Dumping essays

Dumping expositions The World Trade Organization Agreement on dumping characterizes it comprehensively as an organization sending out an item at a value lower than the value it ordinarily charges on its home market for a like item. At the point when merchandise are imported at a cost beneath the residential makers value, cries of out of line rivalry and dumping are frequently heard. Weight is applied among the nations government to plan something for ensure their market against the imported items. The legislature may force obligations to the imported item under three WTO understandings. The Anti-dumping Agreement and The Agreement on Subsidies and Countervailing Measures make a move against those shippers who are bringing in at uncalled for import costs. The third understanding, The Safeguard Agreement, makes a move when the import cost is reasonable yet the imports are truly harming local creation. Residential organizations can demand defend activity if the piece of the overall industry of imports woul d some way or another considerably increment. This generally includes the commitment of quantitative limitations on imports, however these can't be focused at a particular nation. Hostile to dumping arrangements, then again, permit countries to fight back against explicit exchanging accomplices who are trading merchandise at costs lower than those that flourish in their local markets. This counter for the most part includes charging a compensatory obligation to bring the cost of a particular decent from a particular nation back to an ordinary cost. At long last, countervailing duties are measures intended to diminish the impact of remote sponsorship programs. All are expected to be transient activities that settle the issues rapidly. Anyway as observed in many dumping cases worldwide that is regularly not the situation. At the point when a nation accepts that products are being dumped into their nation, the initial step they can take is to document a conventional grumbling against the shipper. The residential government, in light of point by point requirem ... <!

Guerilla Warfare Essays

Guerilla Warfare Essays Guerilla Warfare Essay Guerilla Warfare Essay Jared NorthridgeEnglish IIMrs. Davidson8 March 2012Guerrilla WarfarePicture yourself as an American fighter strolling through a wilderness. The main commotions you hear are the drops of dampness ricocheting off the leaves of the trees and the strides of different officers in your unit. You are in a remote nation you have never known about, battling for a reason you don’t completely comprehend. You are in a little Asian nation called Vietnam performing look and decimate missions, scanning for your foes and afterward killing them. You are in a town looking for the Viet Cong. You have all the inhabitants of the town arranged. They’re all in a frenzy and you do not understand what they’re saying. Out of nowhere you’re being shot at from one of the cottages. A portion of the individuals you thought were only inhabitants of the little wilderness town are currently executing off your unit, your siblings. Through frenzy of the residents and sound of shots flying p ast your head, you conclude it is simply best to rests and pause. The before you know it the shooting has halted, and you hear the sound of certain individuals running profound into the timberland. You were only the casualty of guerrilla warfare.A part of wars have been lost in light of guerrilla fighting. Two models are the United States Vietnam War and the French’s attack of Spain. Guerrilla fighting is â€Å"the utilization of attempt at manslaughter strategies by little, versatile gatherings of sporadic powers working in an area constrained by an antagonistic, normal force† (â€Å"Guerilla† p1).The Vietnam War was battled from November 1, 1955, to April 30, 1975. The Vietnam War was battled between North Vietnam, and their socialist partners, and South Vietnam, upheld by the United States and other non-socialist nations (â€Å"Vietnam† p1). The North Vietnamese had a distinct advantage called the Viet Cong (p7). The Viet Cong are â€Å"South Vietname se guerrilla force† (p7). The war was a difficult task for the United States and South Vietnamese, in light of the fact that the Viet Cong were utilizing their guerrilla

A Slip Of The Lip

A Slip Of The Lip A Slip Of The Lip A Slip Of The Lip By Sharon Its simple to entangle when talking or composing, however what do you call the outcomes when you do? Half a month back, I expounded on eggcorns. These are blunders in which individuals surmise wrongly the importance, cause and spelling of specific articulations. A model would compose or saying defect in the salve rather than fly in the balm. Another mistake, put on the map by Sheridans Mrs Malaprop, is the malapropism. On the off chance that you intend to state a certain something, however utilize a comparable sounding word that implies something totally extraordinary, at that point that is the thing that youve done. Model: A drifter assembles no moths. (greenery) Like an eggcorn, yet normally occurring with tunes and sonnets, is the mondegreen. In the tune The Bonny Earl of Murray, the line (hae laid) him on the green was confused as Lady Mondegreen. Different instances of mondegreens, gathered by writer Jon Carroll, include: Climb Every Woman (Im Every Woman, by Chaka Khan) I Was Barney Rubble (I Was Born A Rebel, by Tom Petty) Falling on my head like a newt moving (falling on my head like another feeling, from Here Comes The Rain Again, Eurythmics) A lot more mondegreens are accessible here (Update: SFGate article not, at this point on the web). At last, spoonerisms come about because of transposing the underlying hints of words. Named after minister William Archibald Spooner, the subsequent words as a rule incite storms of chuckling. Models from Spooner himself include: It is presently kisstomary to cuss the lady of the hour. (standard to kiss the lady of the hour) You have tasted two worms (squandered two terms) Our Lord is a pushing panther (adoring shepherd) A lot more Spoonerisms are accessible on Fun with Words. Need to improve your English in a short time a day? Get a membership and begin getting our composing tips and activities every day! Continue learning! Peruse the Expressions class, check our famous posts, or pick a related post below:10 Rules for Writing Numbers and Numerals15 Types of DocumentsPeople versus People

Materials of Logistics in Management Essay Example for Free

Materials of Logistics in Management Essay The productivity of any assembling association relies upon the accessibility of segment parts and materials in the correct amount, quality, value, range and time. Disappointment in any of these regions expands expenses and diminishes benefit as unquestionably as old fashioned creation strategies or ineffectual selling procedures. This basic however evident point has as of late come to be appropriately comprehended. This book presents the standards, techniques and methodologies that speak to the cutting edge way to deal with materials the board in all divisions of the economy. In breaking down business activities, the expression Value-added concept1 is frequently used to describe the distinction between the expense of part materials and the selling cost of the completed item. This distinction in esteem speaks to the one of a kind commitment of every association to the creation procedure. Numerous organizations produce segment parts and materials for different firms fabricating specific items Remanded by the clients. On a normal, an assembling firm purchases marginally the greater part of the rupee estimation of its deals. As it were, the worth included is ordinarily under 50 percent of its deals. On the other hand, the normal organization buys materials esteemed at the greater part of what it sells. In this manner, an organizations benefit is to a huge degree dictated by how successfully it obtains and deals with these materials. The hierarchical methodology known as materials the board has picked up legitimacy as of late. Creation and activities supervisors thought that it was important to build up a composed collection of information identified with arranging, securing and use of materials during the time spent creation and it has brought about the order known as mate-rials the board. All exercises engaged with bringing materials into and through the plant are consolidated under one head known as materials chief. By giving the materials supervisor by and large position, obligation is concentrated to guarantee that the general expense of materials is kept at the most reduced conceivable level. The essential reason for this hierarchical change is to conquered the issues of clashing destinations. For cample, buy divisions worry to guarantee consistent gracefully of segment materials may strife with he stock control offices target to limit stock levels or the goal of delivery in full vehicle load parcels. Today associations see acquirement as an expert action incorporating exercises engaged with getting materials at least cost, shipping them and giving stockpiling and advancing toward the creation procedure. It likewise incorporates monetary examination of flexibly (I. e. , buy financial aspects), request and costs and the appraisal of global occasions that influence materials. * advancement of materials the executives Historically, the five ‘M’s of assembling firms viz. Men, Materials, Machines, Money and Methods have moved their situations every now and then in their relative significance. In the beginning of industrialization, the attention was on men (work) as they were the primary wellspring of profitable force. Over some stretch of time, the accentuation moved towards machines, which turned into the principle wellspring of modern force after the Industrial Revolution. As the techniques for creation turned out to be increasingly more perplexing because of the expanded client interest for modern results of top notch, there was more prominent need of proficient administration to deal with the unpredictable creation frameworks. In the mid 1920s, buying and keeping up supply of materials was the duty of buying directors or boss controllers of buying and stores in numerous ventures. During and following World War II the attention moved on different capacities related with materials, for example, buying, accepting, investigating, putting away, protecting, taking care of, giving, bookkeeping, shipping and arranging overflow and out of date materials. These capacities gathered under one basic head known as materials director and the division answerable for every one of these exercises came to be known as materials the executives office. Yet, the head of materials the board office played out a staff capacity to help the creation office and needed to answer to the creation head (executive of creation) in the authoritative chain of importance. The oil emergency of the 1970s changed the needs of enterprises everywhere throughout the world. The extreme climb in oil costs and the substantial spending portions on oil made the businesses to control their consumption on the information sources, for the most part materials of assorted types as a result of the huge degree to decrease the costs on materials. Since the start of twentieth century, materials have been getting increasingly more consideration and will keep on doing as such later on moreover. Presently a days material has* become a significant and unavoidable contribution of a creation framework since the expense of materials and cost on materials (cost brought about in buying and putting away the materials) set up represent 50 to 85% of the creation cost contingent upon the idea of the item and the kind of the creation framework. Current assembling associations received frameworks way to deal with the board, which brought about the coordinated materials the board idea. All capacities identified with materials, for example, materials arranging, buying, putting away and stock control were coordinated under materials the executives work. The situation of the leader of the coordinated materials the executives office was raised to be comparable to heads of other utilitarian territories viz. creation, account and HR. * significance of materials in assembling associations Materials are any wares utilized straightforwardly or in a roundabout way in delivering an item or administration, for example, crude materials, segment parts, congregations and supplies. In the assembling associations, the significant sources of info are alluded to as 5 Ms viz. Men (Labor), Machines, Money, Materials and Methods. The relative significance among these five Ms have moved every once in a while. In the start of industrialisation the attention was on machines, men (work) and strategies, however from around 1970 onwards the accentuation is on materials. Material is a significant and inescapable information gi J creation framework since the expense of materials and cost on materials (cost caused in buying and putting away the materials) set up represent 50 to 85* of the creation cost contingent upon the idea of the item and the kind of the creation framework * significance of materials the executives The executives of materials in many associations is significant to their prosperity on the grounds that the expense of buying, putting away, moving and delivering materials represent over portion of the items cost. Improving profitability is an essential factor in confronting the test of rivalry and this includes driving down the expense of all parts of business exercises. Since there is most extreme extent of cost decrease in the territory of materials, carrying out the responsibility of proficient and powerful administration of materials is viewed as the way to higher efficiency.

Logistics in Practice

Official Summary Foreign speculators have grasped the open entryway arrangement and minimal effort work, existing in China to grow their organizations. In China, most worldwide organizations have spread across significant urban areas, for example, Beijing, shanghai and Guangdong districts, which give good business condition to development. On the other hand, since joining the World Trade Organization, WTO, in 2002, additional open doors for Chinese have taken root.Advertising We will compose a custom report test on Logistics in Practice explicitly for you for just $16.05 $11/page Learn More Thus, the nation increases in; expanded exchanging territory, assurance guidelines and arrangement power (Yu Xia and Li-Ping, 2011).Despite of significant advancement accomplished in flexibly chain the executives by the legislature, there still a requirement for development, to viably manage pacing globalization, advancing innovation and rivalry allowed by comparable firms all around. Difficulties influencing Chinese firms have looped around coordinations the board, lawful condition and framework. In any case, with legitimate changes, grasping current innovation and globalization, it is unmistakable that the calculated condition will watch out for another upper hand to coordinations firms in the nation. Western nations have, extra time in redoing their gracefully chain tasks. Investigating openings past their outskirts, grasping financially savvy techniques and government support has been a main thrust for their prosperity. Be that as it may, issues, for example, versatility of flexibly chain, information security danger and regular disasters have hindered their quality. Presentation Globalization of exchange and mechanical movement of organizations over the world have improved exchange between nations. Deliberately, this has fixed an open door for nations to smooth out their coordinations the executives practices to make an upper hand (Sandelands, 1997). Nations have unendi ngly connected their gracefully chain to worldwide systems to profit by the open doors existing inside their national extension. The worldwide systems have given a detailed coordinations framework, which has bring about enlarging operational productivity, quick item conveyance and accomplishing the business destinations. This paper inquires about on coordinations and tasks the executives in China and Western nations. The paper investigates the prescribed procedures, difficulties, patterns and basic issues of gracefully chain activities and the executives forms existing between these two countries.Advertising Looking for report on business financial matters? We should check whether we can support you! Get your first paper with 15% OFF Learn More Information about China Despite ongoing worldwide downturn, money related fiascos, and monetary downturn, China has remained as one of the most dynamic and developing economies on the planet. This has undermined financial powerhouses of the W est. In any case, Sandelands (1997) contends that remote firms or speculators in China have experienced strategic difficulties in wording because of an extensive degree of business wisdom in the neighborhood Chinese market. They have refered to reasons, for example, un-smoothed out coordinations tasks and the board rehearses due to the expanded or quick monetary development, and request in conveyance ( Sandelands, 1997). On the other hand, the Chinese government, as of late, has perceived the test, and has genuinely started patching up its coordinations tasks and the board, as an instrument for key financial development. This has been accomplished through financing coordinations firms, refining coordinations frameworks, making an across the nation multimodal transport system and building an enormous scope calculated focus (Lin and Ho, 2009). Writing Review Best Practices Technology is fundamental in smoothing out gracefully chain exercises. As per Jiang and Prater (2002), while choo sing and actualizing innovation in gracefully chain activities, it is crucial to characterize a strategic component, and business forms. It is an insightful choice to survey the requirements of the client and assess the requirement for innovation in explaining the customers’ need. La Londe and Masters (1994) bears witness to that, surfacing with unequivocal prerequisites may demonstrate extreme and numerous organizations neglect to take care of business. This is on the grounds that most organizations harp on distinguishing direct expenses and investment funds instead of, measuring basic components, for example, stock and work, and shrouded costs. While choosing innovation, it is acceptable to grasp the arrival on speculation, RIO, as the benchmark; this guarantees substantial advantages are accomplished all the while (Moncrieff et al, 2003). China has recently, fused innovation in gracefully chain tasks and the executives. The web driven innovation, for example, EDI is regula r across gracefully chain preparing organizations in the country.Advertising We will compose a custom report test on Logistics in Practice explicitly for you for just $16.05 $11/page Learn More The Electronic Data Interchange (EDI) has disentangled sharing of business archives, for example, charges, buy requests and solicitations (La Londe and Masters, 1994). In addition, sharing data over the EDI has empowered fast reaction to showcase requests and forecast of market changes. The West flexibly chains have additionally productively used innovation in gracefully chain activities. Most strategic firms have executed advances to rearrange business procedures and activities. One of the advancements making upper hand for Western firms is the RFID. As per Lin and Ho (2009), RFID is an innovation that improves following procedure of items, as they move from the producers to the purchaser. Drã ¶ge, and Germain (1991) delineate that best practice in material’s taking care of diminish contact work, underpins esteem include activities and aides in taking care of various assembling situations. Be that as it may, to win this best practice, materials-taking care of frameworks ought to be moderate other than spanning free data stream in the business, and the providers. Most West coordinations firms, for example, the US have grasped E-trade; this has diminished the issue of material dealing with by making an upper hand (La Londe and Masters, 1994). In the US, organizations, for example, Wal-Mart, Amazon, e-straight has effectively limited material dealing with through online business (Lieb, 1992). As per Manuj and Sahin (2011) having a flexibly chain that furnishes a client with item customization, and assorted variety through additional worth administrations, is having the best practice that is effective. That is, does exactly what a client request (Manuj and Sahin, 2011). In Spain for instance, it is a necessary for a business to look at its activities with a refresh ed records of yesterday’s challenges just as estimating on future upgrades (Drã ¶ge, and Germain, 1991). Difficulties of flexibly chain the board in China and the West China has encountered a few difficulties in gracefully chain the executives for quite a while. This, to a bigger broaden has influenced flexibly chain organizations in the nation. The difficulties have waterlogged different parts of flexibly chain the board; warehousing, transport, buying, stock control, request preparing and import/send out services.Advertising Searching for report on business financial aspects? We should check whether we can support you! Get your first paper with 15% OFF Find out More As per Jiang and Prater (2002), these obstructions have emerged on account of the inside wastefulness. For instance, Jiang and Prater (2002) attract that most assembling firms China have been confronting significant difficulties in transport and responsibility for administrations. These difficulties have influenced the degree of satisfaction in giving vehicle administrations. In his study, Drã ¶ge and Germain (1991) investigated difficulties confronting Joint Ventures in China; he noticed that there was a test in maintaining a concurrent quality level, though diminishing expenses by buying assets locally. Exceptional Features of Supply Chain The models of the coordinations and flexibly chain are firmly related. Gracefully chain supports all the jobs and exercises tied in satisfying a customer’s demand. These exercises incorporate; fabricating, shipping, warehousing and flexibly of crude materials and the (Yu Xia and Li-Ping, 2011). The job of a gracefully chain involves a con sistent progression of data, change and conveyance of merchandise from crude materials stage all the way to the finish client. The significant explanation that fixes the accomplishment of a flexibly chain is the procedure of incorporation among purchasers and providers, the framework that connections accomplices and the market keenness on the base of data instead of stock. Gracefully Chain has remarkable highlights, which makes it exceptional in succeeding its assignments. One of the highlights is stock administration. This component empowers a firm to follow and oversee supplies of crude materials and constituents required for creation, completed or finished products to achieve open deals requests and extra parts required for field administration and food. This aides in limiting waste, stockpiling expenses and opens up the firm for other fundamental purposes (Jiang, 2002). Request the board is likewise another exceptional element of a gracefully chain. Request the executives moves in accelerating the execution of the entire procedure of request to conveyance cycle by making firms to gainfully create and follow deals orders (Ip et al, 2011). This office likewise makes dynamism in booking gracefully conveyance, to achieve a request and increase a fast age of estimating and item arrangement. Globalization has made organizations to grow immensely, accepting up open doors existing in remote terrains. Coordinations, an administration highlight associated with gracefully chain streamlines coordination of overflowing distribution centers and transport courses reinforcing on-time conveyance execution making consumer loyalty (Yu Xia and Li-Ping, 2011). In addition, coordinations the board assists with accomplishing client item perceivability and shows how a finished item, put away and dist

Course 18

Course 18 As some of you may know, I am majoring in math and economics. Michelle has already written a lovely post about Course 14 (economics); I want to also talk a little about my experience being Course 18 and how it has differed from my experience doing math in high school. Basics: There are four types of math major at MITâ€"pure math, general math, applied math, and math with computer science. I do pure math, which will be the subject of this blog post. It’s important to note that there are significant differences among the different tracksâ€"applied math has a whole different set of requirements, of which I have taken very few, and general math has super flexible requirements. Math with computer science, or 18C, requires several computer science classes and math classes that double as computer science classes; I have also taken very few of those. My perspective is that of someone who has been firmly on the pure math track for a few years and who hasnt taken many of the more applied or CS-related classes. So let me now talk about my pure math classes. The requirements are: one differential equations class, a real analysis class, two algebra classes, one topology class, one additional analysis class (manifolds, functional analysis, or Fourier analysis), one or two seminars (depending on whether you took the “communication-intensive” version of real analysis or another “communication-intensive” class), and at least two additional math classes of your choosing. Heres a page describing the communciation-intensive math classesbasically, theyre math classes with a heavy writing/presentation component, so that math majors learn how to talk and write (in LaTeX) about their work. I recently realized that I am almost done with my major requirements (as in, I just dropped the one remaining class that would fill them out. It has been very abstract and mentally demanding but also satisfying). My college math classes require a lot more mental legwork than my high school ones did, in the sense that I’ve had to do much more struggling and wrestling with many new abstract concepts in my head for long periods of time, and it has been difficult! But worth it!! Differences from high school: I think I came into college with the expectation that my classes would be noticeably harder and more time-consuming than they were in high school, and for the most part that turned out to be true, though they ramped up in difficulty gradually rather than all at once. However, I also used to have the sense that I could learn anything I wanted as fast as I wanted, and I have definitely changed my mind on this front and come to terms with my limits in the past 2.5 years of school. One thing I want to note is that if you don’t think high-school math is particularly exciting or do math competitions, but you like to think about abstract concepts, please do keep an open mind about college math classes! My math classes in high school demanded a lot of memorization, and the problem-solving often turned out to be pretty algorithmic. Apply the concept you learned in class to a problem like the one from class, but with different numbers. After a certain amount of “training,” a sizeable chunk of competition math was like this for me, too. Specifically, I got better at math competitions by taking a lot of old practice tests, so that many of the problems I encountered were variations on old problems I had seen before. I guess I performed moderately well at math competitions, and they were part of what made me want to come to MIT, but I don’t think they were particularly good at showing me what being a math major would be like. Some things haven’t changedâ€"as in high school, it helps to do practice problems, so you’re familiar with all the possible concepts and theorems you might be able to apply on an exam. It’s just that now there isn’t often enough time to practice enough, depending on what the rest of your schedule looks like. Also, theres less emphasis on memorizing material for exams, and homework is often weighted equally with exams. As a whole, homework is served in larger chunks than it is in high school, so its important to learn to manage your time. There are also fewer examples in class and fewer problems that are near identical to those in the textbook. Finally, a big change is that everything is proof-based (as I write this, I struggle to remember what it meant for math to not be proof-based). You’re basically given an ever-expanding toolbox of definitions and lemmas and theorems and have to tinker until you can assemble them into solutions to the problems you’re asked to solveâ€" it is a creative activity with strict rules and very little grounding in reality and applications. A great benefit of college math classes (besides GIRs) is that they’re full of people who actively like to think about math, and hopefully, if you’re a math major, you think math is pretty cool, too. It’s nice doing math with no expectation that it will be applicable in any way. I recently had to teach a section of a textbook for my math seminar, and it was all about applying the theory in the previous sections of the book to a physics problem (the displacement of a cantilever beam at rest with only the force of gravity acting on it, if you’re interested!!!). Even though I was tasked with presenting this part of the book, it was definitely not the section of the book I would consider the most interesting. I personally thought the fact that the material was applicable to a physics problem was much less exciting than the proofs in the previous sections. I am pretty sure no one is taking that seminar to learn about the ways in which math is applicable to physics. The main trend I have noticed is that math in college is much more intellectually stimulating and abstract than what I encountered in high school. By the way, if youre at all peeved by the way math is taught in your high school, or curious about what math is like when its separated from its applications, I urge you to read Lockhart’s Lament, which was required reading for the communication-intensive real analysis class (18.100C, now renamed 18.100Q) I took my freshman spring. It criticizes math education in grade school and argues that math is an artistic and creative pursuit that is not taught as suchâ€"but should be. He laments the fact that students find math boring and suggests that the mainstream pedagogy is at fault. Struggles: It really helps to develop a strong intuitive understanding of the material you’re learning, although sometimes it gets difficult because there are no good analogies to real life. Sometimes you get stuck rereading a definition over and over and over, trying to flip back to earlier definitions that the current definition refers to in an effort to regain understanding of all the concepts that the concept at hand relies on, but to no avail, because there’s some other relevant concept from a math class you took two years ago that you need to revisit, so you look it up on Wikipedia, but by the time you understand it again, you forget what you were originally looking at, so you’re left scrambling to retrace the string of things you referred to, and at this point you still haven’t even started to solve the actual problem… Sometimes. But most of the time it’s not that bad. Sometimes it’s just tedious, and sometimes you have to write out long expressions with a lot of symbols in order to rigorously explain something that’s much easier to explain intuitively. Lockharts Lament is nice, but at some point you also have to buckle down and slosh around in tedium and make sure that all your symbols are written correctly. Getting used to math in college and dealing with impostors syndrome: I took 18.022 my freshman fall and found that it helped ease me into the sort of proofs and thinking that the rest of my math classes required. Perhaps if I had jumped immediately into 18.100 I would have been overwhelmed; I know for sure that I wouldn’t have been able to handle 18.701. There are people who can, and seeing other freshmen sail through more advanced classes definitely freaked me out at times and stoked my first touches of impostor’s syndrome. Now, though, I don’t think I can adequately stress the importance of not going too fast. Because math classes often rely on definitions and material from prerequisites, these prerequisites are often super useful, unless youve actually learned the exact material from the class you want to skip. Of course, there are exceptions, but I often find it a lot more difficult to grasp mathematical concepts that Ive forgotten or skipped than to pick up other new material, like a programming language. I took 18.701 sophomore fall, and I attempted to take 18.702 last spring, but I ended up dropping it because I was overwhelmed by all the other stuff I was trying to do/learn. I was taking 18.125 concurrently. This semester, I once again made the poor choice of taking three math classes simultaneously, but I ended up dropping one of them last week because I simply could not handle it. I did not have enough time or energy to wrap my head around all the material, and I’m finally (finally) coming to recognize the importance of learning things well and deeply rather than learning them as fast as possible. Bear in mind that this sequence just happens to be what I ended up with, and it is not a recommendation that everybody should take those classes in this order. I am hesitant to give general advice about what classes to take and when because it depends so much on your personal background and how much time you have to devote to the class! A relevant article about impostors syndrome and the feeling of racing to learn math is “The Wrong Way to Treat Child Geniuses” by Jordan Ellenberg, a former “child prodigy” who is now a math professor at UW-Madison. This one might be particularly relevant to people who didn’t grow up being praised for being “good at math” or winning awards at math competitions. (This one’s also particularly hard to access without a WSJ subscription, sigh…) I’ve reproduced a relevant paragraph below: One of the most painful aspects of teaching mathematics is seeing my students damaged by the cult of the genius. That cult tells students that its not worth doing math unless youre the best at mathbecause those special few are the only ones whose contributions really count. We dont treat any other subject that way. Ive never heard a student say, I like Hamlet, but I dont really belong in AP Englishthat child who sits in the front row knows half the plays by heart, and he started reading Shakespeare when he was 7! Basketball players dont quit just because one of their teammates outshines them. But I see promising young mathematicians quit every year because someone in their range of vision is ahead of them. I think that MIT students, especially freshmen, are prone to psyching themselves out comparing themselves to all the people around them who have won the IMO or who were doing calculus in middle schoolâ€"but Ellenberg points out that this type of thinking sounds absurd when applied to other fields and skillsand there is no reason that it should apply to math more than any other field. One of the first math majors I met at MIT had never done math competitions in high school and hadnt had much exposure to higher-level math (i.e. calculus and beyond) coming into MIT, but he loved the math classes he was taking in college, so he began to register for more and more of them until he was thinking seriously about pursuing it as a profession. He was initially intimidated by his peers but enjoyed math so much that it was not a chore at all for him to devote significant amounts of time to mastering his coursework. He later became involved in research and is now pursuing his PhD in math at MIT! In summary, if you think math is cool, please consider continuing to study it in college, but bear in mind that college classes arent exactly like high school classes. And if you dont think math is cool, maybe it hast to do with the way math is taught in your school. Or maybe notnot everyone is destined to be a math major! And if youre intimidated and convinced that youll never be good enough at math, because other people seem to be so far ahead, well thats almost certainly not the caseits much more important that you enjoy the subject and dont try to jump ahead so quickly that you lose enjoyment of the subject in an attempt to catch up. If anyone has specific questions about classes or anything like that, I would also be happy to try to help you individually. I know I have been pretty absent from the blogslife update coming soonbut Im getting back in the swing of things. Sending you all strength and luck for pi day and all subsequent college and major choosing! Post Tagged #Course 18 - Mathematics #Imposter's Syndrome

Course 18

Course 18 As some of you may know, I am majoring in math and economics. Michelle has already written a lovely post about Course 14 (economics); I want to also talk a little about my experience being Course 18 and how it has differed from my experience doing math in high school. Basics: There are four types of math major at MITâ€"pure math, general math, applied math, and math with computer science. I do pure math, which will be the subject of this blog post. It’s important to note that there are significant differences among the different tracksâ€"applied math has a whole different set of requirements, of which I have taken very few, and general math has super flexible requirements. Math with computer science, or 18C, requires several computer science classes and math classes that double as computer science classes; I have also taken very few of those. My perspective is that of someone who has been firmly on the pure math track for a few years and who hasnt taken many of the more applied or CS-related classes. So let me now talk about my pure math classes. The requirements are: one differential equations class, a real analysis class, two algebra classes, one topology class, one additional analysis class (manifolds, functional analysis, or Fourier analysis), one or two seminars (depending on whether you took the “communication-intensive” version of real analysis or another “communication-intensive” class), and at least two additional math classes of your choosing. Heres a page describing the communciation-intensive math classesbasically, theyre math classes with a heavy writing/presentation component, so that math majors learn how to talk and write (in LaTeX) about their work. I recently realized that I am almost done with my major requirements (as in, I just dropped the one remaining class that would fill them out. It has been very abstract and mentally demanding but also satisfying). My college math classes require a lot more mental legwork than my high school ones did, in the sense that I’ve had to do much more struggling and wrestling with many new abstract concepts in my head for long periods of time, and it has been difficult! But worth it!! Differences from high school: I think I came into college with the expectation that my classes would be noticeably harder and more time-consuming than they were in high school, and for the most part that turned out to be true, though they ramped up in difficulty gradually rather than all at once. However, I also used to have the sense that I could learn anything I wanted as fast as I wanted, and I have definitely changed my mind on this front and come to terms with my limits in the past 2.5 years of school. One thing I want to note is that if you don’t think high-school math is particularly exciting or do math competitions, but you like to think about abstract concepts, please do keep an open mind about college math classes! My math classes in high school demanded a lot of memorization, and the problem-solving often turned out to be pretty algorithmic. Apply the concept you learned in class to a problem like the one from class, but with different numbers. After a certain amount of “training,” a sizeable chunk of competition math was like this for me, too. Specifically, I got better at math competitions by taking a lot of old practice tests, so that many of the problems I encountered were variations on old problems I had seen before. I guess I performed moderately well at math competitions, and they were part of what made me want to come to MIT, but I don’t think they were particularly good at showing me what being a math major would be like. Some things haven’t changedâ€"as in high school, it helps to do practice problems, so you’re familiar with all the possible concepts and theorems you might be able to apply on an exam. It’s just that now there isn’t often enough time to practice enough, depending on what the rest of your schedule looks like. Also, theres less emphasis on memorizing material for exams, and homework is often weighted equally with exams. As a whole, homework is served in larger chunks than it is in high school, so its important to learn to manage your time. There are also fewer examples in class and fewer problems that are near identical to those in the textbook. Finally, a big change is that everything is proof-based (as I write this, I struggle to remember what it meant for math to not be proof-based). You’re basically given an ever-expanding toolbox of definitions and lemmas and theorems and have to tinker until you can assemble them into solutions to the problems you’re asked to solveâ€" it is a creative activity with strict rules and very little grounding in reality and applications. A great benefit of college math classes (besides GIRs) is that they’re full of people who actively like to think about math, and hopefully, if you’re a math major, you think math is pretty cool, too. It’s nice doing math with no expectation that it will be applicable in any way. I recently had to teach a section of a textbook for my math seminar, and it was all about applying the theory in the previous sections of the book to a physics problem (the displacement of a cantilever beam at rest with only the force of gravity acting on it, if you’re interested!!!). Even though I was tasked with presenting this part of the book, it was definitely not the section of the book I would consider the most interesting. I personally thought the fact that the material was applicable to a physics problem was much less exciting than the proofs in the previous sections. I am pretty sure no one is taking that seminar to learn about the ways in which math is applicable to physics. The main trend I have noticed is that math in college is much more intellectually stimulating and abstract than what I encountered in high school. By the way, if youre at all peeved by the way math is taught in your high school, or curious about what math is like when its separated from its applications, I urge you to read Lockhart’s Lament, which was required reading for the communication-intensive real analysis class (18.100C, now renamed 18.100Q) I took my freshman spring. It criticizes math education in grade school and argues that math is an artistic and creative pursuit that is not taught as suchâ€"but should be. He laments the fact that students find math boring and suggests that the mainstream pedagogy is at fault. Struggles: It really helps to develop a strong intuitive understanding of the material you’re learning, although sometimes it gets difficult because there are no good analogies to real life. Sometimes you get stuck rereading a definition over and over and over, trying to flip back to earlier definitions that the current definition refers to in an effort to regain understanding of all the concepts that the concept at hand relies on, but to no avail, because there’s some other relevant concept from a math class you took two years ago that you need to revisit, so you look it up on Wikipedia, but by the time you understand it again, you forget what you were originally looking at, so you’re left scrambling to retrace the string of things you referred to, and at this point you still haven’t even started to solve the actual problem… Sometimes. But most of the time it’s not that bad. Sometimes it’s just tedious, and sometimes you have to write out long expressions with a lot of symbols in order to rigorously explain something that’s much easier to explain intuitively. Lockharts Lament is nice, but at some point you also have to buckle down and slosh around in tedium and make sure that all your symbols are written correctly. Getting used to math in college and dealing with impostors syndrome: I took 18.022 my freshman fall and found that it helped ease me into the sort of proofs and thinking that the rest of my math classes required. Perhaps if I had jumped immediately into 18.100 I would have been overwhelmed; I know for sure that I wouldn’t have been able to handle 18.701. There are people who can, and seeing other freshmen sail through more advanced classes definitely freaked me out at times and stoked my first touches of impostor’s syndrome. Now, though, I don’t think I can adequately stress the importance of not going too fast. Because math classes often rely on definitions and material from prerequisites, these prerequisites are often super useful, unless youve actually learned the exact material from the class you want to skip. Of course, there are exceptions, but I often find it a lot more difficult to grasp mathematical concepts that Ive forgotten or skipped than to pick up other new material, like a programming language. I took 18.701 sophomore fall, and I attempted to take 18.702 last spring, but I ended up dropping it because I was overwhelmed by all the other stuff I was trying to do/learn. I was taking 18.125 concurrently. This semester, I once again made the poor choice of taking three math classes simultaneously, but I ended up dropping one of them last week because I simply could not handle it. I did not have enough time or energy to wrap my head around all the material, and I’m finally (finally) coming to recognize the importance of learning things well and deeply rather than learning them as fast as possible. Bear in mind that this sequence just happens to be what I ended up with, and it is not a recommendation that everybody should take those classes in this order. I am hesitant to give general advice about what classes to take and when because it depends so much on your personal background and how much time you have to devote to the class! A relevant article about impostors syndrome and the feeling of racing to learn math is “The Wrong Way to Treat Child Geniuses” by Jordan Ellenberg, a former “child prodigy” who is now a math professor at UW-Madison. This one might be particularly relevant to people who didn’t grow up being praised for being “good at math” or winning awards at math competitions. (This one’s also particularly hard to access without a WSJ subscription, sigh…) I’ve reproduced a relevant paragraph below: One of the most painful aspects of teaching mathematics is seeing my students damaged by the cult of the genius. That cult tells students that its not worth doing math unless youre the best at mathbecause those special few are the only ones whose contributions really count. We dont treat any other subject that way. Ive never heard a student say, I like Hamlet, but I dont really belong in AP Englishthat child who sits in the front row knows half the plays by heart, and he started reading Shakespeare when he was 7! Basketball players dont quit just because one of their teammates outshines them. But I see promising young mathematicians quit every year because someone in their range of vision is ahead of them. I think that MIT students, especially freshmen, are prone to psyching themselves out comparing themselves to all the people around them who have won the IMO or who were doing calculus in middle schoolâ€"but Ellenberg points out that this type of thinking sounds absurd when applied to other fields and skillsand there is no reason that it should apply to math more than any other field. One of the first math majors I met at MIT had never done math competitions in high school and hadnt had much exposure to higher-level math (i.e. calculus and beyond) coming into MIT, but he loved the math classes he was taking in college, so he began to register for more and more of them until he was thinking seriously about pursuing it as a profession. He was initially intimidated by his peers but enjoyed math so much that it was not a chore at all for him to devote significant amounts of time to mastering his coursework. He later became involved in research and is now pursuing his PhD in math at MIT! In summary, if you think math is cool, please consider continuing to study it in college, but bear in mind that college classes arent exactly like high school classes. And if you dont think math is cool, maybe it hast to do with the way math is taught in your school. Or maybe notnot everyone is destined to be a math major! And if youre intimidated and convinced that youll never be good enough at math, because other people seem to be so far ahead, well thats almost certainly not the caseits much more important that you enjoy the subject and dont try to jump ahead so quickly that you lose enjoyment of the subject in an attempt to catch up. If anyone has specific questions about classes or anything like that, I would also be happy to try to help you individually. I know I have been pretty absent from the blogslife update coming soonbut Im getting back in the swing of things. Sending you all strength and luck for pi day and all subsequent college and major choosing! Post Tagged #Course 18 - Mathematics #Imposter's Syndrome