Marijuana persuasive essay

Back in the late 90s, in the process of marijuana persuasive essay reading for my MA dissertation, I put together a collection of hundreds of sentence frames that I felt could help me with my academic writing later on. College Review? And they did. Immensely. After the course was over, I stacked my sentences away, but kept wondering if I could ever put them to marijuana persuasive, good use and perhaps help other MA / PhD students. So here are 70 sentences extracted and adapted for from the original compilation, which ran for almost 10 pages. This list is organized around keywords. Before you start: 1. Pay close attention to the words in bold , which are often used in conjunction with the main word. 2. [ ] means “insert a suitable word here”, while ( ) means “this word is optional.” 3. Keep in mind that, within each group, some examples are slightly more formal / less frequent than others. b. There seems to be no compelling reason to an action research, argue that ___. c. Marijuana Persuasive Essay? As a rebuttal to essay on poverty alleviation, this point, it could be argued that ___. d. There are [three] main arguments that can be advanced to support ___. e. Marijuana Persuasive? The underlying argument in favor of / against [X] is that ___. a. In this [paper], I put forward the essay on poverty programmes claim that ___. c. Marijuana Persuasive Essay? There is ample / growing support for the claim that ___. e. Taking a middle-ground position, [X] claims that ___. a. An Action Research Thesis? The data gathered in the [pilot study] suggest that ___. b. The data appears to suggest that ___. c. The data yielded by this [study] provide strong / convincing evidence that ___. d. A closer look at the data indicates that ___. e. The data generated by [X] are reported in marijuana [table 1]. f. The aim of alleviation programmes this [section] is to generalize beyond the data and marijuana, ___. b. There has been an inconclusive debate about whether ___. c. College Essay Application Review Service? The question of whether ___ has caused much debate in [our profession] [over the years]. d. (Much of) the current debate revolves around ___. a. In this section / chapter, the discussion will point to ___. b. The foregoing discussion implies that ___. c. For the persuasive essay sake of discussion , I would like to argue that ___. d. On Creating The Future We Want? In this study, the marijuana persuasive essay question under discussion is ___. e. In this paper, the discussion centers on ___. f. [X] lies at the heart of the discussion on ___. a. The available evidence seems to suggest that ___ / point to ___. b. On the basis of the evidence currently available, it seems fair to suggest that ___. c. College Stuedents Buying Term? There is marijuana essay, overwhelming evidence for the notion that ___. d. Further evidence supporting / against [X] may lie in the findings of introduction [Y], who ___. e. These results provide confirmatory evidence that ___. a. I will now summarize the ground covered in this [chapter] by persuasive essay, ___. b. On logical grounds , there is no compelling reason to argue that ___. c. [X] takes a middle-ground position on [Y] and argues that ___. d. Stuedents Papers? On these grounds , we can argue that ___. e. [X]’s views are grounded on essay, the assumption that ___. a. Essay? This study is an attempt to address the issue of ___. b. In the present study, the issue under scrutiny is ___. c. The issue of marijuana essay whether ___ is clouded by the fact that ___. d. To portray the issue in [X]’s terms, ___. e. Given the centrality of this issue to [my claim], I will now ___. f. This [chapter] is concerned with the issue of [how/whether/what] ___. a. [X] is psychology apa research paper, prominent in the literature on [Y]. b. Persuasive? There is a rapidly growing literature on research, [X], which indicates that ___. c. Marijuana? The literature shows no consensus on [X], which means that ___. d. The (current) literature on [X] abounds with examples of ___. a. The main theoretical premise behind [X] is on poverty alleviation, that ___. c. [X] is premised on the assumption that ___. d. Essay? The basic premises of analysis essay [X]’s theory / argument are ___. e. The arguments against [X]’s premise rest on [four] assumptions: ___. a.This study draws on research conducted by marijuana persuasive essay, ___. b. Although there has been relatively little research on / into [X], ___. c. In the style analysis introduction last [X] years, [educational] research has provided ample support for the assertion that ___. d. Current research appears / seems to persuasive, validate the paper view that ___. e. Research on / into marijuana ___ does not support the view that ___. f. Further research in this area may include ___ and ___. g. Evidence for [X] is borne out by research that shows ___. h. There is insufficient research on / into ___ to draw any firm conclusions about essay review service peer, / on ___. a. The consensus view seems to be that ___. b. [X] propounds the marijuana persuasive essay view that ___. c. Current research (does not) appear(s) to validate such a view . d. Psychology Apa Research? There have been dissenters to the view that ___. e. The answer to [X] / The difference between [X] and [Y] is not as clear-cut as popular views might suggest. f. The view that _____ is in line with [common sense]. g. I am not alone in my view that ___. h. Marijuana Persuasive? [X] puts forward the view that ___. i. [X]’s views rest on the assumption that ___. If you found this list useful, check out The Only Academic Phrasebook You’ll Ever Need , which contains 600 sentences, as well as grammar and research, vocabulary tips. Marijuana Persuasive? E-book and paperback available on Amazon. 171 thoughts on “70 useful sentences for academic writing” This is incredible! Many, many thanks! I’ll start putting these into use immediately in college essay review peer my DipTESOL assignments. Higor, glad I could help. Um abraГ§o! Thanks for letting out such a list. Seems to be of great help. Great list, OtГЎvio! Thank you! You’re welcome, Eduardo! рџ™‚ Wonderful! It will help indeed! Thanks very much! Be sure to check out my e-book, too, which contains 600 sentences, as well as grammar and vocabulary tips:https://goo.gl/tAvU3P. This is very helpful, I wish I had known about this fabulous choice of marijuana persuasive essay words during my first year of graduate study. If you feel you need more help, check this out: Thanks, Luiz! This list is gonna be so useful! You’re welcome, Michele! What a marvelous list. Thanks for essay introduction, your generosity. Melanie, thank you! my friend i cant access this book from persuasive essay my country pakistan… can u please tell me another source. Really nice, Luiz. I particularly like ‘yielded’. I’ll definitely try to put them to good use during my next assignment. I remember teaching you “yielded” back in 1875, in MAC something. Maybe that’s why. рџ™‚ 1875? You’ve been around awhile. Wonderful Listing Dear Brother рџ™‚ Why were some alphabets left out papers, ? Sure there would have been a GR8 reason ! Am converting this into a ppt and marijuana, share it for many to more to access – hope no problems brother …. LOL n Laughter all the way from college stuedents buying Mumbai, INDIA. Thank you for dropping by. Marijuana Persuasive Essay? You can share the stuedents list with as many people as you like, of course. Please do acknowledge the marijuana source, though, ok? Maybe this will encourage more people to visit the blog. What a wonderful list, very much needed for EAP learners (not to mention any academic writer). Essay On Poverty? I’ll definitely make use of it. Thanks. рџ™‚ Tyson, thank you for your kind words. Marijuana Persuasive? Much appreciated! This is a great source and I will definitely use it in my current literature review class. My professor provide us with your Blog. I am very glad for two reasons, your Blog is a great source, and I think you are Brazilian ? I am from SГЈo Paulo, and psychology paper, as an International student I struggle written in marijuana English. Muito… muito obrigada pelas dicas. Thank you, Dora! Yes, I am Brazilian. Such a great work! It helps me to psychology paper, improve my English…Keep It Up. Data is the plural of datum. Therefore, it should read “The data appear…” Thanks for stopping by. Both usages are correct. Marijuana Persuasive Essay? If one treats “data” as a singular / mass noun, a singular noun should be used. Here’s what the Oxford Dictionary has to say: “In Latin, data is the plural of datum and, historically and in specialized scientific fields , it is also treated as a plural in college stuedents term English, taking a plural verb, as in the data were collected and classified . In modern non-scientific use, however , despite the complaints of marijuana traditionalists, it is often not treated as a plural. Instead, it is essay introduction, treated as a mass noun, similar to a word like information, which cannot normally have a plural and marijuana, which takes a singular verb. Stuedents? Sentences such as data was (as well as data were ) collected over a number of years are now widely accepted in standard English.” So I think it ultimately depends on the stylistic constraints of the piece of writing at hand and on persuasive, the norms adopted by the academic institution you’re writing for college stuedents, / on behalf of. But if history is anything to go by, I think very soon “datum” will be as rare as, for example, “agendum.” What a wonderful list: thank you for sharing. Persuasive Essay? I’m going (with your permission) to use it with my EAP class. Essay On Poverty Alleviation Programmes? I have other lists (including from the Manchester phrase bank) but this is a list of phrases that have been used rather than could be used. Christine, I appreciate your kind words. Of course you can use it! If you feel that your audience would profit from any of the stuff on this blog (aimed at teachers of English as a foreign language), please just say where the sentences were taken from, ok? Every little thing than can increase traffic helps! And you’re so right about the “what people do say” vs. “what people could say” dilemma. Before I put this list together, I made a point of essay googling each one to check its approximate frequency. This alone sifted out at stuedents buying term papers least half of my original list. Best regards from SГЈo Paulo, Brazil. These are invaluable, and they’ll be put to immediate use in ICELT tasks. Thanks a million! JГ©ssica, I’m so glad you’ll be able to marijuana persuasive essay, use some of college buying papers them. Um abraГ§o! Thanks a zillion for persuasive, sharing, Luiz! Assessors worldwide will be amazed at psychology apa research paper how much the marijuana quality of candidates’ writing has improved! hehehe. We sure hope so, right, MГЎrcia? рџ™‚ Thanks for stopping by. Thanks for putting this work together. I am preparing my readings for the Dissertation and in my collection your list of phrases will be useful. Very useful Christine and thanks for sharing. Thank you, Salma. What a fabulous resource for international students as well! Thank you. Cally, thank you! Just great! Thanks for sharing it. You’re welcome, Bruno! Thanks for sharing. Definitely I will use some ideas for my TEFL essay. Patricia, I’m glad you found the list helpful! Courageous, generous and much appreciated. Thank you for research, your kind words, Chris. Bonjour, English is not my first language and the information contained on this page helps me to construct proper essay sentences. Obrigada ! Bonjour, Denise. Marijuana Essay? As a non-native speaker myself, I know the feeling and stuedents buying, I’m glad I was able to help! thank you for this! it helps me tremendously рџ™‚ You seriously saved my life when I was writing a paper due the very next day. Essay? I have bookmarked it and an action research, it will be my go-to blog for future writing assignments! Thank you for marijuana persuasive, your contribution. Glad I could help, Johana! Thank you for college essay review peer, this- it is marijuana essay, fabulous! Really helpful tips for writing good research papers also useful to students of psychology literature. Essay? Great tips indeed. College Stuedents? I think these tips must be shared with every student of literature as there are lot many things they have to know. Thanks a lot. What an incredible work!! I will use it with my students рџ™‚ Thank you, Serena. Incredible! Senor Barros, thank you for sharing. I’ve never seen something like this before–good prompts for writing. Ken (ESL Teacher from Thailand) Thanks, Ken. I appreciate your feedback. These sentences are Fantabulous…. Persuasive? (Thumbs Up For You) Completely agree. The Future? Fantastic expressions. Gonna have to study them for some upcoming papers!! Luizo, it was really generous of marijuana you to essay alleviation programmes, have shared such a useful collection. English is my third language and was I having difficulty writing my dissertation. Hopefully your gift will help. I cannot thank you enough. Persuasive? I hope one day I too can help by uploading something this useful, free. Psychology Apa Research? You are a saint. your sentences are great I am going to use them as much as possible. Рќighly descriptive post, I lС–ked that a lot. Will there. 10000 times thanks. Thank you a lot for marijuana persuasive essay, sharing these useful and practical verbs and phrases ! Habib, glad I could help! Nice Work! Exactly what I was looking for essay, classroom debates! Honestly, I would seriously LOVE to persuasive essay, see the essay on poverty alleviation original 10 page list. Thank you so much – you have just saved me hours of trying to make my Masters assignment sound convincing! Thanks for what you’ve done Luiz… And give a try at marijuana updating the list, if possible. Thank you alto, this is a great list. I prepare for TOEFL but my writing is essay on creating, awful, I hope by using this list it improve. Can I send my writing to you? The list is really wonderfully helpful for any teacher or student in writing a dissertation. Thank you so much are very goods to my tesis. THANKS FOR HELPING PEOPLE. Thanks so much for your generosity. Essay? Just about to embark upon my MA dissertation and feeling very insecure, nervous and low in confidence: the cosmic kick in the bottom, desperately needed! This is an college essay, awesome collection dude! I was looking something like this for my writing in TOEFL test! Thanks for the list! It’ll really give me a boost for marijuana persuasive, my future works! Thank you very much. It is very helpful. thank you for the list, most helpful. Luella. i been using these for a yr and my grades incresed dramatically now i have got an op 2 i can’t thank u enough for these thank u. This is very useful. IF I rate it I will 10. On Creating The Future? But I hope u will also common phrases that commonly use in school reporting. Btw, I am a filipino. This is essay, brilliant! thanks! Thank you so much. Great work. Thanks, I find many of the phrases very useful for my own work. However, I see in general a tendency of being too wordy. This probably depends somewhat on essay alleviation, the branch of science you’re working in. For example, a phrase such as “The available evidence seems to suggest that” uses two hedges (suggest, seem) to persuasive, mitigate the strength of “evidence”). If there’s a lot of such phrases in a paper, the psychology apa research paper readers just won’t believe what your saying. First, I would like to say thank you so much for marijuana persuasive, helpful idea and psychology, I really need to marijuana persuasive essay, improve me academic English vocabulary but I t is still problem to improve it. Who will help me that. Very good work and can be updated to help postgraduate students in an action their writing. Thank you! There’s some exciting news on the horizon, Abdulghadar. Stay tuned! I find the marijuana essay examples very helpfu and would like to have your permission to essay on poverty alleviation, share these information for my students please. Juliana,check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. What a great list, greetings from marijuana persuasive Poland! Titoszka,check out style essay, “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. These phrases are going to be very very very useful for me… Thanks a lot. Akshita,check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Thank you very much, these sentences will help a lot. Thank again. Djibril,check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Thank u so much:) Thank you for this list. I m sharing it with my friends right now. It’s a great source of essay good wordings))) Anastasia,check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Hey this source is great! Thanks for sharing. Jen,check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. A brilliant resource for teaching academic writing, thank you! Sharon,check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. It is perfect list! Thanks a lot. Glad you found it useful! Kostas, check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Dear LUIZ OTГЃVIO, Nice list, It could be much greater If you could add any other vocabulary to use for academic writing in you blog. Dear Professor Avinash, check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Luiz your list is a time saver. you are very thoughtful. Thank you! Diana,check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Thank you so much for analysis introduction, posting this list, I’ve been using it for marijuana persuasive, last 3 years of my uni! Mac, check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Ottotito, check out essay on poverty alleviation programmes, “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. from Saudi Arabia, i would like a to thank you for those great expressions LUIZ, I admit using some of essay them to improve my daily English Emails as well рџ™‚ Majed, check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Dear Louiz, I am writing my PhD proposal and this is just what I need. Thanks a lot. Marie, check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Thanks a lot. It is essay introduction, very useful. Scorneo, check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Thanks a lot. It is very useful… This is what I am looking for !! Thank you so much.. I will use them in may graduation research .. Hela, check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Thank you for sharing your superb list! Naz,check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Thanks a lot. It is very useful. Kasra, check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Thank you so much, i am using your sentences in my thesis. Minoo,check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Thank you for your help you realy helped me interms of marijuana persuasive essay academic work.please now will you help me on psychology, prepositions?this is when am learning English. Hi Micheal, check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZ. I heaved a sigh of relief. Marijuana Persuasive? Because this is my major struggle in essay we want writing academic papers. Remain blessed for sharing. Blossom, check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Luiz, this is AWESOME! I’m so grateful for this. Currently I’m roasting over my dissertation and this prompts lubricate the brain and neuro pathways. Thank you so much for marijuana, your generosity. Essay On Poverty? Blessings to you! Sarah, check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Sarah, check out: “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. im impressed Luiz. Thank you. Check out “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published: http://goo.gl/3frFZW. Sharing this list with my IELTS students in 3, 2, 1… Thanks, Jorge. For those who want more sentences + grammar and vocabulary tips, you can also recommend “The Only Academic Phrasebook You’ll Ever Need”, which I’ve just published. It’s available on Amazon: http://goo.gl/3frFZW. Thank you. This is a bookmarked item. Be sure to check out my e-book, too: It contains 600 sentences, as well as grammar and vocabulary tips. A thousand million thanks. You’re welcome, Pat! If you feel you need more help, check this out: 5 bucks only and it contains 600 sentences + lots of grammar and persuasive essay, vocabulary tips. This seems a lot like the book They Say, I Say which was first published in 2006. Hi Joelle. Thanks for the reference. Just checked a sample on Amazon. Seems like a great book. College Stuedents Buying Term? The sentences above, however, are all formal. As far as I could tell, They Say, I Say includes a number of more neutral “templates” that students can use, say, in high school essays. E-book is not available.. only the paperpack рџ™Ѓ This is good, it will really help in preparing my research manuscripts for publication. Glad you find it useful! Yo have no idea how much I use this page for marijuana persuasive essay, my papers. Buying Term Papers? Special thanks to you! I’m glad you find it useful! Thanks a lot for your tremendous work, it is helpful and sophisticated. May you be rewarded. Found the compilation very helpful. kudos! Thank you, Abdus. Great list! You have just saved my Final degree project. I’m non-native English speager, and taking writing class. it really helped alot. Thanks.

September 12, 1995. Section 1: Introduction: Why bother? Good mathematical writing, like good mathematics thinking, is a skill which must be practiced and developed for optimal performance. The purpose of this paper is to provide assistance for young mathematicians writing their first paper. Marijuana! The aim is not only to aid in the development of a well written paper, but also to we want, help students begin to persuasive essay, think about mathematical writing. I am greatly indebted to style, a wonderful booklet, "How to Write Mathematics," which provided much of the substance of this essay. I will reference many direct quotations, especially from the section written by marijuana, Paul Halmos, but I suspect that nearly everything idea in this paper has it origin in my reading of the booklet. It is available from the American Mathematical Society, and serious students of mathematical writing should consult this booklet themselves. Most of the other ideas originated in my own frustrations with bad mathematical writing. Although studying mathematics from bad mathematical writing is not the best way to learn good writing, it can provide excellent examples of procedures to be avoided. Thus, one activity of the active mathematical reader is to note the places at which a sample of written mathematics becomes unclear, and to avoid making the same mistakes his own writing. Mathematical communication, both written and spoken, is the college application review, filter through which your mathematical work is viewed. If the creative aspect of mathematics is compared to marijuana persuasive essay, the act of composing a piece of music, then the art of essay on creating we want writing may be viewed as conducting a performance of that same piece. As a mathematician, you have the privilege of conducting a performance of your own composition! Doing a good job of persuasive essay conducting is just as important to the listeners as composing a good piece. An Action Thesis! If you do mathematics purely for your own pleasure, then there is no reason to write about it. If you hope to persuasive, share the beauty of the mathematics you have done, then it is not sufficient to we want, simply write; you must strive to write well . This essay will begin with general ideas about mathematical writing. The purpose is to help the essay, student develop an outline for the paper. The next section will describe the difference between "formal" and "informal" parts of a paper, and give guidelines for each one. Section four will discuss the writing of an individual proof. The essay will conclude with a section containing specific recommendations to an action, consider as you write and rewrite the paper. Section 2. Before you write: Structuring the paper. The purpose of nearly all writing is to essay, communicate. In order to communicate well, you must consider both what you want to communicate, and to whom you hope to alleviation, communicate it. This is no less true for mathematical writing than for any other form of persuasive writing. The primary goal of mathematical writing is to assert, using carefully constructed logical deductions, the essay on creating the future, truth of a mathematical statement. Careful mathematical readers do not assume that your work is well-founded; they must be convinced. This is your first goal in mathematical writing. However, convincing the reader of the simple truth of your work is not sufficient. When you write about your own mathematical research, you will have another goal, which includes these two; you want your reader to appreciate the beauty of the essay, mathematics you have done, and to understand its importance. If the whole of mathematics, or even the subfield in which you are working, is thought of as a large painting, then your research will necessarily constitute a relatively minuscule portion of the entire work. Service Peer! Its beauty is seen not only in the examination of the specific region which you have painted (although this is important), but also by marijuana persuasive essay, observing the way in which your own work 'fits' in college essay application review peer, the picture as a whole. These two goals--to convince your reader of the truth of your deductions, and to allow your audience to see the beauty of your work in relation to essay, the whole of mathematics--will be critical as you develop the application review peer, outline for persuasive essay your paper. At times you may think of yourself as a travel guide, leading the reader through territory charted only by you. A successful mathematical writer will lay out for her readers two logical maps, one which displays the connections between her own work and the wide world of mathematics, and application peer, another which reveals the internal logical structure of persuasive her own work. In order to advise your reader, you must first consider for yourself where your work is located on the map of mathematics. If your reader has visited nearby regions, then you would like to stuedents term, recall those experiences to his mind, so that he will be better able to understand what you have to add and to connect it to related mathematics. Asking several questions may help you discern the shape and location of your work: Does your result strengthen a previous result by persuasive essay, giving a more precise characterization of something? Have you proved a stronger result of an old theorem by weakening the hypotheses or by strengthening the conclusions? Have you proven the equivalence of two definitions? Is it a classification theorem of structures which were previously defined but not understood? Does is term papers, connect two previously unrelated aspects of mathematics? Does it apply a new method to an old problem? Does it provide a new proof for persuasive an old theorem? Is it a special case of a larger question? It is necessary that you explicitly consider this question of placement in the structure of mathematics, because it will linger in your readers' minds until you answer it. Style! Failure to address this very question will leave the reader feeling quite dissatisfied. In addition to providing a map to help your readers locate your work within the field of mathematics, you must also help them understand the internal organization of your work: Are your results concentrated in one dramatic theorem? Or do you have several theorems which are related, but equally significant? Have you found important counterexamples? Is your research purely theoretical mathematics, in the theorem-proof sense, or does your research involve several different types of activity, for example, modeling a problem on the computer, proving a theorem, and then doing physical experiments related to your work? Is your work a clear (although small) step toward the solution of a classic problem, or is it a new problem? Since your reader does not know what you will be proving until after he has read your paper, advising him beforehand about what he will read, just as the travel agent prepares his customer, will allow him to enjoy the trip more, and to understand more of the things you lead him to. To honestly and deliberately explain where your work fits into the big picture of mathematical research may require a great deal of persuasive humility. You will likely despair that your accomplishments seem rather small. Buying Papers! Do not fret! Mathematics has been accumulating for thousands of years, based on the work of thousands (or millions) of practitioners. Essay! It has been said that even the best mathematicians rarely have more than one really outstanding idea during their lifetimes. The Future! It would be truly surprising if yours were to come as a high school student! Once you have considered the structure and marijuana persuasive essay, relevance of your research, you are ready to outline your paper. The accepted format for research papers is much less rigidly defined for mathematics than for many other scientific fields. You have the latitude to develop the outline in a way which is appropriate for your work in particular. However, you will almost always include a few standard sections: Background, Introduction, Body, and Future Work. The background will serve to psychology, orient your reader, providing the first idea of where you will be leading him. In the background, you will give the most explicit description of the history of persuasive essay your problem, although hints and references may occur elsewhere. The reader hopes to have certain questions answered in this section: Why should he read this paper? What is the an action research, point of this paper? Where did this problem come from? What was already known in this field? Why did this author think this question was interesting? If he dislikes partial differential equations, for example, he should be warned early on that he will encounter them. If he isn't familiar with the first concepts of probability, then he should be warned in advance if your paper depends on that understanding. Remember at this point that although you may have spent hundreds of hours working on persuasive essay your problem, your reader wants to have all these questions answered clearly in a matter of minutes. In the second section of your paper, the introduction, you will begin to lead the reader into psychology, your work in particular, zooming in from the big picture towards your specific results. This is the place to introduce the definitions and lemmas which are standard in the field, but which your readers may not know. The body, which will be made up of marijuana several sections, contains most of your work. By the style, time you reach the final section, implications, you may be tired of your problem, but this section is critical to your readers. You, as the world expert on the topic of your paper, are in a unique situation to persuasive, direct future research in your field. A reader who likes your paper may want to essay introduction, continue work in your field. Persuasive Essay! (S)he will naturally have her/his own questions, but you, having worked on this paper, will know, better than your reader, which questions may be interesting, and which may not. If you were to continue working on this topic, what questions would you ask? Also, for some papers, there may be important implications of your work. If you have worked on a mathematical model of a physical phenomenon, what are the consequences, in the physical world, of your mathematical work? These are the questions which your readers will hope to have answered in the final section of the paper. The Future! You should take care not to disappoint them! Section 3. Formal and Informal Exposition. Once you have a basic outline for your paper, you should consider "the formal or logical structure consisting of definitions, theorems, and proofs, and the complementary informal or introductory material consisting of motivations, analogies, examples, and marijuana essay, metamathematical explanations. Essay Alleviation! This division of the material should be conspicuously maintained in persuasive, any mathematical presentation, because the nature of the subject requires above all else that the research, logical structure be clear." (p.1) These two types of persuasive material work in parallel to enable your reader to understand your work both logically and cognitively (which are often quite different--how many of you believed that integrals could be calculated using antiderivatives before you could prove the on creating, Fundamental Theorem of Calculus?) "Since the formal structure does not depend on the informal, the author can write up the former in complete detail before adding any of the latter." (p. 2) Thus, the next stage in the writing process may be to develop an outline of the marijuana, logical structure of your paper. Several questions may help: To begin, what exactly have you proven? What are the lemmas (your own or others) on research which these theorems stand. Which are the corollaries of these theorems? In deciding which results to call lemmas, which theorems, and which corollaries, ask yourself which are the central ideas. Which ones follow naturally from others, and which ones are the marijuana essay, real work horses of the college application review peer, paper? The structure of writing requires that your hypotheses and deductions must conform to a linear order. However, few research papers actually have a linear structure, in persuasive essay, which lemmas become more and more complicated, one on top of thesis another, until one theorem is persuasive, proven, followed by alleviation programmes, a sequence of increasingly complex corollaries. On the contrary, most proofs could be modeled with very complicated graphs, in which several basic hypotheses combine with a few well known theorems in a complex way. There may be several seemingly independent lines of reasoning which converge at the final step. It goes without saying that any assertion should follow the lemmas and theorems on which it depends. Persuasive! However, there may be many linear orders which satisfy this requirement. In view of this difficulty, it is programmes, your responsibility to, first, understand this structure, and, second, to arrange the necessarily linear structure of your writing to reflect the marijuana, structure of the work as well as possible. The Future! The exact way in which this will proceed depends, of course, on the specific situation. One technique to assist you in revealing the persuasive, complex logical structure of your paper is a proper naming of results. By naming your results appropriately (lemmas as underpinnings, theorems as the on poverty alleviation programmes, real substance, and corollaries as the finishing work), you will create a certain sense of parallelness among your lemmas, and help your reader to appreciate, without having struggled through the research with you, which are the really critical ideas, and persuasive, which they can skim through more quickly. Another technique for developing a concise logical outline stems from a warning by Paul Halmos, in HTWM, never to buying papers, repeat a proof: If several steps in marijuana essay, the proof of essay Theorem 2 bear a very close resemblance to parts of the proof of Theorem 1, that's a signal that something may be less than completely understood. Other symptoms of the marijuana persuasive, same disease are: 'by the same technique (or method, or device, or trick) as in the proof of Theorem 1. ', or, brutally, 'see the proof of Theorem 1'. When that happens the chances are very good that there is a lemma that is worth finding, formulating, and proving, a lemma from the future we want, which both Theorem 1 and persuasive essay, Theorem 2 are more easily and more clearly deduced. (p. 35) These issues of structure should be well thought through BEFORE you begin to write your paper, although the process of research thesis writing itself which surely help you better understand the structure. Now that we have discussed the marijuana persuasive essay, formal structure, we turn to the informal structure. The formal structure contains the formal definitions, theorem-proof format, and rigorous logic which is the language of 'pure' mathematics. The informal structure complements the formal and runs in psychology, parallel. Persuasive Essay! It uses less rigorous, (but no less accurate!) language, and plays an important part in elucidating both the mathematical location of the psychology apa research paper, work, as we discussed above, and in presenting to the reader a more cognitive presentation of the work. Persuasive! For although mathematicians write in the language of essay on creating the future we want logic, very few actually think in the language of persuasive essay logic (although we do think logically), and so to understand your work, they will be immensely aided by subtle demonstration of why something is true, and on poverty, how you came to marijuana persuasive essay, prove such a theorem. Outlining, before you write, what you hope to communicate in these informal sections will, most likely, lead to more effective communication. Before you begin to write, you must also consider notation. The selection of notation is a critical part of writing a research paper. In effect, you are inventing a language which your readers must learn in order to thesis, understand your paper. Good notation firstly allows the reader to forget that he is learning a new language, and marijuana, secondly provides a framework in which the essentials of essay the future we want your proof are clearly understood. Marijuana Essay! Bad notation, on the other hand, is disastrous and may deter the reader from even reading your paper. College Stuedents Papers! In most cases, it is wise to follow convention. Using epsilon for a prime integer, or x(f) for a function, is certainly possible, but almost never a good idea. Section 4: Writing a Proof. The first step in writing a good proof comes with the marijuana essay, statement of the style analysis, theorem. A well-worded theorem will make writing the proof much easier. The statement of the theorem should, first of essay all, contain exactly the right hypotheses. Of course, all the necessary hypotheses must be included. On the other hand, extraneous assumptions will simply distract from the point of the theorem, and paper, should be eliminated when possible. When writing a proof, as when writing an entire paper, you must put down, in marijuana, a linear order, a set of hypotheses and deductions which are probably not linear in form. I suggest that, before you write you map out the hypotheses and the deductions, and attempt to order the statements in a way which will cause the least confusion to the reader. In HTWM, Halmos offers several important recommendations about introduction writing proofs: 1. Write the proof forward. A familiar trick of bad teaching is to begin a proof by saying: "Given e, let d be e/2". This is the traditional backward proof-writing of classical analysis. It has the advantage of persuasive being easily verifiable by college application review peer, a machine (as opposed to understandable by a human being), and marijuana, it has the college term, dubious advantage that something at the end comes out to marijuana persuasive essay, be less than e. The way to make the human reader's task less demanding is college stuedents papers, obvious: write the proof forward. Start, as the author always starts, by putting something less than e, and then do what needs to marijuana essay, be done--multiply by 3M2 + 7 at the right time and essay application peer, divide by 24 later, etc., etc.--till you end up with what you end up with. Neither arrangement is elegant, but the persuasive essay, forward one is graspable and rememberable. (p. 43) 2. College Buying Term! Avoid unnecessary notation. Marijuana Persuasive Essay! Consider: a proof that consists of a long chain of expressions separated by equal signs. Such a proof is easy to write. The author starts from the first equation, makes a natural substitution to get the second, collects terms, permutes, inserts and immediately cancels an inspired factor, and by steps such as these proceeds till he gets the last equation. This is, once again, coding, and the reader is analysis essay introduction, forced not only to learn as he goes, but, at the same time, to decode as he goes. The double effort is needless. By spending another ten minutes writing a carefully worded paragraph, the author can save each of his readers half an hour and a lot of confusion. Marijuana! The paragraph should be a recipe for action, to replace the unhelpful code that merely reports the college buying papers, results of the act and leaves the reader to guess how they were obtained. The paragraph would say something like this: "For the proof, first substitute p for persuasive q, the collect terms, permute the factors, and, finally, insert and essay on poverty alleviation, cancel a factor r. (p. 42-43) Section 5. Specific Recommendations. As in any form of communication, there are certain stylistic practice which will make your writing more or less understandable. These may be best checked and corrected after writing the marijuana persuasive, first draft. Many of essay on poverty alleviation these ideas are from HTWM, and are more fully justified there. Notation that hasn't been used in several pages (or even paragraphs) should carry a reference or a reminder of the meaning. The structure should be easily discernible by headings and punctuation. There should be a clear definition of the problem at hand all the way through. The title is the first contact that readers will have with your paper. It must communicate something of the substances to the experts in your field as well as to the novices who will be interested. Thus, while the terminology should be technically correct "Don't over work a small punctuation mark such as a period or comma. They are easy for the reader to overlook, and the oversight causes backtracking, confusion, delay. Example: "Assume that aÂX. X belongs to the class C, . ". The period between the two X's is marijuana persuasive, overworked. A good general rule is: never start a sentence with a symbol. College Essay Application! If you insist on starting the sentence with a mention of the marijuana persuasive essay, thing the symbol denotes, put the appropriate word in apposition, thus: "The set X belongs to the class C, . An Action! ". The overworked period is persuasive, no worse than the overworked comma. Not "For invertible X, X* also is invertible", but "For invertible X, the adjoint X* also is invertible." (p. 44) "I recommend "then" with "if" in all mathematical contexts. The presence of "then" can never confuse; its absence can."(p.44) Another critical feature is the layout or architecture of the page. "If it looks like solid prose, it will have a forbidding, sermony aspect; if it looks like computational hash, with a page full of symbols, it will have a frightening, complicated aspect. The golden mean is golden. Break it up, but not too small; use prose, but not too much. Intersperse enough displays to give the eye a chance to help the on creating, brain; use symbols, but in essay, the middle of enough prose to keep the mind from drowning in a morass of suffixes." (p. 44-5) The same symbol should never be used for more than one thing; if you have used n as a counter in one proof, use m in the next proof, unless the two play a similar role in each All notation should be meaningful (no free variables): "avoid the essay we want, use of marijuana persuasive essay irrelevant symbols. Example: "On a compact space every real-valued continuous function f is bounded." What does the symbol "f" contribute to the clarity of essay we want that statement. A showy way to say "use no superfluous letters" is to say "use no letter only once". (p. 41) "In everyday English "any" is an ambiguous word; depending on context that may hint at an existential quantifier ("have you any wool?", "if anyone can do it, he can") or a universal one ("any number can play"). Conclusion: never use "any" in mathematical writing. Persuasive! Replace it by "each" or "every", or recast the on poverty programmes, whole sentence" (p. 38) "Other offenders, charged with lesser crimes, are 'where', and 'equivalent', and 'if. then. if. then'. Marijuana! "Where" is usually a sign of a lazy afterthought that should have been thought through before. "If n is sufficiently large, then | an | < e, where e is a preassigned positive number"; both disease and cure are clear. "Equivalent" for theorems is logical nonsense. (By "theorem" I mean a mathematical truth, something that has been proved. Research! A meaningful statement can be false, but a theorem cannot; "a false theorem" is self-contradictory). As for "if. then. if. then", that is just a frequent stylistic bobble committed by quick writers and rued by persuasive, slow readers. "If p , then if q , then r ." Logically, all is essay the future, well, but psychologically it is just another pebble to stumble over, unnecessarily. Usually all that is needed to persuasive, avoid it is to recast the buying term papers, sentence, but no universally good recasting exists; what is best depends on essay what is important in the case at hand. It could be "If p and q then r ", or "In the style introduction, presence of p , the hypothesis q implies the conclusion r ", or many other versions."" (p. 38-39) Use counter-examples to demonstrate the necessity of conditions on marijuana theorem Use words correctly: distinguish between function and value.