Questions related to the teaching and learning of mathematics.

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33
votes
7answers
3k views

What are some good math specific study habits?

What are/ were some of your good mathematician's study habits that you found really worked for you? I'm a CS major at a respected school and have a solid GPA... However, I definitely lack when it ...
3
votes
1answer
78 views

Symbolic understanding

In mathematics, the symbols represent things with clear and precise meanings. My question is regarding the experience of reading/doing mathematics. When you are reading some piece of mathematics, is ...
8
votes
0answers
155 views

Undergrad research gateways

This question is intended as public service to mathematics. It is meant to benefit undergrad research students and maybe even researchers wishing to broaden their expertise and learn something away ...
53
votes
14answers
8k views

Why do we need to learn integration techniques?

After a lifetime of approaching math the wrong way, I took two college math courses this quarter with a newfound zest for math. These classes are integral calc and multivariable calc. Integral calc ...
7
votes
4answers
1k views

Expanding problem solving skill

I have a great passion for Math but my lack in problem solving skill always keeps me away from the "good stuff". I always wanted to be better at Math and one of the things I figured out was to keep ...
2
votes
0answers
189 views

MathJax (or something like it) as a classroom “blackboard”

At the risk of possible overlap with this (9-month-old) question Chatting about mathematics (with real-time LaTeX rendering) what is the best desktop application now for running MathJax in the ...
5
votes
4answers
2k views

When is linear algebra usually taught

Just curious, when should I learn linear algebra in college? And when is linear algebra usually taught? What precedes linear algebra and what usually goes after linear algebra courses?
1
vote
1answer
177 views

Good, free online resources on AMO-level olympiad training problems?

The title is self-explanatory, but what I'm looking for is a collection of good training problems for middle school students. AoPS is not an option, because I want the problem lists to be free!
6
votes
2answers
718 views

Personal advice ragarding Qualifying Exams

I am a Graduate student in Mathematics and in second Year. I have three qualifying exams in topics Abstract algebra, Real and Complex Analysis and Algebraic and differential topology.I already ...
7
votes
5answers
548 views

Math book for an eager learner with non-mathematical background

I was reading answers to How do you explain the concept of logarithm to a five year old? and realized that I really don't understand mathematics. Okay, I lied when I said that I had no mathematical ...
6
votes
1answer
213 views

Fundamental theorem Galois Theory

From time to time, I try to give my non-mathematician scientist friends descriptions of important theorems that I come across. One friend, watched a video on Galois and now I'm at a loss on how to ...
3
votes
1answer
256 views

Functions that generate “easy” matrices of full rank

While explaining how to invert matrices I once used this ill-fated example $A=\begin{pmatrix} 1&2&3\\4&5&6 \\7&8&9 \end{pmatrix}$ which can not be inverted ($\det(A)=0$). That ...
5
votes
3answers
872 views

why 0=0 is not possible??

Hi one of my friend showed me one proof i.e. $1)$ $2^2 - 2^2 = 10 - 10$ $2)$ $(2+2) (2-2) = 5 (2-2)$ $3)$ dividing both sides by (2-2) $4)$ $(2 + 2) = 5$ I know this is wrong in first line as ...
0
votes
1answer
54 views

Knotted up over “unique”

"Every boy has a unique shirt." Does this mean no two boys share the same shirt, or does it mean no two shirts belong to the same boy? I suppose the former, but then what is the most succinct way ...
1
vote
1answer
91 views

Given a set of numbers can you derive the values in a set using division and addition of the products of division?

This is my first question on the Math SE, and it may be a bit simple. Apologies if my question reveals my misunderstanding of your field or the universe in general. Me Programmer. I am working on a ...
1
vote
4answers
917 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 ...
27
votes
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 ...
22
votes
6answers
4k 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 ...
12
votes
3answers
522 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 ...
42
votes
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 ...
3
votes
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 ...
23
votes
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 ...
2
votes
2answers
514 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 ...
1
vote
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
votes
5answers
678 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 ...
1
vote
1answer
442 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
votes
1answer
151 views

Riddles involving Truth Tables

I'm looking for a simple riddle I can use to introduce the concept of a truth table. Thanks
7
votes
2answers
433 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 ...
1
vote
0answers
234 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 ...
16
votes
5answers
674 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 ...
2
votes
3answers
141 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 ...
7
votes
0answers
397 views

Studying quantum mechanics without physics background

I am a first year PhD math student, and I am wondering if I should study quantum mechanics even though I don't have an undergrad background in physics. I posted this question in physics ...
14
votes
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) ...
3
votes
3answers
2k 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 ...
5
votes
4answers
371 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 ...
6
votes
1answer
15k 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 ...
1
vote
1answer
171 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 ...
45
votes
24answers
8k 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: ...
16
votes
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 ...
99
votes
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 ...
4
votes
1answer
542 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 ...
7
votes
4answers
399 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 ...
1
vote
2answers
708 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
517 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 ...
5
votes
0answers
391 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
votes
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
447 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 — ...
3
votes
2answers
543 views

Proofreading services for mathematical texts

Are there any reputable proofreading services out there for texts with mathematical content? I may need such a service soon. My native language is not English and, even if it were, I would want the ...
0
votes
1answer
47 views

Loss estimation for replacement of stolen item [closed]

If an item of price $x$ is stolen from me or lost (assume that it is never going to be found again or returned to me), and I replace it by buying it again, but at its current price $y$, what is my ...
2
votes
1answer
326 views

any Math game for kids?

I need to plan a "game" for kids about 10-11 years old that involves mathematics and some physical activity or game. It must be short-time and not very difficult because it's a stage of a big game. ...