Questions related to the teaching and learning of mathematics.

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0
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2answers
44 views

I want to study higher mathematics. Where do I start?

Since last year, I've been interested in higher mathematics and don't really know where to start and don't know what knowledge I still need to obtain, before being able to understand the concepts. ...
23
votes
0answers
199 views

What did mathematicians study as an undergraduate/graduate before modern mathematics such as modern algebra and analysis?

I am curious as to what mathematicians such as Leibnitz and Gauss and the Bernoulli's studied when they were students in university. I find it fascinating how we are taught calculus and abstract ...
-1
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2answers
75 views

Logical order to understand math? [on hold]

Imagine a 30 year old human coming from the wild, never visit a school and nether came in touch with math what so ever. And now imagine this person wants to learn math on an academic level. But where ...
0
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1answer
364 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 ...
17
votes
6answers
334 views

Big list of serious but fun “unusual” books

I would like to have some suggestions about serious (that is, with good mathematical content) but fun books that cover topics (or propose problems) in "recreational mathematics"; in any other field ...
3
votes
2answers
33 views

Theorem of the convergence of the series of fourier! [duplicate]

During the demonstration of the theorem of the convergence of the series of fourier, my teacher wrote :$$ \frac{1}{2}+ \sum_{k=1}^{n} \cos(ky)=\frac{\sin((n+\frac{1}{2})y)}{2\sin(\frac{y}{2})} $$ he ...
2
votes
1answer
244 views

The NES mathematics accredidation test

I have to take the NES mathematics test to get accredidation as a High School teacher to become highly qualified to teach mathematics. I have a PhD in physics so I thought that I wouldn't have to ...
10
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5answers
3k views

Advice for Self-Study

I am a senior in high school who has taught myself through Calculus BC and I got a 5 on the exam. However, I have taken all the math I can at my school. I have also taught myself multi-variable ...
1
vote
4answers
791 views

Solved to be 7 after arithmetic

I recently made a blunder while trying to explain a question asked to me in an interview, The question was Think of $X$ Add $X$ to itself ($X+X = y$) Times the result by $3$ ($y\times 3 = z$) ...
1
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1answer
508 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
votes
4answers
169 views

Intiutive argument that $\exp' = \exp$

Is there any intuitive argument or visual "proof" that $\exp' = \exp$? Suppose you have defined the Euler number $\mathrm{e}$ as limit of the sequence $(a_n)$ where $a_n = \left (1 + \frac{1}{n} ...
0
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3answers
31 views

How to compute Final Grade with assignment weightings?

I have just finished the Final for my Computer Hardware course, and I'm trying to figure out where my grade currently stands. The way the class is broken up is 50% weight for the homework, 25% for the ...
0
votes
1answer
20 views

Probability Intersections

$A$ and $B$ are two events from certain probability space $\Omega$. Knowing that: $P(A)=0.6$, $P(B)=0.7 $ and $P(A\cup B)-P(A\cap B) = 0.2$ Determine $P(A\cap B)$ It says in this sheet that the ...
0
votes
2answers
20 views

Equations of lines that are parallel [closed]

Please help me with the following: 4) Write an equation of a line that is parallel to $y = 4x + 10$.
0
votes
1answer
22 views

Some maths help [closed]

I am in primary school and need a little bit of assist, if you can help me, please do not hesitate to respond! :D I need to currently fill out the table of values for the following equations and plot ...
1
vote
2answers
10k views

Hexadecimal value of a negative number?

How can I find the hexadecimal value of negative number? I was studying from a slide that shows these values and there hexa's...! ...
0
votes
1answer
30 views

Choosing final year project [closed]

I'm studying pure math now yet I would like to develop a career in actuarial science. For my final year project, I can choose to either the topic of probability analysis or statistic. While I know ...
457
votes
139answers
28k 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 ...
1
vote
0answers
127 views

Distance Bachelor's degree in mathematics in Europe

This question is largely off-topic for Mathematics stack exchange, but not entirely. Much of the answer depends on personal experiences in learning mathematics. I am looking to go back to school for ...
0
votes
1answer
31 views

Find smallest number bigger than y that is multiple of x

I can't seem to find an answer for this, as all the topics regarding multiples deal with integers... I need to find the smallest number after x that is multiple of 0.36. For example if x = 3000, ...
1
vote
2answers
897 views

Maths brain teaser. Fifty minutes ago it was four times as many minutes past three o'clock

Fifty minutes ago it was four times as many minutes past three o'clock. How many minutes is it to six o'clock..? I have got the solution online but have doubts in it : ...
4
votes
0answers
48 views

From algebraic master degree to algebraic geomery Phd

I am a foreign master student in algebra at the final year. I'm familar with categorical algebra and have interesting in algebraic geomery and number theory. I have learned some knowledge about scheme ...
3
votes
4answers
87 views

Is there an example to demonstrate why $\frac{1}{(1/2)}$ equals $2$?

To explain why $\frac{1}{2}=\frac{2}{4}$ I use slices of pizza and show how eating one slice of a pizza cut in half is the same thing as eating two slices of a pizza cut in quarters. Is there a way ...
1
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1answer
424 views

Linear algebra and Multivariable calculus prerequisites for Stochastic Calculus

Which topics are considered "graduate-level" for the following subjects: Linear algebra Multivariable calculus On Internet, it is said that you need "graduate level" Linear algebra and ...
1
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2answers
22 views

What does conjugation in the time-domain of a signal mean?

I've never been explicitly told what the conjugation of a signal in the time-domain means. I'm mainly asking because in my signals class, my professor stated that for a signal x(t) to be real: x(t) = ...
2
votes
3answers
50 views

Math learning after Differential Equations?

I made it up to DE(Pre-Calc, Calc I and Calc II with basic stats before that same school) in community college through a special program(I'm poor). I'll have to self-teach from now on but am still ...
1
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0answers
29 views

Distance Mathematics Education

I want to study mathematics however being employed I could not join a full time course nor I am eligible to study mathematics in India as I study accounting and commerce. So I am looking for an ...
5
votes
1answer
102 views

Is an undergraduate in engineering sufficient preparation for a masters in mathematics?

I'm a high school student who is considering doing an undergraduate in engineering. However my the long term plan is to pursue math at a higher level. I want to do engineering at undergrad because I ...
0
votes
0answers
35 views

Is the field of Algebraic Topology still an active field of research?

I have been studying some Algebraic Topology in my free time, and I began to wonder whether it was still an active field of research? If not, what are some of the most active research fields nowadays. ...
19
votes
7answers
2k views

Very *mathematical* general physics book

I am searching for a book to study physics. So far, I've been suggested Resnick, Halliday, Krane, Physics, but it doesn't seem to be very suited for a math major. Can you suggest some more ...
1
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3answers
34 views

A silly question about potential functions

Why have physicists had the idea to define a potential function of a gradient vector field $\vec F$ to be a function $g$ such that $\vec F=-\nabla g$? What changes if we don't put the negative sign? I ...
4
votes
0answers
45 views

How can I retain the mathematics that I've supposedly learnt?

So my question simply is "What is the best method to make sure you retain what you have learnt?" Okay so I've tried learning mathematics up to where I should be at in the past. Every time though I ...
3
votes
1answer
57 views

Definition of a function and the notation $f:A\to B$.

In some textbooks on analysis, I have encountered a definition of function/mapping that distinguishes the terminology mapping on $A$ to $B$ and mapping from $A$ to $B$; the first one refers to a ...
1
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1answer
45 views

Matrices of the form $A^p=(a_{ij}^p)$

I am wondering if there is a name for these kind of matrices and if they are interesting or not? Do they even exist? Let $A$ be a $n\times n$ matrix with elements $a_{ij}$. $A= (a_{ij})_{i,j\in\{1, ...
16
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3answers
257 views

Is$\frac{\sqrt{a}}{\sqrt{b}}$ the same as $\sqrt{\frac{a}{b}}$?

My idea is that the two functions are not the same since for the first function, the domain of the function is only non negative reals for the numerator and positive reals for the denominator. ...
4
votes
1answer
26 views

continues function statement in real analysis [closed]

I ran into a challenge, i read following sentence in one note. anyone could describe or prove it for me? F is a continues function at point $ x_0 \Leftrightarrow (x_n \to x_0 \Rightarrow ...
0
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2answers
40 views

Is this correct - confused in this riddle - where does the one rupee come from…? [closed]

I have 50 rupees, and spending like this and where does that ONE rupee come from.... am right or wrong ??????
0
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0answers
22 views

Is this correct? A snail climbs up a 20 metre wall. [duplicate]

A snail climbs up a 20 metre wall. Every hour it climbs up 5 metres then slides back 3 metres. How long does it take the snail to climb up the wall. My solution: By 16 m, the snail would have taken 8 ...
1
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2answers
60 views

Path to 3d Mathematics programming, where to start?

This might read like duplicate of this question https://math.stackexchange.com/search?q=where+to+start However since that one wasn't answered, and I have a more specific problem in regards to ...
0
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0answers
21 views

Times around an oval track

I have an oval track. In that track their are runners, points of call, and fractional time triggers. The points of call specify what position a runner is behind the leader, and the fractional times ...
8
votes
5answers
2k 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
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0answers
44 views

Master in financial mathematics or actuarial science?

I study mathematics and want to study a master degree in Europe that allows me to develop in a different teaching (at least for now) workforce. I am interested in financial mathematics but I've also ...
0
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1answer
21 views

The normal plane to a path

PROBLEM: Let $\vec x(t)$ be a path with $\vec x'$x $\vec x'' \ne 0$ and suppose that there is a point $\vec x_0$ that lies on every normal plane to $\vec x$. Show that the image of $\vec x$ lies on a ...
16
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2answers
720 views

A problem V.I. Arnold solved as a primary school student

According to a 1995 interview that Vladimir I. Arnold gave to the Notices of the AMS, his primary school teacher I.V. Morozkin gave in 1949 (when Arnold was 12 years old) to a Soviet classroom, most ...
4
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2answers
84 views

What intuition stands behind implicit differentiation

I'm trying to undestand implicit differentation Let's take as a an example equation y^2 + x^2 = 1 1. How i think about how the equation works I think the function as : if x changes then the y term ...
9
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2answers
177 views

Good Reference for Justifying (less well-known fields of) Math?

How do we as mathematicians justify the study of math to students? Or, indeed, how do we justify it to the general public? How do you justify your particular field? I'm particularly interested in ...
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5answers
2k views

Explain why perpendicular lines have negative reciprocal slopes

I am not sure how to explain this. I just know they have negative reciprocals because one one line will have a positive slope while the other negative.
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0answers
24 views

Which functions could be discussed in a calculus course?

In a typical calculus course, students are exposed to many functions. Some have their origin in a field of study, while others are simply combinations of polynomials, trig functions, exponentials, and ...
431
votes
45answers
292k views

Visually stunning math concepts which are easy to explain

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain, but are ...
47
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23answers
17k views

What is a good complex analysis textbook?

I'm out of college, and trying to learn complex analysis on my own. I took out Ahlfors' text from the library, but I'm finding it difficult. Any textbook recommendations? I'm probably at an ...