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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11
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1answer
1k views

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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1answer
1k views

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 ...
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3answers
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.
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1answer
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 ...
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17answers
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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, ...
1
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1answer
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 ...
4
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3answers
4k views

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 ...
3
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2answers
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 ...
2
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2answers
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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19answers
17k views

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?
4
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1answer
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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5answers
2k views

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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1answer
355 views

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. ...
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8answers
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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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5answers
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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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2answers
240 views

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 ...
2
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0answers
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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1answer
593 views

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) ...
3
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1answer
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 ...
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7answers
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 ...
5
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1answer
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 ...
2
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2answers
595 views

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 ...
3
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1answer
1k views

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 ...
7
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1answer
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 ...
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4answers
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 ...
3
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3answers
124 views

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
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1answer
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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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3answers
4k views

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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7answers
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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, ...
11
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3answers
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 ...
5
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2answers
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 ...
12
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11answers
53k views

How do I explain to students that $0 \text{ mod } n$ equal $0$?

I am teaching a beginning programming class in Visual Basic (for non-CS majors). I told my students that the mod operator basically gives the remainder of the division. So, when seeing $0 \text{ mod } ...
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6answers
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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 ... ...
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6answers
13k views

What is the best way to develop Mathematical intuition? [closed]

I want to develop my pure mathematics knowledge and would like to know what is the best way to develop mathematical intuition? I am going through exercises that ask for proofs and I don't have the ...
6
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1answer
451 views

Learning roadmap for mathematical biology

Which courses (at an undergrad level or master's level) in mathematics or statistics should be taken by a student aiming for a PhD in mathematical biology? The basics I imagine are calculus courses, ...
24
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1answer
618 views

How much math education was typical in the 18th & 19th century?

Was it unusual for people in those days to learn Calculus? Could a grad student take a course in differential equations or multi-variable Calculus, or did they have to learn from journals? I am always ...
6
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1answer
506 views

Good books for 4th graders focusing on fun, interesting and challenging math topics and exercises

My son shows strong interests in math and he is currently a 4th grader. I wonder if there are any good books that could be used to keep up his interests and at the same time challenge him a little bit....
12
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4answers
477 views

A Book of Neat Theorems for Laymen

I'm looking for reading assignment ideas for my students. I'd like them to read up on results in mathematics in layman's terms. For example, the Monty Hall problem, or Borsuk Ulam as the "Ham ...
13
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2answers
934 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 ...
2
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1answer
314 views

Depth of the winding river… Not satisfied with answer…

I'm currently studying for the SAT. I'm taking a practice quiz and came across this problem: Now, using simple logic (and a bit of cheating by trial and error) we can easily determine the answer to ...
4
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0answers
193 views

$\max_{y} \min_{x} f(x,y)$ as motif for exploring mathematics

It's been several years since my undergraduate math days, and I would like to spend a bit of time refreshing and then tackling a few things I never completely mastered. Rather than proceeding topic ...
0
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2answers
109 views

What is this called? (Equations involving percentages)

I am trying to describe our formulas to our users, and have forgotten the basic math term for these 2 types. First one is: $$y=x+10\% $$ $$z=y+10\%$$ if $x$ was $10$, then $z$ would be $12.1$. Other ...
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4answers
5k views

Do you need real analysis to understand complex analysis?

I'm debating whether I should take a course, in complex analysis (using Bak as a text). I've already taken Munkres level topology and "very light" real analysis (proving the basic theorems about ...
25
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5answers
1k views

Elementary problems with group theoretic solutions

I am helping a friend develop a course in abstract algebra that is designed for high school students who have no knowledge of abstract algebra or any real exposure to formally rigorous mathematics. To ...
8
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2answers
436 views

Outline and Goals of a One-Year Calculus Sequence

Our department is considering restructuring our traditional three semester calculus sequence so that the calculus requirement for our majors is satisfied in two semesters. Does your department ...
10
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4answers
7k views

Difficulties with Chapter 2 in Rudin

I have been reading Rudin (Principles of Mathematical Analysis) on my own now for around a month or so. While I was able to complete the first chapter without any difficulty, I am having problems ...
8
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0answers
446 views

The difference between 10 and 9.99999 … (recurring) [duplicate]

Possible Duplicate: Does .99999… = 1? At supper today my daughter was discussing her maths (she's 13) - she had been studying putting decimal numbers into what she called standard form $A*...
9
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4answers
525 views

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) ...
9
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2answers
734 views

What should be the next step?

This is a soft/educational question and I'll flag it to be made community wiki. A little bit of background, first. I am in my last undergraduate year, and I took a graduate course in category theory; ...
4
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2answers
1k views

How should I teach a high school student about inverse functions?

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^...