For questions related to the teaching and learning of mathematics. Note that Mathematics Educators StackExchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

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Is it to the students' advantage to learn the language of infinitesimals?

A colleague of mine asked an interesting question reproduced below with his permission. It is reasonable to ask whether it is to the students' advantage to learn the language of infinitesimals - ...
0
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1answer
14 views

Is there a unique solution to this upstream/downstream canoe rowing proposition?

A man jumped into his canoe and paddled upstream for one mile. After this, he continued for another fifteen minutes. Having arrived at his destination, he then turned around and paddled downstream, ...
12
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6answers
816 views

How does advancing through the math major work?

I am an undergrad math major that just completed Calculus 3 last semester. This semester I signed up for Discrete Mathematics, and will be taking Intro to Advanced/Abstract Math next. Of course-- I ...
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0answers
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How do I get my mathematical thinking back on track? [on hold]

I used to be very good in math at school (though I suppose in a "big fish in a small pond" kind of way). The last years, however, the material was not that challenging, the pace was slow, and I ...
0
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0answers
23 views

Reference in Latex [migrated]

For my thesis references, When I run latex, in pdf appear like below Aliabadi, M. H. The Boundary Element Method, Applications in Solids and Structures, Vol. 2, J. Wiley, New York, 2002. 4 Baudouin, ...
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0answers
34 views

Polar System with Short Answers, How $U(0, \theta)=\pi$ will be calculated?

I read some notes on Laplace. I ran into a short answer question as follows. We have a Laplace equation in Polar Systems: $\frac{1}{r}\frac{\partial}{\partial r}(r\frac{\partial u}{\partial ...
25
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19answers
484 views

What are some surprising appearances of $e$?

I recently came across the following beautiful and seemingly out-of-the-blue appearance of $e$: $E[\xi]=e$, where $\xi$ is a random variable that is defined as follows. It's the minimum number of ...
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0answers
15 views

Good introductory book in geometric probability

I recently came across the proof of the Buffon theorem and I was fascinated by geometric probability. Could someone indicate me a good introductory book? Maybe with many exercises?
14
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12answers
10k views

Which 4 maths courses to take as an Economics PhD student?

I am doing a PhD in economics and I have the chance of taking one subject a semester in the maths department (I would like to do more, but "unfortunately" I have to work on my thesis). I want to have ...
8
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7answers
9k views

Real life applications of general vector spaces

Students familiar with Euclidean space find the introduction of general vectors spaces pretty boring and abstract particularly when describing vector spaces such as set of polynomials or set of ...
7
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2answers
492 views

Studying quantum mechanics without physics background

I am a PhD math student, and I am wondering if I should study quantum mechanics while I don't have an undergrad background in physics. I posted this question in physics stackexchange, but there ...
0
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0answers
12 views

Dynamic systems formula

One simple questions that i dont seem to find a answer for, is there a general equation for dynamic systems and/or is there a way to describe dynamic systems in equations? Thank you!
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9answers
8k views

Are there contradictions in math?

Someone told me that math has a lot of contradictions. He said that a lot of things are not well defined. He told me two things that I do not know. $1+2+3+4+...=-1/12$ what is infinity $\infty$? ...
0
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2answers
49 views

I am looking for a book designed for self teaching applied/engineering mathematics. Can someone help me find a few?

I have used Shaum's differential equations. Are there others that I could use that are designed for self-study?
6
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1answer
153 views

Is it worth proving every theorem you learn?

Ever since I determined mathematics - mainly set theory and number theory - was my main passion, and I began learning mathematics formally outside of the curriculum posed within secondary schools I ...
13
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1answer
219 views

Is it a good approach to heavily depend on visualization to learn math?

I am a third year undergraduate and I am a beginner on these "real mathematics" (no pun intended). Before contacting the "real math", my math level should be considered to be "good", although I was ...
2
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0answers
36 views

Methods for solving for partial fraction coefficients.

When I present partial fraction decomposition, there are typically two approaches to solve for the coefficients of the fractions: Clear the fractions, multiply out the products, and equate ...
25
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6answers
5k views

Is a good GRE score enough for a non-math graduate to be accepted in a decent pure mathematics graduate program?

I have a computer engineering degree , and i have studied several mathematics courses like single variable and multiples variables calculus , complex variables , probability , numerical analysis ... ...
2
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2answers
28 views

How to express $\log_5 2$ in terms of a and b (Refer to qn)

In my textbook, I came across this interesting question which I am currently struggling to solve: If $\log_6 2 = a$ and $\log_5 3 = b$, express $\log_5 2$ in terms of a and b The solution given is ...
0
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1answer
20 views

convert Hex value to two's Complement

for example, let's say: 0xE5 assume the system is 8 -bit in decimal it's = 229 and in Binary it's = 1110 0101 the Two's Complement rules said: sign-bit, which's the most left, indicates a negative ...
9
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3answers
314 views

Developing Mathematic Intuition

I'm an engineering student, currently working my way through the fundamental mathematics courses. I've done reasonably well so far—mostly A's and a couple of B's in Algebra, Statistics, ...
4
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2answers
81 views

recommend math books [closed]

So i completed an year ago my schooling and i am pretty good at maths well at my level and i am very interested in maths and want to learn as much maths as possible and i like stuff like number ...
0
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0answers
26 views

Game Theory Projects for Undergrads

I am looking for some project ideas for beginning math students in the topic of game theory. I am not very knowledgeable in the topic so it would be great if I could get an good introductory source to ...
1
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1answer
28 views

Why are surds put on the numerator in the final answer when it is a fraction. [duplicate]

I have learnt that a fraction with a surd in its most simplest form should have the surd in the numerator and not the denominator? Why is it convention not to leave the surd on the denominator? Is it ...
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0answers
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mathematician who changed the world [closed]

I’m interested to know about mathematician and mathematical problems that changed the world. For example enigma machine + code braking, if you know amazing stories like this please comment them below
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1answer
117 views

Why do we teach Calculus in High School instead of, say, programming? [closed]

I was wondering "Why do we teach Calculus in High School instead of programming?" 'Calculus' only goes up to about partial derivatives, then its called different things like real analysis and other ...
595
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158answers
37k views

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's ...
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0answers
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Why are math textbooks that are considered good books so hard to read? Why do authors make their books difficult to read? [closed]

I've noticed that many books that are difficult to read are considered some of the best. Why does hard to read indicate that it is rigorous? For example: Rudin, Apostol, Lang, Hungerford, Ahlfors, ...
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0answers
12 views

consider the coordinates of the bounding area inclusive the range coordinates

I am stuck with a very trivial issue here. I have following coordinates: (xMin,yMin) = (-500,-500) (xMax,yMax) = (764,-26) and the step size is 79. I need to consider all the coordinates inclusive ...
7
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2answers
315 views

Why do knowers of Bayes's Theorem still commit the Base Rate Fallacy?

Source: 6 July 2014, "Do doctors understand test results?" by William Kremer, BBC World Service. A 50-year-old woman, with no prior symptoms of breast cancer, participates in routine mammography ...
2
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0answers
29 views

E versus e when using scientific notation

When I was calculating pressures in different units, I decided to use Google out of laziness. First I tried: 1.013e-10 mbar and received a result of: ...
2
votes
2answers
48 views

Mathematical usage of “$\dots$” during enumeration, is it ok to be imprecise?

I am guilty of writing things like the following in proofs: so by lemma 1.2 we have that for $k<n$ all of the integers $k,k+1,k+2,k+3,\dots ,n$ are pompous. I really like how this looks, the ...
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5answers
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Is high school contest math useful after high school?

I've been prepping for a lot of high school math competitions this year, and I was just wondering if all the math I learn would actually mean something in college. There is a chance that all of it ...
2
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1answer
45 views

Theorem 2.27 (a) in Baby Rudin: Is his proof complete enough?

Here's Theorem 2.27 (a) in the book Principles of Mathematical Analysis by Walter Rudin, 3rd edition: If $X$ is a metric space and $E \subset X$, then $\overline{E}$ is closed. Now here's ...
2
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0answers
56 views

What's the mathematical symbol to say “It doesn't depend on …”?

If I want to say x doesn't exist I would use the symbol $\nexists$ If I want to say x is a member of... I would use $\in$ But what's the symbol to say y doesn't depend on x? I know I could write ...
1
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3answers
54 views

Logic with numbers

Nick wrote each of the numbers from 1 to 9 in the cells of the 3x3 table below. Only 4 of the numbers can be seen in the figure. Nick noticed that for the number 5, the sum of the numbers in the ...
1
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5answers
79 views

How to prove $\sin3θ=3\sinθ-4\sin^3θ$

I was solving an A Level past paper (November 2014 P32) when I stumbled upon this question. It first asks us to expand $\sin(2θ+θ)$ which is easy using the identity $\sin(A+B)=\sin A\cos B+\cos A\sin ...
5
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2answers
782 views

Using the Constant Function Theorem to prove the Increasing Function Theorem

I quote Thomas W.Tucker: ... By the way, I view the Constant Function Theorem as even more basic than the IFT. It would be nice to use it as our theoretical cornerstone, but I know of no way to ...
7
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10answers
19k views

Explain for students: Why does 0 mod n equal 0 (zero)?

I told my students that the mod operator basically gives the remainder of division, so upon seeing: 0 mod 10 Some students (apparently) reasoned that, "10 goes ...
653
votes
48answers
408k views

Visually stunning math concepts which are easy to explain

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain, but are ...
2
votes
1answer
91 views

How important is the choice of books in studying Analysis?

I am in a fix. I have done a graduate course in Pure Mathematics.I love to study abstract algebra.I want to do postgraduate in Mathematics especially in Abstract Algebra . In order to enter a ...
9
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1answer
415 views

Best program for creating educational math animations?

I'm looking for recommendations on what program to use for creating mathematical animations. These animations will be used in creating educational videos for high school math -- Trigonometry first, ...
13
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4answers
958 views

Best way of introducing determinants in a linear algebra course

What is the best way of introducing determinants in a linear algebra course? I want to give real life examples of where the determinant is applied. It should have a real impact.
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3answers
3k views

Research Experience for Undergraduates: Summer Programs (that accept non-American applicants)

There are many summer research programs in the United States, targeted at good motivated undergraduate students majoring in mathematics. The main aspects that characterize such programs are: (a) a ...
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1answer
347 views

Understand Logarithm of Bar values manipulation step.

Currently I am learning Logarithm , but I can't understand the manipulation of the following Highlighted step how it comes How the result come after after ...
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0answers
23 views

What does meant “Uncounditional proof” and why should believe it that is a complet proof?

I have tried many times to understand what it does meant "Uncounditionally proof" but i don't succed , only I think that is the proof which produced from Insufficient conditions and and havn't enough ...
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0answers
66 views

Got some problem with math [closed]

First of all sorry, if this is the wrong place to post this, didn't found a better tag for it. So I used to be/am quite good in math, however recently I discovered a big weakness I have. Whenever I ...
16
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2answers
84 views

why don't standard analysis texts relax the injectivity requirement of the multivariable change of variables theorem? [duplicate]

In standard multivariable analysis texts, the change of variables for multivariable integration in Euclidean space is almost always stated for a $C^1$ diffeomorphism $\phi$, giving the familiar ...
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2answers
7k views

GRE Probability question

How many 3-digit positive integers are odd and do not contain the digit 5 ? My attempt: 100-999 3 -digit integers, 900/2=450 odd numbers. Now how to calculate odd numbers which do not contain digit 5 ...