Writing Workshop

the following content is provided under a Creative Commons license your support will help MIT open courseware continue to offer highquality educational resources for free to make a donation or view additional materials from hundreds of MIT courses visit mitop courseware at ocw.mit.edu so what is an 18821 p um well it's no more and no less than uh a presentation of the project that you've been working on as you've defined it and an account of the results that you've obtained in uh in studying that Pro problem and so these findings can come in many different forms um uh theoretical mathematics uh um you know the the gold standard is a proof a rigorous proof uh that's great if you can do it um that's great if the problem admits that kind of thing um but there are many other kinds of uh findings that you may want to report on in this report as well you may very well come up with things that you are damn sure are true but you can't figure out aof of they're called conjectures and if you're if they fit into the frame of the paper into a coherent uh story then uh absolutely present your conjectures as well as your proven findings a lot of the physical applied math projects and things the best you can really do is make observations you may have a simulation that results in something and the the thing to do is to present uh your conclusions from the simulation it's not a formal proof but it's a perfectly valid uh uh finding for the purposes of this paper so how um who is this addressed to um well the the the paper should be addressed to people just like you so actually it's a pretty wide variety of uh of uh interests uh in the class here and so the actual target audience of different uh papers by various groups will be somewhat different from each other that's fine just make a paper that you'd like reading yourself target audience is a big uh deal both in uh in in verbal presentations and in writing uh and keeping a consistent uh target audience is is something that we always look for uh if you uh give some detailed definition or account of something that's kind of Elementary and then in the next breath you skip over something that's more sophisticated well there's a g there's a there's a uh in consistency in the target audience and that's a flaw that's something to avoid so we'll keep looking out for that so there are a lot of things that you might think that a this report is that it's really not one thing for sure it's not is an exposition of uh of known results about the project it's pretty for many some of these projects it's easy easy to go to Google and find out things uh that other people have done that can be part of your background research but uh just giving an account of that is not what we have in mind you may want to want to describe uh what you've discovered from the literature if you did that search but it's that's not the main point of the of the paper but it's on the other hand um these aren't really intended to be research papers it does happen that um sometimes teams study these projects and come up with uh publishable results so these things these papers that you're writing now could become a research paper but that's not really what we have in mind at the at the first round also usually it takes more than three weeks to write it research generally speaking most of us and it's not a lab notebook either uh so this is a literary exercise it's not just a listing of things that you did it's got structure to it um it's going to go through a rewriting process um so how long should it be well it should be as long as it should be I don't know how else to put it you have a certain amount of time you want to tell a story um it in practice this means that it's not going to be much shorter than 10 pages because you need to introduce the problem and tell what you've done about it uh if it gets to be much more than 10 pages then you're probably putting in things that are sort of tangential to what the main point is and you should be more more uh more concise so 10 or 12 pages is typical uh length for these these papers and if there's you know we go through this revision process and the three papers you'll get a better sense of what what uh what the right sort of level of of concision is I'm going to ask to say so I haven't worryed that much about the the length issue you you'll get used to that now um literature comes in many different styles and uh in this course we made the decision that we would ad adopt one particular style which is the mathematical research uh Journal style uh it's actually quite a well- defined literary style um with particular usages and a particular structure and uh that's the style that's the type of writing that this course uh um is designed to get you good at it's if you've taken uh seminars here that's uh generally speaking it's the same style as you may have written in papers for seminars but that's the style that I'll be talking about here so um as a structural thing uh uh mathematics Journal article almost always has these components to it it's got a title it's got an abstract um and we'll talk in detail about what each one of these things means um it's got um an introduction it may have a separate section that F fills in background um that is not original with the paper but needed to understand the paper um then there's the body of the work which may have several sections and we have a complicated structure in its own uh then with correct spelling you've got appendices that may or may not be there that carry out things that you uh that don't fit so naturally into the paper like like code for example might go into a an appendix and there are references at the end uh to literature that you've used so uh let's begin with the top one here so what I'm going to do here is uh talk about a a a paper that came out of the very same project that Nat and Saul talked about on Tuesday so it's a paper about coloring knots uh and and you've you've seen the work so you know mathematics now the qu only question is how does it appear when you write it write it up in a paper and so we'll look at um the various different parts of this of of this paper and and um we'll look at a number of different ways of approaching the problem of writing this Pap writing the different sections of this paper uh and think about how successful they are in meeting the demands of that section so let's begin with the title and the abstract so um here's a title here's the paper um and there's an abstract um by the way a remark about these slides uh there's this is a workshop on literature so there's going to be a lot of words on these slides many more words than you generally want to put into a slide when you're making a presentation of mathematics uh so uh don't take this as an example and the quent slides will have a lot more words don't take that as an example of what your slid should look like in a presentation well let's see um so what should a title do um it should convey the subject matter uh and it's a there's a this tension between being Punchy and and brief and eye-catching and being accurate and uh and honest about what your paper actually does a general rule is you should try to avoid symbols in in a title because people will quote the title and symbols are often not easily quoted they don't don't translate very well so and moreover they're just sort of unfriendly have a symbol in a title so we'll uh so uh I'm going to go to the the abstract here as well the purpose of an abstract is to give a very brief outline of the contents of the paper and there's no ATT doesn't need to be any attempt to say give the meaning of the words it's something that um a professional might look at to see what's in the paper um typically uh there are collections of uh abstracts and there a way for somebody in the field to look through papers quickly a list of papers quickly and decide whether they want to get into them or not so they're generally very brief uh and sort of can be fairly ruthless in in their language so I don't think that the the K there does anything except annoy the reader as far as I can tell it might make it look more professional or something but actually it doesn't make it look more professional so uh there's an improvement what other improvements could we make do you think to this this title just the title get rid of all the there's an awful lot of ofs in there too aren't there so but how would you do that enumerating coloring enumerating coloring well enumerating coloring so that's nice uh what I one thing I like about that is that there's a verb enumerating it is a verb although it's a gerund or something but but making getting getting something active into a title is is great it's part of being punching but enumerating wait anything missing from enumerating colorings what has the arc coloring okay would you color anything other than arcs well if you just have the title you could color I don't know uh the Statue of Liberty I mean well a numerating color I mean if if you if you a numerating coloring versation colorings sing you can factor out absolutely enumerating colorings of arcs of project okay right I thought you were meaning to have enumerating colorings as the complete title and then I was concerned that there were no knots in the title but that would not be yes uh enumerating colorings with not projections assuming not projection the question is standard terminology matters right because they assume these kns and these projections are welln standard mathematic object so whatever the terms of art are here yeah that that would do that's sufficiently standard right so that's that's a good one that would be a big improvement over this projections versus projections of a not K right um um right exactly making sequences of nouns uh does make things more compact it U can be overused though and becomes kind of ugly after a while but I think enumerating not projections is much much better title this I agree completely how about the abstract does it does it succeed in take there's either a typo or somebody didn't just use grammar correctly I agree ways of coloring the arcs plane projection of a not and I guess that that um readers of grammar manuals will take issue with the use of the word which as opposed to that in that context okay but uh but this that for me what do you think this abstract doesn't seem too bad says it's there pretty well what do you think that it's okay you have any abstract what our papers do our Pap abstract absolutely put in abstract let's look at another example of uh another solution to this these two problems um here's the second second version so let's even puncher it's probably not it's not as accurate as yours because it doesn't talk about enumerating them um but this would defin if it was like a talk this would definitely be a much better it just would draw the audience in wouldn't it they'd all come to the talk huh the abstract like doesn't first of all doesn't say anything and what it does say is wrong man um so it's not that enumeration of these colorings gives rise to a not invariant really right like I mean if you could already enumerate the colorings oh I mean it it just sounds so so we'll see in the body of the paper that if that you count the number of different uh proper three colorings and that number is not variant oh it is it is in fact the enumeration of them the number of them that okay so I guess it's a maybe it's a misuse of the word enumeration maybe I age eneration was not clear enumerating all we know all possible like types of coloring classes that were okay good good yeah I'm not talking about uh coloring coloring schemes I'm talking about colorings of a given scheme so isn't language great um okay so uh at least it got rid of the spelling error oh should should the authors Al great question uh why in the world does B occur second in front of celo uh in in you know every discipline has their own standards about uh about what order the authors come in um uh I understand biology puts the lead author last for example um mathematics almost always has straight alphabetical and it's alphabetical in the last name okay alphabetical the so I suppose that this was alphabetized by the first name well that's a little bit non-standard all right that's a good point so that's a further I think a further defect of this uh of this of this title thing okay uh but surely the title is is a lot better although maybe enumerating enumerating not Notting not colorings might be better even though it's a little inaccurate right because they're not we're not coloring knots we're coloring knot projections but but you see it's it's okay it's okay all right so that's the title and the abstract uh next section is the introduction so the introduction is supposed to be the hook a lot of papers um you know this they get read or not read completely according to how good the introduction is and so here's your one chance to to uh get the reader involved in your paper not going to read past it if you can't see what what's going on from the introduction so the introduction has several different purposes though it's a summary of uh what the paper what the paper is about the context of the problem it's a summary of what the paper achieves it should say something about the methods that are used in the in the work and then it ends um with a a description of the structure of the paper in into sections basically and then um generally it there will be acknowledgements as well which happen at the end of the introduction that's the way I write papers um in in this case um you will have uh probably have a lot of um um you know you'll have gotten a lot of help from your Mentor but that's sort of understood and I think generally speaking the mentor doesn't have to be thanked specifically we understand that but you do have to thank each other as well and you'll see what I mean by that so let's look at an example uh oh yeah well so questions to ask so we're going to look at a at a at a sample introduction and as we look at it here are the questions that we want to ask so does it succeed in giving a an intuitive uh understanding of the question why would anyone think of looking at this problem and um why is it deep and what's your approach and does it do this thing at the end here's an introduction to this paper about not coloration so I'll let you read this for a minute so um from the bottom up um this is the kind of uh acknowledgement of your of your teammates that I want to see at the end of the introduction say who was who was in charge of writing which parts of the paper yeah the can't the bottom two paragraphs just be replaced by like um what usually don't have yeah yeah tablec is is a pretty heavy piece of apparatus for a short paper if you have a 60-page paper then it probably makes sense I section mentioned well so there's an either either clo didn't get um her work into the paper or uh they forgot to say what section section section seven is about uh but anyway um so let me say something about this also these papers uh um they form a ho they'll be written by a team um we all know uh about the the uh course that was designed by a team a committee it it you have to work to make your different pieces of writing cohere and come together so the whole team is responsible for the paper as a whole but um but but the but individuals will have written different part sections of the paper and we want to hear um the you know who is the who is the one in charge of each of those different sections um we will be making um discriminations within the team to some extent because we all get different grades in the class so this is a tension that exists whenever a classes depends upon teamwork and we do the best we can to be fair to everybody and uh give give credit where where it's due so I hope that was a completely ambiguous statement but uh it's the best I can do uh so this this acknowledgement should be there working up from the bottom um this is a this to my eye um it it it describes the SE the sections it's a little boring isn't it um but at least it's clear I always find this particular part of a of a um of an introduction um a little boring but useful so clear and simple is fine I would say how about the top paragraph kind of stupid stylistic issue which is um the sentence many Nots have devoted a lot of time so like most of us has written in a sort of semi formal fashion and the word a lot does not seem or the phrase a lot does not seem to into the writing like that sentence to stand out being a little moreal in fact this whole evocation of the community of not theorists seems a little out of place yeah it's probably not that a little bit odd well I'm TR to I mean because you I feel like that statement is an important one but describing what not theorists have done is kind of I don't know much interest has been devoted into classifying KN or something might be yep I agree a better I agree the second sentence should probably not be separated the col there it might make more sense to replace the word is with asks where are you looking the main I would say you know the main question not theing asks question I see people ask uh main question is how can we tell I think that's it's a problem with that grammatically um they say that that should be capitalized if it's a complete sentence yeah F American versus British style this really is one of those points also I feel like the number of people who like know that and Care is what that ofal all right that's fine um but how many people know uh what a knot [Music] is I mean there's a basic assumption that's being made here that uh we all know what a not is uh so this is a matter of uh deciding on your uh audience uh if the audience is this class well now this class does know what a knot is because we attend attended a presentation about knots on Tuesday but otherwise that's probably not something you should have seen and then and then there's this notion of deoration is well it's a little it's a bit of a stretch I I I would say this beginning thing um should I be saying things should do the work say go for it sa um this line about the table makes it look like it's the culmination of the entire subject of not the Bible of not theory yes probably I don't know much about not lit it's probably a misrepresentation right um so so so this is a question of of of of the audience if um I think you should be writing this paper um to your peers and I think it's we could have a discussion about this but my sense is that you probably want to say something about what a knot is because I have knots on my shoes here but they're not knots in the sense that we mean here's the set of questions that we were looking at um well how about the second second uh question does it express the author's approach to this problem no Z nothing nothing zero there's no no hint not coloring is buried at the end of the list no hint it's it's like it's like there's a missing paragraph in there having not colorings in that list is also kind of odd unless something El the not colorings are what being deved in this paper and they're kind of listing with all this prior wellknown body word right exactly and and that there's no hint about what they mean by coloring right yeah so I I assume the would be a good place to put a definition of that kind of thing or at least an intuitive definition I think so let's see what what the next version of this does so here's the second version same paper different version of it of an introduction so this is missing the second paragraph go after this that's right it's missing the acknowledgements and it's missing uh the structure of the paper this is actually helpful what do you think comments oh to I feel like they should at least have sh to what are here now um at the very it that's the last word that appears here being German he would say Meister um yes um this is getting into he's describing the method of proof here um let's see in fact that's the only description of the method of proof that that one sentence is the only description of what he is yeah I'm just wondering about this whole like just the whole mathematical content of this and maybe this is completely beside the point but like it's weird it seems weird to me that this is a paper talking about um three colorability using Rister moves as given like it seems like the whole proving the ROM Meister move you know that they like generate knots is it is what it seems like it's much more substantial and harder to do than any like it seems like the three-color ability thing is an easy consequence of that I don't know well but isn't that the way science is you you stand on the shoulders of giants and a small step I mean did they like not discover three colorability before they like figured out how to show this Romer thing uh it in fact R moer came about 100 years before three-color ability wow okay never mind [Laughter] then about just be fixed by putting something like for example case bye class that generates not in fact R Master moves don't happen on a knot do they they happen on a not projection so the whole concept of a notot projection is skipped over here it seems to me that's part of the method that's the main part of the method should be should be part of it in fact actually yeah actually the three color are technically defined onction on not projection right so it's a theorem that they that the invariant under under Romer moves and therefore an inar if they not so so yeah I I agree this is a little this is too brief to be really uh to fulfill the promise of an introduction what else you're just some random biologist who happens to be reading a paper in mathematics papers that do things almost that I've seen real papers that do things almost that silly though I think people do this to like get funding or something yes why is it wrong say well approx the word approximately isy but it's like but but I me what you put in the approximate the whole point of not are these like formal algebraic objects you totally lose that so I I do wonder what the reference one is here there is work about using that theory to analyze there's uh Topo Topo isomerases that cut specific knots in DNA strands as a matter of fact uh so it's not a it's not an empty thing it's it's not false to say that not theory has applications to to study of DNA um but but you were asking how far out from the uh from the from the focus of the paper should these motivating things be uh I don't know I think maybe biology is a little bit of a stretch that's that's my sense NIH well okay they may get funding from them maybe that's what accounts for that's what you're thinking tooo is it's a little bit of a stretch too but this is a actually very very common uh thing to see in in papers sort of things get mixed in in a strange way we're Ma we're mathematicians though okay other comments about this this introduction so does should [Music] um should it should the introduction have any definitions or any actual precise statements what do what do you what do you think sometimes it does sometimes I feel like I've seen some have like an introduction section test definition seen some that have an introduction section and then another section under that has definition and then goes into yes uh yes yes uh it's it's a nice practice to separate out a precise a separate section that contains a precise statement of results um many papers will do that um I think it is a judgment call uh if the definition is um is is so in these 10-page papers you know a definition has an environment it's uh it has to have some space it occupies some space I think it's kind of a bit heavy for these papers and and if the precise theorem or statement that you're interest that you that you want to bring out is convenient to make it precise fine but if it's but there's no need to do it you should feel compelled to do it I think how am I doing yeah um stylistically is it good to present future results where so so the phrase I'm looking at is it will turn out that three colorability of the KN is very how about the tense I kind like thats natural to Meely we prove the best part is that the wi can even if it a single um where does it say we provve oh you're saying it will turn out that um oh I see so that would put it in the present tense um what do you think about the tense issue s i I think that present tense is more common than future because the paper exists in the present exists you say it turns out that that this particular sense will not flow with right so so that is an argument for an exception so so I I don't actually mind the future tense here but once you get there you have to stay there it will turn out but then the proof that is and you go back to the present tense after that so there's an inconsistency in the tense the proof that three colorability is invariance find is the frof that us will will use that's the that's correct that's the wrong tense right right so I guess future is you know it's a little it's a little um edgy and you have to be careful of it and these it correctly yeah hi I think like the bigger problem there is that it's not clear if that is something that you come up with or something that just follows or okay just like something that was there and you just mentioned it okay this is a really important point which uh which is relevant to to an introduction what in writing these papers uh it's absolutely critical that things which um you learned from somewhere else else are distinguished from things which you discover for yourself that's absolutely the most critical distinction that you can make in the in the paper and uh that already can take place in the introduction and it's not clear that that this does this our project studies it will turn out it's not invariant so the as I read this the implication is that they did this work and if that's correct um I think that's fine if it's not correct it's not fine you have the same sense that this it implies that the that the team did this work yeah yeah right yeah so where like here three color right when you have concept that's it's weaker than a defition definitely but it calls attention to the fact that this is maybe something that you hadn't seen before it's not it's uh it's saying uh this is a new word I'm not um I'm you shouldn't you know you shouldn't U search through your memory to try to figure out where this word appear before because you're not remembering it stuff like that that's a ver a function of italicization what do what do you think about a test convention that is used sometimes in textbook publishing is to italicize the word when it appears before being formally defined which is what you're suggesting it's but um that has to be done carefully because if it hasn't been formally defined italicizing it is not sufficient you still need to context so people what yeah and it has to be explained uh just italicizing it um doesn't people will often do this I've seen this happen in in the mathematical literature a hundred times people will will italicize a word give give you this word and then you're supposed to attach some significance to it by some kind of magic despite the fact that there's no explanation given to it just the fact that it's a tze somehow it's supposed to make it mean something it's it's a very the I don't think that that happens here though um he says three colorings of nuts if there were just a period here then I would object to that but he says it's ways of labeling segments with three possible labels and so that's sort of explain and that doesn't conclud from form absolutely this this thing is very far from me because ways of labeling segments with three labels what the constraints are on those actually very important it's very important idea and and so we could have a discussion about whether this is within the the bounds of uh informality that's appropriate for an an introduction or not um I don't think there so I of feel like you can't actually have any understanding of what papers have been trying to do except at the level of it's a non invariant unless you know so I think because it's using it as a key not as a Def and then like said this doesn't stop you from formally it later but to call attention to the fact that this is a key that's going to be of course there's an inaccuracy here segments of a knot they don't mean a knot they mean a knot projection and so so I still think that that in this introduction they have to say something about projections because that's the key thing is and sort of skip over that question well I come fromg and I've a lot of there and people mostly use voice but in English passive yeah and in English people mostly use active voice so do I need to what about the issue of active versus passive well English speaking Pap s other mathematics you see passive used way through really more than yeah do we think any kind of math like heav bu it's not the Royal right it's not I at least the information I've always heard is that it's me the author and the reader yeah yeah and uh of course there's an ambiguity here because it's we three as well as we the author and the reader but the point is even if there only one author it still be we terrible through I it's it's it uh so uh you'll see both but we I think is uh more traditional and maybe more formal I would say um I the issue of passive is a very interesting one I think in English um passive is regarded as a little bit passive it's it there's no uh there's no um inhibition you shouldn't have an inhibition against using the active voice it's more immediate it's more efficient and um my my impression in mathematics is that active is usually preferred because it's seen as livelier and more interesting but in order to do active you need to use so like a picture could be a good addition to even an introduction section absolutely should we go on to the next one let's see what are the things we're looking at here does it give a good intuitive grasp this one's better isn't it there's something um author's approach to the problem not completely but better they don't talk still don't talk about Pro not not projection which is an essential part of there U and then we know that it doesn't uh talk about the structure and Technology you can more less paced on you could pce that on right let's look at one more so uh yeah um isn't it amazing um there's no right way to do these things there's uh every inuh so we we can pce them together what do you not like about this one you don't like the theorum there yeah okay also so the is not but I don't like is that this is actually it's going into this extra formality but it's actually not unlike the one it's not actually telling you any of what this means or yeah right three coloring right it violates all of the uh all the things that we say that you have to prepare the way and and and get the reader uh on board before you make a statement it's all missing mean if they had the that had all the stuff right under it I that be terrible a little worse than the other around so so uh following uh the use of a word with a description of what the word means um it's a I would say it's a it's high-risk Behavior [Music] okay is that accurate yes feel like I've seen you definitely you've seen it definitely you've seen it people engage in high-risk Behavior the reason it's high-risk behavior is because a normal reading strategy is to make sure that you've understood everything you've read and so if you come to a period and you haven't understood what you just read you may stop and puzzle over it before you read on so there's an there's anxiety created there's tension created in the reader which may be your intention it that can be a good thing but you have to there has to be a payback at some point and and things get get rewarded and Consolidated pretty quickly it's it's high risk it's also good weird that the theorem starts with a number like three pillar umh you think that that that um that's a little strange uh especially in the second sentence of the introduction I mean this is really part of the structure of the paper that he's inserting up here right at the at the head I I I agree that's kind of strange to have there so there's a lot missing from this isn't it um at least they he makes some attempt uh to say uh you know what this deformation thing is it's genuinely knotted I feel like going into a specific example a high level overv is not the most effective the example like maybe that sentence theile thing could have been added like version two of the introduction after explaining what but MH here the example is not really sufficient to you can't really fairly expect the reader to immediately extrapolate what all those sentences mean just from that example absolutely no there's you one needs much more description of of of of what's going on up here there's so colorability not invariant V must and so on are just mysterious in in that I agree very brief description of the strategy I like that part not there's some virtue to it right uh maybe a little brief but it has to happen be confined to this slide let's see yeah so that's all we have for that in that version of the introduction so they do some good things a little better some things a little worse I I agree um so now we're I'm not not going to keep doing these introductions I do want to talk about some other section of it but here we go here are some pictures at the beginning do you believe that's the unot I have a problem with these two pictures in that they're not parallel with each other it it they're taken from different sources that's kind of odd so you can see that uh pictures in the introduction really do per it up you can come back to this is on the website all right look at all this text I'm not going to I think I want to move on to the next section here there's you can see there's a lot of things he talks about what TR oil is says what a not varant is he doesn't still he doesn't say about not projections talks about segments of a knot naughty right got to be all right I'm going to move on here and then uh then there's the description of the sections and the acknowledgements all right so so okay uh it's it's quarter after the hour I'm I want to um there's a lot more to this presentation I'm going to go on a little bit further but I'm not going to get to the end of it okay but let's keep talking about the the um the qualities of writing I think this is a really great discussion about uh the quality of writing and what's important in writing uh in in the small as well as uh in the the the the role that the different sections of the paper play so sometimes you're going to need to to use to to gather information um that isn't really part of uh the research that you're doing but it's background maybe it's notation maybe it's uh um State definitions or theorems that you will use and just don't want to have interrupt the flow of work when you come to describe your own work later on it sets up um it sets up the context that you're going to work in in more detail than you would do in in a introduction so it's quite common for people for for papers to have a background section like this although it's not not a necessary part of these papers but we have to know that the that this that the contents are going to be used um the level of detail is now full detail have to be completely uh clear and accurate about things that you say um you can't just introduce things that aren't going to be used later and um it has to be well organized okay so maybe we'll just look at one of these and think about how um so this is a typical uh thing you want to know what a knot is before we can start talking about coloring of knot projections it feels like there's a big a paragraph in front of the definition that's missing what are we doing here what's okay so another weird point is the time rsal here maybe that's sometimes an intuitive way to think but that is not the term I would use or that not the way I think about not I don't think yeah this was a problem in the presentation on Tuesday too Noah what were you going to say oh I was going to say I don't know if you need to introduce oriented knot if you're only considering unoriented knots or find unoriented well if you're going to define a knot as a function from the reals it's going to be an oriented knot so maybe don't Define it as a function from the so this is a this is a a huge question what use of is the rest of the body of the paper going to make of this exact definition I feel like just to make sure the reader knows what not is and and have just have an understanding how they could translate the things into formality so ultimately it's going to use a not projection and r removes right and so this how you know what about what does it mean for two not projections describ to say not if you can't answer that question then you like don't have any wait what why can't you just Define it as like an embedding of S1 or something it seems like much more reasonable that's what the oh S1 does have an orientation so sure but but but but I'm asking the question when we actually start to work and talk about not colorations we're going to use a not projection right and I have the question about whether we really need this kind of formal definition of a not if that's the work that we're going to do in the end I have my doubts about it there is a literature out there that you can refer the reader to to to to to be precise about what a not is and prove the theorem that um that you know not projections of that particular form uh exist and prove the theorem that ROM masterer moves uh translate between them um but I'm not so sure you really need a precise definition if you're not going to use definition is very low cost if you don't care about the definition it's in this nicely label definition section see it starts with and and then skip I think there's a high mental cost including definitions that are somewhat extraneous I think there's like a reability cost there absolutely that's a cost it's a great way to put it I think the definition of k is that gives the nice picture image of K to to say take K of R and so that focuses your attention well so so that's so there's a little bit I agree with you um it's important that they make that that they say that that what really matters somehow in your mind is the image in fact in cases we consider but I'm wondering about the word we consider here it's a little bit strange I mean you can argue that that's with the informality that that particular use does not seem damaging at all other Poss they could try to react defition so so so this definition in Tech um this is created by um an environment you say uh begin definition and what follows is going to be a definition and then we say n definition and inside that that um that environment what should be there is the definition and it should be an accurate definition not just an approximate definition so I have a problem with what happens down here uh definition two knots are isotopic okay unoriented knots and then it says the intuitive image is Da this isn't part of the definition be better to give an intuition first inside of the definition block yep and then gave a formal definition yep I agree if you need the formal definition and I'm questioning whether you really need it here at all but see I don't know also the word pink is vague enough that okay so I want to move on to a different section here so there's more of this if you want to have fun uh critiquing stuff this is a little better isn't it look he set the uh it's the same definition but he set these out separated them a little bit and he gives a kind intutive he begins with with this introductory stuff uhhuh that's that's much nicer so more background so here's a here's a background choice that doesn't um this is almost an introduction isn't it it's uh could be part of an introduction but but it I think that that well this is just one paragraph in a longer uh background section and I suspect that in when they come to do the work they won't need more detail than this that's I have a problem about ordinary self intersections because although actually self isue well moreover this this allows tangencies which is not allowed in a not projection so it's a little bit inac accurate is that part of all right there's more to this there's a a picture that's wonderful picture isn't it all right all right all right presentation of results so you're any two mathematicians will write the same results quite differently it's there's really a lot of variation in how you present mathematics but but there are a lot of rules and conventions that really have to be satisfied if you're going to be legible and it's going to be good mathematical literature so we'll have we'll just look at one of these things and um here are some questions to ask about the section involving the body of work that you're presenting so we like we were saying the most the really important thing maybe the most important thing is that uh you you it's clear what the what the status of statements are are they things which you claim to have proven are they things which you are quoting from literature are they are they guesswork are they what are they and making it clear what what role each um each paragraph or each sentence plays is really important connectivity is incredibly important and um I I think that in the commentaries in our in our critiques of your first drafts you'll see a lot of uh a lot of commentary about um getting connectivity between uh different sentences and and different paragraphs uh uh we'll make a lot of comments about that it's a it's a big deal it's it's surprisingly important in making a paper easy to read to uh get the connectivity uh correct and of course um are the arguments correct and are they correctly presented meaning um do they does the presentation follow the the standard uh rules of mathematical presentation so maybe just one example U or maybe we'll do two examples of this so here's okay so here's another so we've done the background where we've done an introduction we've done a background we're starting in on the work here's the here's the first section of the body the paper I feel this is bad for people who are not familiar with whatever the conventions around RS are people know what type one type two and type three already refer to absolutely that's part of the backg of them is kind of really weird well it's part of the background theyve they've seen one two and three that's so there if that already been put in yeah that's part of the background should we just look at another one to see a a contrast this is completely missing the high level you have the same sense is something we're just thrown into the water here uh somehow it's nice to say slightly indirect but and and again I would I would like to see some guidance like you were suggesting in in the frun of that what about the title of the section so this sorry this to be interpreted as a a section like a section heading main theorem and then right under that another bold item I feel like having two bold items in a row is just sort of bad if you can avoid it at all maybe just a couple of words in between would be probably good it's it's called guidance it's it's a essential part of a paper to to um ease the ease the reader a lot they they probably wouldn't actually do anything except separate the two bold items not that's like okay but over here we had the previous example of the other section y actually like not terrible as a high level overview of power you can basically pop that in details I um I wonder if the if there's a more imaginative title for the section the main theorem something that carries some more content to it somehow um there's a Lemma isn't it don't do allers need to have P for the sections because of course the UNC solution is name like section three is that not really so readers often want to be active imagine you're a reader you read the introduction and you think oh this part sounds interesting or you so you skim through the paper and you want to find things if the if you have meaningful titles then people can find okay good I think an image would go very well here trying to describe this matrixes constru oh wouldn't it be great to have an example here's a definition the I entry of AIG isure on the side that Tex so um math papers are usually pretty uh one column Affairs they're pretty linear this sidebars aren't really part of the picture but you could easily have uh interrupt this with an example of the troil or something and say what the what the it would add enormous amount to that I agree um here's a Lemma um sort of early I would say here uh no proof following the lia is that okay else is say say what it should be proven somewhere I guess it should be proven somewhere unless I guess the absence of any indication say me makes me think well maybe he'll come back to that but I would like to hear that he'll come back to that it it would make it better if if there was some assurance that yeah we'll come back and prove that all the time they'll just give a reference sorry A lot of times they'll just give a reference but is in some sense not yeah uh you could you you right if if it if it was something that they got from the literature then it would need a reference but by not giving a reference here they're saying that they proved it so I mean you could um you could try to give it some slightly more polite version ofc to yes absolutely you can say we leave this absolutely easy reconstruct detail absolutely when you have a statement like that so sometimes when you try to write at of proof it's a total mess and yet it's an extremely easy basically to L so and so where do you go with that I don't know I'm observing I'm observing that you might make this section look a lot more messy by including a full proof there and so maybe you want to give a verbal idea of a proof bad form to say this follows immediately from the definition there's also like a where you could I'm not sure seen you say something like um so you know an intuitive explanation is this and say then you can say like you don't actually have somehow say you don't actually have to read this follow proof but here it is if you want it yeah I always feel like I'm uh being jerked around somehow by uh a paper that says you don't have to read this if you don't want to I I mean I want him to tell me what I should read and that's why I feel uh I uh uh Saul is saying that a proof would be pretty distracting immediately following includ a proof for completeness I think I have seen yeah I know I've seen these things too I agree with Saul that to put a proof of this right here would right here in the second paragraph third paragraph of the proof of your main theorem is probably a little out of place and seems kind of could probably verify well maybe who knows uh but but uh maybe something I think like one so I think two things here I think that the author was smart not to put a proof here but it would have but dumb to have not told us something about where whether we were going to see a proof or not and where to find it that that's that's my sense about that now so okay so I've sort of run through this you can have fun reading this and making your own uh judgments about how successful they are in meeting these requirements in these papers it will certainly happen that you will um know things that you um can't prove although you wish you could or just statements that don't admit proofs because they're simulations or something and I just wanted to give an example of uh how that looks um same questions the same questions pertain is are the statements is the status of each statement clear um are are is the connectivity clear we didn't actually talk about connectivity in the in the words that we were just looking at and are the arguments correct and correctly presented so here's a um section four this is stuff that these authors wish that they could have had something to say about all they have is experimental evidence it's pretty standard in 18821 papers okay exper the statement that comes after that is not actually a statement about D experiment a general statement which may or may not be true yes I agree so I feel like you should either not describe you describe as a conjecture instead of an experimental fact I you want to change the phras the I agree this is Mis badly worded maybe that's what you were you were saying um it's badly worded this isn't the the experimental facts are down here um this is a conjecture it's in incorrectly phrased but at least it's saying this is something that we believe to be true but we know we can't prove and um that's that's important but I don't like the first sentence oh because that sounds like you can actually make a stronger proof but a conjectured strengthening see it's ambiguous because at the end they quote literature which would prove that the number of three colorings is a nonvariant wait no the literature they I thought well uh two two fact 4.2 is a refinement of 4.1 no I get I I'm sorry I guess it's not but anyway uh yeah so I what I said is not quite correct this literature would would certainly show that the number of three colorings is an not variant so so so there's an there's the so that first sentence fails the the test of being clear uh about or the first pair of sentences it fails that test it's not clear what they mean it can be strengthened as follows yes because you find you find that it's in literature or no because we don't know maybe it can be strengthened actually seems like it seems like they actually that simple enough they actually could put in an actual proof because it seems follow direct well I mean the now that's a that's a non-literary comment but whether whether they could have gone on to prove this or not is so they they very nicely I think described the experimentation that they did and then um uh I like to think that the team discovered this which I find quite amazing the number of colorings is 3 to the nus what do you know and they have a lot of experimental evidence for it and somebody went out and looked at the literature and found a proof of it so I agree I think that experimental fact is not a well chosen word here and and I have a problem with the ambiguity of the status of statements at the at the beginning but the actual descrip yeah I it's pretty good yeah you said that this shouldn't be a lab notebook right this looks kind of like a lab notebook to me this isn't everything yeah I would say a lab notebook would say uh you know here's a list of the three colorings which they I guess they do in appendix one okay and they're summarizing their findings here okay so uh the the lopy things if they if you want to include them they're they're appendix things okay uh so let's see so we've had complaint various critiques along these lines well there's more of this yeah better yes we would like to refine it as far there's also a better version of the to that's nice isn't it I like that introductory sentence that little paragraph at the beginning but now I kind of liked how the other one described their experimental evidence whereas here it says that they decided to not include that at all that and they tell you a few of the arguments that they thought of at least it's divisible by six okay I don't like starting a sentence with [Music] oh with a number how could you how could youil is not very so this this three here you don't like the three there how would you change that how would you what would you do in place of that what would you do like so in general so here you can not the americ or in general say I say we have we know I don't actually Pro do you think that writing out T re would solve it no you don't like that you can't have a number you if something is like a a number hyen thing you can't put a word the ru I guess so I never heard that rule I'll go it's not an actual rule that that but I mean I don't think you just don't see people do that very often okay know why yeah okay so beginning beginning uh sentence with a symbol of any kind is generally frowned upon for reasons that I've never been able to figure out I I think it's because when people read they expect the sentence to begin with a capitalized word and to end with a period and that expectation is capitalization so it's just a reability [Laughter] issue of course also get what's wrong with that well of course why what's wrong with that I don't know it's kind of inal not bad you say it's a little dismissive one could of course get experiment I don't actually mind it it's a little it's a little what do you what does that do to you Susan it makes me wonder well then why didn't do why why didn't you do it yeah it's a little dismissive like this is below us to do this you could do it if you wanted to it's just a general reminder the obious superiority yeah maybe that's what you're objecting to it's a there's an arrogance of the author that comes out by by that a little bit as it wouldn't say it's really wrong it's just sort of revealing some feature of the personality of the [Laughter] author all right all right there's more of this and so on ah so they separate the con experimental EV yeah which is good right and they have theoretical evidence so but they still have this empirical fact so that's another so empirical fact is that different from a conjecture does that seem ambiguous enough that I would I think empirical fact is uh it's an [Laughter] oxymoron it's basically I mean there's no reason not to yeah I agree all right we're going to we're we're going to finish citations you have to cite your references you have to cite the references that you use in the paper and make a bibliography I the example I don't have bibliographical entries here on these slides there are examples on the website that you can find standard standard form for bibliographical referencing cite all the references you use but don't side any references you don't use so if there are entries in your bibliography that you haven't used that's that's not great if you don't use anything you don't need any bibliography that's fine so a lot of times um when if you use things that are sort of know general knowledge or something y I've never understood exactly what the rules or conventions of when you're supposed to find a citation with a textbook or so I think you you have this is a question of what your who your audience is because you have to the citations serve two purposes they serve the purpose of declaring where you got your information and um protecting you against plagiarism but they also serve a purpose of helping the reader find out information about what you're talking about and so it depends on what your audience is whether you what sort of General references you want to site and that's a decision that you make as part of your your imagining of who your audience is so um so you know he might earlier on when he was talking about F3 he might have referred to some book which talked about finite Fields maybe he did and he reason I think you're I think the decision could go either way it depend it's a question of of being uh consistent with uh your target audience um right and again it's always essential to say whether to make it clear whether you're using results that you got from somewhere else or results that you've um obtained yourself yeah and well when you make a reference so what's wrong what's wrong with these citations it says poor citation what's wrong with them useful where For What and like we would use that for the comment I feel like I it's not bad problem bad is using them without further comment what's wrong with the first one it's simar separate for if you should separate the three different citations and uh I put them all in separate brackets um hm that's that's a kind of thing that maybe some journals would object to and some would be think it's okay for me uh uh gosh that's an awful lot of literature to have thrust in front of me it just seems vague to me is there something actively wrong with the way it's cited or no I think it's okay the US it's just kind of useless is that why it's here as an example of a of a poor citation um because I didn't write this I'm not sure but uh it could be because it it it really doesn't if the question is what does the reader me yeah if the reader wants a probability textbook then choose one that is going to be good and suggest that one yeah and and be as precise as you can as a general thing be as precise as you can about pointing the reader to a specific place instead of just saying this book might be useful to you that's not actually that helpful use result without F comment second one that will generically make your reader life more difficult because then they have to like do some pattern managing trying to figure out what here goes to what in there it's basically I you've already done the work why not give that to your reader absolutely [Music] absolutely I just have to wonder what what it was in three that was inspiring to and where in three it was at the least tell us where it was in three I guess like that's like analogously to and how about the five theorem 7 now you're being accurate but you might as well just put the actual text of the theorem yeah yeah it's it's it's what is it if I'm actually going to get something out of this I have to know what theorem 7 was you could say is like theorem blah Point BL this paper brackets five from five yeah right maybe maybe maybe before this there was a long text that explained what theorem 7 was and this five theorem 7 is just the reference but I don't think that's agreed so there I'm I'm just going back to the first one there is another issue uh here which um we haven't talked about yet which is that the purpose of citation is is not only for facts but also presentation and one possible motivation behind the the first citation is um if the author used those textbooks and based the background section very closely on the textbooks and the author put that citation in as a way to somehow indicate that the background section came from these textbooks that's not sufficiently informs the third one is so yeah what would exle a good way to do what is there is there good exle next that oh maybe let's see this is supposed to be good examples so that first one if from the textbook you're using the notation then that's it's more specific it makes clearer what you're taking sources yeah you can see that every one of these is is is more specific than anyone on the first slide really specificity is really essential you can refer to web sites um put down the URL and uh the practice I've seen is to have people give the date on which they accessed the web site typical um standard um so if we look at a paper online but it's published in the journal should you still side like the yeah then um um you that's a good good question um my practice is to give the journal entry and not not worry about the web [Music] presence but I've seen other people people do other things as well the exception might be if uh so sometimes what you find online is someone retyped the paper yeah yeah and you can tell because there are all sorts of typos in that case uh ideally you should go and find the original and site the original but for some reason you could then you would site the web page all right there's lots more to say uh right so this is a you're write this paper you'll write a first draft but that first draft won't really be your first draft because it'll be the product of a series of revisions in internal to your group uh everybody rewrites things over and over again you write something out and realize that the order could be done differently and if you have the time and the energy that's what you do is fix it um you're working as a team uh read each other's [Music] writing and and and um right if you can't read your others your teammates text then better believe that we can't read it either so the first draft is a first draft um but make it your best shot the final draft don't you know don't put the onus on us to fix things that you know how to fix but on the other hand um I can guarantee you that every single Paper is going to have suggested uh changes um you may not think that there are always improvements and that's fine we can have a discuss about that but uh but but but you'll always have there's always more to do and not just in the writing but uh part of the point of these um of these um um debriefings is to uh for us all to discuss what the mathematics is and there there may be some completion of the math as well that'll be suggested as part of the degre so it's not just more writing practice makes perfect or at least it makes better and uh the the skills of mathematical writing really um convey convert over they translate over to um all kinds of writing um being precise and organization and avoiding too much um padding okay uh any last minute questions so this is up on the web if you want to look at it some more there's also that essay about uh about math writing and some examples and there's plenty of material you if you uh have other ideas of things that should go up on the website by way of examples and things let me know