Questions related to the teaching and learning of mathematics.

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4
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1answer
96 views

the nature of numbers?

I am currently relearning basic math - including; fractions, decimals and percentages. I am learning from various different sources, and what gets me is that they only teach math in forms of methods. ...
0
votes
1answer
42 views

the difference between showing and checking

So we had a quiz in math a couple of days ago and I had gotten none of the questions wrong on the quiz. I was very angered to find out that I had been marked down 5 points for not checking my work and ...
8
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5answers
3k views

Are there any memorization techniques that exist for math students?

I just watched this video on Ted.com entitled: Joshua Foer: Feats of memory anyone can do and it got me thinking about memory from a programmers perspective, and since programming and mathematics ...
1
vote
1answer
132 views

Randomly place $n$ balls in $n$ buckets - how many empty buckets?

A question posed on John D. Cook's blog asks: Suppose you have a large number of buckets and an equal number of balls. You randomly pick a bucket to put each ball in one at a time. When you’re ...
2
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2answers
99 views

The evaluation of proofs

I searched this community upon proofs and found some interesting topics. Yet I would like to know how you guys achieved to write your own proofs. What I mean is, my course describes proof as something ...
3
votes
2answers
717 views

Roadmap for maths self-study for a physics undergrad wanting to pursue research in maths [closed]

I am a second year physics undergrad. After spending about an year exploring mathematical physics (QFT,solitons, etc), I have realized that maybe theoretical physics isnt my passion after all, and I ...
0
votes
1answer
133 views

teaching a little nonlinear PDE to an undergraduate

I would like to teach a little nonlinear PDE to an undergraduate who is taking a course in second-order linear boundary value problems. I have never taught nonlinear PDE before, although it is my ...
14
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5answers
545 views

Inspiring a new generation

Tomorrow is a very special day for both my students and I: we will be starting a calculus course. I'm looking for some nice quotes to read to them to convey just what a complete game changer calculus ...
0
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2answers
135 views

What engineering major in undergraduate is compatible for taking a master in Mathematics?

Short question: What the engineering major in undergraduate is compatible for taking a master in Mathematics?
1
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2answers
184 views

Why begin with distributions and then move to tempered ones?

After reading several books on distribution theory, I got a strange feeling. Why do they all begin with the theory of distributions and then move on to tempered distributions? Why can't we just start ...
12
votes
3answers
1k views

What should a math graduate know? [closed]

There are a lot of undergraduate courses out there and most of them agree on certain things, with regard to the subjects covered. Courses that include mathematics (engineering, physics, etc) are ...
2
votes
0answers
59 views

Where can I get “computer based math” education as defined by Conrad Wolfram?

Textbooks, courses, and other resources would be helpful. http://www.computerbasedmath.org/
4
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3answers
6k views

What is the most effective way of teaching mathematics to my 7 year old kid?

I want to help my kid excel in Math. I can see she has some trouble with additions,subtraction, multiplication and division. Will it help if I let her memorize the multiplication table? or use ...
2
votes
0answers
90 views

Where read recent developments in Math presented in a way that is easy to understand?

I posted a similar question a few months ago, but I don't think people understood my question. I often find articles such as this which discuss exciting developments in science. I have a great ...
15
votes
1answer
326 views

Do lay persons really believe that all of mathematics is known?

I once found a professor of medicine to be under the impression that everything in mathematics is already known. It's probably commonplace to hear that the masses labor under that misconception. In ...
2
votes
1answer
146 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
6k 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
5k 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 ...
5
votes
3answers
2k 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
195 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
610 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
3k 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
436 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
949 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
15k 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
4k 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
159 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
9k 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
182 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
745 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
563 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
217 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
261 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
882 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
945 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 ...
23
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
538 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
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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 ...
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 ...