Are there any other good sources for learning Calculus from the intuitive point of view that I can reference as I try to make sense of the garbage they are force feeding me in this class? Thanks for your time. Wow, thanks for the note! Yet in 20 minutes with just this page, I not only understood something that looked completely foreign to me, but actually enjoyed it. People talk about how money is a limited resource. Thank you for proving as definitively as ever that the only limited resource is human intelligence, and the creativity to do a little critical thinking and generate something as lucid and sensible as this site.
I should make a quick video with pipe cleaners to show what I mean: Good luck with your class: The only thing that threw me is, how do you know the unrolled rings will create a straight lined hypotenuse rather than some sort of curve? Intuitively, I see the rings as being very, very thin lines. We can see as the radius increases smoothly 2, 2. Basically, because the circumference is directly proportional to the radius, as the radius increases in a straight line from 0 to the full radius , the circumference should increase also.
I have another post in the works which takes another approach to introducing calculus. Should be out this week. Not only does the cutting up the rings stuff work in 2D to find area. But you can extend to 3D to find volume. Then to get the volume, find the volume of this stack of peelings using the formula for a pyramid.
Our educational system just focuses on memorization and not real thinking or problem solving, because that is what they test on. It is all very sad. Your visual explanation of the circle to triangle was beautiful. It was a huge moment of clarity for me. I would love more of this for calculus. I took it and passed many, many years ago and do not remember much. Your article just makes me know I could understand the meaning of what I had memorized long ago and since forgot. If I could read more of this, I know it would give meaning and understanding to all that long lost information. I noticed how long ago this was posted.
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Do you have any other articles on calculus with other visuals to explain concepts? Some have commented that derivatives were simple to understand. Well, for one who still needs more visuals, can you provide either more comments or point me to another article that will help me to see how simple they are too? I need to understand what they really mean. I know it relates to looking at the slope at a given point on the curve.
But I feel like I need more substance. How does that help? It makes me want to say, so what? What do I do with that now? Just a small remark: This put an extra difficulty in your visual proof. I do like the alternative proof though! Absolutely Brilliant…After a long time I reread this article and its just as its whats needed to be done in any teaching. Your way of explaining is like breathing fresh air. Keep up the good work. Cool article I love the way you explain the relationship between the circle and triangle area ,wish more books would start off like that.
After twenty years i still groan at doing calculus for a new course and I am doing one now with a lot of vector based calculus for Electromagnetism ,surfaces Gausses Theorem, Gaussian surfaces ,your explanation of divergence clicked right away. Calculus Made Easy Being a very-simplest introduction to those beautiful methods which are generally called by the terrifying names of the Differential Calculus and the Integral Calculus Author: Silvanus Phillips Thompson Release Date: July 28, [EBook ] Language: Some calculus-tricks are quite easy. The fools who write the textbooks of advanced mathematics—and they are mostly clever fools—seldom take the trouble to show you how easy the easy calculations are.
Master these thoroughly, and the rest will follow. What one fool can do, another can. Thanks for the wonderful comment! That book is been on my list: The concentric rings in your example have a conveniet thickness. Instead, let those thickness be close to zero. Or a mile thick and in both cases the answers pertaIn not at all. What am i missing here please? The key idea is that instead of measuring a wiggling shape directly, we break it into easy-to-measure pieces and measure those.
The key is the finer-grained our measurements mini-shapes , the closer we match the real shape. So, taking measurements a mile-wide would give a pretty poor approximation: Thanks Kalid, reading your blog is much like a dream come true for me like most of the others. Today I am going to Start teaching Calculas to my my first student. He is just 2 yeas younger than me and I am thinking how to show him that differentiation is just the opposite of integration. But how to show that slope calculation is the opposite of calculating the area under the same curve? I will post as soon as I find some analogy.
But you never know, if you find an analogy that works, use it! Kalid, your approach is refreshing and enlightening! The way Calculus is taught is wrong, wrong, wrong. Thanks for a wonderful and well-written article! As both a college student and a math tutor, I have found many of your posts helpful. And after reading the comments, I could not resist putting in my own two cents.
However, I do not have a problem with mixing science and religion. To my mind they are inseparable, for religion is the lens through which we interpret the world. God governs all things and knows all that is or can be done. And, just for the record, here is a quote from Einstein: But what really makes me angry is that they quote me for the support of such views. I struggled with calculus until a class in Statistics, all of a sudden the area under the curve made sense. Learning computer programming simplifies this entirely.
Take a for-loop, all this is is integration from one value to another. Calculating the area under the curve is exceedingly easy when plugging the iterator value into the function. I loved and still do love physics, but was so discouraged by memorization of formulas without any practical examples, that i could not continue. One of my biggest insights was that once you get over the frustration, learning can become truly, genuinely enjoyable. So im only in grade 8 but i really wanna know calculus because i hate when people know it and it makes me feel dumb.
This page has sorta helped me understand it but i still want to know how to do an equation that someone gives me. My math teacher teaches all levels of math from to calculus and he teaches me now so im ready because i asked him for help but its still hard to understand calculus and what the equation equals to. By Page 2 I was laughing my head off, then crying with joy. I have begun the understanding of calculus. God knows how long it will take me to get through the rest of the pages but I am expecting the finest of steak dinners. Thank you for being.
Wow, thank you for the heartfelt comment, it made my day: Really glad it clicked for you. I had my aha! Glad it was helpful: I totally know what you mean, I love the excitement of having a tough idea finally click. But the intuition comes when you can separate the ideas and play with them a bit. Thanks for the comment. I know I was!! I find anything can be fascinating if presented properly!
Engineering by cashea - Pearltrees. Hi, I like the idea. Thanks, I like tau as well. It helps people break away from a memorized formula and think about what the concept of pi really is. Yes, unfortunately the definitions we see in math books are ones that have been refined over thousands of years to the most precise possible. Lucky me I discovered your web site unintentionally, and I am stunned why this accident did not took place earlier! Azad, Do you plan to teach, or are you teaching now, a complete course on Calculus that follows the illustrative method you use above?
If so, please let me know as I would very much like to take such a course. Also, let me know what the cost would be for such a course. I am anxious to start. Thank you for the comment! Most likely, it will focus on developing intuition and using other online courseware Khan Academy, MIT Open courseware, etc. Hi, excellent article as always, many thanks. Kalid — great site and great service to mankind! What am i missing here? In Calculus, we take tiny, microscopic steps which means the error term is some microscopic amount squared micro-microscopic. For small steps, our error rate is shrinking faster than our step rate, and eventually becomes negligible.
So, jumping from 2 to 3 in steps of. If we jumped in steps of. Hey I have a question. Is it possible to integrate the volume of the sphere using the same method only with a pyramid? Wikipedia went about deriving the volume of a sphere on a completely different manner and when I differentiate the formula for the volume I get the formula for the surface area of a sphere. What is the relation between these results?
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Because that would make calculating shapes above the third dimension very easy. I have never really bothered to read anything into calculus. After reading this, I actually feel that I would actually like to learn a lot more into this as this gave me a really good view of what Calculus is. I like what you said. Two Weeks ago I read an article on quantum entanglment and since then have been trying to figure out how to learn more.
This is exciting yet daunting especially since I am doing this on my own and not in a class. I do this so that I can really understand what people are saying about entanglement, and well learning is always a good thing.
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Thank you for describing it in a manner my liberal arts mind not only understood but enjoyed. I look forward to my journey in the math world. This single article has taught me more in terms of real understanding than my last 24 years of schooling. These are some wise words. The education system does try and crush my love for maths but this has assisted to allow me to look past that and focus on the beauty of the subject. Calculus is a very lovely subject…. You will see how rigid and awesome it is later….
Ask questions and show curiosity till you understand everything…. How did you pass College Algebra? If nature is programmed, how does your statement [Like evolution, calculus expands your understanding of how Nature works. And, Who is th programmer? Who wrote or created the CODE? Had to take Calc 1 three times to pass, three times to pass Calc 2, never used any of it in the next 40 years.
But I feel to this day presentations were awful, full of theorems, not a bit of common sense real world problems solved or real world applications shown. Probably half the students flunked out of Parks College because of Calc. Reading your stuff tonight was a great refresher, and you have an excellent knack of simple explanation. I wish I had you as an instructor 40 years ago!
Hi Pete, thanks for the note. Really happy things resonated with you: Congratulations and keep up the good work! As the area of a triangle is half the one of a parallelogram. But I have to add, because I read your article, the formula for the area of the parallelogram made total sense, as being a bunch a lines stacked one next to the other, resulting in the formula: D I had to figure it out by myself.
With the few words of your text, you already unlocked a better math logic in me, and more admiration for Newton, as I begin to understand more of his genius: Again, thank you a lot for sharing your knowledge in a simple and understandable way! Hi Yashvardhan, thanks for the note and kind words — happy the articles are helping grow your math interest: Yep, I write all the articles!
Been pouring over your site last 3 to 4 hours. Worth every second of it. Just bought the book too. Keep up good work. Hi Louis, it can actually be really fun once you get into it.
Physics and chemistry, especially, are presented as surrogate math courses when they could be presented as the wonder of discovery. Max Planck suggested that light travels in packets of energy because it was the only way he could solve an equation. He expected someone to come up with a better answer in time. It explains so much. And there are so many others that could be told as well. I had a hard time accepting the reality of elliptic geometry until one author made the comparison with latitudes and longitudes.
I am 49 years old, been a housewife most my later adult life, office manager in younger years, and am planning to go back to college next Fall. I wish to major in physics. I took algebra and geometry in high school and did fairly well, but that was many years ago. I love math but due to Parkinsons, tend to have memory issues. Anyway, in preparation for this endeavor, I wish to re-educate myself to prepare for college calculus. It has been very interesting for me as a teacher to use a little calculus gadget to teach them a new way of seeing things.
For example, with the formulas you write perimeter, area, volume of a sphere of radius, I always get the most surprised faces when I show them how the derivative of the volume function leads to the surface area function, and the derivative of the area function leads to the perimeter function. It is quite exciting for them to see that and they start asking themselves questions, which is great.
The counting of syllables, like numbers in math, is critical to the practice and appreciation of verse. Will be using this site more in the Fall when I start my first of several Calculus classes for my physics degree. Very glad I found this site. Can we find the function from the integral? If so, how can we find the integreal with so little data? Hi Tim, great question. If we only have 2 data points the start and end , then we have to assume a linear progression from 0 to 60mph over the course of 6 seconds i. In this case, integrating to figure out how much distance was traveled may not be accurate.
As we gather more data points, we can get a better idea of the actual shape of the acceleration curve. I seriously love you man. I have hated math my whole life and failed calculus miserably. I felt like something was always missing, and that was insight. You nailed everything on the hammer and gave such a helpful guide. I actually know what is going on in class now, instead of starting at the board and zoning out at the giant mass of information. It is like studying a language before you can speak it, or study the physics of art before art itself.
But this is honestly the best thing ever, and thank you. In college, I enrolled in calculus and dropped it within my first week. I was lost by the end of lesson 1 and drowning by day 3. Everything is within our grasp when explained properly. Very, very happy the approach is clicking for you. Dear friend, Your text was so fascinating. I am a student at Engineering faculty in Afghanistan.
Please help me up. Really appreciate your great work and intuitive to help people understand things better. Will you try to explain some concepts in Linera Algebra in future? I think that is a weakness in some colleague students, i am one of it honestly: Hi Keith, thanks for the note.
Yep, I have a quick intro to linear algebra http: I thought I hated math for a long time, but as with many other things, it turned out I just hated how humans were approaching it. Hi Kallid, I love the way you derived the formula for the area of a circle using the circumference of a circle. My question is on how to derive the surface area of a sphere in a similar manner.
I also have ADHD which makes the classroom setting a nightmare, especially in math. Explanations like this are greatly appreciated because it takes the horror away from math and helps me to understand it in a logical and practical way. Wow, thanks for the thoughtful comment! I always knew I was smart but never could get even the basics of math.
Well, until we got to the end of the unit, or the next math up. I needed to actually see the practical application to appreciate what I was doing. Even graphing calculators stunk because those curves served no practical purpose. I found his website in eighth grade and it was really helpful in teaching me to love math, even if calculus seemed like a kind of fascinatingly foreign idea at the time.
Beautifully explained i like the way…. I am a ninth grade student, trying to learn stuff ahead of our syllabus, and calculus was my first pick. The way you have given an intro to calc is just epic. I understood everything as well as possible. I will surely continue on your series. This is actually very interesting Im 11 and Dad is trying to teach me calculus and I can understand you, unlike my prealgebra book.
Hope you enjoy the rest of the calculus series! Both grown adults, are exceptional in mathematics, to this day. Love the way you have explained the fundamentals of calculus. I love the insights. Not understanding the essence of mathematics makes the majority of people not appreciate it. In order to understand what an abstract word really means, one must get a hold first of its manifestations in the concrete world, and then how the abstract thereafter relates to the concrete.
I feel moved to share some facts, inferences and insights regarding its validity. Our scientific formulae are so predictive only because each scientific formula represents a scientific generalisation that has been based on factual observations. We keep on observing sets of phenomena in this way.
However, that does not explain how they can be consistent.
Therefore one is left with two general categories to explain the consistency of each of them: What do we call these certainties in the universe? What intuition do you think drove us to call physical laws laws? Nothing comes from nothing. The law of conservation of energy signifies this. This therefore makes us conclude that the universe has always existed from eternity past. However, the universe began. Our universe is characterised by cosmic expansion. The second law of thermodynamics indicates that the longer time has elapsed, the greater the overall entropy of the universe shall be.
Given that the universe is currently not at a state of maximum entropy, the first and second laws of thermodynamics indicate that the universe must not have always existed from eternity past. Matter, energy, space and time, which constitute the universe, have not always existed. Therefore, because the universe began to exist, either some Being or something must have caused it. This cause of the universe must be immaterial, because the cause of the universe cannot be the universe itself, which is the totality of all material things, as nothing can cause itself that has not arisen from nothing.
In other words, something causing itself is like saying that it appeared out of nowhere. Something arising out of nothing can only be true if that thing is not under the law of conservation of energy, or, if some Being xor some other thing caused it that, being able to create energy, is above the law of conservation of energy. Because of laws such as the laws of thermodynamics, only the Creator can and will create the universe from nothing. The theory of evolution holds that millions and millions of years ago, fish began evolving by means of little cumulative changes over long periods of time.
Over approximately years, fish managed to evolve to amphibians. Over approximately years, amphibians evolved to reptiles. Some of these reptiles evolved to nonmonkey mammals, still over a long period of time, which then evolved to monkeys—simply put, our ancestors. Of course, fish came all the way from a common ancestor.
This is what Darwin has proposed. After the discovery of DNA, however, the theory of evolution itself evolved to include nonliving chemicals that happened to live by time and incredible luck.
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There is no substantial evidence, however, to support this. The assertion that genus evolves to another genus over a very long period of time is contrary to science genome is the total of all the genetic possibilities for a given species, and should not be confused for genotype. I understand that, in order to appear as though it was falsifiable, and thus be convincing, this assertion depends on natural selection. One purpose of natural selection is to eliminate the abnormal mutations cause abnormalities.
Too much of this and extinction would occur. Living beings adapt to their surroundings because of the way they were designed — not because of natural selection; without design in the first place, natural selection would be meaningless. No one has ever observed actual evolution happen naturally. One only sees supposed evolution in some man-made books with pictures and in man-made realistic 3D animation movies. All proponents of the theory of evolution can show are some fossil remains with similarities, which have already undergone decomposition. The lips, the eyes, the ears, and the nasal tip leave no clues on the underlying bony parts.
You can with equal facility model on a Neanderthaloid skull the features of a chimpanzee or the lineaments of a philosopher. These alleged restorations of ancient types of man have very little if any scientific value and are likely only to mislead the public… So put not your trust in reconstructions. The fact that one language was used to design, and to dictate all the functions of, all living beings on Earth is just undeniable.
After all, all living beings on Earth have one thing in common— life. If one has ever used a programming language before, one would understand the necessity of reusing a set of specific codes to a number of different programs. Computer programmers though have a way of converting lengthy codes to just a short one by saving codes in header files because it would be tiring for humans to retype lengthy codes over and over again.
Information is contained in our DNA, and our bodies were designed, and functions, as well, according to the specifications of this information. What happens when a living being is exposed to harmful things such as radiation? Mutations are alterations that take place in the DNA—damaging the information in it. Information never originates by itself in matter; it always comes from an intelligent source.
The outdated microscopes of their time made the very complex structure of the cell look so simple. However, if we would subscribe to the current scientific discoveries, as well as the technologies, of our time, we would begin to apprehend that the indications never really pointed to the theory of evolution.
As science progresses, intelligent design becomes more evident. What else is the meaning of evidence? Everywhere we look, the more attentive we are to the details, the more evident intelligent design becomes. That initial failure caused me to answer the basic question, providing the mental fortitude to keep going despite the hurdles and problems I would later face.
My answer is you should get a Ph. Your answer may differ from mine. As long as you have an answer that you believe in passionately, then that's enough. If you don't have an answer, then save yourself a lot of grief and don't get the Ph. Academia is a business, and "graduate student" is a job title. This is especially true at private universities. Academia is very peculiar type of business.
It is certainly not the Real World and does not work in the same way that the ordinary corporate world does. However, it is a business nonetheless and as a graduate student, you must treat it that way. Graduate school made a lot more sense and became much easier for me after I realized this. If you think of graduate school as an "Ivory Tower" free of politics, money problems, and real-world concerns, you are going to be severely disappointed.
A few graduate students are independently wealthy or have fellowship and scholarship money that cover all their expenses for their total stay in graduate school. Such students are rare, however. In general, RA's are more desirable to students since those can directly fund the research you need to finish.
Where does the money come from to fund RA's? Your professors have to raise funds from external organizations. Private companies also fund some university research, although this tends to be less common, in smaller amounts, and in the form of equipment donations. These organizations don't just give money away as charity. They expect their money to accomplish something. Increasingly these days, this takes the form of a contract for a working demonstration that must be shown at the end. That means once the money is delivered, your professors must come through with the working demonstration.
It is rare that they do this by themselves. Instead, they find some very capable, young, self-motivated people who are willing to work long hours for small amounts of pay. In other words, they fund RA's. The RA job is crucial to the academic business. If the RA's cannot successfully conduct the research, then the demonstration will not work in the end and the funding agencies may not be happy. They may choose not to fund your professor in the future, which will bring his or her research program to a halt.
And there are many professors and other researchers chasing too few research dollars these days; it is a competitive market. Thus, each professor wants the best students available. These students are the most capable ones who can get the research done required to fulfill the funding contracts. That means you must treat an RA like a job.
You must prove to your professors that you are capable of getting the work done, being a team player, communicating your results, and most of the other characteristics needed to do well in regular jobs. That's why many of the upcoming sections in this guide sound like ones written for the regular workplace. What do you get out of this? At the start, you may have to do tasks specifically related to the funding contracts. But eventually your professor must be flexible enough to fund your own specific research program that leads to the completion of your dissertation.
Your stipend and tuition waiver should be enough to live on frugally without going into debt. You will learn the state of the art in your chosen speciality and conduct cutting-edge research on a subject that you find interesting and enjoyable. If you don't find this compensation sufficient, then you shouldn't be in graduate school in the first place. If you do your job well and have good negotiation and interpersonal skills, as discussed in future sections , both your needs and your professors' needs will be met.
But don't enter an RA position thinking that the computers, research equipment, staff members and other resources that you are provided with are your birthright. Don't take them for granted! Most of those exist only because your professors have been able to raise the money to provide those to you. In turn, you must fulfill your end of the deal by doing great research with those resources. If you don't do your job well, don't be surprised if your professors choose not to fund you in the future. They do not have to provide you with an RA job or let you use the computing equipment they acquired.
And the student who has no funding, no tuition reimbursement and no access to required computing resources is the student who leaves the university that semester. If we wanted something that would predict life success, we'd have to invent another test completely. If you go through a Ph. If you just get an M.
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But for a Ph. The students who do well are the ones who learn this earlier rather than later and make the necessary adjustments. Graduate school is not primarily about taking courses. You will take classes in the beginning but in your later years you probably won't have any classes. People judge a recently graduated Ph. And, without any offense to my professors, most of what you learn in a Ph. Success in graduate school does not come from completing a set number of course units but rather from successfully completing a research program.
Graduate school is more like an apprenticeship where each student has his or her own project, and the masters may or may not be particularly helpful. It's like teaching swimming by tossing students into the deep end of the pool and seeing who makes it to the other end alive and who drowns. It's like training clock designers by locking students inside a clock factory with some working clocks and lots of clock parts and machines for building clocks.
However, the instructions are at best incomplete and even the masters themselves don't know exactly how to build next year's models. Excelling in a Ph. Undergraduate education tests you through class projects that do not last more than a semester , essays, midterms and finals. For the most part, you work alone. Your professor may not know your name.
Every other student in your class takes the same tests or does similar projects. But in a Ph. For most of us, this means you have to learn how to do research and all that entails: I'm not saying that tests and grades are completely unimportant in graduate school. One of the two biggest hurdles in completing a Ph. The other is finding an acceptable dissertation topic. But because graduate school is not nearly as exam-based as undergraduate education and requires different skills, the GRE and undergraduate grades are not as good an indicator of who will excel and who will drop out as admission committees seem to think.
Those tests do not measure creativity, tenacity, interpersonal skills, oral presentation skills, and many other important traits. The dissertation represents a focused, personal research effort where you take the lead on your own, unique project. If you expect that your adviser is going to hold your hands and tell you what to do every step of the way, you are missing the point of the dissertation. This does not mean that guidance from professors is unimportant, just that this guidance should be at a reasonably high level, not at a micromanaging level.
If you never do any tasks except those that your professor specifically tells you to do, then you need to work on initiative. Many years ago, UNC got a force-feedback mechanical arm to use with molecular visualization and docking experiments. The problem was how to move it to UNC. Unfortunately, there was a trucker's strike going on at the time.
Joe Capowski, on his own initiative and without telling anyone , flew out to Argonne, rented a car, drove the mechanical arm all the way back to North Carolina, and then handed the computer science department the bill! Many years later, Joe Capowski ran for the Chapel Hill city council and won a seat. Fred Brooks gave him an endorsement. I still remember the words Dr. While the Joe Capowski anecdote is perhaps a bit extreme, it does show that it is often better to ask forgiveness than permission, provided you are not becoming a "loose cannon.
MIT are good at fostering a "can do" attitude among their graduate students, and therefore they become more assertive and productive. One of the hallmarks of a senior graduate student is that he or she knows the types of tasks that require permission and those that don't. That knowledge will come with experience.
Generally, it's the senior graduate students who have the most freedom to take initiative on projects. This privilege has to be earned. The more that you have proven that you can work independently and initiate and complete appropriate tasks, the more your professors will leave you alone to do what you want to do. You don't need to be a genius to earn a Ph.
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But nobody finishes a dissertation without being tenacious. A dissertation usually takes a few years to complete. This can be a culture shock to former undergraduates who have never worked on a project that lasted longer than one quarter or semester at the end of which, whatever the state of the project, one declares victory and then goes home. No one can tell you in advance exactly how long the dissertation will take, so it's hard to see where the "end of the road" lies.
You will encounter unexpected problems and obstacles that can add months or years to the project. It's very easy to become depressed and unmotivated about going on. If you are not tenacious about working on the dissertation, you won't finish. Tenacity means sticking with things even when you get depressed or when things aren't going well. For example, I did not enjoy my first year of graduate school. I didn't tell anyone this until after leaving UNC.
I was not on a project and was focused on taking classes, some of which I didn't do all that well in. I didn't feel a part of the Department, and really wondered whether or not I fit in. Still, I stuck with it and when summer rolled around and I got a job in the Department, I became much more involved in research and enjoyed graduate school much more. Part of earning a Ph.
One lesson I learned as a graduate student is the best way to finish the dissertation is to do something every day that gets you closer to being done. If all you have left is writing, then write part of the dissertation every day. If you still have research to do, then do part of it every day. Don't just do it when you are "in the mood" or feeling productive.
This level of discipline will keep you going through the good times and the bad and will ensure that you finish. Some people hear it; some do not. It's not enough to hear opportunity knock. You must let him in, greet him, make friends and work together. Flexibility means taking advantage of opportunities and synergies, working around problems, and being willing to change plans as required. As a graduate student, you are on the bottom of the academic totem pole. Even undergraduates can rank higher, especially at private universities because they actually pay tuition!
You cannot order anybody to do anything. In general, you will be in the position of reacting to big events rather than controlling them. Therefore, you must be flexible in your approach and research program. For example, you may not have as much access to a piece of laboratory equipment as you would like, or maybe access is suddenly cut off due to events beyond your control.
What do you do? Can you find a replacement? Or reduce the time needed on that equipment? Or come in at odd hours when no normal person uses that equipment? Or redefine the direction of your project so that equipment is no longer required? Events can be good as well as bad. The difference between the highly effective graduate student and the average one is that the former recognizes those opportunities and takes advantage of them.
But after he arrived I realized my research would progress much faster if he became my adviser so I made the switch and that was a big help to my graduate student career. Opportunities for synergy and serendipity do occur, but one has to be flexible enough to recognize them and take advantage of them. Computer Science majors are not, in general, known for their interpersonal skills. Some of us got into this field because it is easier to understand machines than people. As frustrating as computers can be, they at least behave in a logical manner, while human beings often do not.
However, your success in graduate school and beyond depends a great deal upon your ability to build and maintain interpersonal relationships with your adviser, your committee, your research and support staff and your fellow students. This does not mean you must become the "life of the party. But I did make a serious effort to learn and practice interpersonal skills, and those were crucial to my graduate student career and my current industrial research position. Why should this matter, you may ask?
If one is technically brilliant, shouldn't that be all that counts? The answer is no, because the situation is different from your undergraduate days. In both graduate school and in business, you must depend upon and work with other people to achieve your goals To put this in perspective, I have excerpted the following from an article called "Organizations: Patterson, published in Fall issue of The Bent: As part of the research design, we asked to talk to low, medium, and high performers.
This in itself was an interesting exercise. To determine performance rankings, we would place in front of a senior manager the names of the people within his or her organization. Each name would be typed neatly in the middle of a three-by-five card. After asking the manager to rank the employees from top to bottom, the managers would then go through a card sort.
Typically the executive would sort the names into three or four piles and then resort each pile again. Whatever the strategy, the exercise usually took only minutes. Just like that, the individual in charge of the professionals in question was able to rank, from top to bottom, as many as 50 people. It rarely took more than three minutes and a couple of head scratches and grunts. Although politics may appear ambiguous to those on the receiving end, those at the top were able to judge performance with crystal clarity.
This performance ranking conducted by individuals not involved in the interviews was then used as a dependent measure. Those of us conducting the interviews attempted to surface information independent measures that would predict the ranking. What about a scientist's career would lead to a top ranking? What trashed a perfectly good career? Surely scientific prowess would have an impact. But technological prowess wasn't as predictive as another factor. We discovered that we could tell what performance group the interviewees belonged to within a minute or two by their attitudes toward people and politics.
Individuals who were ranked low by their managers spoke of organizational politics as if it were poison. They were exceptionally annoyed by the people side of the business. They frequently stated they would rather be left alone to conduct their research untrammeled by human emotions. They characterized the social side of organizations as "soft and gushy. Top performers, in contrast, found a way to work within the political system. They hadn't exactly embraced politics. They didn't appear like that toothy kid you knew back in college who lived to fight political battles.
They didn't come off as glad-handling sales folks. These were professional scientists who were often top ranked in their field. They looked and talked liked scientists. The difference between them and those ranked at the bottom of the totem pole was clear. They had found a way to make peace with organizations, people, and politics. They climbed to the top of their field by mastering both hard things and soft and gushy people.
Engineers and scientists aren't the only ones who find the human side of the organizations to be annoying. As we expanded our research to include professors, accountants, and other professionals, the findings were remarkably similar. All found political machinations to be distasteful. It's just that some had found a way to master the social aspects -- the top performers. For example, which group of people did I try my best to avoid offending? Was it my committee? No, because healthy disagreements and negotiations with your adviser and committee are crucial to graduating within a reasonable amount of time.
Nor was it my fellow students, because I did not need help from most of them, and most of them did not need me. It creates fear as much as it creates curiosity. The truth is most people want more. Even if it is on a subconscious level. Humans tend to trail blaze. From cradle to the grave, our society emphasizes the importance of education. Learning and discovering is what we do, but still it is increasingly hard to understand what you don't understand. So how do you learn to know what you don't know?
Start by asking yourself: What don't I know? What do you want to learn more about? Most importantly, understand that it's OK to be wrong. In error there is growth. Your good times are temporary and your bad times are temporary. So when you're up, enjoy it, bask in it, and be grateful for it. And when you're down, know you will get through it. Know that it's not the end, and that it's just a rough patch.
Life is full of twists and turns, ups and downs, and surprises. There is a lesson in everything.
I think it's hard for a lot of people--especially young people--to appreciate life. Recognizing the full worth of your hardships and your blunders is key to appreciating the journey. It's just as important to stay humble and be grateful for the joys life brings you. If you are anxious, you are living in the future. If you are at peace, you are living in the present. More often than not, we tend to worry about what's to come, or dwell on something that's already happened.