California Davis 2018 Read the abstract to get an idea of the paper then the conclusion to see where it leads what it accomplishes. Contemplate the title of the paper in light of that. Then read the outline section titles to get an idea of its structure.
2 Usually no. Again if a paper is well-written then the arguments explained in it plus the statements of the quoted theorems from other papers should be enough to understand everything. Certain people hate to use other papers as black boxes though and go through even if quickly the other quoted papers.
3 This is a delicate point. I think what your supervisor means is that there are certain big motivating questions behind math. Read slower this time.
Highlight important points for further study. Dont overdo the highlighting. Distinguish key points and highlight them.
That should be well under 50 of the text. Color-code if that helps you Some students find it helpful to take notes on separate paper while reading. If youve never done this you might want to give it a try.
You may find that it helps focus your mind. Note that in some ways the easiest way to read a proof is to check that each step follows from the previous ones. This is a bit like following a game of chess by checking to see that each move was legal or like running the spell checker on an essay.
Its important and necessary but its not really the point. A math heavy paper could mean. A paper with long equations lots of algebra and manipulation of complicated equations.
When you read a paper you never read it only once. You read the title first than you decide if you should read the abstract. You read the abstract and decide if you will skim through the results.
You do that and decide if youll skim through the whole text. 722 met once a week for two hours and in the course of the semester we read thirteen papers. Cooley Tukey 1965 the Fast Fourier Transform 2.
Courant Friedrichs Lewy 1928 finite difference methods for PDE 3. Householder 1958 QR factorization of matrices 4. Curtiss.
De Boor 1972 calculations with B-splines 6. Remember I am expecting it to take several hours just to read the paper Keeping the above in mind as you read the paper should make the process easier. Your one page review should include the following.
A one or two sentence summary of the paper. A deeper more extensive outline of the main points of the paper including for example assumptions. HOW TO WRITE MATHEMATICAL PAPERS BRUCE C.
THE TITLE The title of your paper should be informative. A title such as On a conjecture of Daisy Dud conveys no information unless the reader knows Daisy Dud and she has made only one conjecture in her lifetime. Generally titles should have no more than ten words although.
Im going to show you some key steps necessary for you to be able to read any mat. Mathematics is its own language and not enough people speak this language. Tate Fourier analysis in number fields and Heckes zeta-functions.
I am not suggesting that any mathematician should read all of them but any one of them will do. In fact the actual content of these papers does not matter so much. It is rather that they give an insight how a new idea is born.
Then leave papers there for yourself. Try reading with a friend. Sit next to each other looking at the same copy of the paper and stay synchronized at the paragraph or sentence level.
Read aloud at times. Logic is the framework upon which every good mathematics research paper is built. Each theorem or equation must flow logically.
In order for the reader to understand the authors work definitions for terms and notations used throughout the paper must be set at the beginning of the paper. It is more effective to include this within the Introduction section of the paper rather than. This suggests that reading research papers is crucial to further ones understanding of the field.
With hundreds of papers being published every month anybody who is serious about learning in this field cannot rely merely on tutorial-style articles or courses where someone else breaks down the latest research for himher. New ground-breaking research is being done as you read this article. Skim most papers in their areas but read none carefully.
Some just read the intro-ductions. Some read whatever is suggested by Google Scholar with its obvious bias towards citations of their own papers. Some skip everything in the paper and go straight to main results.
If su ciently interested they then go back to read whats it all about. At this point you should feel confident talking about the paper with colleagues thinking critically about the results and being able to compare the work to other research in the field if you have read other papers. To retain and enforce what you have learned I suggest you write about the paper.
It can simply be a few paragraphs about what you learned and the significance of the results. You can reference the list of questions you were answering as you read through the paper. Mathematics is written with sentences in paragraphs.
And yes paragraphs are important. It is not amusing to read a three-page paper consisting of just one paragraph There is however one element in mathematical writing which is not found in other types of writing. However it may surprise you to know that in a math paper formulas.
In this video Prof. Pete Carr faculty member at the University of Minnesota Department of Chemistry shares an algorithm to read a scientific paper more e.