Questions related to the teaching and learning of mathematics.

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0
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1answer
56 views

Calculating $\lim\limits_{x \to 0} \frac{10^x - 2^x - 5^x + 1}{x \cdot \tan x}$ [duplicate]

I am trying to solve this limit without using Taylor expansions to explain it to a secondary school student $$\lim_{x \to 0} \frac{10^x - 2^x - 5^x + 1}{x \cdot \tan x}.$$
2
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2answers
113 views

$f(x)=\sin(43x)+\cos(2x)$ is periodic function?

$f(x)=\sin(43x)+\cos(2x)$ is periodic function. I got the period of $\sin(43x)$ is $\frac{2\pi/}{43}$ and period of $\cos(2x)$ is $\pi$. Then the period of $f(x)$ is $2\pi$. Am I right? Any comment? ...
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0answers
18 views

Does Volterra’s example prompted development of a generalization of the Riemann integral?

Volterra's function is a real-valued function X defined on the real line R with the following curious combination of properties:(a)X is differentiable everywhere. (b)The derivative x ′ is bounded ...
2
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1answer
306 views

Real world applications of exponential function; continous case

I am looking for interesting applications in everyday life, technology or science of exponential functions of the type: $$ f\colon \mathbb{R} \to \mathbb{R}, \quad x \mapsto ab^x $$ for the case $a ...
0
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1answer
19 views

How to work out 3 dimensional vector angles

I've come across this question and cant for the life of me think how to work it out. I understand working out the angle between two vectors e.g. given, vector a(2i+3j-k) and vector b(8i-6j+2k) but am ...
2
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1answer
84 views

About the epsilon definition of a convergent sequence. Is this definition equivalent?

I read that it is appreciated to include the context and motivation of a question. I may have overdone this a little bit in this question. To summarize, my question is: Are the two blockquoted ...
62
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14answers
6k views

Should an undergrad accept that some things don't make sense, or study the foundation of mathematics to resolve this?

I'm a second year math student. And I've the following problem. When I prepare myself for an exam, I can distinguish two phases. First I'm mainly interested in whatever is necessary to pass the ...
0
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1answer
156 views

I want to pursue Computer Science as a major but I don't know if i should…HELP!? [closed]

I'm currently a second semester sophomore who's currently pursuing a Global Affairs major and minoring in Japanese Studies. I plan on going to law school after college and I'm interested in ...
0
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1answer
44 views

Pre requisites of linear algebra

I want to learn abstract linear algebra. Do I require the knowledge of discrete mathematics before I start? I have the impression that abstract maths and their proofs can be understood easily by the ...
5
votes
1answer
170 views

When should I start learning Set Theory?

I started to learn a few disciplines on my own over the break after my first year in college and one of them was Real Analysis. In the process I came across many issues in Analysis texts concerning ...
2
votes
1answer
69 views

Elementary “bugs” in computer algebra systems?

There's a discussion of bugs in CAS's here, but these are technical errors of interest mainly to the professional mathematician. I am more interested in simple errors which might arise in the use of ...
5
votes
1answer
213 views

Is making the math learning process deliberately more challenging an effective teaching strategy?

I've often come across a view on teaching/learning math to the effect that forcing students to struggle rather then "spoon-feeding them" (as they put it) makes for much more able students in the long ...
3
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2answers
311 views

best books for learning algebra

My name is Aniket and I have started 11th class recently. I have studied only my school textbooks(NCERT Books) and I am not happy with them. I want to learn Algebra,i.e, all the topics covered in ...
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vote
2answers
81 views

Do users of RTL languages adopt an LTR standard for mathematics (in the same way they often do when using LTR words or phrases in RTL text)?

Non-mathematician here. There is a discussion on this forum titled "Is “applying similar operations from left to right” a convention or a rule that forces us to mark one answer wrong?" I found it ...
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1answer
373 views

How to use point estimation on an interval? Statistics question

I got part a and part b just fine, but I am confused on how to do part (c), (d), and (e). I don't really understand what the question is asking, nor do I understand how to do that sort of interval ...
2
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0answers
113 views

What are some cool projects that can be done in a high school math class?

I'm studying to be a secondary math teacher and will be starting student teaching next month (an algebra 2 class). It's difficult to find activities and projects that are actually informative and time ...
0
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2answers
89 views

Find Vector and Parametric Equation

I'm having some trouble finding answers to these problems. When i try to find help online, all i find are (x,y,z) problems and I'm simply looking for a PreCalculus (x,y) problem solving technique: ...
4
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2answers
220 views

Careers in Mathematics?

I am a college freshman, and I really like to have goals for my life, one of the big ones is my career of choice. Previously, I have always wanted to be a programmer, and I have written a lot of code. ...
0
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0answers
39 views

Events for high school students which can look good on a cv.

I'm a european high school student and I'll apply to university in July. Are there any interesting activities/events which can look good on the curriculum I'll submit with the application? Further ...
2
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0answers
65 views

Learning to write the style of mathematics texts

When learning how to write articles in mathematics (in style of articles published in journals) is there a good reference listing things like common outlines, style guides, phrases, common mistakes ...
0
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1answer
29 views

This is regarding a verbal math problem

A Shopkeeper buys sweets at 11 for a rupee. He bought an equal number of sweets at 10 for a rupee. he sold all the sweets at 8 for a rupee. find loss or gain % Please solve this for me. I am not able ...
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2answers
43 views

Fundamentals of Algebra - Cancelling Like Terms in Divison

When can, or can't, terms be cancelled. ie: $\frac{3x^2-1}{x^2}$ $x^2$ cannot be cancelled. Why not, and what are the rules?
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1answer
70 views

Looking for data science-oriented “Applied Maths for dummies” summer school

I'm a PhD candidate who critically lake of maths skills for his data science projects. I'm looking for a summer school that would enable me to take off in this aspects. This could be ...
1
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2answers
117 views

Re-learning Math and becoming more comfortable

As someone finishing up their BSc in Electrical Engineering, it is becoming very clear that I need to improve my mathematically abilities significantly if I want to pursue any more education. I ...
1
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1answer
25 views

function inversion and the horizontal shift

I am currently doing inverse functions and graphing radical equations of the form $y=a\sqrt{x-h}+k$ with my algebra class and one of my students asked me the following question. "Why is it that we ...
2
votes
2answers
84 views

Why doesn't this work? — The V.I. Arnold Primary School Problem (Two women started at sunrise…)

I've got a, perhaps silly, question. I understand the various solutions to this problem: Two women started at sunrise and each walked at a constant velocity. One went from A to B and the other ...
0
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1answer
76 views

Interpretation of First Isomorphism Theorem

I understand that the first isomorphism theorem basically says that any homomorphism f from group G to group G' induces an isomorphism from G/Ker(f) to the f(G). What I don't quite understand is the ...
2
votes
3answers
453 views

How to explain to a small child that the area of a square of side a is a²?

I have a small child and I am always trying to find the best way to explain new things to her. The area of a square is a very basic concept that is related to the idea of area unity and can be used to ...
1
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2answers
21 views

Getting the Amps from Watts, Amps and the voltage of a line

What amperage capacity should the supplied wired be rated for a refrigerated fixture which has a 208V power supply and the following loads? 4 Evaporator fan motor rated at 9W each 4 Evaporator fan ...
0
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0answers
24 views

Suggestion for a work on variational calculus

Hi dear forum :D stack I must complete the Master FISYMAT in Spain my assistant professor has told me to do about calculus of variations. What suggestions on this matter can you give me ? To get the ...
7
votes
6answers
345 views

Evaluating the reception of (epsilon, delta) definitions

There is much discussion both in the education community and the mathematics community concerning the challenge of (epsilon, delta) type definitions in real analysis and the student reception of it. ...
7
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6answers
458 views

Thinking of mathematics in terms of analogs

I think the way that I've come to think about mathematics is becoming problematic and I'm wondering if I should abandon it. When I study mathematics, I find myself trying to compare the mathematical ...
0
votes
1answer
92 views

Severe problems understanding abstract algebra [closed]

I just came out of high school and one of my courses during my first semester of a maths B.sc. is Abstract Algebra. Now all my other courses seem logical and even easy, but this course...I just don't ...
7
votes
1answer
374 views

Why do professors sometime hide the book from which they are really teaching? [closed]

Well, the title is almost self explanatory. I am in a graduate school and have two professors this semester both of who are telling me that they are not following any particular book, and yet when I ...
1
vote
2answers
168 views

What exactly do math education PhDs do?

I have been researching this for the past hour or so, but I have not really found a sufficient answer. What I have found is that vaguely, math education PhDs set policies for math education. ...
2
votes
1answer
74 views

Bridge the gap to university mathematics [closed]

Can anyone suggest some good books to help an high school student to "bridge the gap" to university math? I've heard of http://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316 and ...
5
votes
4answers
822 views

Solve without a calculator: What is the possible value of 2*((1+1/100)^100)?

What is the possible value of $2·((1+\tfrac{1}{100})^{100})$? Google will give $2·((1+\tfrac{1}{100})^{100}) = 5.40962765884$. How can I find the possible value without Google or a calculator? How ...
1
vote
1answer
73 views

maths for a strong visual spatial thinker with sequential processing weakness?

Can someone with superior visual spatial thinking ability but weak sequential/word ability be successful in university maths and beyond? For example, for real analysis, would definitions with lots of ...
4
votes
3answers
379 views

Most useful books for a math undergrad

What are the most useful books an undergraduate in math should read? I found Alock's "How to study as a math major" and "how to study for a math degree" very useful. Are there any other good readings ...
0
votes
1answer
73 views

Max(x,y) and argmax(x,y)

I am writing my report and I got confused on this simple maths concept. What I need is: I have 2 values i.e x and y and I want to use the maximum of either x or y as my length. So which statement is ...
0
votes
1answer
34 views

How to define a set for a matrix

I have a big matrix and I have partitioned it. So, I want to say that I am taking the summation of entries that do not belong to the blocks in the diagonal. How can I say it mathematically. Is it ...
0
votes
1answer
283 views

Determine sin cos and tan from slope? NON CALCULator

I am used to finding this by drawing the triangle and knowing the angle measurement. With the angle measurement i can find sin cos and tan. But i dont have angle all I have is line. I have put a ...
1
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1answer
23 views

The right angled triangles ABD and BCD?

AB=5cm BD=4cm and angle ABD=x Find the exact value of cos(ABC) this is the trangle...: https://twitter.com/JxstyBiebs/status/432919494466752514
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vote
4answers
51 views

The graph of the function is $g(x)=x^3-2x^2+x+1$ and the tangent to the curve is at $x=2$?

a) Find the equation of the tangent to the curve at $x=2$ HELP and then b) Determine the angle that this tangent makes with the positive direction of the $x$-axis Please help I really need to ...
1
vote
2answers
65 views

General solution to the integral of 4/x

A friend asked me what was the solution to the problem (which was on his test)$$\int\frac4xdx$$ I proceeded to tell him that you can take out the 4 in the numerator, and then just take the integral of ...
0
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1answer
52 views

Mean and Variance Statistics

$X_1, X_2, \dots , X_n$ ~ i.i.d $U[0,1]$ a) Find the mean and variance of $lnX_1$. b) Let $0\le a \lt b$. Find the $\lim_{n \to \infty} P(a \le (X_1,X_2, \dots ,X_n)^{(n^ -0.5)}*e^{ ( n^{0.5})}\le ...
6
votes
1answer
163 views

Are mathematics competitions important?

So I'm seventeen and currently a junior in high school. I love mathematics very much, it's developed into a strong passion over the past few years, after witnessing the president of the math club at ...
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vote
1answer
179 views

How to learn problem solving (IMO and IPhO)

I'm not interested in IMO and IPhO actually, but one of the most prestigious universities in my country admits students using a test which is composed by 5 IMO and IPhO questions (or slighly lower). ...
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1answer
50 views

What is a right way to think when going about trying to solve a math problem? [closed]

What is good step-by-step method to deconstruct a math problem.
3
votes
3answers
304 views

How would you prove that the graph of a linear equation is a straight line, and vice versa, at a “high school” level? [duplicate]

This is something I've been wondering about. Namely, I've always accepted "on intuition" that the equation $$ax + by = c$$ is, when graphed, a line. You can plot the points $(x, y)$ satisfying the ...