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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6answers
8k 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 ...
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4answers
995 views

Masters' in Applied or Computational Math

I've been looking at various applied masters' in math programs, but the tuition of many of the best programs in the US is prohibitively expensive given a lack of information about student placement ...
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3answers
2k views

Good ways to help people learn math.

I have a student position at my university, which involves helping people who are struggling with basic calculus, precalculus, and discrete math. In general, the students that I help are hostile ...
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6answers
5k views

Complete undergraduate bundle-pack [closed]

First of all I'm sorry if this is not the right place to post this. I like math a lot. But I'm not sure if i want to do a math major in college. My question is: Can you give me a list of books that ...
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6answers
981 views

Is the Mean Value Theorem interesting to engineers, scientists, and others?

I am trying to decide whether to include whether to include the Mean Value Theorem in a calculus course I will be teaching. I am sort of leaning away from it, in light of the interesting discussion ...
12
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3answers
554 views

Elementary Geometry Nomenclature: why so bad?

A long-ish wall of text, and I apologize. Some background: when I was a first-year university student, my chemistry professor was lecturing and was trying to find the word to describe a shape. A ...
43
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13answers
4k views

Research done by high-school students

I'm giving a talk soon to a group of high-school students about open problems in mathematics that high-school students could understand. To inspire them, I would like to give them examples of ...
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2answers
1k views

History of Quadratic Formula

My wife is planning a lesson on the quadratic formula for high school students, who have previously learned how to complete the square. It would be nice to open the lesson with some historical ...
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8answers
3k views

I'm teaching a college geometry course. What should I cover?

I've been asked to teach "Foundations of Geometry" at the University of South Carolina. Apparently, professors in the past have all done very different things, and I have a lot of choice in the ...
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2answers
540 views

How to get better at algebraic manipulations?

I've always been able to manipulate equations found in school homework easily. But when tackling more challenging questions from puzzle books - where I might need three quarters of a page to ...
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3answers
218 views

How to introduce basis vectors

What is attractive way to introduce basis vectors? I am looking for a hook that students will find motivating. It needs to have an impact. I have normally introduced it by just stating independent ...
12
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5answers
695 views

Can the order of learning be changed?

I have been advised by many people to learn from scratch. So I decided to learn it. But I have the following questions in my mind. Can we skip "the Trinity" and learn something else directly? ("the ...
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1answer
455 views

Getting a masters in Mathematics

I'm not entirely sure that this is the right medium for this question, so feel free to close it at will. I'm basically wondering where there are some strong programs to get a masters in mathematics. ...
4
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1answer
156 views

Riddles involving Truth Tables

I'm looking for a simple riddle I can use to introduce the concept of a truth table. Thanks
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2answers
448 views

Too many topics taught in class? Frustrated student in need of advice and encouragement. [closed]

Location: New York CUNY (as education systems might be different in other places) I started my life studying philosophy and psychology and then at 22 transitions to computer science. It took me a ...
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5answers
1k views

Best books in the genre “______ for Mathematicians”

I once heard someone (perhaps from someone famous -- anyone have a citation?) say that there ought to be a series of books called "__ for Mathematicians," each one of which would explain a different ...
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0answers
117 views

References on the equivalence of different definitions of integrability

While writing a chapter of a book about mathematical analysis, I decided to compare some definitions of integrability that are usually taught to sophomore students, in Italy. I briefly collect four ...
3
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1answer
530 views

How did the teaching of mathematics change since the 19th century?

Background: 1) In the book Gems of Geometry, chapter 9 Relativity, the author wrote: "The General Theory concerns gravitation and the mathematics behind it is considered rather difficult ( post- ...
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0answers
246 views

Programmer understanding academic writings on maths

I would like to know in which order I should learn different areas of maths so I can have a robust overview of all the theory in case I need something for a computer programming problem. So I've ...
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4answers
227 views

Examples of logs with other bases than 10

From a teaching perspective, sometimes it can be difficult to explain how logarithms work in Mathematics. I came to the point where I tried to explain binary and hexadecimal to someone who did not ...
3
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1answer
314 views

What is a motivating way to introduce vectors?

What is a good way to introduce vectors on a linear algebra course so that students are motivated from the start? I need an opening which will have a real impact. Are there any motivating examples?
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5answers
723 views

Math department space design ideas

I'm looking for resources on design space for academic departments, particularly, We've been asked to provide ideas on designing a "dream math department". I'd like to gather some ideas for doing ...
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3answers
145 views

Resources for kids education

Most of the questions on MSE about educational resources are for high school. At least I haven't found questions which deals with sites on very elementary mathematics. I will be grateful if someone ...
6
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1answer
451 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 ...
1
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1answer
95 views

Polynomials and exponentials: showing that $n^k \le c\cdot a^n$

If $k$ is any real and $a>1$, prove that there exists a $c>0$ such that for any integer $n\ge 1,$ $$ n^k \le c\cdot a^n $$ To forestall any complaints about the imperative nature of this ...
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7answers
2k views

Teaching abstract maths concepts to young children.

I am interested in opinions and, if possible, references for published research, about the pros and cons of teaching abstract maths concepts to young children. My younger brother (five years old) ...
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1answer
254 views

An elementary (?) minimization problem

This morning, in Italy, there was the national exam of mathematics for students of high schools. One of the exercises asked to solve Heron's problem: given a straight line and two points lying on the ...
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3answers
3k views

What is the importance of determinants in linear algebra?

In some literature on linear algebra determinants play a critical role and are emphasized in the earlier chapters. (See books by Anton & Rorres, and Lay). However in other literature it is totally ...
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4answers
374 views

Would nonmath students be able to understand this?

For a course, I am required to do a presentation. The topic could either be something mundane, like a career strategy report, or something more interesting, such as a controversial topic, or an ...
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6answers
1k views

Purpose of Linear Algebra

How much emphasizes should be on proof on a first course in Linear Algebra? I sometimes feel that they (proofs) crowd out a coherent vision for linear algebra. However I also think a central theme of ...
7
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1answer
17k views

Numerator vs. denominator vs. nominator

What is appropriate usage of "numerator", "denominator", and "nominator" to refer to parts of a fraction? I'm posting this question and answer here because I had little luck finding a clear ...
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1answer
176 views

Should students be taught that $\int dx/x = \log(|x|)$? [closed]

I think in precalculus students should be taught the following: Euler's identity for $e^{i \theta}$. The principal value of $log(x)$ for $x<0$. Then in Calculus they should be taught that $\int ...
10
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1answer
3k views

Tips and examples for a poster presentation in pure mathematics

I will be presenting a poster in a few weeks but have no experience with them. I've seen and given plenty of talks, read and written papers, but I have never made or even seen a poster in pure ...
48
votes
24answers
9k views

“Negative” versus “Minus”

As a math educator, do you think it is appropriate to insist that students say "negative $0.8$" and not "minus $0.8$" to denote $-0.8$? The so called "textbook answer" regarding this question reads: ...
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1answer
1k views

Purpose of Inverse matrix

What use is the inverse matrix? I would not use it to solve linear systems but there must be some concrete or real life applications where it is used.
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2answers
267 views

Teaching permutations, How to?

I posed this question to my niece while teaching her permutations: Given four balls of different colours, and four place holders to put those balls, in how many ways can you arrange these four ...
3
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1answer
240 views

Forum for students - your experiences, recommendations, suggestions [closed]

Have you ever used online discussion forum or something similar for students of your course? (Or, if you are a student, have you attended a class, where something like this was used?) If yes, I'd ...
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8answers
1k views

When is something “obvious”?

I try to be a good student but I often find it hard to know when something is "obvious" and when it isn't. Obviously (excuse the pun) I understand that it is specific to the level at which the writer ...
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3answers
293 views

Linear Algebra Journal

Is there any journal which has significant material on the teaching of linear algebra. I am investigating the most effective way to teach a course on Linear Algebra. What are the most important things ...
37
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19answers
8k views

Examples of mathematical induction

What are the best examples of mathematical induction available at the secondary-school level---totally elementary---that do not involve expressions of the form $\bullet+\cdots\cdots\cdots+\bullet$ ...
102
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7answers
3k views

What remains in a student's mind

I'm a first year graduate student of mathematics and I have an important question. I like studying math and when I attend, a course I try to study in the best way possible, with different textbooks ...
9
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1answer
729 views

Who came up with the arrow notation $x \rightarrow y$?

I read that the arrow notation $x \rightarrow y$ was invented in the 20th century. Who introduced it? Each map needs both an explicit domain and an explicit codomain (not just a domain, as in ...
4
votes
1answer
548 views

Mathematics for beginners

I am not great at math. Last test I did I got a 5.5, just made it. My questions is: Is there a Website(software/on line-books) that can help me practice my math? It doesn't matter how many sites ...
12
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5answers
262 views

Issues with text problems

When I tutor, I often see people who kind of know the stuff they cover in school at the moment and succeed at straight problems like: Find the derivative of $f(x) = \frac 12 x^2$ But when it ...
7
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4answers
402 views

Extracurricular ideas for UK GCSE level maths student

My daughter is 15 years old and enjoys her maths classes (perhaps only because her maths homework takes her the least amount of time). Until now I have managed to introduce her to subject matter ...
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2answers
776 views

Where does binary arithmetic/manipulation enter the mathematics/engineering curriculum?

Binary arithmetic is both an educational basis for elementary logic and an pervasive tool for practical mechanics in managing computer systems (at a very particular level). That is the state of ...
6
votes
3answers
542 views

The Importance Of Good Teachers and Guidance In the Academics

I'm a first year student for a math degree. I'm very curious on how good students overcome their bad teachers in the journey of learning and grasping the courses material fully, all in the pressure of ...
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1answer
478 views

Derivation vs. proof

I imagine that Ramanujan and many other gifted mathematicians achieved results by derivation, meaning they followed a trail that led to a result, then proved it later if at all. Is this so and if so, ...
14
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8answers
2k views

What math should a programmer know?

I am an application programmer focussing on Line Of Business (LOB) applications. I am from non-mathematics and non-CS background. What mathematics should I learn which help me improve my programming ...
3
votes
4answers
466 views

Factoring $ac$ to factor $ax^2+bx+c$

I was watching a first-year high-school-algebra student struggle with factoring quadratics last night. Given a quadratic $ax^2+bx+c$ (I'll give you the exact example in a moment), her method — ...