Questions related to the teaching and learning of mathematics.

learn more… | top users | synonyms (1)

3
votes
1answer
422 views

Do only certain people exceed at math well? [closed]

It's obvious if you look around that math has always been one of the toughest subjects in all areas, from federal-traditional public schools to simply people learning it as an autodidact, hobby, or as ...
3
votes
0answers
131 views

Which is the best transitional mathematics book for self-teaching among the ones listed?

What is Mathematics, An Elementary Approach to Ideas and Methods - Courant Robbins Stewart How to Solve It, A New Aspect of Mathematical Solving - Polya Introductory Mathematics, Algebra and Analysis ...
3
votes
3answers
114 views

Explaining to kids that $2^n$ can quickly yield high values

I have to explain to kids that $2^n$ can yield high values. Not with math and numbers but with a story rather. There was a story about a pharaoh and wheat..
4
votes
5answers
420 views

How to defend Mathematics from “ignorant” people? [closed]

Some of my friends are blaming me to stop talking about and studying Math. But I love Math so much and I do Math almost everyday. The problem is that some of my friends told me "go and get a life". I ...
0
votes
1answer
119 views

Going to math grad school with low GPA [closed]

I am a pure mathematics major and I want to do Ph.D in math, however I want to change to Applied math. I have a low 3.2 < GPA < 3.3 though. I have taken most of Pure math requirements, and ...
1
vote
0answers
44 views

What are some good statistics resources?

A year ago, I took a statistics course at my university. The course was based on Rice's "Mathematical Statistics and Data Analysis". Apart from the fact that I did not find the book terribly good, I ...
0
votes
1answer
50 views

What is the difference between math learning and math exam? [closed]

I really have a strong feeling that the process of learning the concept and structure of them is quite different from the actual exam feeling. What's more, how can I do better in dealing with exam ...
1
vote
2answers
31 views

An ice cream cone is 8 inches tall and

An ice cream cone is 8 inches tall with a slant height of 10 inches . The opening of the cone is a circle.What is the diameter of the opening of the cone?
0
votes
1answer
63 views

Are upper division math courses textbook- or lecture-based?

I'm a sophomore studying computer science. I have the option of finishing up my degree, or switching to math and taking my minor in CS. I'm contemplating switching for a variety of reasons - don't ...
2
votes
1answer
108 views

Structured Self-Learning Program for Calculus I & II

I'm interested in a organised program which comprehensively covers the topics of Calculus I and Calculus II. I've recently finished taking my secondary school's university-level Calculus I course, ...
-1
votes
1answer
82 views

Why lots of people don't like (and sometimes hate) mathematics? [closed]

This is a question which I really can't give an answer. Personally i really like Math and I found it interesting since I was a child, but now I really feel like I'm the only one even if I am not (just ...
1
vote
1answer
58 views

Graduate course selection for prospective probability student

I am about to begin my masters in applied mathematics, with the hopes of eventually researching probability theory and it's applications to physics. With that in mind, I was wondering which of the ...
2
votes
3answers
61 views

Why in formulas a return value of a function sometimes shown as an argument?

Sorry for a perhaps newbie question, I had a hard time in the school. Well, the title says the problem, let's look at example, which I stole from the coursera video-lectures about an algorithms: ...
0
votes
1answer
46 views

Is there a way to simplify this equation?

$$ A = \left( 4000 \left( 1+\frac{x}{y} \right) \right)^4 \cdot \left( 1 + \frac{x+0.002}{y} \right)^4 \cdot \left(1+\frac{x+0.002+0.002}{y} \right)^4 $$
1
vote
0answers
185 views

Math Competitions such as Intel Science Talent Search for High School Freshmen

I am extremely interested in mathematical competitions. I was wondering if there was something like the Intel Science Talent Search, where one can present his/her research, for freshmen in high ...
0
votes
0answers
49 views

What are real applications of factorization of integers?

Why is factorization of integers important on a first number theory course? Where is factorization used in real life? Are there examples which have a real impact? I am looking for examples which will ...
1
vote
2answers
62 views

I still forget concepts even after answering numerous math problems

Note: this is particularly aimed at high-school/entry level college problems When I'm learning a new topic: 1) I read the theory given in the textbook at the start of each topic 2) proceed to read ...
7
votes
3answers
235 views

Graduate School?

I'm completely clueless on the process, but on track to graduate in two years, so I have a few questions about what I should do. 1) What's the difference between a Master's degree in Mathematics and ...
7
votes
3answers
295 views

Is formal logic necessary for pure/“higher” mathematics?

I'm asking this as an autodidact who wants to learn math rigorously for its own sake. And I was just wondering if understanding proofs could be achieved without a formal grounding in symbolic logic. I ...
4
votes
1answer
152 views

How should one go about obtaining “mathematical maturity”?

tl;dr: Is mathematical maturity better obtained by doing hard subjects slightly out of your reach, or by doing more simple subjects to gain experience? The end of the semester is close, and I ...
0
votes
2answers
41 views

Problem with symbology

I know this may be a pretty basic question, but what is the difference between $\approx , =,\cong, \text{and}\sim $ ? I had problem while changing schools and now I am confused.
0
votes
1answer
22 views

Causality of a discrete recursive system

I am new in this site and this my first question. How can I mathematically prove that the system with a transfer function like the below one is causal? P.S: I know that for a system to be causal ...
25
votes
6answers
1k views

Should I understand a theorem's proof before using the theorem?

I find myself embarrassed when using results in books. For example, there are so many results in Sobolev spaces that I think I would not be able to understand all of them. Yes, I could try to ...
9
votes
1answer
145 views

A graph of all of mathematics

In mathematics, one often makes (proves) statements on the basis of: Previously proven statements Axioms I like to think of these dependencies as a directed graph, with edges from the accepted ...
3
votes
2answers
95 views

How many times should students repeat reviews? Frequency of repetitions? [closed]

The usual advice is that a math student has to read or study something "a couple of times" to appreciate it. But is there a narrow range of the optimal number? Any research on this? And what's the ...
1
vote
1answer
71 views

Grade School Math: Bad math, or new meanings?

I came across this online quiz discussing the new Common Core education standards, and it all seemed pretty reasonable, until I came across this question: In the number below, how many times ...
1
vote
0answers
85 views

Exam Advice or Tips, specific for Undergraduate Math or Higher [closed]

What are some noteworthy, even rare suggestions for exams in undergraduate math or higher? I'm not interested in general advice that can apply to many different subjects, like ...
1
vote
1answer
45 views

Abstract Algebra before or after [duplicate]

Do you recommend I take a course in Abstract Algebra before or after a course in Linear Algebra? I have never taken any abstract mathematics courses before. So this would be my first one.
1
vote
1answer
109 views

Advice on taking a Course in Logic.

Is a course in Mathematical Logic necessary for a well-rounded Mathematical education? I asked a question about taking a Set Theory course before and was advised to do so. However the course offered ...
0
votes
1answer
76 views

Using math to help people [duplicate]

So I am currently a graduate student at the University of Colorado. I love math. From calculus to category theory to everything in between, I have tried and, for the most part, loved it. However, I ...
0
votes
1answer
8 views

Incrementing Number Formula

I am trying to find a formula to express the nth term, the pattern is as follows: n = 4, 5, 6, 7 its corresponding values are as follows: 6, 10, 15, 21 I know this is not worded very well, if ...
1
vote
1answer
90 views

How to remember modular arithmetic and divisibility results?

I tried reviewing the same material $\ge 5$ times, once every 2 weeks or whatnot. Withal, I query intuition like this. But I forget these results quickly or don't remember them 100% perfectly. But ...
1
vote
2answers
45 views

Why are the areas non-positive?

I learnt that the integral of a function $f(\cdot)$ is the measure of an area, i.e. $\int\limits_{a}^{b}f(x)\,\mathrm{d}x$ is the area of the intersection of $x=a$, $x=b$, and $y=f(x)$. How come some ...
3
votes
2answers
232 views

What is the history of the use of the term “scalene triangle”?

A "scalene triangle" is a triangle with three unequal sides. As far as I can tell, this term is not in much use in serious mathematics — in fact, before I became a high school math teacher, I'd ...
2
votes
1answer
77 views

Getting interested in mathematics again after I finished Computer Science program.

So, I finished Computer Science study about 3 years ago (I'm 28 now) and lately I've been craving math. As a daily job I work for a start up company building a web application. I mostly done web apps ...
3
votes
1answer
163 views

Do the things that you don't know in mathematics frighten you? [closed]

I have zillions of things that I don't know in mathematics. I feel I would never know any of them completely. Especially after this age (26)... and I immediately run away since I am a perfectionist. ...
0
votes
0answers
38 views

What is $(k+1)^2[(k+1)+1]^2$ in factored form?

What is $(k+1)^2[(k+1)+1]^2$ in factored form? I'm a bit confused as to what the term "factored form" means in this context. Thank you.
1
vote
0answers
31 views

Arithmetic and Algebra exercises on latex source code.

I´m currently writing a little book for two student that I teach. The book covers school arithmetics and algebra, and it include theory and examples. Since I don´t have time to prepare a good sets of ...
2
votes
2answers
64 views

mental math: approximating fractional exponents

Does anyone have any good tricks for estimating expressions with fractional exponents (besides guess and check)? For example, I want to easily calculate $9.1^{1/3}$. Currently, the best I've got is ...
0
votes
1answer
18 views

Limits as x approaches 0

I was wondering how this worked when submitted, anything over 0 was infinite.
0
votes
1answer
35 views

Trigonometry when to divide and times

OK, so I am revising for an upcoming test and am a bit confused. I have previously learn Trigonometry, however that was around a year ago, and i have completely forgotten it now. I went on to ...
1
vote
0answers
57 views

Instructive video content for High School kids?

I need some math Youtube channels (or any other visual media, movies maybe...) that I can recommend to High School students, not solely as a method of learning math but more to illustrate the beauty ...
20
votes
4answers
2k views

Is all of mathematics based on logic?

I do not understand the discipline in mathematics that is called "mathematical logic". For me, all of mathematics is based on logic and that is what makes it the exact science. Every theorem or lemma ...
1
vote
3answers
80 views

$2 \cos^2 x − 2 \cos x− 1 = 0$ Find the solutions if $0^\circ \le x < 360^\circ$

Find the solutions of $$2 \cos^2 x − 2 \cos x− 1 = 0$$ for all $0^\circ ≤ x < 360^\circ$. For $0^\circ \le x < 360^\circ$, I'm getting $x=111.5^\circ$ and $x=248.5^\circ$. Is this ...
0
votes
2answers
125 views

Measure Theory or Set Theory?

Having taken Real Analysis I before (the seven first chapters of baby Rudin) I have the option to take Measure Theory now. However I am torn between that and Set Theory. Which course would you go for ...
32
votes
10answers
3k views

Becoming Better at Math

How can I become excellent at math? It really interests me but when I fail I become demotivated and begin to give up. EDIT: Could anyone suggest books for someone with a math education that just ...
0
votes
1answer
38 views

Other conditions than necessary and sufficient conditions, $\Rightarrow$, $\Leftrightarrow$?

I know that $$A\Rightarrow B$$ means that $A$ is a necessary condition for $B$ and $B$ is a sufficient condition for $A$. Also, $$A\Leftrightarrow B$$ means that $A$ is necessary and sufficient ...
1
vote
0answers
37 views

Tools (electronic notebook and ontology viewer) of mathematical formulas (definitions and facts)

I am reading math books and articles (for applications in other disciplines, mostly about logics for computer science and AI) and the hardest part is to memorize formulas, to look up some ...
10
votes
9answers
953 views

A Poster About Prime Numbers [closed]

We're going to design a poster about prime numbers, which will appear in a mathematics magazine for middle school students. The poster should be both visually attractive and mathematically rich. Do ...
0
votes
5answers
175 views

How to teach newbie multiply of complex number

I want to teach a newbie the arithmetic law of complex numbers. the law of add is acceptable psychological. but multiply is not. for example, assume $$z = a+bi, w = c+di$$ He (She) may ask me: why ...