Questions related to the teaching and learning of mathematics.

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2
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1answer
143 views

“limit along a path” equivalent to usual definition of limit?

At the institution where I teach, regrettably, we do not teach students the real definition of the limit in our calculus classes. I am teaching a little complex analysis, and I would like to use the ...
6
votes
6answers
5k views

Steps to Re-Learn Mathematic the right way

I was always branded weak mathematics back at school though i loved it. The reason was that I was not having many basics in maths. Due to this problem I stopped learning Maths after my 10th grade. But ...
2
votes
3answers
4k views

Sum of digits and product of digits is equal (3 digit number)

My child got a question in school (grade) that is: Find biggest and smallest 3 digits number, which has sum of it's digits equal to product of those digits. Help please since I cannot explain my ...
5
votes
2answers
174 views

How effective is Wikipedia for first line of attack?

I am learning some pretty disconnected concepts of mathematics for a project I am working on. I was reading about matrices and suddenly had to know about Markov Chains and that lead me to read about ...
7
votes
4answers
4k views

Degree choice — Math or physics

I realize that it is of bad form to cross-post. However, on this matter I very much hope to hear arguments from all sides... I hope to become a physicist focusing mainly on the theoretical side in ...
4
votes
3answers
1k views

Advice for choosing an MSc or PhD.

I have recently graduated from the University of Warwick with a 1st Class in my Master of Mathematics(MMath) degree and would really like to continue my education in mathematics by doing a PhD. The ...
4
votes
1answer
187 views

Skip count “starting at one”

My daughter is taking a second grade math class and they are learning to "skip count" I am guessing this means to count by [n]. The directions say "Start at 1. Skip count by 2." and the worksheet has ...
3
votes
1answer
568 views

Fuzzy C Means mathematics tutorial [closed]

Hello I am looking for help on understanding the maths of Fuzzy C Means as explained here: Fuzzy C Means I was hoping for a broken down explantion of the actual math. I have tryed googling for ...
16
votes
4answers
1k views

Is the golden ratio overrated?

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 ...
1
vote
2answers
2k views

GRE Probability question

How many 3-digit positive integers are odd and do not contain the digit 5 ? My attempt: 100-999 3 -digit integers, 900/2=450 odd numbers. Now how to calculate odd numbers which do not contain digit 5 ...
15
votes
7answers
424 views

Common inadequate definitions

I had the good fortune of assigning the following problem on the first day of my freshman honors calculus course: Is $a$ contained in the interval $[a,a)$? Explain. The majority of my students ...
4
votes
1answer
872 views

Relevance of Euclidean geometry to modern mathematics

I'm interested whether, barring the reasons such as the importance of historical narrative and having an illustrative example, one should learn (synthetic) Euclidean geometry. To make such an inquiry ...
5
votes
7answers
13k views

Geometry triangle question

In the figure below, AB=BC=CD. If the area of triangle CDE is 42, what is the area of triangle ADG? I think triangles are similar. Are there any properties of similar triangles regarding their area. ...
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
75 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
154 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
188 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
172 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
697 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
547 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
208 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
253 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 ...
4
votes
3answers
866 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
90 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
898 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 ...
26
votes
3answers
1k 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 ...
21
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
506 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 ...
41
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
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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 ...
2
votes
2answers
508 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
674 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
441 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
150 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
428 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
232 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
669 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
140 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
386 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 ...
13
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
370 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 ...