Questions related to the teaching and learning of mathematics.

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1answer
74 views

How long will it take me to learn calculus? [on hold]

First and foremost I want to point out that I am 14 years old currently and love mathematics. Summer is coming and that means I'll have 2 months to try to learn calculus to as far as I can get ...
2
votes
4answers
103 views

I call them squares. They called them arrays. What do they mean?

So I was in C++, and we had third graders come today to play our programs. Whilst the others just drilled them with problems, my game was subtract a square. It was fun watching them discover that ...
3
votes
5answers
70 views

Difference between Pure and Applied Mathematics?

So, I have been looking into college courses to see what I want my major to be, and I noticed that M.I.T offers two specified types of Mathematics. Pure and Applied. What is the major differences in ...
0
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1answer
46 views

Learning math by analyzing/proving theorems?

Hello I want to learn mathematics. In order to do this I want to get familiar with formulas/theorems by taking one and just analyze it and try to manipulate it to understand it better. I wanted to ...
1
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1answer
65 views

Is it useful to learn math by proving a formula/theorem?

Hello I want to learn mathematics. In order to do this I want to get familiar with formulas/theorems by taking one and just analyze it and try to manipulate it to understand it better. I wanted to ...
-2
votes
0answers
27 views

What is the maximal number of residents of the city [on hold]

The population of the city Roachrach consists of cockroaches and cucarachas. The number of residents of the city is no greater than 2,000,000. Each cockroach is acquainted with 1,000 cucarachas, and ...
3
votes
1answer
32 views

I need some help understanding proofs for an upside-down cycloid being the tautochrone curve. Could someone show me or point me to a simple proof?

The tautochrone curve has fascinated me since I first heard about it and I want to share it with my Calculus class as an end of the year project. I think something similar to this (Demonstrating that ...
-4
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0answers
34 views

Geometry and Algebra, Algebraic Geometry Question [on hold]

Can we compare geometry and algebra? Which is harder? Which should I take? Are we comparing geometry and algebra already? If so, what do I need to know?
0
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0answers
80 views

Applications of math [on hold]

I am a soon-to-be math teacher (high school level). I know my request is broad and vague, but I still feel the need to ask you all. I want to be able to answer my students´ somewhat feared question, ...
0
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0answers
11 views

Two questions on the UK's Taught Course Networks [closed]

In the UK, the EPSRC is funding 6 Taught Course Networks which allows graduate students from different universities to follow a same math-related course: Taught Course Center (a few including ...
0
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1answer
62 views

Severe problems with math undestanding

Recently (although still in high school) I've been at university, more precisely at information science engineering as apprenticeship. I want to become an operating system programmer but I severely ...
0
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2answers
56 views

books about relation between Mathematics and reality and life? [closed]

Which books I should read to understand better Mathematics? Intuition books to understand better Maths. The books show clearly the relation between Mathematics and reality and life.
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0answers
22 views

Maths Economics Question

The demand for rail travel is $Q^d = 600 - 2P$ where quantity is thousands of train journeys per quarter and $P$ is in £ per journey. How much would the consumer surplus change if rising cost of ...
0
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1answer
17 views

Explanation of $\textrm{argmax}_j{z_jt}$ and how to implement it

I'm struggling with one equation within a subtour elimination constraint. $$\sum_{i \in S} \sum_{j \in S, j<i} y^t_{ij} \le \sum_{i \in S} z_{it} -z_{kt} \quad S \subseteq M \quad t \in T \quad ...
1
vote
1answer
83 views

Difference between maths in physics degree and maths in a maths degree

I asked this question on the Physics site, but it got closed, so I'll try here. Basically, I was wondering what are the main differences between the maths you learn in a mathematics degree and the ...
0
votes
1answer
34 views

On the definition of sphere in analytic geometry…

Last year, when I was teaching mathematics (analytic geometry) for one of my clever freands, I arrived to the definition of sphere. I said Fix $r>0$, An sphere is the set of all triples ...
0
votes
2answers
47 views

Condition for Rectangle and Square to have the same area

Prove that if a rectangle and a square has the same area if and only if the length of the square is the geometric mean of the side length of the rectangle. I'm not sure how to start this problem. ...
1
vote
0answers
42 views

Prerequisites to Learning Real Analysis

I am a freshman, rising sophomore that is interested in learning Real Analysis, since it is required for many higher mathematics subjects. I have currently Calculus I, II, and Linear Algebra. Is ...
4
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0answers
48 views

Physical analogies of a math concepts [closed]

In a post Terence Tao explained a very nice way to think about convolution and noted that "one should try to use physical intuition to model mathematical concepts whenever one can". I found this very ...
0
votes
1answer
12 views

Finding amount of Days it will take for a Dam to empty

So say I have a dam, with a max capacity of 3,538,000 acres FT of water. It's currently storing 1,796,250 acre FT of water. Water is flowing IN at a rate of 1,050 cubic-FT per second, and out flowing ...
1
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3answers
50 views

What happens with a sign?

I have something simple to ask, but it often confuses me. What happens with number-sign when it crosses over the equal sign or less-than and greater-than sign. I have an example. $$1-3x\geq0$$ ...
3
votes
2answers
23 views

Basic simultaneous equation with logarithms

Question Solve giving your answers as exact fractions, the simultaneous equations : $$8^y = 4^{2x + 3} \tag{1}$$ $$\log_2 y = \log_2x + 4 \tag{2}$$ I think that the RHS of eq 1 can be split up, ...
4
votes
0answers
90 views

Mathematical Thinking - How does it work? [closed]

Not only am I hoping you can answer my question, but perhaps refine my question itself. Unfortunately it is something I do not know how to ask, but I will give it my best attempt. Either I ask it, or ...
1
vote
1answer
78 views

Is it ill-advised to read books casually for entertainment? [closed]

I'm a student who has about a year (and a few months) to go before entering a university and I've been reading some math books recently. I'm on Chapter 6 on Rudin's PMA, Chapter 5 in Munkres' Analysis ...
0
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0answers
45 views

Real or Complex Analysis next quarter?

I apologize if this is the wrong place for to ask a question about a math course I should take, but I didn't see a better stack-exchange forum for this. Long story short, I am a fourth-year chem PhD ...
0
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0answers
21 views

Scale Factor meaning

I need to do this fast because tomorrow I got math exam and suddenly my friend said that scale factor is tested (Basic ones)None of my friend understands...But my question is 1.If I were to get a ...
3
votes
0answers
35 views

Criterion for Improvement

I was recently asked the question "How do you know when you've become a better mathematician/better at mathematics?," and I realized that at that moment I did not have a valid answer, since I have ...
5
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0answers
70 views

Is it worth proving every theorem you learn?

Ever since I determined mathematics - mainly set theory and number theory - was my main passion, and I began learning mathematics formally outside of the curriculum posed within secondary schools I ...
0
votes
1answer
30 views

Differential equation concerning echolocation

I am in the process of trying to solve a differential equation using MATLAB. Given information is the following: $$ c(z) = 4800 - 20.2090 + \frac{17.3368z}{1000}+272.9057e^\frac{-0.7528z}{1000} $$ ...
0
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0answers
35 views

Differentiate between Fourier analysis and Fourier decomposition

I am a beginner. I am confused between two terms i.e. Fourier analysis and Fourier decomposition.I don't understand when to use Fourier analysis term and when to use Fourier decomposition term. It ...
6
votes
4answers
408 views

The meaning of various equality symbols

I'm interested in knowing what is the meaning of the various equality symbols: $=,\sim, \cong,\approx,\equiv$. For example, the speed of a car $V$ in m/s: what would be the meaning of each of these ...
3
votes
1answer
72 views

What are the primary disadvantages of Dummit and Foote's abstract algebra text (3rd ed.)?

I have done a fair amount of research concerning which abstract algebra book to "settle down into"; that is, I wanted to pick an algebra text and really commit to it as my "primary text," more or ...
2
votes
2answers
58 views

Explaining intersections to a 6th grader

$A=\{1,2,3,4,5\}$ $B=\emptyset$ How to explain to a learner from 6th grade the result for $A \cap B$ ? For a 6th grade student, it could be difficult to understand why the result is $\emptyset$. ...
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2answers
29 views

Help Finding the Equation of a Line with a Given a Point and a Slope

I have been receiving a lot of help today and I really appreciate it, I am nearing the end of my class and need help studying for my final. In my review I came across a problem that i am having ...
1
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3answers
42 views

Simplify the Complex Fraction

I am having trouble with the following complex fraction. I have simplified everything for the most part, but I am stuck on the last part and need to know what I have to do next. ...
12
votes
1answer
187 views

How to fill my mathematical gaps?

To do the story short, I became interested in mathematics in a serious way like two years ago, I'm currently in graduate school, but the problem is that my mathematical background is not as good as ...
11
votes
1answer
248 views

A question on the remainders of integer division

This is a question on the remainders of integer division from my student. Notations. Let $p$ be a positive odd prime integer. We write $r_{i,j}$ for the remainder of $i \times j \div p$. Now for an ...
5
votes
1answer
59 views

How to get the most out of attending a conference talk or a research presentation?

I'll say up front that I imagine there's a resource for this somewhere, but I was unable to find it. I've been attending conference talks and research presentations for about a year at my university, ...
5
votes
1answer
60 views

Best program for creating educational math animations?

I'm looking for recommendations on what program to use for creating mathematical animations. These animations will be used in creating educational videos for high school math -- Trigonometry first, ...
0
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2answers
28 views

Get an alternate form of an equation

I am trying to prove the following limit value: $$\lim_{n\to \infty} \frac{n^3 + 1}{n^2 +1} = \infty$$ But how does $$\frac{n^3 + 1}{n^2 +1}$$ become this $n + \frac{1 - n}{n^2 +1}$?
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0answers
37 views

How many counts the square number?

For example I have a number is $55$. Can I check this for how many counts number's square create this number. For example I have $55$ So, I know this number total from 5 number, which are $$55 = ...
0
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1answer
20 views

Why is it important to recognize CRT establishes an isomorphism between $Z/p\#Z$ and $Z/qZ$

As I understand it, it is well known that CRT can be used to show that $Z/p\#Z$ as a ring is isomorphic to the product of the finite fields $Z/qZ$ where $q$ ranges over the primes up to $p$. For ...
1
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1answer
56 views

Is self study of proof-based mathematics difficult?

I heard from a renowned Mathematician that self study of proof based Mathematics is extremely difficult as there is not only right and wrong but also degree's of correctness. So without a teacher ...
3
votes
2answers
80 views

Why do we need to rationalize fractions? [duplicate]

Teachers often take off points from students who write 1/sqrt(2) instead of sqrt(2)/2. Why do we need to write it as sqrt(2) / 2 ? Where did that convention come from? Do we need to even do it? Why do ...
0
votes
1answer
51 views

High School Geometry problem with a triangle and trapezoid in a larger triangle.

In school, I have an assignment to write a problem for geometry students. I have written the following problem. Draw triangle ABC. Let the height have magnitude h. Draw a line segment, DE, which is ...
2
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0answers
102 views

Are “Transition Books” (Spivak/Apostol/Courant) really necessary?

Why do so many people recommend Spivak, Apostol, and Courant calculus textbooks, especially as a preparation toward the advanced courses like analysis and abstract algebra? Are they really necessary? ...
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3answers
66 views

I can't understand how to factor a quadratic

I can't figure out why some actions are possible in factoring $\frac{r–3}{r^2+11r–42}$. Factor the quadratic out of the denominator $\frac{r-3}{(r-3)(r+14)}$. This does not make sense how can $+11$ be ...
0
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1answer
33 views

Textbook error or my own error, Law of sines question.

A triangle with side 8 inches and corresponding angle 13 degrees, side x inches and corresponding angle 120 degrees. To answer this I set up a proportion: $sin(13)/8=sin(120)/x$ ...
6
votes
3answers
174 views

What are the differences in mental skills required to master abstract algebra and analysis?? [closed]

I had took undergraduate-level abstract algebra and analysis courses before. And I find I can do proofs in analysis faster than in abstract algebra. However some other students is opposite to me. I ...
0
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2answers
35 views

Are the geometric sequences a subspace of all infinite sequences of real numbers

I'm a little confused about how to prove that the given infinite sequence is a subset of "the space of all infinite sequences." so V = subspace of all infinite sequence of real numbers so $$(x_0, ...