軍隊文職考研數(shù)學_軍隊文職考試

解放軍文職招聘考試考研短文寫作總論-解放軍文職人員招聘-軍隊文職考試-紅師教育

（1）考官閱卷規(guī)律考研作文的讀者是閱卷考官，因此充分掌握考官的閱讀和評分心理是我們制勝的一大法寶。那么，閱卷考官在評分過程中都會呈現(xiàn)出什么樣的特點呢？具體的注意事項總結如下：（2）英文作文的行文特點和思維模式美國一位著名的語言學家Kaplan曾經(jīng)在20世紀70年代作過一項關于在美國的本土學生、亞洲學生和阿拉伯學生在寫英文作文中體現(xiàn)出的思維方式及其背后的文化影響的調查，并發(fā)表了一篇著名的論文，提出了三種思維模式引發(fā)的寫作模型。雖然考研作文的閱卷考官們大部分都是中國人，但是他們的英語水平都很高、造詣也很深，對于英文的行文規(guī)律了如指掌。因此，考生要盡量學會英文的寫作模式，尤其要重視主題句的作用。簡單來說，英文議論文的行文有以下特點：1、結構分明、意圖明確。2、扣緊主題、切勿離題。3、句子不必過長，嚴防語法錯誤。4、適量引用名人名言、成語諺語。5、用清晰的語言指出問題。6、使用更多的連接詞。（3）圖畫作文和圖表作文的寫作策略我們認為，接下來幾年的研究生考試中，圖畫作文出現(xiàn)的概率遠遠大于圖表作文?？忌匾晥D畫作文的能力訓練，但是也不能完全忽略圖表作文。下文將具體闡述應對這兩種作文形式的要點和攻略。一、圖畫+提綱作文圖畫作文往往給出的是一幅簡潔明了的照片、圖片或者漫畫，要求考生將圖畫轉變成為文字形式。盡管中國學生從小學開始就接受了看圖作文的系統(tǒng)訓練，但是我們不能因此掉以輕心。首先，英文看圖作文和中文看圖作文的模式和思維體系是不同的。其次，考研作文的圖畫選擇都是含有豐富的寓意的，對考生提出了 把握寓意、聯(lián)系現(xiàn)實、深刻思考、豐富表達 等一系列較高的要求。我們認為攻克圖畫作文的關鍵在于仔細分析、觀察細節(jié)。雖然考研寫作時間非常緊張，但是花2-3分鐘細心觀察圖畫是具有決定性意義的。觀察圖畫的同時可以在草稿紙上作相應的筆記：1、寫出你認為圖畫中反映的是一個什么樣的社會現(xiàn)象和問題；2、簡單寫下圖畫中的一些細節(jié)，如2001年作文中的蠟燭燭光是以一個笑臉的形式體現(xiàn)出來的。迅速分析這些細節(jié)，標明哪些是重點、哪些是次重點、哪些無關緊要，在寫作的時候便能夠自如把握需要詳細描述的信息。3、查漏補缺。檢查是否有遺漏的信息，因為越是簡單的圖畫就越容易使人忽略一些細節(jié)。例如在2005年的圖畫中，如果仔細觀察可以發(fā)現(xiàn)，是大兒子把父親踢了出來，而其他幾個兒女是做防守動作，防止老父被踢到自己的球門。當然在發(fā)現(xiàn)遺漏的信息之后也需要進一步判斷是否需要將這一信息加入自己的作文中。需要說明的是，我們這里指的提綱不是考題中已經(jīng)給出的提綱，而是根據(jù)考題的提綱寫出自己的行文思路、大意和要點等。接下來就是正式的寫作步驟。我們來詳細分析一下三段的具體寫作要點（我們在本書的 高分句型 和 萬能模版 部分將分別提供對每一個段落行之有效的句型和模版）：1、第一段主要是描述圖畫中的信息和表達的含義?？忌诘谝痪湓捴袘撻_門見山地說明圖畫中談論的是什么事情；第二句話進一步描述細節(jié)、但不要用于第一句話相同的表達方式；第三句話點明圖畫的象征意義。注意點：如果圖中有中文說明的話，要盡量將中文句子譯出或者以其他方式表達出來。但切忌生硬地翻譯中文，如1998年作文中的那首打油詩就沒有必要翻譯出來。2、第二段的全文的重點，一般都是要求具體分析圖畫中暗含的社會現(xiàn)象?？忌谔岢鲆粋€總論點之后，可以通過 firstly, secondly, thirdly 等形式提出分支論點，進行詳細闡發(fā)。在論證過程中可以采用并列論證、對比論證、舉例論證、邏輯論證等方式。注意點：第二段和第三段的開頭最好寫一個主題句，既可以防止離題，又符合英文寫作的習慣。同時，全文的段與段之間、句與句之間做好銜接和過渡的工作。二、圖表+ 提綱作文考研作文已經(jīng)出現(xiàn)過的圖表作文包括1997年的柱狀圖（bar chart）和餅狀圖（pie chart），1999年的曲線圖（line chart / line graph）。其它常見的圖表還包括表格（table）、流程圖（flow chart）等。在進行寫作之前，我們同樣要觀察和分析圖表。此時我們需要帶著問題去觀察：這個圖表或者這組圖表是關于什么內容的；圖表中有哪些具體項目組成、分別有什么作用和含義；圖表中有哪些重要數(shù)據(jù)（可以用鉛筆在圖中圈出）；如何分析這些數(shù)據(jù)，是把重點放在數(shù)據(jù)本身，還是重點分析數(shù)據(jù)變化的趨勢。如果是一組圖表，還要分析彼此之間有什么樣的關聯(lián)；如果從圖表中得出一個中心思想或者主題句。接下來的幾個寫作步驟可以參考上文關于圖畫作文的分析，具體包括列提綱和如何組織三段論、以及最后的檢查和修改等。此外，針對圖表作文的特點，我們還提出了以下一個注意點：1、不同的圖表本身就暗示了考生應該關注的分析點。如柱狀圖和曲線圖重點在于指出變化趨勢，而餅狀圖則側重于各個部分的數(shù)值和所占百分比、即體現(xiàn)了整體和局部的關系，流程圖在于過程和各個階段的不同情況。以上四種圖表一般都會有說明文字，如橫坐標和縱坐標上的說明等，需要格外關注。表格的難度相對要更高，需要考生自己找出重點數(shù)據(jù)、并仔細觀察數(shù)據(jù)來發(fā)現(xiàn)變化和趨勢等。無論哪種形式的圖表，考生萬勿簡單地羅列數(shù)據(jù)和信息，因為考研作文考察的重點是分析能力。2、要密切關注圖表上一些重點區(qū)位，如果曲線的峰值、谷值、突然的轉折，曲線的交匯點。其它圖表中數(shù)值的極值，數(shù)據(jù)或者百分比大幅度增加或者減少的地方等等，這些往往都是圖表暗含的中心意思所在。3、圖表寫作的事態(tài)采用一般現(xiàn)在時，如果題目中有具體關于過去和將來時間的提示，則根據(jù)情況采用過去時和將來時。4、圖表的描述也有一些固定的表達法，考生需要在平時練習中積累（本書 高分句型 部分也提供了豐富的表達法）。5、由于圖表往往提供了比圖畫更加豐富的信息，考生需要提高鑒別分析信息的能力，找出最重要的數(shù)據(jù)。由于數(shù)據(jù)繁多，也更容易遺漏，所以最后的查漏補缺工作也顯得尤其重要。（4）寫作注意事項u詞匯英語寫作講究用詞準確而且正式。同時，英語的詞匯非常豐富，一個詞語通常都有許多同義詞和近義詞。考生如果平時注意積累并加以練習，就能夠熟練在考試中運用。下面我們舉一些英語詞匯變化的例子。help out assist; set up to establish; go up increase;cut down reduce; find out determine; look into investigate;bring up raise; come up with create; go up and down fluctuategood considerable; get obtain; a lot of numerous;things that will happen consequencesu語法英文寫作非常講究語法，尤其是考研作文作為正式文體，需要注意以下幾點小細節(jié)：1、盡量少用縮寫形式。如don t, can t, won t寫做do not, cannot, will not等。2、用更加正式的否定形式。如not any寫做no, not much 寫做 little, not many 寫做few等。例如：He did notsay anywords.He said nowordsThere are not manychances available.There are fewchances available.3、盡量少用 etc. , and so on 等表達方式。例如：Activities include dancing, singing, etc.Activities include dancing, singing, and other fun stuff.4、盡量把副詞和動詞放在一起。例如：Consequentlywe may arrive at the conclusion thatWe may consequentlyarrive at the conclusion thatu標點英語中沒有頓號，在漢語需要頓號的情況下可以用逗號。漢語中的引言通常都是： 的格式，而英語中不用冒號，用逗號，如, .u常用程度和語句副詞常用的程度副詞包括：absolutely, almost, awfully, completely, considerably, deeply, entirely, exactly, extremely, fairly, greatly, hardly, immensely, increasingly, more and more, much, nearly, partly, perfectly, profoundly, quite, rather, scarcely, slightly, somehow, somewhat, thoroughly, to some extent, utterly, very.常用語句副詞包括：actually, admittedly, certainly, clearly, definitely, evidently, fortunately, frankly, honestly, luckily, more importantly, naturally, surprisingly, obviously, perhaps, preferably, probably, possibly, strangely, superficially, surely, technically, theoretically, undeniably, unexpectedly, unfortunately.u常用邏輯連接詞因果關系： and so ; another important factor/reason ; as a consequence; as a result; as; because; because of; being that; consequently; due to; for the reason that; for the same reason; for; hence; for this reason; in consequence; in that ; in view of; owing to; since; so; so that ; the reason seems obvious; there are about ; therefore; thus; obviously; evidently并列關系：and; also; as well as; both and ; either or ; neither nor ; not only but also ; in the same way; too序列關系: first , second , third , and so forth; A , B , C , and so forth; next; then; following this; at the same time; now; at this point; after; afterwards; subsequently; finally; previously; before this; simultaneously; concurrently; thus; therefore; hence; next; and then; soon遞進關系：accordingly; as a popular saying goes ; as far as is concerned; at the same time; besides; even; further; furthermore; in addition; in order to ; in other words; in the first place , in the second place ; in this way; meanwhile; moreover; not only , but also ; not but ; lastly; for one thing , for another時空關系：afterwards; as soon as; at least; before; eventually; every; first; first of all; first and foremost; for a start; meanwhile; in the meantime; while; now; next; not until; later; formerly; previously; prior to; since then; since; subsequently; till; to begin with; to start with; when; then轉折關系：yet; but; unless; despite that; in spite of; though; although; although this may be true; even so; even though; however; sometimes; once in a while; independent of; reckless of; regardless of條件關系：as long as; even if; even though; if it necessary; if not all; if possible; if so; if; lest; once; provided that; unless重復關系：in brief; as I have said; as I have noted; as has been noted; as is mentioned above比較關系：apart from; by the same token; compared with; in comparison with; in the same vein; like; likewise; rather than; similarly; similarly important; equally; when compared with; when in fact舉例關系：a good example would be; for example; for instance; in this case; in anothercase; on this occasion; in this situation; take the case of; to demonstrate; to illustrate; accordingto; as an illustration; as for; as regards; as to; in particular; including; namely; notably; such as; like; take as an example; you may say對比關系：after all; as opposed to; balanced against; up against; vis a vis; where; conversely; on the one hand on the other hand ; contrary to; conversely unlike; different from this; however; in contrast; nevertheless; on the contrary; oppose to; whereas; while強調關系：definitely; extremely; obviously; absolutely; positively; naturally; surprisingly; always; forever; perennially; eternally; emphatically; never; unquestionably; without a doubt; certainly; surely; undeniably; without reservation; believe it or not; especially; particularly; in particular; specifically; in fact; as a matter of fact; actually; in deed; moreover; not to mention ; what is more important; notably; that is;總結關系：accordingly; altogether; as a result; consequently; hence; in one word; in brief; in short; in other words; in summary; on the whole; in conclusion;overall; the conclusion can be safely drawn that ; therefore; to conclude; to sum up; summing up; as I have shown; as I have said; hence; all in all（5）提高寫作能力的整體策略和技巧眾所周知， 一口吃不成一個大胖子 ，應對考研寫作不僅僅需要考生在考試之前進行強化訓練，更需要在平時堅持練習和積累。1、背誦范文背誦范文就是一個很好的方法，通過朗讀和背誦，考生能夠迅速掌握并牢記各種精彩詞匯、詞組和句型，更能夠大大增強英語語感。而掌握語感是學會另一門語言的關鍵所在，也是一條捷徑。2、擴大詞匯量例如，我們可以查到 show 的同義詞有：, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , 等。conclude 的同義詞有：, , , , , , , , , , , , , ,greatly 的同義詞有：, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,我們可以發(fā)現(xiàn)這其中的很多詞語都可以用到考研作文中。3、擴大閱讀量。學習語言就要增大閱讀量。考生可以在平時選取一些休閑類的英語讀物用作準備考研的緊張生活中的一種調劑，如曾經(jīng)風靡一時的 書蟲 系列等?，F(xiàn)在這類讀物在書店中隨處可見，非常容易買到。在閱讀過程中，考生要做一個有心人，隨時記下自己認為較好的詞匯、詞組和句型。此外，還可以多看看英語報紙雜志，不僅可以學到最新的詞匯，也可以找到更多當前社會比較流行的話題，汲取不同的思路和觀點，這些都與考研作文有很大的關聯(lián)?，F(xiàn)在這類出版物在國內也越來越多，比如21st Century, China Daily等報紙，國外的雜志像有名的Times, Newsweekly, Economist等也都能夠較容易地買到過刊。不過我們不建議考生去讀大部頭的英文著作，一來消耗時間，二來大書中的詞匯反而不如報紙雜志上的靈活生動、貼近生活。4、糾正中文思維5、考前作文復習步驟在自己搜集的資料基礎上，多看多讀多背，并盡量建立適合自己的各類作文模板。

解放軍文職招聘考試2009年考研英語真題和答案-解放軍文職人員招聘-軍隊文職考試-紅師教育

發(fā)布時間：2017-06-14 23:00:022009年考研英語真題和答案Section I Use of EnglishDirections:Read the following text. Choose the best word(s) for each numbered blank and mark A, B, C or D on ANSWER SHEET 1. (10 points)Research on animal intelligence always makes me wonder just how smart humans are. 1 the fruit-fly experiments described in Carl Zimmer s piece in the Science Times on Tuesday. Fruit flies who were taught to be smarter than the average fruit fly 2 to live shorter lives. This suggests that 3 bulbs burn longer, that there is an 4 in not being too terrifically bright.Intelligence, it 5 out, is a high-priced option. It takes more upkeep, burns more fuel and is slow 6 the starting line because it depends on learning a gradual 7 instead of instinct. Plenty of other species are able to learn, and one of the things they ve apparently learned is when to 8 .Is there an adaptive value to 9 intelligence? That s the question behind this new research. I like it. Instead of casting a wistful glance 10 at all the species we ve left in the dust I.Q.-wise, it implicitly asks what the real 11 of our own intelligence might be. This is 12 the mind of every animal I ve ever met.Research on animal intelligence also makes me wonder what experiments animals would 13 on humans if they had the chance. Every cat with an owner, 14 , is running a small-scale study in operant conditioning. we believe that 15 animals ran the labs, they would test us to 16 the limits of our patience, our faithfulness, our memory for terrain. They would try to decide what intelligence in humans is really 17 , not merely how much of it there is. 18 , they would hope to study a 19 question: Are humans actually aware of the world they live in? 20 the results are inconclusive.1. [A] Suppose [B] Consider [C] Observe [D] Imagine2. [A] tended [B] feared [C] happened [D] threatened3. [A] thinner [B] stabler [C] lighter [D] dimmer4. [A] tendency [B] advantage [C] inclination [D] priority5. [A] insists on [B] sums up [C] turns out [D] puts forward6. [A] off [B] behind [C] over [D] along7. [A] incredible [B] spontaneous [C]inevitable [D] gradual8. [A] fight [B] doubt [C] stop [D] think9. [A] invisible [B] limited [C] indefinite [D] different10. [A] upward [B] forward [C] afterward [D] backward11. [A] features [B] influences [C] results [D] costs12. [A] outside [B] on [C] by [D] across13. [A] deliver [B] carry [C] perform [D] apply14. [A] by chance [B] in contrast [C] as usual [D] for instance15. [A] if [B] unless [C] as [D] lest16. [A] moderate [B] overcome [C] determine [D] reach17. [A] at [B] for [C] after [D] with18. [A] Above all [B] After all [C] However [D] Otherwise19. [A] fundamental [B] comprehensive [C] equivalent [D] hostile20. [A] By accident [B] In time [C] So far [D] Better stillSection II Reading ComprehensionPart ADirections:Read the following four texts. Answer the questions below each text by choosing A, B, C or D. Mark your answers on ANSWER SHEET 1. (40 points)Text1Habits are a funny thing. We reach for them mindlessly, setting our brains on auto-pilot and relaxing into the unconscious comfort of familiar routine. Not choice, but habit rules the unreflecting herd, William Wordsworth said in the 19th century. In the ever-changing 21st century, even the word habit carries a negative connotation.So it seems antithetical to talk about habits in the same context as creativity and innovation. But brain researchers have discovered that when we consciously develop new habits, we create parallel synaptic paths, and even entirely new brain cells, that can jump our trains of thought onto new, innovative tracks.But don t bother trying to kill off old habits; once those ruts of procedure are worn into the hippocampus, they re there to stay. Instead, the new habits we deliberately ingrain into ourselves create parallel pathways that can bypass those old roads.The first thing needed for innovation is a fascination with wonder, says Dawna Markova, author of The Open Mind and an executive change consultant for Professional Thinking Partners. But we are taught instead to decide, just as our president calls himself the Decider. She adds, however, that to decide is to kill off all possibilities but one. A good innovational thinker is always exploring the many other possibilities.All of us work through problems in ways of which we re unaware, she says. Researchers in the late 1960 covered that humans are born with the capacity to approach challenges in four primary ways: analytically, procedurally, relationally (or collaboratively) and innovatively. At puberty, however, the brain shuts down half of that capacity, preserving only those modes of thought that have seemed most valuable during the first decade or so of life.The current emphasis on standardized testing highlights analysis and procedure, meaning that few of us inherently use our innovative and collaborative modes of thought. This breaks the major rule in the American belief system that anyone can do anything, explains M. J. Ryan, author of the 2006 book This Year I Will... and Ms. Markova s business partner. That s a lie that we have perpetuated, and it fosters commonness. Knowing what you re good at and doing even more of it creates excellence. This is where developing new habits comes in.21. The view of Wordsworth habit is claimed by beingA. casual B. familiar C. mechanical D. changeable.22. The researchers have discovered that the formation of habit can beA. predicted B. regulated C. traced D. guided23. ruts (in line one, paragraph 3) has closest meaning toA. tracks B. series C. characteristics D. connections24. Ms. Markova s comments suggest that the practice of standard testing ?A, prevents new habits form being formedB, no longer emphasizes commonnessC, maintains the inherent American thinking modelD, complies with the American belief system25. Ryan most probably agree thatA. ideas are born of a relaxing mindB. innovativeness could be taughtC. decisiveness derives from fantastic ideasD. curiosity activates creative mindsText 2It is a wise father that knows his own child, but today a man can boost his paternal (fatherly) wisdom or at least confirm that he s the kid s dad. All he needs to do is shell our $30 for paternity testing kit (PTK) at his local drugstore and another $120 to get the results.More than 60,000 people have purchased the PTKs since they first become available without prescriptions last years, according to Doug Fog, chief operating officer of Identigene, which makes the over-the-counter kits. More than two dozen companies sell DNA tests Directly to the public , ranging in price from a few hundred dollars to more than $2500.Among the most popular : paternity and kinship testing , which adopted children can use to find their biological relatives and latest rage a many passionate genealogists-and supports businesses that offer to search for a family s geographic roots .Most tests require collecting cells by webbing saliva in the mouth and sending it to the company for testing. All tests require a potential candidate with whom to compare DNA.But some observers are skeptical, There is a kind of false precision being hawked by people claiming they are doing ancestry testing, says Trey Duster, a New York University sociologist. He notes that each individual has many ancestors-numbering in the hundreds just a few centuries back. Yet most ancestry testing only considers a single lineage, either the Y chromosome inherited through men in a father s line or mitochondrial DNA, which a passed down only from mothers. This DNA can reveal genetic information about only one or two ancestors, even though, for example, just three generations back people also have six other great-grandparents or, four generations back, 14 other great-great-grandparents.Critics also argue that commercial genetic testing is only as good as the reference collections to which a sample is compared. Databases used by some companies don t rely on data collected systematically but rather lump together information from different research projects. This means that a DNA database may differ depending on the company that processes the results. In addition, the computer programs a company uses to estimate relationships may be patented and not subject to peer review or outside evaluation.26.In paragraphs 1 and 2 , the text shows PTK s ___________.[A]easy availability[B]flexibility in pricing[C] successful promotion[D] popularity with households27. PTK is used to __________.[A]locate one s birth place[B]promote genetic research[C] identify parent-child kinship[D] choose children for adoption28. Skeptical observers believe that ancestry testing fails to__________.[A]trace distant ancestors[B] rebuild reliable bloodlines[C] fully use genetic information[D] achieve the claimed accuracy29. In the last paragraph ,a problem commercial genetic testing faces is __________.[A]disorganized data collection[B] overlapping database building30. An appropriate title for the text is most likely to be__________.[A]Fors and Againsts of DNA testing[B] DNA testing and It s problems[C]DNA testing outside the lab[D] lies behind DNA testingText 3The relationship between formal education and economic growth in poor countries is widely misunderstood by economists and politicians alike progress in both area is undoubtedly necessary for the social, political and intellectual development of these and all other societies; however, the conventional view that education should be one of the very highest priorities for promoting rapid economic development in poor countries is wrong. We are fortunate that is it, because new educational systems there and putting enough people through them to improve economic performance would require two or three generations. The findings of a research institution have consistently shown that workers in all countries can be trained on the job to achieve radical higher productivity and, as a result, radically higher standards of living.Ironically, the first evidence for this idea appeared in the United States. Not long ago, with the country entering a recessing and Japan at its pre-bubble peak. The U.S. workforce was derided as poorly educated and one of primary cause of the poor U.S. economic performance. Japan was, and remains, the global leader in automotive-assembly productivity. Yet the research revealed that the U.S. factories of Honda Nissan, and Toyota achieved about 95 percent of the productivity of their Japanese countere pants a result of the training that U.S. workers received on the job.More recently, while examing housing construction, the researchers discovered that illiterate, non-English- speaking Mexican workers in Houston, Texas, consistently met best-practice labor productivity standards despite the complexity of the building industry s work.What is the real relationship between education and economic development? We have to suspect that continuing economic growth promotes the development of education even when governments don t force it. After all, that s how education got started. When our ancestors were hunters and gatherers 10,000 years ago, they didn t have time to wonder much about anything besides finding food. Only when humanity began to get its food in a more productive way was there time for other things.As education improved, humanity s productivity potential, they could in turn afford more education. This increasingly high level of education is probably a necessary, but not a sufficient, condition for the complex political systems required by advanced economic performance. Thus poor countries might not be able to escape their poverty traps without political changes that may be possible only with broader formal education. A lack of formal education, however, doesn t constrain the ability of the developing world s workforce to substantially improve productivity for the forested future. On the contrary, constraints on improving productivity explain why education isn t developing more quickly there than it is.31. The author holds in paragraph 1 that the important of education in poor countries ___________.[A] is subject groundless doubts[B] has fallen victim of bias[C] is conventional downgraded[D] has been overestimated32. It is stated in paragraph 1 that construction of a new education system __________.[A]challenges economists and politicians[B]takes efforts of generations[C] demands priority from the government[D] requires sufficient labor force33.A major difference between the Japanese and U.S workforces is that __________.[A] the Japanese workforce is better disciplined[B] the Japanese workforce is more productive[C]the U.S workforce has a better education[D] ]the U.S workforce is more organize34. The author quotes the example of our ancestors to show that education emerged __________.[A] when people had enough time[B] prior to better ways of finding food[C] when people on longer went hung[D] as a result of pressure on government35. According to the last paragraph , development of education __________.[A] results directly from competitive environments[B] does not depend on economic performance[C] follows improved productivity[D] cannot afford political changesText 4The most thoroughly studied in the history of the new world are the ministers and political leaders of seventeenth-century New England. According to the standard history of American philosophy, nowhere else in colonial America was So much important attached to intellectual pursuits According to many books and articles, New England s leaders established the basic themes and preoccupations of an unfolding, dominant Puritan tradition in American intellectual life.To take this approach to the New Englanders normally mean to start with the Puritans theological innovations and their distinctive ideas about the church-important subjects that we may not neglect. But in keeping with our examination of southern intellectual life, we may consider the original Puritans as carriers of European culture adjusting to New world circumstances. The New England colonies were the scenes of important episodes in the pursuit of widely understood ideals of civility and virtuosity.The early settlers of Massachusetts Bay included men of impressive education and influence in England. `Besides the ninety or so learned ministers who came to Massachusetts church in the decade after 1629,There were political leaders like John Winthrop, an educated gentleman, lawyer, and official of the Crown before he journeyed to Boston. There men wrote and published extensively, reaching both New World and Old World audiences, and giving New England an atmosphere of intellectual earnestness.We should not forget , however, that most New Englanders were less well educated. While few crafts men or farmers, let alone dependents and servants, left literary compositions to be analyzed, The in thinking often had a traditional superstitions quality. A tailor named John Dane, who emigrated in the late 1630s, left an account of his reasons for leaving England that is filled with signs. sexual confusion, economic frustrations , and religious hope-all name together in a decisive moment when he opened the Bible, told his father the first line he saw would settle his fate, and read the magical words: come out from among them, touch no unclean thing , and I will be your God and you shall be my people. One wonders what Dane thought of the careful sermons explaining the Bible that he heard in puritan churched.Mean while , many settles had slighter religious commitments than Dane s, as one clergyman learned in confronting folk along the coast who mocked that they had not come to the New world for religion . Our main end was to catch fish.36. The author notes that in the seventeenth-century New England___________.[A] Puritan tradition dominated political life.[B] intellectual interests were encouraged.[C] Politics benefited much from intellectual endeavors.[D] intellectual pursuits enjoyed a liberal environment.37. It is suggested in paragraph 2 that New Englanders__________.[A] experienced a comparatively peaceful early history.[B] brought with them the culture of the Old World[C] paid little attention to southern intellectual life[D] were obsessed with religious innovations38. The early ministers and political leaders in Massachusetts Bay__________.[A] were famous in the New World for their writings[B] gained increasing importance in religious affairs[C] abandoned high positions before coming to the New World[D] created a new intellectual atmosphere in New England39. The story of John Dane shows that less well-educated New Englanders were often __________.[A] influenced by superstitions[B] troubled with religious beliefs[C] puzzled by church sermons[D] frustrated with family earnings40. The text suggests that early settlers in New England__________.[A] were mostly engaged in political activities[B] were motivated by an illusory prospect[C] came from different backgrounds.[D] left few formal records for later referencePart BDirections:Directions: In the following text, some sentences have been removed. For Questions (41-45), choose the most suitable one from the list A-G to fit into each of the numbered blank. There are two extra choices, which do not fit in any of the gaps.Mark your answers on ANSWER SHEET 1. (10 points)Coinciding with the groundbreaking theory of biological evolution proposed by British naturalist Charles Darwin in the 1860s, British social philosopher Herbert Spencer put forward his own theory of biological and cultural evolution. Spencer argued that all worldly phenomena, including human societies, changed over time, advancing toward perfection. 41.____________.American social scientist Lewis Henry Morgan introduced another theory of cultural evolution in the late 1800s. Morgan, along with Tylor, was one of the founders of modern anthropology. In his work, he attempted to show how all aspects of culture changed together in the evolution of societies.42._____________.In the early 1900s in North America, German-born American anthropologist Franz Boas developed a new theory of culture known as historical particularism. Historical particularism, which emphasized the uniqueness of all cultures, gave new direction to anthropology. 43._____________ .Boas felt that the culture of any society must be understood as the result of a unique history and not as one of many cultures belonging to a broader evolutionary stage or type of culture. 44._______________.Historical particularism became a dominant approach to the study of culture in American anthropology, largely through the influence of many students of Boas. But a number of anthropologists in the early 1900s also rejected the particularist theory of culture in favor of diffusionism. Some attributed virtually every important cultural achievement to the inventions of a few, especially gifted peoples that, according to diffusionists, then spread to other cultures. 45.________________.Also in the early 1900s, French sociologist ?mile Durkheim developed a theory of culture that would greatly influence anthropology. Durkheim proposed that religious beliefs functioned to reinforce social solidarity. An interest in the relationship between the function of society and culture known as functionalism became a major theme in European, and especially British, anthropology.[A] Other anthropologists believed that cultural innovations, such as inventions, had a single origin and passed from society to society. This theory was known as diffusionism.[B] In order to study particular cultures as completely as possible, Boas became skilled in linguistics, the study of languages, and in physical anthropology, the study of human biology and anatomy.[C] He argued that human evolution was characterized by a struggle he called the survival of the fittest, in which weaker races and societies must eventually be replaced by stronger, more advanced races and societies.[D] They also focused on important rituals that appeared to preserve a people s social structure, such as initiation ceremonies that formally signify children s entrance into adulthood.[E] Thus, in his view, diverse aspects of culture, such as the structure of families, forms of marriage, categories of kinship, ownership of property, forms of government, technology, and systems of food production, all changed as societies evolved.[F]Supporters of the theory viewed as a collection of integrated parts that work together to keep a society functioning.[G] For example, British anthropologists Grafton Elliot Smith and W. J. Perry incorrectly suggested, on the basis of inadequate information, that farming, pottery making, and metallurgy all originated in ancient Egypt and diffused throughout the world. In fact, all of these cultural developments occurred separately at different times in many parts of the world.Part CDirections:Read the following text carefully and then translate the underlined segments into Chinese. Your translation should be written carefully on ANSWER SHEET 2. (10 points)There is a marked difference between the education which every one gets from living with others, and the deliberate educating of the young. In the former case the education is incidental; it is natural and important, but it is not the express reason of the association.46It may be said that the measure of the worth of any social institution is its effect in enlarging and improving experience; but this effect is not a part of its original motive. Religious associations began, for example, in the desire to secure the favor of overruling powers and to ward off evil influences; family life in the desire to gratify appetites and secure family perpetuity; systematic labor, for the most part, because of enslavement to others, etc. 47Only gradually was the by-product of the institution noted, and only more gradually still was this effect considered as a directive factor in the conduct of the institution. Even today, in our industrial life, apart from certain values of industriousness and thrift, the intellectual and emotional reaction of the forms of human association under which the world"s work is carried on receives little attention as compared with physical output.But in dealing with the young, the fact of association itself as an immediate human fact, gains in importance.48 While it is easy to ignore in our contact with them the effect of our acts upon their disposition, it is not so easy as in dealing with adults. The need of training is too evident; the pressure to accomplish a change in their attitude and habits is too urgent to leave these consequences wholly out of account. 49Since our chief business with them is to enable them to share in a common life we cannot help considering whether or no we are forming the powers which will secure this ability.If humanity has made some headway in realizing that the ultimate value of every institution is its distinctively human effect we may well believe that this lesson has been learned largely through dealings with the young.50 We are thus led to distinguish, within the broad educational process which we have been so far considering, a more formal kind of education -- that of direct tuition or schooling. In undeveloped social groups, we find very little formal teaching and training. These groups mainly rely for instilling needed dispositions into the young upon the same sort of association which keeps the adults loyal to their group.Section Ⅲ WritingPart A51. Directions:Restrictions on the use of plastic bags have not been so successful in some regions. White pollution is still going on. Write a letter to the editor(s) of your local newspaper to1) give your opinions briefly and2) make two or three suggestionsYou should write about 100 words. Do not sign your own name at the end of the letter. Use Li Ming instead. You do not need to write the address.Part B52. Directions:In your essay, you should1) describe the drawing briefly,2) explain its intended meaning, and then3) give your comments.You should write neatly on ANSHWER SHEET 2. (20 points)Section I Use of English1 5 BADBC 6 10 ADCBD11 15 DBCDA 16 20 CBAACSection II Reading ComprehensionPart A21 25 ABCAA 26 30 ACDAB31 35 DBBAC 36 40 BBDACPart B41 45 CEABGPart C46. 可以說，任何社會制度的價值在于它對擴大和改進經(jīng)驗方面的影響，但是這種影響并不是它原來的動機的一部分。47. 一種制度的副產(chǎn)品，只是逐步被注意到的，而這種效果被視為實施這種制度的一個指導性因素更加緩慢得多。48. 在和他們接觸的時候，雖然容易忽略我們的行動對他們的傾向的影響，但是也不像與成年人打交道那么簡單。49. 既然我們的主要任務在于使年輕人參與共同生活，我們禁不住考慮我們是否在形成獲得這種能力的力量。50. 因此，我們可以在上面所考慮的廣闊的教育過程之內區(qū)別出一種比較正規(guī)的教育，即直接的教導或學校教育。Section Ⅲ WritingPart A51. 應用文參考范文Dear editor，I am writing this letter to advise you of the pressing situation we are facing now. As we know, being accustomed to using plastic bag in our daily life, some of us still take the white pollution for granted. Plastic bag has become the indispensible part of our life, and the white pollution now is a ubiquitous phenomenon, which greatly worsens our environment.To save the situation from further aggravating, I would like to suggest that: firstly, our government should make a set of laws to punish the groups and individuals who are still polluting the environment; secondly, new technologies should be used to produce degradable and renewable materials; thirdly, the local media can make full use of its own influence to intensify the publicity in order to enhance people s awareness of environment.I hope that my suggestions are helpful, thank you for your attention!Sincerely yours，Li MingPart B52. 短文寫作參考范文In the drawing, what first appears in front of us is a huge spider web, on which innumerable people are attached, like the catch of the owner of the web. What is more ironic is they are imprisoned in respective cabins, choosing contacting on line rather than communicating face to face.There is no doubt that the Internet provides us with considerable convenience. However, it drives too many individuals to be addicted to the fictional experience, and hence forget the traditional and most efficient communication method. Indifference has become a not uncommon phenomenon in the modern world. The following reasons may be contribute to the phenomenon. To begin with, people in mounting numbers, who are vividly called netters, indulge in on-line activities, because science and technology develops too fast for people to adapt to it. The Internet, in particular, moving forward with an unimaginable speed, provides people with a convenient tool of getting in touch with others, which lacks weighing its correctness. Moreover, the fierce competition also plays a role of forcing people to fear the situation, which results in people s habit of wallowing in the unreal world.Hence, it is the high time that we highlighted the imperative of face-to-face communication between people. The joint efforts of the specialists, the netters and the educators are needed to cultivate the whole society with the essentiality. Only in this way can we expect a healthy development of the relationship among individuals.

解放軍文職招聘考試英雄時代——十八世紀的數(shù)學-解放軍文職人員招聘-軍隊文職考試-紅師教育

發(fā)布時間：2017-11-22 19:37:00英雄時代 十八世紀的數(shù)學17世紀最偉大的數(shù)學成就是微積分，18世紀的大部分數(shù)學工作則是多方面利用微積分方法所進行的新的創(chuàng)造．產(chǎn)生了現(xiàn)在仍在研究的許多數(shù)學新領域：微分方程、微分幾何、變分法，等等．18世紀數(shù)學研究的特點是，取得的成果相當豐富，涉獵的領域十分廣泛，但其中有些內容卻經(jīng)不起嚴格的推敲．18世紀的卓越數(shù)學家主要有英倫三島的泰勒(B．Taylor，1685 1731)、馬克勞林(C．Maclaurin，1698 1746)；歐洲大陸有瑞士的貝努利(Bernoulli)家族，以及18世紀數(shù)學界的中心人物、在數(shù)學史上與阿基米德(Archimedes)、牛頓(I．Newton)、高斯(F．Gauss，1777 1855)一起被稱為 四個最偉大的數(shù)學家 的瑞士數(shù)學家歐拉(L．Euler，1707 1783)．隨著牛頓的去世，以及牛頓與萊布尼茨(G．W．Leibniz)關于微積分優(yōu)先權之爭日趨激烈，英倫三島數(shù)學界固守牛頓的流數(shù)方法，拒不接受歐洲大陸的數(shù)學思想，英倫三島在牛頓尤其是在馬克勞林之后，數(shù)學發(fā)展相對比較緩慢．繼貝努利家族和歐拉之后，主宰18世紀的數(shù)學是法國數(shù)學家，他們中有棣莫弗(A．DeMoivre，1667 1754)、克萊羅(A．C．Clairaut，1713 1765)達朗貝爾(D Alembert，1717 1783)、蘭伯特(J．H．La-mbert，1728 1777)著名的 三L ：拉格朗日(J．L．La－grange，1736 1813)、拉普拉斯(P．S．Laplace，1749 1827)、勒讓德(A．M．Legendre，1752 1833)，以及蒙日(G．Monge，1746 1818)和卡諾(L．Carnot，1753 1823)．法國一直到19世紀上半葉仍是世界數(shù)學中心．18世紀數(shù)學工作的推動力是解決物理 自然科學的問題，工作的目標不是數(shù)學，而是解決物理問題．法國百科全書學派的狄德羅(D．Dideret，1713 1784)和達朗貝爾明確地把數(shù)學看作是自然科學的一個分支，這樣數(shù)學在歷史上第一次從屬于自然科學，而且這種觀點到今天仍有影響．這個世紀的數(shù)學家?guī)缀鯚o一例外地都從事于科學、工業(yè)技術、軍事問題的研究，并且其認真程度絲毫不亞于研究數(shù)學．同時，數(shù)學家還逐漸拋棄了宇宙是上帝按照數(shù)學定律設計的信念，機械決定論開始占據(jù)人們的心靈，而這一切都得益于數(shù)學的巨大成就．18世紀可以說是數(shù)學史上的英雄時代．第一節(jié) 數(shù)學分析一、微積分18世紀數(shù)學的核心是以微積分為主的數(shù)學分析，這一世紀的中心人物是歐拉．牛頓、萊布尼茨創(chuàng)造了微積分，而歐拉則使這一數(shù)學領域充滿了光輝燦爛的景色．拉普拉斯(P．S．Laplace)的話道出了當時的狀況： 讀讀歐拉，讀讀歐拉(指其著作)，他是我們大家的老師． 這一評價甚至在今天也不過分．歐拉于1707年4月15日誕生于瑞士巴塞爾．小時由父親任啟蒙教師，12歲入當?shù)刂袑W，16歲畢業(yè)后遵從父愿，入巴塞爾大學神學系學習．在神學課程之余，他被約翰 貝努利(JohannBernoulli)的數(shù)學講座深深吸引了，在貝努利兄弟的影響下，數(shù)學逐漸擠走了神學，占據(jù)了他的學習日程表，而且貝努利也開始對他刮目相看，熱情地指點他．歐拉回憶約翰 貝努利時曾深情地說，貝努利讓他每星期六下午到晚上自由地去他的住處，他讓歐拉每解決一個問題，歐拉就能很順利地解決10個問題．的確，在貝努利兄弟的指導下，歐拉已經(jīng)具備了優(yōu)秀數(shù)學家的素質，并開始從事數(shù)學研究．18歲時他就發(fā)表了數(shù)學論文．1726年，年僅19歲的歐拉由于在船的立桅方面的研究論文而獲得巴黎科學院的獎金，從而在歐洲數(shù)學界嶄露頭角．這一年他正好大學畢業(yè)．在瑞士，年輕的歐拉未能獲得自己所謀求的職位，恰巧這時約翰 貝努利在俄國彼得堡科學院任教授的兒子尼古拉 貝努利(Nicolaus Bernoulli)和丹尼爾 貝努利(Daniel Bernoulli)來信說，俄國歡迎歐拉．1727年5月17日歐拉來到彼得堡科學院任丹尼爾 貝努利的副手，1731年被任命為副教授，1733年他接替丹尼爾 貝努利擔任彼得堡科學院的數(shù)學教授．他為俄國的數(shù)學發(fā)展、科學進步做了大量的工作，他的許多成果出現(xiàn)在彼得堡科學院的刊物上，幫助俄國政府解決了大量的物理學、工程學方面的難題．過度的案頭工作使得這位數(shù)學大師得了眼病，不幸于1735年右眼失明，這一年他還只有28歲．1741年，歐拉應腓特烈大帝之邀擔任柏林科學院物理數(shù)學研究所所長．除此之外，他還在宮廷為公主們講授數(shù)學、物理、天文、哲學乃至宗教方面課程．講述的內容曾以《給一位德國公主的信》，(Letters to a German Princess)發(fā)表，是一部風趣、文筆優(yōu)雅的科普作品．他為普魯士研究了保險、河運等方面的一系列問題．1766年，俄國沙皇誠摯的邀請終于使歐拉又回到了彼得堡科學院．實際上，他時刻也沒忘記俄國．在1741 1766年的25年時間里，身在柏林的歐拉，卻仍為彼得堡科學院寫了上百篇論文，時刻關注著俄國的事務．的確，俄國、彼得堡科學院是他的第二故鄉(xiāng)，是他施展聰明才智的地方．俄國人民也深深地熱愛他，以致于俄國數(shù)學史家差不多總是將歐拉當作俄國數(shù)學家、俄國數(shù)學的創(chuàng)始人和彼得堡數(shù)學學派的奠基人．回到俄國后不久，嚴寒的氣候對歐拉微弱的視力如雪上加霜，很快左眼視力衰退，最后于1766年底雙目失明．這對于一位以案頭工作為主的數(shù)學家的打擊可想而知．此時他已59歲，年近花甲．然而，在他生命的最后17年，盡管雙目失明，在全盲中他的成果卻絲毫不減往年．1771年，圣彼得堡突起大火，殃及他的住宅，雙目失明而又身染疾病的歐拉被圍困在大火中．雖然一位工人冒著生命危險將這位大師從大火中搶救了出來，然而他的書庫、大量研究成果卻全部化為灰燼．沉重的打擊，并沒有使天性樂觀的歐拉屈服，而是更加勤奮的工作．他以驚人的毅力與黑暗作斗爭，以超常的記憶力和心算從事數(shù)學研究．人們發(fā)現(xiàn)，對不少有才能的數(shù)學家在紙上做起來也很困難的數(shù)學證明與計算，他卻能心算出來！在數(shù)學史上，歐拉與阿基米德、牛頓、高斯一起被稱為四位最偉大的數(shù)學家．而歐拉又是數(shù)學史上成果最多、數(shù)學著作最多的數(shù)學家．研究的數(shù)學領域遍歷微積分、微分方程、解析幾何與微分幾何、數(shù)論、級數(shù)與變分法，他還是卓越的理論物理學家，通過將數(shù)學應用到整個物理學領域，創(chuàng)立了分析力學及剛體力學學科．他寫了數(shù)學分析、解析幾何與微分幾何、代數(shù)、變分法、力學方面的許多課本，并且在百余年的時間里被用作標準教材．除課本外，從20歲開始，他以每年約800頁左右的速度發(fā)表高質量的研究性論文，論文所獲得的獎金成了他的生活收入主要來源．雙目失明后，他還寫了好幾本書和400余篇研究論文．歐拉全集達厚厚的74卷．今天，我們幾乎可以在數(shù)學的任何分支中看到歐拉的名字：初等幾何中的歐拉線，立體幾何中的歐拉定理，解析幾何中的歐拉變換，方程中的歐拉解法，微積分中的歐拉積分，數(shù)論中的歐拉函數(shù)，微分方程中的歐拉方程，級數(shù)論中的歐拉常數(shù)，以及歐拉線、眾多的歐拉方程、歐拉公式 ，令人目不暇接．然而，歐拉并不像牛頓、萊布尼茨那樣終身一人．大量的數(shù)學、科學創(chuàng)造并未犧牲他所有的天倫之樂．他是一位稱職的丈夫，13個孩子喜愛的父親．與妻子一同安排家務，給孩子們做科學游戲，一起念誦《圣經(jīng)》，在黃昏的林蔭道上留下了幸福家庭的串串腳印．歐拉愛好思考哲學問題，曾數(shù)次與啟蒙思想家伏爾泰(F．M．A．Voltaire)切磋，甚至欣賞伏爾泰對他的哲學觀點的尖銳批評．可見其生性是多么豁達樂觀．1783年9月18日傍晚，為慶祝計算氣球上升定律的成功，他請朋友們吃飯，席間他興致勃勃地講述了計算要領，然后喝茶、逗孫子玩，突然疾病發(fā)作，煙斗落地，口中喃喃： 我死了． 于是 他停止了計算，也停止了生命 ．在歐拉的時代，隨著微積分的發(fā)展，函數(shù)概念顯得越來越重要了．18世紀時占主導地位的函數(shù)概念是，函數(shù)是由一個解析表達式(有限或無限)給出的．今天我們熟知的各種初等函數(shù)，大都得益于歐拉的系統(tǒng)總結．1748年，他寫下了兩卷本《無窮小分析引論》(Introduction Analysin Infinitorum)，首先，將函數(shù)定義為由一個變量與一些常量通過任何方式形成的解析表達式．隨后系統(tǒng)地研究了各種函數(shù)．在三角函數(shù)方面，他一方面使sinx，cosx，tgx等徹底擺脫了直角三角形的局限，使之成為一般意義上的函數(shù)；同時弄清了三角函數(shù)的周期性，并且引入了弧度概念．他區(qū)分了顯函數(shù)與隱函數(shù)，單值函數(shù)與多值函數(shù)．不僅如此，他還在意識到超越數(shù)的基礎上，引入了超越函數(shù)，認為三角函數(shù)、對數(shù)函數(shù)、指數(shù)函數(shù)及某些特殊函數(shù)是超越函數(shù)，這些函數(shù)的特征是不能通過對某個表達式作代數(shù)運算得到．實際上，代數(shù)函數(shù)、超越函數(shù)的提出表明歐拉已經(jīng)定義了多元函數(shù)f(x，y， )，其中二元函數(shù)f(x，y)、三元函數(shù)f(x ，y，z)在當時是最重要的．(其中，P(x)為x的有理函數(shù)，R(x)則為四次多項式)．分進行更一般的研究乃至建立橢圓函數(shù)論則是19世紀的事情了．今天已經(jīng)遍及數(shù)學、物理的許多部門的兩個非常重要的非初等函數(shù) (Gamma)函數(shù)、 (Beta)函數(shù)，也是18世紀引入的．這兩個函數(shù)都是歐拉創(chuàng)造的，最初是因為求解常微分方程的需要，隨后哥德巴赫(C．Goldbach，1690 1764)考慮插值問題時就這個問題求教歐拉，于是歐拉在1729年10月13日寫給哥德巴赫的信中解決了這個問題，并在1730年1月8日第二封信中引入了積分問題了 (n＋1)＝n (n)．明顯地 (1)=1．于是對任何正整數(shù)n都有 (n＋1)＝n (n)＝n (n-1) 2 1 (1)在1830年1月8日給哥德巴赫的信中，歐拉還提出了今天的 函數(shù)不過歐拉在1771年已經(jīng)發(fā)現(xiàn)了 函數(shù)與 -函數(shù)的重要關系：B(p，拉第二型積分，這一名稱一直沿用到今天．勒讓得還得到了下述結果：普通導數(shù)與偏導數(shù)的區(qū)別開始并不被人們重視，許多人對兩者都用同樣的記號，但萊布尼茨卻察覺了這一點，1694年他曾用 m 表示 64年才出版的著作中，封田(A．Fonta－ine)對于x，y，z，u等變量的函數(shù) ，給出了公式格朗日等人的改進，逐漸演變成了今天的偏導數(shù)符號．克萊羅在偏導數(shù)方面的主要貢獻是得到了dz＝pdx＋qdy是全微分的條件，其中p，q是x，y的函數(shù)， 全微分 是由封田提出的，系克雷羅得到了這樣的結果：pdx+qdy是全微分(即 方程的研究極為有用，它是積分因子法的理論基礎．拉對由弧圍成的有界區(qū)域上的二重定積分已經(jīng)有了比較清楚的概念，并給出了用累次積分計算這種積分的程序，但對 f(x，y)dxdy的次序交換問題仍比較模糊．由于探討引力、多體力學問題，拉格朗日、拉普拉斯、勒讓德開始了三重積分研究．拉格朗日用三重積分表示引力．值得注意的是，積分變換在三重積分中發(fā)揮了重要的作用．1773年，拉格朗日在他關于旋轉橢球引力的研究中，發(fā)現(xiàn)用直角坐標計算很困難，于是轉用球坐標，他引入積分變換的實質是用r2sin d ddr代替dxdydz，于是他開始了多重積分變換的課題，1772年拉普拉斯也給出了球坐標變換．從此， 變換 在數(shù)學中逐漸為人們重視，18世紀的變換主要集中在兩個方面，一個是坐標變換，這對于多重積分非常重要，另一是微分方程中的變換，其中最著名的是拉普拉斯變換．

解放軍文職招聘考試十五至十七世紀的初等數(shù)學-解放軍文職人員招聘-軍隊文職考試-紅師教育

發(fā)布時間：2017-11-22 19:29:28十五至十七世紀的初等數(shù)學第一節(jié) 歷史背景15世紀，希臘著作大量進入歐洲．特別是從1453年土耳其人征服君士坦丁堡以后，希臘學者紛紛攜帶文稿逃到意大利．復興古典文化的旗幟首先在意大利打出來，興起了一場歷史上被稱為文藝復興的革命運動．到16世紀，這場運動已經(jīng)席卷歐洲，極大地促進了思想解放和科學的發(fā)展，為近代數(shù)學的產(chǎn)生創(chuàng)造了良好的社會條件．關于這個時期的數(shù)學，有五個方面的背景必須提到．一、經(jīng)濟的發(fā)展在文藝復興時期，由于個性解放，激起人們探索自然和改造世界的熱忱，生產(chǎn)和貿(mào)易迅速發(fā)展起來，一個新的經(jīng)濟時代開始了．在這一時期，中國四大發(fā)明的傳入對歐洲有重要意義．羅盤使得遠洋航行成為可能，火藥促進了管形火器的發(fā)展，從而使拋射體研究變得很重要．造紙和印刷術則直接促進了知識的傳播．1438年，德國人約翰 古登堡(JohannGutenberg)發(fā)明了鉛字，《幾何原本》(Elements)的第一次印刷本終于在1482年出現(xiàn)于威尼斯．經(jīng)濟的發(fā)展不僅為數(shù)學發(fā)展提供了物質條件，而且提出了許多有待數(shù)學解決的問題．歐洲人在開辟新航路的探險中，必須確定船只的地理位置，這就要求用準確的數(shù)學方法測量地球的經(jīng)緯度．為了航行安全，船身必須端正，這就要求測量和計算物體重心．對二次曲線的研究則是為了解決彈道學和天文學問題．另外，商業(yè)和稅收中日益頻繁的計算，要求人們改善計算方法，這也是數(shù)學發(fā)展的動力之一．二、知識的傳播從阿拉伯反傳歐洲的希臘著作多是希臘文或阿拉伯譯本，一些學者將其譯成拉丁文，以擴大影響．從16世紀開始，許多學者又用本地語言翻譯希臘的經(jīng)典著作．例如，塔爾塔利亞(N．Tar－taglia，1499 1557)便于1543年把歐幾里得《幾何原本》由拉丁文譯成意大利文．這種翻譯工作大大加快了數(shù)學知識的傳播速度．在意大利的羅馬和佛羅倫薩等城市，還通過建立圖書館的方法來啟發(fā)公眾．佛羅倫薩的設計學院也很有名，它創(chuàng)建于1563年，后來成了數(shù)學研究的中心．學院的成員把拉丁文著作譯成本地語言，向公眾作報告．建于1603年的羅馬山貓學院也起到了這種作用．但當時的各大學仍在神學統(tǒng)治之下，對于傳播科學作用不大，這是很遺憾的．三、人文主義的影響人文主義提倡人性，反對神權，在這一思想鼓勵下，不少杰出人物脫穎而出，突破宗教束縛的科學事件不斷涌現(xiàn)．1543年，波蘭的哥白尼(N．copernicus，1473 1543)發(fā)表了《天體運行論》(DeRevolutionibus)，以日心說否定了在西方占統(tǒng)治地位千余年的地心說；比利時維薩留斯(A．Vesalius，1514 1564)的《人體構造》，則根據(jù)三百多張解剖圖，指出圣經(jīng)的許多錯誤．于是，隨著生產(chǎn)力的發(fā)展及思想的解放，近代科學開始從神學中解放出來，走上獨立發(fā)展的道路．引人注目的是，哥白尼、開普勒(J．Kepler，1571 1630)、伽利略(GalileoGalilei，1564 1642)等著名科學家都具有這樣的觀念：科學工作的最終目標是確立定量的數(shù)學規(guī)律．四、數(shù)學與宗教由于科學的發(fā)展，人們不再對圣經(jīng)文字上的含義作無休止的考據(jù)和爭辯，而開始面向自然．但自然科學并沒有完全擺脫神學的束縛．有趣的是，數(shù)學家們在神學和科學之間建立了某種妥協(xié)，使他們的數(shù)學研究不受宗教界干擾．他們把上帝推崇為一個至高無上的數(shù)學家，說上帝在構造宇宙時已經(jīng)把數(shù)學規(guī)律放在其中了，因此尋找大自然的數(shù)學規(guī)律便成為一件合法的宗教活動．每一條規(guī)律的發(fā)現(xiàn)都被說成是證明了上帝的智慧而并非研究者的智慧．例如開普勒在每次獲得發(fā)現(xiàn)后，從不忘記對上帝寫頌歌．伽利略也曾說過： 上帝在自然界的規(guī)律中令人贊美地體現(xiàn)出來的，并不亞于他在圣經(jīng)字句中所表現(xiàn)的． 這種理論甚至影響到17世紀的萊布尼茨(G．W．Leibniz，1646 1716)，他說： 世界是按上帝的計算創(chuàng)造的． 就這樣，宗教與科學似乎融為一體了．但實際上，上帝只是形式，而科學才是內容，這一點是很明顯的．五、科學與實驗文藝復興中實驗的興起對數(shù)學發(fā)展是一個很大的推動力．隨著大批實踐者尤其是手工業(yè)者的經(jīng)驗積累，以及他們提出的問題的啟示，系統(tǒng)的觀察和實驗逐步產(chǎn)生了．在古希臘純數(shù)學的影響下，一些有識之士開始把數(shù)學思想引入實驗，純科學和實踐的興趣被融合在一起．例如，達 芬奇(LeonardodaVinci，1452 1519)便熱衷于在實驗中尋找數(shù)量關系，他認為在科學中， 凡是和數(shù)學沒有聯(lián)系的地方，都是不可靠的． 在他之后的培根(F．Bacon，1561 1626)和笛卡兒(R．Descartes，1596 1650)，則分別強調了實驗方法與數(shù)學方法的重要性，為近代科學打下方法論的基礎．培根認為，任何真正的科學都應建立在實驗的基礎上，而歸納法則是由實驗獲得知識的主要方法．笛卡兒則宣稱科學的本質是數(shù)學，并力求找出一種兼?zhèn)錃w納法和演澤法二者之長的新方法．兩人的共同之處是重視科學的應用，培根說： 把得到的真理應用到人類的福利上，是始終要記在心里的目標． 笛卡兒也認為，把數(shù)學方法只用到數(shù)學本身是沒有價值的．實驗和數(shù)學的結合逐漸成為歐洲科學的一個特點．科學家們尤其重視理想實驗，在這種實驗中，由于排除了次要因素對實驗的干擾，有利于數(shù)學規(guī)律的發(fā)現(xiàn)．伽利略正是通過斜面實驗發(fā)現(xiàn)了自由落體定律和水平方向的慣性原理．開普勒行星運動定律的發(fā)現(xiàn)，則是數(shù)學方法與系統(tǒng)觀察相結合的結果．