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10 Tips for Writing the College Application Essay. Oedipus Funny! No subject is more fraught with anxiety for the high school senior than the essay on the college application. Whether it is as bizarre as the University of Chicago's How do you feel about Wednesday?; University of Pennsylvania's You have just completed your 300-page autobiography. Please submit page 217.; or Tufts University's Are We Alone?—or whether it is a more mundane question about a formative experience you've had in your life, or about some controversial social or political issue, students tremble at how to write pm, the very thought of writing the essay and oedipus being judged on it. Get updates from U.S. News, including newsletters, rankings announcements, new features and special offers. We wondered what tips could be offered to ease the pain. Your Essay! For advice, we turned to visiting blogger Jonathan Reider, director of college counseling at essay funny, San Francisco University High School, who before that was the findings chapter, senior associate director of admissions (and humanities instructor) at Stanford University.
He should know; he's been on both sides of the oedipus, high school/college door. Here are his 10 best tips. 1. Chapter Dissertation! Be concise. Essay Oedipus Funny! Even though the Common Application main essay has only a suggested minimum of 250 words, and no upper limit, every admissions officer has a big stack to read every day; he or she expects to spend only a couple of minutes on of darkness essays the essay. If you go over 700 words, you are straining their patience, which no one should want to do. 2. Essay Funny! Be honest. Don't embellish your achievements, titles, and offices.
It's just fine to be the copy editor of the newspaper or the treasurer of the Green Club, instead of the president. Not everyone has to be the star at everything. You will feel better if you don't strain to inflate yourself. 3. Be an how to write pm, individual. In writing the essay, ask yourself, How can I distinguish myself from those thousands of others applying to College X whom I don't know—and even the ones I do know? It's not in your activities or interests. If you're going straight from high school to college, you're just a teenager, doing teenage things. It is oedipus your mind and how it works that are distinctive. Your Essay! How do you think? Sure, that's hard to explain, but that's the key to the whole exercise. 4. Be coherent.
Obviously, you don't want to babble, but I mean write about just one subject at a time. Don't try to essay oedipus cover everything in an essay. Doing so can make you sound busy, but at the same time, scattered and superficial. And Religion Coexist! The whole application is a series of oedipus funny snapshots of what you do. It is inevitably incomplete.
The colleges expect this. Go along with them. 5. Be accurate. I don't mean just use spell check (that goes without saying). Attend to the other mechanics of good writing, including conventional punctuation in the use of can science and religion coexist commas, semi-colons, etc. If you are writing about Dickens, don't say he wrote Wuthering Heights. If you write about Nietzsche, spell his name right. 6. Be vivid. A good essay is often compared to a story: In many cases it's an oedipus funny, anecdote of an important moment.
Provide some details to help the reader see the setting. Use the names (or invent them) for the other people in the story, including your brother, teacher, or coach. This makes it all more human and humane. It also shows the reader that you are thinking about his or her appreciation of your writing, which is something you'll surely want to do. 7. Be likable. Colleges see themselves as communities, where people have to get along with others, in dorms, classes, etc. Are you someone they would like to have dinner with, hang out with, have in a discussion section? Think, How can I communicate this without just standing up and saying it, which is corny. Chapter Dissertation! Subtlety is good.
8. Be cautious in your use of humor. You never know how someone you don't know is going to respond to you, especially if you offer something humorous. Humor is always in essay, the eye of the beholder. Be funny only if you think you have to. Then think again. 9. Me A! Be controversial (if you can). So many kids write bland essays that don't take a stand on anything. It is essay funny fine to write about politics, religion, something serious, as long as you are balanced and thoughtful. Of Darkness Ivory' Essays! Don't pretend you have the final truth. And don't just get up on your soapbox and spout off on a sensitive subject; instead, give reasons and arguments for your view and consider other perspectives (if appropriate).
Colleges are places for the discussion of ideas, and admissions officers look for oedipus, diversity of mind. 10. Be smart. Colleges are intellectual places, a fact they almost always keep a secret when they talk about their dorms, climbing walls, and how many sports you can play. It is helpful to show your intellectual vitality.
What turns your mind on? This is apostle paul resume not the same thing as declaring an intended major; what matters is funny why that subject interests you. © Copyright 2010 Professors' Guide LLC. All rights reserved. Resume! Master SAT Command of Evidence Items. Essay Funny! Students will find this question type in the reading and writing and language sections of the exam. Washington College Road Trip: University of Washington. Dreams! Discover what it's like to essay funny attend this public institution in Seattle. Ivory'! Washington College Road Trip: Gonzaga University. Learn what it's like to attend this Spokane, Washington school. Take a College Road Trip to Washington. Find out oedipus funny, what it's like to attend college in this Northwestern state.
Washington College Road Trip: Whitman College. Discover what it's like to attend this school in Walla Walla, Washington. Washington College Road Trip: University of Puget Sound. Learn what it's like to attend this Tacoma, Washington school. Pitino Is 'Coach-2' in Federal Court Documents. Heart Essays! The Louisville head basketball coach Pitino may have helped funnel money to a top recruit in bid to essay oedipus secure his commitment. Different groups and organizations – from tech companies to sororities – offer college aid for women. 10 Universities With Biggest Endowments. The endowment at each of these schools exceeded $8.7 billion for the 2016 fiscal year, U.S.
News data show. Ideal Choices in ivory', College Admissions. Learn how to make the best decision in common undergraduate admissions scenarios. Get updates from U.S. News, including newsletters, rankings announcements, new features and special offers. Video: Creating a College Short List. Essay Funny! See the best National Universities, Liberal Arts Colleges and how to write pm more.
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Foreign Direct Investment in essay funny, Russia. Term Paper, 2006. 25 Pages, Grade: A- 1 FDI during the period of transition: a failure or success? 2 Spatial and sector distributions of FDI in Russia. 3 Factors behind investment performance of Russia. Foreign direct investment constitutes a highly important part of contemporary world economy. Globalization of international economic relations have led to your dreams essay the situation in which many countries face the necessity to compete with each other and, thus, to enhance their competitiveness through attraction of foreign capital. FDI in oedipus, this respect appears to be the most desirable option for many economies, as they are more stable than other forms of investment. For the developing and emerging markets they provide specific opportunities, such as.
- integration into the global economy, - enhancement of the aggregate rate of investment, - transfer of essays soft technology (management, organization, sourcing and marketing), - development of patterns of networking and subcontracting with other firms in the host country  . Currently, there is essay oedipus a debate among researches on the relationship between foreign direct investment and crucial economic indicators, such as output growth, accumulation of human capital stock, higher productivity rates, etc. According to the most widespread point of view, inflows of findings chapter dissertation foreign direct investments are deemed to improve economic growth and restructuring of the host countries. However, the empirical literature has not proved this opinion, since in many countries with high rate of FDI other economic indicators appear to be worse than in those which accept less inflows. Borensztein found that a positive impact of FDI on growth is observed only in countries with a certain level of accumulated minimum threshold stock of human capital. Funny! Blomstorm, on his part, stated that FDI positively influenced growth only in the ‘low quality data’ countries  . Apostle Paul Resume! Saltz even found that FDI have a negative impact on domestic capital formation. Naurto F. Campos and Yuko Kinoshita argue that the discrepancy between the authors appears to essay oedipus funny be a result of the fact that the former tended to apostle equate FDI to technology transfer while in most countries and regions of the world FDI encompasses arrangements that goes well beyond pure technology transfer. However, even taking into consideration different results of the studies provided by the authors, it is evident, that some more developed fast growing countries tend to export FDI more than import, while the others, which import more, show very modest achievements in economic growth (the examples are Bolivia and Papua New Guinea with FDI inflows of oedipus funny nearly 2% of GDP)  . Transition economies, in this respect, can be viewed as a unique case. On the one hand, according to Naurto F. How To Write Pm! Campos and essay funny Yuko Kinoshita, they possess some kind of apostle resume ‘enabling environment’ that is lacking in many developing economies, and thus ‘present an excellent testing ground for the impacts of FDI on growth’  . On the other hand, all these countries encounter many problems, as they develop in specific environment, characterized by strong influence of the Soviet past. Essay Funny! In certain cases distortions, inherited from the past (such as lack of entrepreneurial culture, sluggishness of the transformation of how to write pm legal system, etc.), can slow down, or even eliminate improvements, associated with the FDI inflows to the country. Generally, it is quite difficult to assess the impact of FDI on the transition economies, as studies like that are lacking.
In Russia it is even harder to funny find information, which is due to the fact that economic growth was not characteristic to the country for the whole decade. However, the paul, success or failure of FDI within the country is largely attributed to the success or failure of the transition process and vice versa, which means that FDI is obviously interrelated with other economic indicators. The United Nations Economic Survey  , for instance, views success of many CEE countries in attracting FDI primarily as a consequence of macroeconomic stabilization. Oedipus! However, while observing the dreams, failures with FDI of the oedipus funny, CIS countries, it involves such explanatory factors as political instability and unfriendly investment environment, which relate more apparently to the sphere of decisionmaking. Taking into your dreams consideration highly controversial character of the subject, in this paper I will try to find out the factors behind investment performance of the country during the period of essay funny transition, and, thus, answer the question of why Russia attracted such a small amount of FDI since the beginning of the can science and religion coexist, transition process.
Starting analysis from the observation of foreign investment profile of the country after the dissolution of the essay, Soviet Union, I will then look at major determinants of FDI inflow to essay the country as well as factors of oedipus funny their spatial and sectoral distribution within the state. Additional questions will be as follows: Has Russia benefited from foreign direct investments during the transition period? How did various factors (spatial distribution of FDI, reform progress in regions, investment climate, etc.) influence its effectiveness? Answering these questions I will embark on different approaches toward the assessment of the FDI effectiveness, and resume then refer to the analysis of sectoral and essay oedipus spatial distribution of FDI within Russia. Trying to answer the main and additional questions, I will involve some comparisons from other transition economies, such as Poland, Czech Republic, Hungary, China. I hypothesize that poor investment climate served as one of the main reasons for both poor investment performance of Russia and capital flight during the transition period.
Thus I suppose that the determinants of bad investment performance and follow dreams capital flight out from oedipus Russia significantly coincide. The paper will largely focus on include assessment of the environment for FDI in Russia during the period of transition and the contemporary period. It will also raise some questions about the factors that might be strongly discouraging for the enhancement of FDI in Russia  . 1 FDI during the period of transition: a failure or success? According to available statistics, foreign direct investment in Russia remained relatively low for much of the 1990s, usually less then $ 2 billion per annum. Generally, as many authors observe, investing in Russia proved uncompetitive for foreign investors. Russia attracted $10.3 billion worth of FDI in the period 1994-1999 that is on average $1.7 billion per annum. After the essay oedipus funny, 1998 crisis the FDI even declined  . The OECD report states that the cumulative figure for FDI in Russia from 1991 through the end of apostle 2001 represents $18.2 billion, or only 5 percent of domestic fixed capital formation. If compared with other countries these figures appear to be rather small: in China FDI accounted for $46 billion in 2000 alone, in the USA they accounted $200 billion for the year 2001, while global total in 2000 was $1,270 billion. The level of FDI in Russia is also very low relative to other transition countries in the region: on a per capita basis, cumulative FDI in Russia is 15 %, compared to 84 % for Poland, 118 % for the Czech Republic and $221 for Hungary  . At the same time Russia appeared to oedipus be the leading investor in the CEE region, providing about 75% of the regional outflows.
However, according to Ditlbacher, Fidrmuc, Walter, and many other authors, interest in Russia as a destination for investments has been steadily growing, and in spite of the follow your dreams, fact that FDI levels have remained relatively low for much of the 1990s, usually little over $2 billion per annum, recently the oedipus, inflows have increased – including returning flight capital from Cyprus and elsewhere – and there are prospects for higher FDI in future  . In 2005 the include findings chapter dissertation, amount of foreign investments into the Russian economy doubled as compared to the previous year. Contrary to the predictions of many Russian officials, net capital that year the country registered net capital inflow, which meant that inflows outpaced the outflows. FDI jumped from $12.8 billion in oedipus, 2004 to $17.8 in 2005. UNCTAD explains this positive shift primarily by two reasons: high oil prices and essay the appearance of Chinese capital inflows. Other sources, trying to explain such an unpredicted rise of essay oedipus inflow, add to the reasons the massive borrowing of Gazprom (over $13,1 billion from a consortium of resume foreign banks) to purchase Sibneft  , the deal, which had a huge effect on essay funny statistics, preventing a net inflow from being negative.
However, the growing level of inflows in 2005 significantly coincided with other positive economic indicators in Russia and the rise of FDI throughout the world (in 2005 – $ 897 billion, which is 29% higher than during the previous year). illustration not visible in this excerpt. According to the UNCTAD data, the largest investor in Russia has always been the United States providing a share of 20% of the Russian FDI stock (in 2001 and find me a 2002). According to essay funny the OECD report, the largest investor in Russia by find resume the end 2000 in cumulative terms was Germany (17,1 percent), the oedipus, United States (15,6) and can science and religion coexist essay Cuprus (14.9 percent). Other large investors to essay oedipus funny Russian economy are the Netherlands, the find me a resume, UK, and Japan. It is interesting that Cyprus, which has never been a particularly active investor on the world scene (according to UNCTAD (2003) the essay, outward FDI stock of how to write pm Cyprus was $731 million whereas the inward stock was much higher - $4827), during many years provided nearly the same amount of essay funny FDI to Russia, as the United States.
The study of Pelto, Peeter Vahtra and Kari Liuhto shows that by apostle paul resume July 2003 the essay, investment stock from essay Cyprus to essay Russia was $ 6 606 million. Of these, $ 4432 million were direct investments, making Cyprus the how to write pm, main source for essay oedipus funny, FDI to the Russian economy with a 20-% share of the Russian total inward FDI. Thus, during the essay, first half of 2003, the FDI stock of Cyprus exceeded that of the USA  . The fact that Cyprus has been one of the main investors to essay funny the Russian economy for many years, and at the same time one of the main destinations of Russian FDI, gives an opportunity to suggest the return of resume Russian capital. In this respect, the essay, study of Elina Pelto, Peeter Vahtra and Kari Liuhto, suggests that Cyprus’s FDI that are declared in Russia, are actually not of apostle resume Cypriot origin, but most likely originate in Russia. This transfer of funds abroad in order to bring them back, partly or wholly, as FDI, and obtain the tax and other benefits offered to foreign investors is known as a phenomenon of ‘round tripping’, that is connected to Russian capital flight. Generally, the share of Cyprus in the Russian inward FDI is strikingly large, considering that Cyprus has a population of only 750000 and does not play active role as a Russian regular trade partner. The phenomenon of ‘round tripping’ is characteristic not only to Russia, but also to essay oedipus funny some more developed countries (as, for example, China). However, for Russia, which, unlike China, has been characterized by slow growth of foreign investment, this phenomenon proves to be particularly harmful.
As it is how to write pm exemplified in literature, Russian investors tend to diversify themselves through both visible and hidden channels into offshore investments. By the fact, many foreign companies trading with Russia use Cypriot subsidiaries in order to take advantage of the favorable taxation in Cyprus and essay doubletaxation agreement between Cyprus and Russia. Table 1 – The Structure of Accumulated Foreign Direct Investment to the Russian Economy  illustration not visible in this excerpt. The other phenomenon largely influencing Russian economy is of darkness ivory' investment withdrawal. Many globally operating multinationals have disinvested in manufacturing projects, due to the risks of funny local environments. Generally, low levels of FDI in Russia, as well outflows of capital and disinvestments are commonly used to illustrate the unsuccessful investment performance of the country during the period of transition. Find! However, so that to understand whether the FDI story was a success or failure, we must also try to essay oedipus answer the question of whether Russia benefited from foreign direct investments during the transition period, i.e. have those amounts of FDI which Russia received, a “success story”? If we look at the share of output of foreign owned firms in total output, we will see that it significantly increased during the period of transition (being around 2-3 percent in find, the beginning of the 1990s, it has grown up to 6-10 percent).
Figure 2 - Share of Output of Foreign Owned Firms in Total Output (%)  illustration not visible in this excerpt. While comparing the essay oedipus, productivity of foreign and find me a Russian owned firms, Yudaeva K., Kozlov K., Melentieva N. and Ponomareva N. found that the funny, former are more productive than the latter, as they have advantages on access to technologies and better management  . In spite of the fact that involvement of foreign capital had negative effect on how to write pm firms in vertically related industries (hence, negative effect for the suppliers), it was shown that Russian economy benefits from foreign direct investment both directly (by receiving money) and essay funny indirectly (through spillovers to domestic firms). Liudmila Bzhilianskaya  while observing a case study of foreign direct investments in find resume, the Science-Based industries of Russia, also found positive effects of transfer of management and oedipus funny marketing skills and hard technology. Most studies in can science and religion coexist essay, the field insist on the positive potential of foreign direct investments in Russia. However, most arguments are based more on qualitative then quantitative research, and thus can suggest primarily interpretations rather then reliable evidence.
Unfortunately, it is also hard to find studies explaining unsuccessful experience, exemplified by disinvestments in funny, Russia. If such studies were found, the answer to our question would be clearer.  David A. Follow Dreams! Dyker, Foreign Direct Investment in the Transition Countries: A Global Perspective, in Foreign Direct Investment and Technology Transfer in the Former Soviet Union’, ed. By David A. Duker, Edward Elgar 1999.  Foreign Direct Investment As Technology Transferred: Some Panel Evidence from The Transition Economies, by Naurto F. Campos and Yuko Kinoshita, The Manchester School Vol 70 No.3, June 2002, pp. Essay Funny! 398-419.  Liberalization of capital flows.  Foreign Direct Investment As Technology Transferred: Some Panel Evidence from The Transition Economies, by Naurto F. Campos and Yuko Kinoshita, The Manchester School Vol 70 No.3, June 2002, pp. 398-419.  FDI and the Macroeconomy in the Transition Economies, Background Paper for heart ivory', Special Session ²²² on FDI and the Restructuring of the Transition and Emerging Economies, prepared by Economic Analysis Division UN/ECE, December 6-7, 2000 // http://www.unece.org/press/specialevent/00rcmfd_documents/Ffdjoe.pdf.  Following Russian legislation, we can define FDI as purchase of at oedipus funny, least 10 percent of findings chapter dissertation shares in a Russian firm.
 On the Determinants of Capital Flight from Russia, by Marcella Mulino, in oedipus, AEJ March 2002, Vol. Include Findings Chapter! 30, No. 1.  ‘Attracting Foreign Direct Investment For Russia’s Modernization. Battling against the odds’, OECD-Russia Investment Roundtable, June 19, 2002, St. Petersburg, Russia // http://www.dundee.ac.uk/cepmlp/journal/html/vol12/article12-1.pdf.  ‘The Great transformation: Russia’s Return to the World Economy’, Paul Hare, Mark Schaffer, Anna Shabinina, Centre for oedipus, Economic Reform and Transformation, Heriot-Watt University, January 2004, A report for Media Strategy on Foreign Direct Investment in Russia // http://www.dundee.ac.uk/cepmlp/journal/html/vol12/article12-1.pdf.  Shaun Walker, ‘A Reverse in me a resume, Capital Putflow’, Russia Profile, Feb 17, 2006 // http://www.russiaprofile.org/business/2006/2/16/3271.wbp.  ‘Cyp-Rus Investment flows to essay Central and Eastern Europe – Russia’s Direct and find Indirect Investments via Cyprus and CEE’, Elina Pelto, Peeter Vahtra, Kari Liuhto, Turun Kauppakorkeakoulu, Turku School of Economics and Business Administration, Electronic Publications of essay funny Pan-European Institute, 2/ 2003 // http://www.tukkk.fi/pei/verkkojulkaisut/Pelto_Vahtra_Liuhto_22003.pdf.  Pelto E., Vahtra P., Liuhto K., Kauppakorkeakoulu T., Cyp-Rus Investment flows to Central and Eastern Europe – Russia’s Direct and Indirect Investments via Cyprus and CEE. emTurku School of Economics and Business Administration, Electronic Publications of how to write pm Pan-European Institute, 2/ 2003, p.12/em // http://www.tukkk.fi/pei/verkkojulkaisut/Pelto_Vahtra_Liuhto_22003.pdf.  Yudaeva K., Kozlov K., Melentieva N., Ponomareva N., Does Foreign Ownership matter?
The Russian Experience, emEconomics of Transition Volume 11 (3) 2003, 383-409, p.389/em //http://www.gdnet.org/pdf2/gdn_library/awards_medals/2004/r_m/fdi/does_foreign_ownership_matter.pdf.  Yudaeva K., Kozlov K., Melentieva N., Ponomareva N., Does Foreign Ownership matter? The Russian Experience, emEconomics of Transition Volume 11 (3) 2003, 383-409, p.389/em //http://www.gdnet.org/pdf2/gdn_library/awards_medals/2004/r_m/fdi/does_foreign_ownership_matter.pdf.  Bzhilianskaya L. Foreign Direct Investment in the Sciencebased Industries of Russia, in Foreign Direct Investment and Technology Transfer in the Former Soviet Union’, ed. By David A. Duker, Edward Elgar 1999. Research Paper (undergraduate), 35Pages. Master's Thesis, 108Pages. Bachelor Thesis, 65Pages. Scientific Essay, 8Pages.
Research Paper (undergraduate), 27Pages. Research Paper (undergraduate), 11Pages. Diploma Thesis, 101Pages. Term Paper (Advanced seminar), 19Pages. - Publication as eBook and essay book - High royalties for the sales - Completely free - with ISBN - It only takes five minutes! - Every paper finds readers. Research Paper (undergraduate), 35Pages. Master's Thesis, 108Pages. Bachelor Thesis, 65Pages. Scientific Essay, 8Pages. Research Paper (undergraduate), 27Pages. Research Paper (undergraduate), 11Pages.
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Oedipus essay funny | Best Essay …
Famous Unsolved Math Problems as Homework. One of my favorite assignments for essay oedipus funny, students in undergraduate mathematics courses is to find me a, have them work on funny, unsolved math problems. An unsolved math problem, also known to mathematicians as an “open” problem, is a problem that no one on earth knows how to solve. Can Science Essay. My favorite unsolved problems for funny, students are simply stated ones that can be easily understood. In this post, I’ll share three such problems that I have used in find me a resume, my classes and discuss their impact on my students. The Collatz Conjecture . Given a positive integer (n), if it is odd then calculate (3n+1). If it is even, calculate (n/2).
Repeat this process with the resulting value. For example, if you begin with (1), then you obtain the sequence [ 1,4,2,1,4,2,1,4,2,1,ldots ] which will repeat forever in this way. If you start with a (5), then you obtain the sequence (5,16,8,4,2,1,ldots), and now find yourself in the previous case. Essay Oedipus. The unsolved question about this process is: If you start from coexist essay any positive integer, does this process always end by cycling through (1,4,2,1,4,2,1,ldots)? Mathematicians believe that the answer is essay funny yes, though no one knows how to prove it. Essay. This conjecture is known as the Collatz Conjecture (among many other names), since it was first asked in 1937 by Lothar Collatz. The Erd o s-Strauss Conjecture . A fascinating question about unit fractions is the following: For every positive integer (n) greater than or equal to (2), can you write (frac ) as a sum of three positive unit fractions? For example, for (n=3), we can write [frac =frac +frac +frac , . ] For (n=5), we can write [ frac =frac +frac +frac ] or [frac =frac +frac +frac , . ] In other words, if (ngeq 2) can you always solve the equation [ frac =frac +frac +frac ] using positive integers (a), (b), and (c)?
Again, most mathematicians believe that the answer to this question is yes, but a proof remains elusive. This question was first asked by Paul Erdos and Ernst Strauss in 1948, hence its name, and mathematicians have been working hard on it ever since. Lagarias’s Elementary Version of the Riemann Hypothesis . Oedipus Funny. For a positive integer (n), let (sigma(n)) denote the sum of the positive integers that divide (n). Your Essay. For example, (sigma(4)=1+2+4=7), and (sigma(6)=1+2+3+6=12). Let (H_n) denote the (n)-th harmonic number, i.e. [ H_n=1+frac +frac +frac +cdots+frac , .] Our third unsolved problem is: Does the following inequality hold for oedipus funny, all (ngeq 1)? [ sigma(n)leq H_n+ln(H_n)e^ ] In 2002, Jeffrey Lagarias proved that this problem is can science and religion coexist essay equivalent to the Riemann Hypothesis, a famous question about the complex roots of the Riemann zeta function. Essay Oedipus. Because it is equivalent to follow your essay, the Riemann Hypothesis, if you successfully answer it, then the Clay Mathematics Foundation will reward you with $1,000,000.
While the statement of this problem is more complicated than the previous two, it doesn’t involve anything beyond natural logs and exponentials at a precalculus level. Impact on essay oedipus, Students. I’ve used all three of these problems, along with various others, as the focus of findings dissertation in-class group work and as homework problems in undergraduate mathematics courses such as College Geometry, Problem Solving for funny, Teachers, and how to write pm History of Mathematics. An example of a homework assignment I give based on essay, the Riemann Hypothesis problem can be found at this link. When I use these problems for in-class work, I will typically pose the problem to the students without telling them it is unsolved, and then reveal the full truth after they have been working for fifteen minutes or so. By doing this, the students get to dreams, experience the funny shift in findings, perspective that comes when what appears to be a simple problem in arithmetic suddenly becomes a near-impossibility. Without fail, my undergraduate students, most of funny whom are majors in math, math education, engineering, or one of the natural sciences, are surprised that they can understand the statement of an find, unsolved math problem. Most of them are also shocked that problems as seemingly simple as the essay oedipus funny Collatz Conjecture or the Erdos-Strauss Conjecture are unsolved — the ideas involved in the statements of these problems are at an elementary-school level! I have found that having students work on unsolved problems gets them engaged in three ways that are otherwise very difficult to obtain. Students are forced to depart from the “answer-getting” mentality of mathematics. In my experience, (most) students in K-12 and postsecondary mathematics courses believe that all math problems have known answers, and that teachers can find the essay answer to oedipus, every problem.
As long as students believe this story, it is hard to motivate them to develop quality mathematical practices, as opposed to doing the minimum necessary to follow dreams, get the “right answer” sufficiently often. However, if they are asked to work on an unsolved problem, knowing that it is unsolved, then students are forced to find other ways to define success in their mathematical work. While getting buy-in on oedipus funny, this idea is occasionally an issue, most of the time the students are immediately interested in the idea of an unsolved problem, especially a simply-stated one. The discussion of how to define success in mathematical investigation usually prompts quality discussions in class about the authentic nature of mathematical work; students often haven’t reflected on the fact that professional mathematicians and scientists spend most of their time thinking about how to solve problems that no one knows how to solve. Of Darkness Essays. Students are forced to redefine success in learning as making sense and increasing depth of understanding . The first of the mathematical practice standards in the Common Core, which have been discussed in previous blog posts by the author and by Elise Lockwood and Eric Weber, is that students should make sense of problems and persevere in essay, solving them. Coexist Essay. When faced with an unsolved problem, sense-making and perseverance must take center stage. In courses heavily populated by preservice teachers, I’ve used open problems as in-class group work in which students work on a problem and monitor which of the practice standards they are using. Essay. Since neither the students nor I expect that they will solve the problem at hand, they are able to really relax and your dreams essay focus on the process of mathematical investigation, without feeling pressure to complete the problem.
One could even go so far as to evaluate student work on unsolved problems using the common core practice standards, though typically I evaluate such work based on maturity of investigation and clarity of exposition. Students are able to work in a context in which failure is completely normal. In my experience, undergraduates majoring in the mathematical sciences typically carry a large amount of guilt and funny self-doubt regarding their perceived mathematical failures, whether or not it is justified. From data collected by the recent MAA Calculus Study, it appears that this is findings particularly harmful for women studying mathematics. Oedipus Funny. Because working on unsolved problems forces success to be redefined, it also provides an follow dreams essay, opportunity to discuss the essay definition of failure, and the pervasive normality of small mistakes in the day-to-day lives of mathematicians and scientists. Apostle Resume. I usually combine work on unsolved problems with reading assignments and classroom discussions regarding developments in educational and social psychology, such as Carol Dweck’s work on mindset, to help students develop a more reasonable set of expectations for their mathematical process. One of the most interesting aspects of using unsolved problems in my classes has been to oedipus, see how my students respond. I typically ask students to write a three-page reflective essay about me a resume, their experience with the essay oedipus homework in how to write pm, the course, and almost all of the essay funny students talk about working on the open problems. Some of coexist essay them describe feelings of essay oedipus relief and joy to have the opportunity to be as creative as they wish on a problem with no expectation of ivory' essays finding the right answer, while others describe feelings of frustration and immediate defeat in the face of a hopeless task.
Either way, many students tell me that working on an unsolved problem is one of the noteworthy moments in the course. For this reason, as much as I enjoy witnessing mathematics develop and progress, I hope that some of my favorite problems remain tantalizingly unsolved for many years to oedipus, come. 13 Responses to Famous Unsolved Math Problems as Homework. Thanks for the great ideas Ben! I currently have some students working on Sylver Coinage as part of a final project in a Number Theory class. They have come up with a few strategies on their own and are intrigued by include chapter dissertation the fact that more strategies haven’t been discovered. It’s even more interesting that there are nonconstructive proofs for essay oedipus, strategies. Because these students know the problem is unsolved, they are more apt to be proud of small steps forward. I’d love to hear more ideas of what is done in other classes.
I hadn’t heard of that problem before, it sounds like an awesome project! Came here from chapter dissertation https://news.ycombinator.com/item?id=9537802. In the Erdos-Strauss conjecture why is it 4/n. Clearly one is limited by the highest number achievable with the fractional terms on the right, but why not the general question x/n = Sum 1/a[i] for i from 1 to essay funny, (x -1)? [attempted to render that in mathml:] Has a form of this been solved generally for other x values ( 3) and chapter 4/n is an outlier?? In my mind geometric solutions for the first two are so obvious (!) however in my current state of mind I’m far more inclined to the pragmatic “well you can show if it’s true for any particular n you care about, close enough” – think I’m losing my youthful inquisitiveness! Some work has been done on essay, the more general case, see Terry Tao’s comments on include findings chapter, his blog https://terrytao.wordpress.com/tag/erdos-straus-conjecture/ and oedipus the references therein. This is fantastic and inspiring! Thank you.
Hey, Beth, thanks for mentioning the Coinage Problem. I have been teaching Discrete Math (including some number theory) at the University of Alabama for years and one of the problems in our book has to do with making change. Once I read your note, I googled (or do I mean capitalized Googled?) the how to write pm coinage problem and, lo and behold, it has a long history! Sylvester! Frobenius! Wow…I am going to try this question in my class this semester to see if the essay oedipus funny kids can guess and then prove Sylvester’s (a-1)(b-1)-1 theorem! I don’t think I’ll ask them to prove the Lagarias version of the Riemann Conjecture, though… I wish that 30 years ago I had studied under you.
At first read, I thought this was cruel and unusual punishment, then I realized your method. Wonderful… you are someone who should keep teaching forever. Please keep doing what you’re doing. If I didn’t live so far from Kentucky I would be begging to audit one of how to write pm your classes. I am not a mathematician but I have a question about the The Collatz Conjecture.
If we take any positive number and lets say it is an essay oedipus, even number then, we will divide it by 2. and apostle paul resume obviously we will get the Even number and then again we will divide it by 2 and again we will get the even number and this process will continue until we come to 4 and then we will divide the 4 by 2 and we will get 2 and then divide 2 by 2 and we will get 1 so it will always end with 4.2.1. Incase of odd number we will do the 3n+1 that means we will get the Even number and then again the Even number process that means we will also end up with 4.2.1. So what is need to be proven here. It is obvious and can be proved with the simple number theory. Your suggestion only works for powers of 2. Essay Oedipus. If you have a number like 10, which is even but has odd factors, then it isn’t clear what will happen. Wonderful post! I will be sharing this in my on-going conversation about authentic curriculum in elementary mathematics. I use open problems frequently in my 4th and 5th grade maths classes, especially during, but not limited to, our units on number theory. Can Science And Religion Coexist. The students love the funny work. Follow Your Dreams Essay. It is fun, engaging, motivating, empowering and capitalizes on their natural curiosity.
Many students stick with the problems after we’ve moved on because they hope one day someone will find the proof and move them beyond conjecture. Like Julie Robinson and the diophantines, it didn’t have to essay, be her, she just hoped for a proof in findings dissertation, her lifetime so she could celebrate it. Furthermore, these problems do a wonderful job of oedipus showing students that mathematics is dreams essay not dead, but full of discovery and oedipus funny humanity. They are motivated to your essay, learn more about the players and their stories. I don’t want to waste you time but I really find it fascinating. So I Just wanted to understand it more. If I take 10, its a even number and I divide it by 2, I will get 5 and then (3x+1) so I will get 16 and then divide it by 2, will get 8 and then 4,2,1. Essay Funny. So whats the problem in it.
Just to understand this better. Thank you so much for such interesting post. This page: https://en.wikipedia.org/wiki/Collatz_conjecture has lots of good information about the details of the conjecture. At the find end of the page, there is a nice list of references where you can find more detailed discussions about why the problem is difficult. I think this is a brilliant idea. It not only gets fresh insight on mathematical problems whose solutions have still not been figured out. It also forces students to think outside of the funny box and try things they wouldn’t normally do.
One of the include chapter biggest issues I have seen in the mathematics courses I have taken at my university is that failure and mistakes are seen as bad and essay oedipus funny terrible. When in fact they are the opposite. They promote learning and greater understanding that just simply getting the right answer. Paul Resume. They promote learning the process and method behind the problem instead of essay just regurgitating a solution. It also forces students to paul, come at problems from different angles and figure out new methods for solving problems than just the tried and true methods. I believe your method is absolutely necessary for essay funny, riding the mindset that there is one set way of apostle paul solving a problem or that failure is essay funny not an option. I believe all professors should adopt this mindset for can science and religion, teaching mathematics at any level. This is oedipus funny because it makes it easier for students to learn and allows them to not be discouraged when they don’t understand something right away or after the first few times.
It promotes persistence and the pursuit of understanding which is critical for any student who is studying mathematics to understand and acquire those qualities. If more students thought like this then in my opinion they would be more likely to succeed and heart of darkness essays flourish in essay, any field they choose not just mathematics. Mathematics at it’s core is the understanding of the universe around us and include findings the laws that govern it. It is reason and logic and without persistence and understanding we will never fully understand it and that is a crime in and of essay funny itself. The opinions expressed on how to write pm, this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society. The AMS encourages your comments, and hopes you will join the discussions. We review comments before they're posted, and those that are offensive, abusive, off-topic or promoting a commercial product, person or website will not be posted.
Expressing disagreement is essay funny fine, but mutual respect is required.