Questions related to the teaching and learning of mathematics. Consider asking your question at Mathematics Educators.SE instead.

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Books on complex analysis (Ahlfors, Conway and Lang)

To make my question slightly different from others, I would like to know how would you rate on the complex analysis books by Ahlfors, Conway and Lang? I had a basic course on complex analysis during ...
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0answers
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Rethinking a counting strategy - sampling of distinct objects with replacement where order doesn't matter

I am looking for an alternative to the stars and bars counting method for determining the number of ways of choosing subsets of size $k$ from a set of distinct objects of size $n$ where ordering ...
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6answers
222 views

Alternate ways to prove that $4$ divides $5^n-1$

I was working for various method to solve this: For all $n\in \mathbb N$: $4\;\mid\;(5^{n}-1)$. My try was: 1st: $$n=1 \to 4|5^1-1\\n \geq 2 \to 5^n=25,125,625,3125,...\\ n\geq 2 \to ...
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What is a good way to Google and obtain Math resources? [on hold]

I'm having a great deal of difficulty finding math resources on Google and stackoverflow. Is there a scheme to search for MathJax equations? Any good ways to search the web via Wolfram Alpha?
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2answers
763 views

Is Mathematics graduation important for a Computer Scientist?

I know this might be a personal problem, but I often find some friends in the same problem as me so I think this might be helpful to them after all. I am going to graduate in Computer Science in ...
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3answers
596 views

How can I find videos of mathematics at graduate level, especially on linear algebraic groups

I am studying mathematics by myself, and I find it very helpful to watch online course videos. There are many such videos on undergraduate courses, such as elementary calculus, abstract algebra, ...
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8answers
5k views

How can I learn to “read maths” at a University level?

When I look at math, it's like my mind goes fuzzy. The only way to describe it is in terms of what I can relate it to. You know how when you read, you see the letters and words, but your brain picks ...
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2answers
532 views

Self-Teaching: Is Geometry the Nexus of all Mathematics?

Necessary prologue: I'd really like to become more fluent in the language of mathematics. I don't have a schedule that permits me taking a class and any on-line tutors that I find seem relatively ...
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2answers
370 views

Study program for algebra for an math-phobic person

I have a female friend (Mid 20's) who wants to get an associates degree, who has an absolute phobia of math, and algebra in particular. I'm trying to find a good program that can help her to study ...
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2answers
253 views

Is there a online reference that chains mathematical knowledge from simple to complex?

I'm a very, very logical person -- but I've never taken any math classes; really, I know. So, on that note -- how do I teach myself math? As my question might suggest, I see the answer as being an ...
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8answers
7k views

When to learn category theory?

I'm a undergraduate who wishes to learn category theory but I only have basic knowledge of linear algebra and set theory, I've also had a short course on number theory which used some basic concepts ...
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0answers
40 views

Good Book for learning Math [on hold]

There is a great book for learning Physics "Halliday - Fundamentals of Physics", and so my question is simply: Is There a great book like that for learning math? Thanks :) Note: "An author whose ...
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1answer
56 views

Factoring bivariate quadratics with real coefficients (for high school students).

I was tutoring a Year 10 student last night (he's learning about quadratics). Unfortunately, we ran into a class of problems that I couldn't explain how to solve (beyond simply guessing and checking), ...
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4answers
1k views

Guidelines for learning about Ramanujan's work?

It is well known that one of the first books Ramanujan studied was "Synopsis of Pure and Applied Mathematics" and that it shaped the way Ramanujan thought and wrote about mathematics. Being interested ...
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5answers
404 views

New idea to solve this equation

I was teaching $\left \lfloor x \right \rfloor$ function properties and equation . I solved this equation in my class . My works are show below. Some students ask me for new Idea...,and now I am ...
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5answers
2k views

When I was teaching absolute function properties, I suddenly made this question …

I was teaching absolute function properties in a K-12 class. I made this question in my mind. Suppose $f(x)$ is a one-to-one function, and its definition is $f(x)=max\left \{ x,3x\right ...
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0answers
2k views

GRE past papers

As it is required for most students who wish to do a Ph.D in maths in the US to sit the GRE subject specific mathematics exam, I hope this question will be of interest to the mathematical community ...
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13answers
4k views

Are all mathematicians human calculators?

I asked my dad why he did not major in math he said "because he is not good at math". I think I like math, and I think I'm ok at it, but I'm not gifted or anything like that, I just like math. I think ...
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5answers
4k views

Math GRE Subject Exam [on hold]

I am studying for the GRE Mathematics subject exam [1]. I am looking for tips regarding how to more effectively study for it. Does anyone know of any good study materials or have any tips in general? ...
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2answers
376 views

Good math software [closed]

I have finally decided to go more deep into math and cs, so to do that I will need proper tool, math tool. Could you please tell me what's the best open source math tool on the web today, since as far ...
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9answers
1k views

Educational Math Software

What is the the most educational software for high school and college math? Not the one that just gives you the answer, but has any of the following: Edit: Software mentioned in answer added in ...
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0answers
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Proper name and access of the constituents of an equation.

In any math problems for example: ... B = (1 + B) A = (A + B) ... How can I definitely define a variable that points to the ...
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0answers
77 views

Opportunities to learn algebraic geometry outside of PhD education [on hold]

After a lot of deliberation, I decided to go to professional school instead of pursue academic mathematics. I don't have research aspirations, but I do have an obsession with "getting" esoteric ...
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1answer
25 views

Any idea how to approach this problem

A rectangular meadow will have a fence around it. The long side is $130$ m longer than the short side. The sides lengths can be written $x$ and $x+ 130$. Write a simplified expression for 1) ...
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153answers
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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
33 views

Demonstrative geometry around the world and its significance.

This is not exactly a mathematical question. I am from Pakistan; and over here students are taught a subject 'demonstrative geometry' (as a part of mathematics) from secondary level education. ...
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5answers
269 views

Is $1 : 7 = 1 / 8$ or is it $1/7$?

In a certain (non-mathematical) Stack Exchange, when I wrote $n : m = n / m$ where $n$ and $m$ are positive integers, one of the moderators said "No! $n : m$ is usually the notation for "$n$ parts in ...
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3answers
182 views

How to overcome the temptation to read many books covering the same topics [closed]

S.E advisers, I am a college sophomore in US with a major in mathematics and an aspiring mathematician in the computational complexity theory. I have been reading some math books on different topics, ...
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1answer
4k views

Strange old multiplication table

Today I read an article about chalk boards from 1917 discovered in an Oklahoma school. One of the chalkboards included the following curious image: (Oklahoma City Public Schools) The article ...
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4answers
347 views

How To Develop A Higher Mathematical Aptitude? [closed]

First off I must say I'm pretty blown away by the vast majority of the people in this forum. I do aspire to reach the knowledge of mathematics as shown on the site, but honestly it's a little daunting ...
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3answers
322 views

I would like to buy references in order to review and study mathematics [closed]

I am an ESL learner and most of the time I am able to understand English but In my courses, we don't study mathematics, and I think that it is a mistake or wrong. 1-What are really the best sources ...
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3answers
669 views

Which background is more suitable to study “Cryptography”

I am a student of Pure Mathematics and also interested in programming .I have learnt C++,SAGE . Recently I have started learning "Cryptography" .But there are many definitions involved here like ...
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1answer
26 views

How to calculate percentile?

I am reading a document issued by UK Gov about minimum salary for work visa, it is using word percentile, which I don't understand, Could anyone explain what would be the 50th or 75th percentile IF, ...
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5answers
1k views

Is the golden ratio overrated? [closed]

While reading many sources and watching many video's about nature and physics I wonder if the golden ratio is really that often occurring in nature and physics ? If I look on the Wikipedia pages I see ...
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33answers
33k views

Pedagogy: How to cure students of the “law of universal linearity”?

One of the commonest mistakes made by students, appearing at every level of maths education up to about early undergraduate, is the so-called “Law of Universal Linearity”: $$ \frac{1}{a+b} ...
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1answer
145 views

Reading mathematics at the graduate level - does every single proof matter?

I would be interested in hearing from PhD students (and upwards) specializing in pure maths (in particular, the more algebraic aspects). My question is this: When reading to learn mathematics at ...
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1answer
130 views

Studying for analysis- advice

I find that studying for analysis is unlike other math classes that I've taken. I dedicate a lot of time to studying for it, but it seems like no matter how much time I put into it I am not getting ...
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1answer
65 views

Is this Applied Mathematics?

I wanted to learn Applied mathematics, mostly due to it being similar to or having relation to Object Orientated Programming (OOP), and thought it would help alot. I searched all over the internet. ...
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4answers
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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0answers
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Looking for Math books recommendations to study Electronics

My background is the very basics, and I mean, literally, I can add, sub,mul,div and a little of algebra (near, nothing) and that's it. As you can see I need the best Total Beginner Book(s) that can ...
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1answer
53 views

Cartesian Product how can this be used in real life situations [closed]

I am learning about the cartesian product as defined by The New Oxford American Dictionary as: the product of two sets: the product of set X and set Y is the set that contains all ordered pairs ...
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3answers
45 views

Factoring Trick - Adding Up Coefficients

My professor told me this for factoring polynomials: Add up the coefficients and if they equal 0 then the polynomial has root of 1. Add up, but switch the signs of the coefficients with odd ...
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1answer
35 views

Proving Odd & Even Functions

For the following: If $f(x)$ is an odd function, then $|f(x)|$ is _______. If $f(x)$ is an odd function and $g(x)$ is an even function then, $(f~o~g)(x)$ is _______. If $f(x)$ is an odd ...
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1answer
31 views

Domain of the definition of a composite function

If $$f(x)= \sqrt{3|x|-x-2} \\ g(x)=\sin(x),$$ then the domain of definition of $(f\circ g)(x)$ is ...? How do you calculate the domain of a composite function like this?
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2answers
414 views

Can any function represent something in the real world?

We know that the volume of a cube can be represented by the function: $V(x)=x^3$, where $x$ is side length. $x^2$ can represent the volume of some material that has a constant side ($1$). The function ...
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5answers
197 views

Difference between Pure and Applied Mathematics?

So, I have been looking into college courses to see what I want my major to be, and I noticed that M.I.T offers two specified types of Mathematics. Pure and Applied. What is the major differences in ...
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1answer
445 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 ...
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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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49 views

Can the difference between a number and a set of numbers be calculated as follows?

I have a number $X$ (lets say $45$) and I have five other numbers, lets say $(3, 4, ,5, 6, 7)$ I want to know the difference between my number and the other numbers like this: ...