Questions related to the teaching and learning of mathematics.

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1answer
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Explanation over this simple equation, which involves multiplication of two square-roots

It was the time in schools, where we were taught about finding square roots of numbers. For a long time, i found the technique very difficult, so always used to find some shortcut to get rid of the ...
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4answers
639 views

Is there any good reason why a protractor starts from right to left, unlike a scale, which starts from left to right?

While studying through the number system, i notice that positive side is from 0 to +ve infinity. The direction is left to right. However, this is opposite in case of angles. The sort of curved number ...
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2answers
325 views

Study regimen for discrete mathematics? - Lack high-school maths…

I have just gotten into college, and will be studying mathematics from next semester. (this course) Unfortunately I did not study mathematics for the last 2-3 years of high-school mathematics. What ...
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0answers
59 views

Bookwork Preparation for Exams

Has anyone got advice for learning bookwork. I have one particular module which is absolutely full of it. Currently I keep looking at it over and over but 'the tricks' aren't sticking.
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0answers
201 views

Comparing the U.S. undergraduate math education to the French “classes préparatoires”

Could anyone comment on how the math track of the "classes préparatoires" compares to the U.S. undergraduate major? I took a look at some of the French entrance exams and was rather intimidated. How ...
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2answers
19k views

Hexadecimal value of a negative number?

How can I find the hexadecimal value of negative number? I was studying from a slide that shows these values and there hexa's...! ...
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2answers
294 views

Does introducing penalties for getting true/false questions incorrect result in higher skill penetration (less luck/variance)?

A student is asked to answer 50 true/false questions and he would get 35 right and 15 incorrect if he had to put his best guesses for each question down. Now, for each question he has a certain ...
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4answers
5k views

Self-Paced Graduate Math Courses for Independent Study

Does anyone know of any graduate math courses that are self-paced, for independent study? I am a high school math teacher at a charter school in Texas. While I am quite happy with where I am right ...
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4answers
1k views

Understanding mathematics imprecisely

For a long time, it has been a complete mystery to me how any of my peers understood any math at all with anything short of filling in every detail, being careful about every set theoretic detail down ...
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4answers
303 views

Communicating mathematics

As a TA, my ratings have been fairly mediocre. There's nothing to suggest I'm a problem, but I have room to improve. What's more disturbing to me is that I even struggle to communicate math with ...
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1answer
54 views

Linear fuzzy system

I need help if any one can help me How to define a crisp number or crisp system? Whats the difference between crisp number and fuzzy number? And if there is any references.
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17answers
5k views

How do you respond to “I was always bad at math”? [closed]

Here in the U.S., it is my experience that over 75% of adults I meet socially will volunteer that phrase or a variation upon learning that I am a mathematician. I find this frustrating, since almost ...
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2answers
797 views

Mathematics Article Collection Books for Talented High School Students

I'm looking for some good books including mathematics articles which are appropriate for talented high school students. I'm NOT looking for puzzle or Olympiad problem books. Here are some of my ...
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0answers
74 views

Looking for online matlab-based differential equations course/text.

I am looking for an online ODE course that would be matlab/project-oriented. A full online text/course in the spirit of this linear algebra text is preferred. I know about the following CODEE and ...
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1answer
175 views

breadth vs depth and time management in undergraduate math education

For the sake of time, is it bad to just accept some fast paced class's theorem's (such as MIT's algebra class) as true even if you don't completely understand the proof or can't remember the proof off ...
6
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4answers
239 views

Math school online?

As a hobbyist programmer with little to no math skills (no science skills either, thank you religious schools) I am finding math encroaching on my life more and more often. I have always laughed and ...
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3answers
1k views

Importance of Neatness / Organization / Speed in Math?

Pretty simple question here but it does relate to math. I ask this as my writing is quite messy, possibly a cause of silly mistakes. How important is neatness in math? Does having messy writing put ...
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0answers
153 views

looking for guidance in my road to pure mathematics

During my teenage years I got into arts and slowly but surely I continue to pursue different art forms (poetry, music, painting, photography, etc) but it was just recently that I got interested in ...
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3answers
352 views

Statistics Workshop for High School Students

We are going to hold an introductory workshop about the statistics. The participants will be students who have just finished their 8th or 9th grade. The workshop consists of 10 two-hour sessions. The ...
6
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3answers
21k views

Largest prime factor of 600851475143 [duplicate]

I'm trying to use a program to find the largest prime factor of 600851475143. This is for Project Euler here: http://projecteuler.net/problem=3 I first attempted this with the code that goes through ...
1
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1answer
367 views

Math Behind the Game “Quoridor”

I'm going to write an article for middle school students to introduce them to the game "quoridor". Tha game certainly is interesting, but it will be great to add to the article some serious "math ...
2
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3answers
388 views

Is Vector Calculus useful for pure math?

I have the option to take a vector calculus class at my uni but I have received conflicting opinions from various professors about this class's use in pure math (my major emphasis). I was wondering ...
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3answers
4k views

What makes a good mathematician?

A soft question but I believe important to help get maturity in maths. Not until I got admitted to a graduate applied math program that I started to learn math. Before that, I was a life science ...
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3answers
91 views

Integrating a school homework question.

Show that $$\int_0^1\frac{4x-5}{\sqrt{3+2x-x^2}}dx = \frac{a\sqrt{3}+b-\pi}{6},$$ where $a$ and $b$ are constants to be found. Answer is: $$\frac{24\sqrt3-48-\pi}{6}$$ Thank you in advance!
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2answers
170 views

At what education level is this “simple” problem adequate?

Given the following problem: Alice, Bob and Carl stand on a straight line. Alice is one rod away from Bob. Dana stands one rod away from both Bob and Carl. Carl is as far from Alice as Alice ...
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3answers
2k views

Why is 1 raised to infinity Not defined and not “1” [duplicate]

$1$ square is $1$, so is raised $1$ to $123434234$. My maths teacher claims that $1$ raised to infinity is not $1$, but not defined. Is there any reason for this? I know that any number raised to ...
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0answers
328 views

Graduate schools in set theory

What options for graduate schools are there for an aspiring set theorist? In the US, the only top 50 schools with active research in set theory seem to be Berkeley and Carnegie Mellon. Are there any ...
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1answer
627 views

Understanding the pseudocode for the Sieve of Eratosthenes

The outer loop on the Wikipedia page for the Sieve of Eratosthenes ends at √n: for i = 2, 3, 4, ..., √n : Is this because if n has a square root it wont be prime? From what I understand this ...
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1answer
3k views

About Euclid's Elements and modern video games

Update (6/19/2014) $\;$ Just wanted to say that this idea that I posted more than a year ago, has now become reality at: http://euclidthegame.com/ 12.292 users have played it in 96 different ...
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0answers
166 views

Advice on learning mathematics

I know it is hard to ask for the perfect method for doing mathematics, but I hope there are some paths that are more preferable over others. I am a engineering student who has switched to mathematics ...
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2answers
9k views

Self-study Real analysis Tao or Rudin?

The reference requests for analysis books have become so numerous as to blot out any usefulness they could conceivably have had. So here come another one. Recently I've began to learn real analysis ...
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1answer
446 views

What are the prerequisite for understanding complex analysis?

Which should I complete first before complex analysis? I am following Visual Complex Analysis by Tristan Needham. Is there any easier book?
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1answer
61 views

Any comprehensive material to revise the mathematics

I left school long back and so my mathematics knowledge also fades out. I am trying hard to re-collect the basics about log / permutaion / combination / probability / polynomial equations. I tried ...
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3answers
828 views

English words in written mathematics

I recently marked over $100$ assignments for a multivariable calculus course. One question which a lot of people did poorly was proving a given set was open. Aside from issues relating to rigour and ...
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3answers
1k views

How to fill gaps in my math knowledge?

Just finishing highschool, even though I am doing "well" (in the context of the math course itself), I have significant holes in my actual math knowledge. As I think many people who explore math ...
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3answers
2k views

Find the shortest distance from the point $P(0,1)$ to a point on the curve $x² - y² = 1$ , and find the point on the curve closest to $P$.

Find the shortest distance from the point $P(0,1)$ to a point on the curve $x² - y² = 1$, and find the point on the curve closest to $P$. What I did so far is : plot the y var from $x^2-y^2=1 ...
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1answer
97 views

Mathematical Journey text

Hi I am looking for a HARDCOVER book I read when I was younger. It is fairly modern and published probably around 2006 - 2007. It is a hardcover with a cheesey title like: Mathematical thinking ...
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2answers
2k views

How to find multiples of numbers under a certain range

I recently found a 'question' that requires me to find the sum of all multiples of 3 and 5 under 1000, I sadly cheated and found some code online to help build a code in python: ...
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22answers
10k views

The Best of Dover Books (a.k.a the best cheap mathematical texts)

Perhaps this is a repeat question -- let me know if it is -- but I am interested in knowing the best of Dover mathematics books. The reason is because Dover books are very cheap and most other books ...
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3answers
155 views

what are the rules/rationale for “simplifying” negative denominators

So I'm losing my mind trying to understand the rules and rationale behind "simplifying" expressions and equations in Algebra. It's been decades since I've had to study for it (going back and ...
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3answers
1k views

Does learning logic and set theory before arithmetic, algebra, and geometry have an advantage?

I'd like to become conversant in a wide variety of serious mathematics, but i'm currently one of those students who did very poorly on mathematical subjects in school, never completing even basic ...
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3answers
215 views

Learning Combinatorial Species.

I have been reading the book conceptual mathematics(first edition) and I'm also about halfway through Diestel's Graph theory (4th edition). I was wondering if I was able to start learning about ...
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2answers
575 views

Is it possible to learn mathematics right from the source instead of reading textbooks. By studying the masters and not their pupils

I was wondering if mathematics learning process require the use of textbooks. When I was a high school student, I read as a preparation for university, Legendre book on Elements of geometry and ...
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7answers
3k views

Easiest and most complex proof of $\gcd (a,b) \times \operatorname{lcm} (a,b) =ab.$

I'm looking for an understandable proof of this theorem, and also a complex one involving beautiful math techniques such as analytic number theory, or something else. I hope you can help me on that. ...
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2answers
2k views

Learning Mathematics using only audio.

Are there any mathematics audio books or other audio sources for learning mathematics. I ask this because I make about 1 hour from my house to the school and staring at a screen on the car makes me ...
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2answers
387 views

The Game of Nim alternative solutions

Nim has a mathematical solution which uses binary number system and addition modulo 2.I was wondering if there is an alternative solution to this game or at least another interpretation of the ...
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2answers
872 views

How can I make sure I never forget.

I am currently refreshing my Elementary Algebra using Schaum's Outlines. I find them useful as they are choc full of exercises (Which I now realize is the only way to master algebra). I am worried ...
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1answer
113 views

Course/homework management systems for computational math courses [closed]

I will be teaching a course which will be based on a mathematical software, (as in MATLAB, MAPLE, Mathematica). The question is how to manage homework. Ordinary email is not efficient it seems. I am ...
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3answers
171 views

Darboux integral too sophisticated for Calculus 1 students?

I strongly prefer Darboux's method to the one commonly found in introductory level calculus texts such as Stewart, but I'm worried that it might be a bit overwhelming for my freshman level calculus ...
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0answers
115 views

What is $0^0$? Should we define $0^0$ on its correctness or convenience? [duplicate]

What is $0^0$ ? I have read many debates about this question. The debate has been going on at least since the early 19th century. At that time, most mathematicians agreed that $0^0$ = 1, until in ...