Questions related to the teaching and learning of mathematics.

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5
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1answer
248 views

Most efficient way to learn mathematics

So there's a lot of advice on how to learn mathematics most efficiently, and it mostly revolves around doing problems, asking questions, and considering all possible generalizations. However, I was ...
2
votes
1answer
91 views

An applied problem in ODE leading to Interval of Existence issue

ODE books have a section on interval of existence of a solution with a standard set of problems, such as what is the interval of existence for $y'+(\tan t) y = t/(t-2), y(3)=5$, or $y'=y^3, y(0)=2$. I ...
7
votes
1answer
447 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, ...
-3
votes
0answers
25 views

How to generate pdf using Texstudio [on hold]

If I save the file as a pdf and I try to open it I get the error that either this filetype isn't supported or damaged. How can I get it to work? Thanks in advance.
1
vote
2answers
43 views

Components of a vector

If I have the angle between two vectors, and I have the components $(x,y,z)$ of the first vector $( xi + yj + zk)$, how can I know the components $(x',y',z')$ of the second vector ?
1
vote
0answers
44 views

A complete math programme [on hold]

I want to correct my biggest mistake in life, which is a complete lack of interest in math when I was a kid. Now, after learning a lot of new things, knowing science and working as a programmer I ...
1
vote
3answers
109 views

Improving Mathmatical Skill [on hold]

I am a student of computer science and engineering. My understanding of mathematics is not very good. I am getting very hard time studying subject that require a background on mathematics. So, I ...
5
votes
1answer
727 views

Soft question : First year student and confused

I hope I won't tire the fellow mathematicians with this question but I am very, very confused... I am a first year undergraduate student of Mathematics. I can't say I am a prodigy, maybe having an ...
2
votes
2answers
47 views

What do we mean by 'defining a function'?

First I will start by quote from Wikipedia about function's defining methods : There are many other ways of defining functions. Examples include piecewise definitions, induction or recursion, ...
60
votes
34answers
6k views

Easy math proofs or visual examples to make high school students enthusiastic about math [closed]

I'm a teacher in mathematics at a high school. Math has fascinated me for almost my entire life, so I would like to bring that enthusiasm to my students with beautiful yet easy to understand proofs or ...
2
votes
2answers
59 views

what is the definition of numbers? [duplicate]

Well the question may seem obvious but I can't really find a proper answer to this. Mathematics all seem kind of difficult to understand so please help. I believe it is a quantity. Thanks in advance.i ...
3
votes
1answer
97 views

Students and Real Analysis

I am currently working on a project investigating why students tend to struggle when they first encounter Real Analysis and what can be done to improve the situation. I would be very grateful if any ...
-4
votes
0answers
33 views

find a method for twin primes and with Golbach conjecture [closed]

There are infinitely many twin primes. Two primes (p, q) are called twin primes if their difference is 2. Let be the number of primes p such that p<= x and p + 2 is also a prime. a sample ...
0
votes
1answer
37 views

How should I start learning Actuarial Science? [closed]

I recently completed my under-graduate studies in pure mathematics, and have been accepted for Masters at one of the top 10 math schools. I have great interest in research and would like to continue ...
1
vote
1answer
19 views

Log, find the following values in term of m and n

I have a hard time on this log question, can you explain it? Given log(x)p = m and log(x)q = n find the following values in ...
0
votes
1answer
21 views

Hessian null - Point of saddle

Given the function $f: \mathbb{R}^3 \to \mathbb{R}$ defined by $f(x,\,y,\,z) := 3 x y^2 + 6 y^2 + x^2 z + 3 z^2 $ is not difficult to show that $f$ presents a unique critical point of coordinates ...
-3
votes
1answer
15 views

what is Semitopological groups in details [closed]

what is B type semi topological group and C type semi topological .please get me know more about this.
0
votes
0answers
30 views

What are some practical math courses in college? [closed]

I am currently a 2nd year college student majoring in finance and is hoping to study for a math minor out of my own interest. I would like to take some courses that have relatively high practical use ...
1
vote
2answers
34 views

simple SAT question. confused.

My friend selected option B, I did C. We're confused. Can someone please explain this for my friend?
4
votes
2answers
89 views

Is theoretical Linear Algebra still an active field of research?

Numerical Linear Algebra seems to be a very active area right now, but is there any work still being done on the purely theoretical side? To put it another way...is it possible for someone to write a ...
2
votes
2answers
113 views

Pre Algebra Text book or online

I have a kid who just started middle school. I would like to introduce them to pre algebra. I would like her to know the fundamental concepts. Just like "What is mathematics" book, if there is a book ...
105
votes
17answers
5k views

How do you respond to “I was always bad at math”? [closed]

Here in the U.S., it is my experience that over 75% of adults I meet socially will volunteer that phrase or a variation upon learning that I am a mathematician. I find this frustrating, since almost ...
18
votes
1answer
3k views

Strange old multiplication table

Today I read an article about chalk boards from 1917 discovered in an Oklahoma school. One of the chalkboards included the following curious image: (Oklahoma City Public Schools) The article ...
6
votes
0answers
428 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 ...
3
votes
0answers
32 views

Where to study type theory?

I want to learn more about (homotopy) type theory, constructive mathematics and univalent foundations. To my knowledge, there are only few faculties with large type theory groups. In Europe, most of ...
0
votes
0answers
35 views

The $\epsilon$-$\delta$ definition of a limit of a linear vs a non linear function

I am teaching elementary analysis and introducing the concept of $\epsilon$-$\delta$ definition of the limit to first time learners. For example, we take $\displaystyle\lim_{x \to 2} (2x - 1) = 3$, ...
0
votes
1answer
55 views

General Inquiry on Mathematics syllabus [closed]

This isn't a technical math question but I would like to consult you masters as to what to study in math? I'm very interested and my knowledge level is at around Calculus II. I wanted to know more ...
0
votes
3answers
76 views

Sketching a nice graph of $f(x) = x^2 + 2x – 8$ [closed]

I would like to sketch a nice graph of $$f(x) = x^2 + 2x – 8$$ including labeling the coordinates of the vertex and intercepts. I tried to graph it using this tool: But I don't know how to label ...
4
votes
3answers
340 views

How can I explain my 9 years old brother that $8a\cdot4a \neq 64a$

My youngest brother had a pre-algebra test yesterday and he was asked to tell if two expressions are equal or not. We agreed on most of the things but on this one I find it hard to make him accept my ...
5
votes
0answers
71 views

Algorithm for finding “fact families”

My friend's 3rd grader encountered the following question regarding "fact families" on her math homework: I was in 3rd grade sometime in the 1980s, so I don't believe I ever encountered this term ...
0
votes
0answers
107 views

What to teach in Set Theory & Logic Course. [migrated]

I will be teaching a third-year introductory course on Set Theory and Logic soon and was hoping to get advice from this community. I would rate my students' proof abilities as weak and was hoping to ...
-2
votes
1answer
72 views

How values of the constants are derived mathematically? [closed]

As said by Jan regarding constant value $\pi$ ,Imagine you have a circle and you are able to measure its circumference "c". Then, you can also find out what its diameter "d" is. When you divide ...
1
vote
1answer
26 views

How big a text file will be for a wordlist composed of 10 HEX characters given certain conditions?

While discussing with another friend the insecurity with some wifi systems against dictionary attacks we couldn't reach a common ground on how big a WPA wordlist dictionary would be for the most ...
0
votes
0answers
31 views

Proving a quadrilateral is an isosceles trapezoid

Warning: You'll probably need pencil and paper to follow this. Recently I came across the following problem in a middle/high school geometry textbook: $\ast$ Suppose $\ QUAD\ $ is a quadrilateral ...
1
vote
0answers
44 views

Why is differential equations typically taught with an applied focus? [closed]

Out of all the maths I've learned, the terminology and examples given in differential equations lectures always grinds my gears. It feels like a rebellion against pure math, haha.
4
votes
1answer
37 views

What book offers strategies and heuristics for theorem proving in the same spirit as Polya's How to Solve It?

Polya's How to Solve It is all about heuristics and strategies for problem solving, but it's mainly written for problems which require students to find values, not to prove theorems. While Polya's ...
-1
votes
1answer
2k views

How to build a mathematical formula

We can see mathematical formulas, graphs in thesis paper. Together those are used to prove some theorem. Graphs are generated based on some test using those formula. My question is how those formulas ...
15
votes
2answers
405 views

High school algebra textbooks for gifted students

Cross-posted to Math Educators Stack Exchange. (link) I am looking for high school algebra/mathematics textbooks targeted at talented students, as preparation for fully rigorous calculus à la Spivak. ...
1
vote
1answer
58 views

What are some good mathematical journals? [closed]

I would like to study mathematics when I'm older, but I want to read some of the current literature to learn what mathematics is truly about, maybe direct my studies into some particular field. What ...
0
votes
0answers
103 views

Where can I get detailed and comprehensive notes of a functional analysis course taught using the book by Erwin Kreyszig?

Where on the Internet can I find detailed and comprehensive lecture notes of an elementary functional analysis course taught using the book Introductory Functional Analysis with Applications by Erwin ...
2
votes
3answers
135 views

How do mathematicians invented and introduced $\pi$ term in the case of circle?

This is basic question. Since childhood I am mugging the mathematical formulae areas of square, rectangle and circle etc. Now,it is possible for me to understand formula of area of square I.e. ...
0
votes
0answers
28 views

Why we should study “sub-energy” function and what are its applications in mathematics?

I read some papers in optimization and I found this term "Sub-energy function" that is a new mathematical term to me. Aside from "its a large area in mathematics," why we should study it? What's its ...
5
votes
2answers
82 views

What's interesting in latus rectum?

I'm a maths teacher in Italian secondary school and I've been spending some time trying to construct "meaningful" problems about conic sections. I particularly like problems which focus on practical ...
1
vote
1answer
29 views

Calculate the fourth proportional of the given numbers (Grade 7)

My son has this: Calculate the fourth proportional of the given numbers: 1/9, 1/6, 1/3 Similarly, another question: Calculate the fourth proportional of the given numbers: 9.1; 6.5; 2.8 It should ...
6
votes
2answers
610 views

I need to integrate, but I don't know where to start. I'm a bit (a lot) rusty.

Please help me solve the following integral. I'm not sure where to start in fact, I haven't done math for 7 years and now I have to jump back in the integrals. I'm not sure if I have to integrate by ...
538
votes
152answers
34k views

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's ...
0
votes
0answers
35 views

What are the desired questions that should to be in SM (stackexchangemath)? [migrated]

According to many questions posted in SM ,I see that SM give a high importance for the related questions to Real analysis and number theory and contests where "MO" give a high importance to ...
17
votes
1answer
601 views

Which universities teach true infinitesimal calculus?

My colleague and I are currently teaching "true infinitesimal calculus" (TIC), in the sense of calculus with infinitesimals, to a class of about 120 freshmen at our university, based on the book by ...
0
votes
1answer
630 views

Line Drawing Using Bresenham Algorithm

Indicate which raster locations would be chosen by Bersenham’s algorithm when scan converting a line from screen co-ordinates (1,1) to (8,5). First the straight values (initial values) must be found ...
8
votes
0answers
71 views

How to explain the topic of Fourier transform interactively? [closed]

This is a soft question . In the walk-in for the lectureship, I have decided to give demo lecture on the topic of Fourier transform. The principal of the institution ask me to take lecture ...