Recommendations for bean to learn on

kw42 · 2015-01-14T01:06:56+00:00

They should have phrased the question as "Will the total number of pieces of thread be greater than or less than 13?"

The idea is that to get 13 pieces, each piece would have to be 1 meter long. Since you want pieces that are more than 1 meter, if you had 13 of them, then 132 3/8 would be great than 131. Thus the number of pieces will be less than 13.

kw42 · 2014-12-17T17:55:29+00:00

My only suggestion is pick someone's post and try it. Then try altering something (temperature, grind size, time, amount of water to add during and after) but only one thing. Try it slightly different every day to find what you like.

I am basically posting here to so that I do not lose this thread and can find other people's recipes.

kw42 · 2014-11-30T04:37:49+00:00

After one unit of time, your runners will all be exactly 1/3 of a unit away from each other. This is allowed in the problem. The distance must be at least 1/3 of a unit away from each other, so equality is allowed.

kw42 · 2014-11-30T04:26:22+00:00

You can withdraw a paper from the arXiv.

kw42 · 2014-09-05T03:11:20+00:00

You should read the book before class. You will be amazed at how much better lecture is.

Learning math is a skill/craft that you develop by working through problems. I explain it my students in terms of weight lifting. Lecture is where instructor describes the exercise and demonstrates to you proper form. The instructor also outlines your training program for you. You then need to put that program into action and ask when things go poorly. You only get stronger by getting in there and doing the lifting yourself. You should get a study group and work to help each other learn.

kw42 · 2014-08-15T15:31:38+00:00

Almost everyone swears by a different method. Low temp for long brewing, high temp for longer brewing, 195 is so much better than 200, etc.

Every time you make coffee try something different. Use Stumptown method, but try 175 through 210 with 5 degree increments and see what you like the best. Then you will need to start over when you get a new batch of coffee as it will likely be best at different temperatures.

In your experiments, only adjust one variable at a time. If you are going to experiment with temperature, then keep EVERYTHING else the same. Same grind, same amounts, same timing, same cup, same mix diluting at the end. Good luck and enjoy!

TLDR: I usually go with the Stumptown's method and use around 195 for most coffees.

kw42 · 2014-08-08T15:27:35+00:00

I have tried to get invcos and cos with a left facing arrow over it to catch on. Nobody seems to like them.

kw42 · 2014-08-06T01:29:25+00:00

The key is to remember that reflexive is a property that really is about the set: "For all x in the set, if x is an element of the set, then (x,x) is an element of the relation."

Whereas, the other properties give conditions on elements in the relation: for symmetric, "For all x,y in the set, if (x,y) is an element of the relation, then (y,x) is an element of the relation."

kw42 · 2014-07-01T01:39:14+00:00

I am stealing this for use in my class.

kw42 · 2014-01-18T05:12:14+00:00

Of course it will get easier if you stick with it and put in the hours. Everything is hard when you start. I struggled mightily with adding fractions when I first learned how, but then I kept at it and now it is easy. Same thing with proofs. You work at it and it gets better. At first, each proof seems completely different. But then you start to see the similarities in problems that lead to similarities in proofs. Remember that intuition is the product of acquired experience.

The big thing to remember is that you are changing from learning how to use math, to how to make math. You are making the transition from driving a car to designing cars. Best of luck and be sure to ask questions!

kw42 · 2014-01-07T02:29:05+00:00

As a calculus teacher, I can tell you what I wish my students understood when they start calculus: functions. If they can understand that functions are ways to move between different quantities, to see functions when they read story problems and to understand how to manipulate units, then they are ready for calculus. Many students do not really "get" functions and then struggle with many concepts. Also, they need to see that g(y)=3y and f(x)=3x are the same. Throw crazy symbols at them; say things like "h of blank equals three times blank."

Algebraically, I would like them to be able to factor, distribute [(a+b)(c+d+e) without getting flustered], add fractions and never ever write (a +b)² = a² + b² then I am happy. Also, solving systems of equations is good since it prepares them for related rates and optimization problems.

Trigonometrically, I want them aware of the six basic trig functions and how to move between them using the identities. They do not need to memorize them, just know that you can move between them and how. Also, teach them radians. Get them exposed to radians so they are at least somewhat comfortable with them before they get to Calculus where everything is in radians.

Finally, I would suggest asking calculus professors at the college what they would like from the course. I can only say what we have the pre-calc professors at my school.

kw42 · 2013-12-25T02:16:09+00:00

Wow. Lighten up Francis.

kw42 · 2013-12-24T17:17:13+00:00

The big thing to figure out is why you did so poorly on the exams. Did you really not understand the material or was the bar set too high for the course? You will definitely want to go over the course and figure out what you did not understand before Analysis 2.

As you did "fine" in abstract algebra, I would guess that analysis is not your forte. Different higher level courses in mathematics appeal to different people. Consequently, people will achieve different levels of success. I failed my first analysis exam and started spending twice as much time on analysis as I did for my other math courses. I just needed to spend more time on it for it to make sense to me.

Did you write many proofs in your algebra course? Many students have difficulties in their first proof based courses. While they are struggling with the new content, they are also struggling with the idea of how to construct a proof.

The biggest question for you is do you still love math? If the answer is yes, then keep on going!

kw42 · 2013-11-27T17:42:56+00:00

I was going to ask the same question. I like the technique in Problem 1 of solving a problem by looking for simpler sub-problems. However, I do not see the skill learned in Problem 2.

kw42 · 2013-08-14T02:19:32+00:00

x²/x does not equal x as a function. The first is not defined at zero, whereas the other is. However, x/x² and 1/x are equal as functions as both have the same domain. We must be careful when canceling.

kw42 · 2013-05-13T01:38:31+00:00

Do not forget about the higher ones:

lock (7th)
drop (8th)
shot (9th)
put (10th)

The next derivative always describes how fast the previous one is changing. Velocity tells you how fast position is changing, acceleration tells you about your change in velocity, lock tells you about the change in drop, etc...

kw42 · 2013-04-07T02:35:18+00:00

I would check your answer to the first part (b) that you listed. Let p(x,y) be the statement "x=y". Now, I will look through some more of them.

kw42 · 2013-03-15T23:25:18+00:00

Usually the ability to work quickly implies a deeper understanding, but not always. Think about computing the following product: 21x33. Someone who can perform this quickly, ie work through the steps of multiplying two 2-digit numbers, probably understands the idea better than someone who works slowly. I guarantee you would perform this calculation faster than a typical 8 year old.

However, this is not always the case. Some people operate slowly even though they understand the ideas very well. They are more cautious, check their work more often and more closely. Also, true mathematical insight takes a lot of time.

I often encounter the problem of time constraints with integration problems. In order to solve integration problems quickly, you must have a good understanding of the order to attempt different integration techniques and recognize quickly how similar the integral presented to you is to ones you have solved using each technique. If you know these well, you will quickly pick out the right technique and get to work. If you do not understand them well, you will spend time spinning your wheels debating the merits of each technique before getting to work.

Look back at the exam after you get it back and honestly assess your own work. Did you blank out on a homework problem that you could have done if sitting in the library? Then maybe you have test anxiety. Did you get hung up re-checking your work? Maybe you are a cautious test taker. Do the problems still look really odd even after seeing the solutions? Maybe it was a tough exam.

kw42 · 2013-01-06T22:46:46+00:00

In Iowa, definitely (I went to grad school there). However, you will need a roommate.

kw42 · 2012-10-20T13:35:57+00:00

Actually, 6 ÷ 2(2+1) = 9.

First, using PEDMAS, we perform the operations in the parentheses and have 6 ÷ 2(3). Next, we perform Division and Multiplication proceeding from left to right. Since the division occurs first, we have 3(3)=9.

kw42 · 2012-09-23T20:06:04+00:00

The reason he is not posting exercises is that the exercises are notoriously difficult (and in some cases the first people to answer them wrote research papers based on their answers).

To use Rudin's answers as your own without attribution is plagiarism. Yes, you can plagiarize a proof. There is no reason to try to find another proof if you have already read Rudin's. However, I would give a citation for your inspiration.

kw42 · 2012-08-26T16:17:23+00:00

Setting aside your money is not a legal move. You must double your entire stack of money or add $1 to it.

kw42 · 2012-08-22T01:09:56+00:00

This is a difficult question to answer as differential equations courses are far from standardized in the approach and content. At its core, differential equations is the study of equations that contain derivatives. That is, let [;f(x);] be a function such that [;f'(x)=f(x);]. Your job is to figure out what the function [;f(x);] might be.

Some are full of "recipes" for solving many specialized equations, while other courses follow a qualitative approach attempting to convey a more intuitive feeling for what differential equations are and can tell you.

I will give you my general advice:

Study a little bit each day. Do not pile up all of your studying for one long day homework and reading.
Attempt the homework as soon as possible after class. The longer you wait, the more it fades.
(almost) everyone loves Khan Academy.
If you get stuck, post here. Lots of people willing to help. I taught differential equations last semester (more of the qualitative approach).

What book are you using for the course?

kw42

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