# Questions tagged [education]

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

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### What higher-level math ought I, an undergraduate, study?

I am a undergraduate student pursuing a degree in mathematics and I hope to pursue graduate level studies and eventually be a professor. I have taken math classes through calculus. I am looking to ...
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### General definition of growth in mathematics

From high school math one knows "linear growth", "exponential growth", "logistic growth", "bounded growth" etc., but is there a common accepted general definition of "growth" which covers the special ...
216 views

### “the product of the factors” versus “the factors of the product”

Could somebody please compare and contrast the meanings of the two phrases: "the product of the factors" and "the factors of the product." In terms of expressing possession. Thank you.
162 views

### “unexpected” isomorphism between finite posets?

The set of all divisors of a square-free number, partially ordered by divisibility, is trivially isomorphic to the set of all subsets of the set of prime factors, partially ordered by inclusion. Are ...
14k views

### Explaining Horizontal Shifting and Scaling

I always find myself wanting for a clear explanation (to a college algebra student) for the fact that horizontal transformations of graphs work in the opposite way that one might expect. For example, ...
198 views

### Expanding squares and simplification of equations

as i'm reading a paper "An Underdetermined Linear System for GPS" By Dan Kalman i understand the paper but when i traced the equations there's something i don't understand ,may be my mathematics is ...
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### Masters in Actuarial Science

I am applying to a grad school for the Masters in Actuarial Science. Now i am getting cold feet. I do love math, i was always good in math (not excellent or a genius). Did all adv. calculus classes ...
419 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 ...
955 views

### What is an effective way to teach children the Cartesian coordinates?

My nephew is preparing for a $4$-th grade state test. They need to learn topics like reflection about $x$ or $y$-axis of a point( say $(3,5)$ reflected about the $y$-axis). I tried to explain but he'...
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### How do you explain the concept of logarithm to a five year old?

Okay I understand that it cannot be explained to a 5 year old. But, how do you explain the logarithm to primary school students?
551 views

### Learning approach of simultaneously enhance creation and imagination skills instead of 'follow' approach

I am a math-major bachelor student. And I want to get some advice about the approach I'm trying now for learning maths, not for efficiency, but for depth and fully-mastered. Firstly, I want to know ...
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### High school math definition of a variable: the first step from the concrete into the abstract…

variable: A symbol used to represent one or more numbers. High school students are justifiably confused by the two distinct concepts: a variable as something that “varies” in an expression, such ...
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### When my teacher gives me a question involving summation notation, do they expect us to calculate it by hand?

Assuming we don't have a calculator that can do summation notation. My class is not up to summation yet, but I'm asking a question involving this concept because I'm not all that experienced using it. ...
15k views

### Which calculus text should a 36-year-old use for self-study?

I am 36 years old, and have forgotten a lot of math from high school, of which I only took up to Algebra 2. However I am teaching myself mathematics and am now, completely fascinated with the logic ...
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### trivial but non-trivial equivalence relations

Define a binary relation $R$ on a set $A$ by saying $xRy$ iff $x$ and $y$ have the same whatever. "Whatever" is of course some specified function on $A$. This is a "trivial" equivalence relation: ...
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### Math Database For Problem Descriptions In An App.

I am developing an app for kids and they will have a variety of problems from percentage problems, absolute value problems, negative number problems, fraction problems, etc. I was hoping to have a ...
225 views

### Starting my nephew out on the journey to higher mathematics. [closed]

My nephew is 8 years old and shows great promise as a student. Sadly, as most of you know most programs in secondary education don't offer any foundational courses for higher mathematics. What books/...
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### How do I get into a masters course in pure mathematics?

My question is as stated in the title and to elaborate more: I would like to know if there are any standardized international exams to enter a masters course in pure mathematics (besides GRE Math) ...
171 views

### A Formal and Precise treatment of Simplification?

I am looking to gain a deeper understanding of, and increase my own skill in "Mathematical Simplification". But I've been finding the concept overly vague and haven't been able to find any good ...
16k views

### Mind maps of Advanced Mathematics and various branches thereof

I would like to get a list of mind maps of advanced mathematics topics. As an example, I have posted one below. I would be happy if you post such other maps. Making one and posting it here is also ...
711 views

### Why don't they teach Fundamental Theorem of Algebra in High School? [closed]

I am currently in AP Calculus BC and one more year to go, I have heard about Fundamental Theorem of Algebra several times, and with the resources that is out there today I tried to search and study ...
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### Opinions on foundational math materials to teach 8th grade, 9th grade kids at a Summer Camp

I have been asked to teach mathematics/physics to a few 8th grade/9th grade kids for a summer camp. I have been thinking about it and I realized that I could go about it in two ways: One of the ways ...
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### learning maths for statistics

Apologies if I have posted this in the wrong place first off. My work has taken me into a unexpectantly large amount of statistics. In order to really understand what I am doing I need to understand ...
557 views

### Implicit use of the Implicit Function Theorem when finding tangent lines to polar curves.

Recently I found myself having to teach students how to find the slope of a tangent line to a curve in $\mathbb R^2$ given in polar coordinates by the equation $r = f(\theta)$. The students' calculus ...
12k views

### Do you prove all theorems whilst studying?

When you come across a new theorem, do you always try to prove it first before reading the proof within the text? I'm a CS undergrad with a bit of an interest in maths. I've not gone very far in my ...
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### Where can I find math plans for US primary / secondary education?

I'd really like to have an overview of how math is being studied in US. I would love to see how it compares to primary / secondary education in Europe (ex Yugoslav countries). TIA
2k views

### Quickest way to understand Kruskal's Tree Theorem

I came across the Kruskal Tree Theorem the other day and thought it looked pretty interesting (especially the stronger finite form due to Friedman). I'm currently a first year mathematics ...
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### Infinite Series: Fibonacci/ $2^n$ [duplicate]

I presented the following problem to some of my students recently (from Senior Mathematical Challenge- edited by Gardiner) In the Fibonacci sequence $1, 1, 2, 3, 5, 8, 13, 21, 34, 55,\ldots$ each ...
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### Why do introductory real analysis courses teach bottom up?

A big part of introductory real analysis courses is getting intuition for the $\epsilon-\delta\,$ proofs. For example, these types of proofs come up a lot when studying differentiation, continuity, ...
20k views

### How to justify small angle approximation for cosine

Everyone knows the picture that explains instantly the small angle approximation to the sine function (as defined by the parametrisation of the unit circle): "what's the length of that arc?" "See how ...
956 views

### Connecting finite automata and regular languages in teaching/applications

I am considering giving a presentation to middle schoolers, aged about ten to fourteen, about finite automata and regular languages. Average American students have no problem with uses of the ...
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### Motivation for solution to constructing a set of 1983 distinct integers such that no three are consecutive terms of an arithmetic progression

Problem: Is it possible to choose $1983$ distinct positive integers, all less than or equal to $100,000$, no three of which are consecutive terms of an arithmetic progression? (Source: IMO 1983 Q5) ...
Today I tried to teach a high school student about inverse functions. I gave him this problem and defined the parts that he didn't understand: Let $f: \mathbb{R} \to \mathbb{R}$, \$x \mapsto x^...