Questions related to the teaching and learning of mathematics.

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0
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1answer
89 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
373 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
167 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
71 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
792 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
72 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
361 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
70 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
33 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
0answers
30 views

Need help with expected value and variance of Chebyshev's Inequality [duplicate]

Let X1,X2,...,Xn and Y1,Y2,...,Ym be independent exponential distributed random samples with mean θ. Let T_α=αx¯+(1−α)y¯, where 0<α<1. a) Find E[T_α] and var(T_α) b) Show that, for any ϵ>0, ...
0
votes
1answer
262 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
vote
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
1
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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
votes
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 ...
0
votes
0answers
18 views

Jacobian, Independence, and expectation [duplicate]

Let $Y_1,Y_2,\dots Y_n \tilde{} exp(θ)$ be i.i.d. random samples. If $Y_i$'s are sorted in ascending order, the ordered random variables $X_1,X_2,\dots,X_n$ with the join pdf: $$ ...
5
votes
1answer
159 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 ...
1
vote
1answer
154 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). ...
-4
votes
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
270 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 ...
5
votes
1answer
88 views

Software for basic math notes at 5th to 10th grade level (10 to 15 years old)

So I've looked around, here and otherwise, but sadly can't seem to find quite what I'm looking for. I don't know if it even exists, I figured it was worth trying to ask, though. I've found plenty of ...
1
vote
1answer
170 views

Applications of infinity in real life [duplicate]

I am writing a mathematical essay and would like to focus on the concept of infinity. I am not sure of any real life applications of infinity to write about or some way to narrow down the topics. Does ...
1
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3answers
214 views

How would you explain confidence intervals to a beginner with very weak algebra skills

Let us say that you are taking AP Statistics. The prerequisite is a passing grade of D or above in Algebra II. The kids that you are working with struggle with algebra and do not retain information ...
0
votes
2answers
99 views

How to deduce this puzzle

Every station on the railway system sells tickets to every other station. Some new stations were added. 46 sets of additional sets of tickets were required. How many new stations have been added? How ...
3
votes
1answer
106 views

To take notes or not to [closed]

Is it really better to take notes as a maths major or are some better without them? I've never gotten used to taking notes and I've never done it. But I'm wondering if I'd improve if I'd start doing ...
0
votes
1answer
73 views

How to calculate the points of the triangles making up an Octahedron?

Ok guys, I'm not a great mathematician but will try to work this as accurately as I can. I hope someone can help me. I am drawing some 3D objects and I am having trouble drawing an Octahedron. I ...
0
votes
1answer
93 views

How to get a top-notch Math education (high school level) online?

For the past years, it is becoming more and more accessible to get college level content from many different sources, and, if one is willing can get very far with his math education (not only by ...
1
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0answers
44 views

What is the less confusing way to explain confidence intervals to a beginner

Let us say that you are back in high school and you have a friend who has missed class for a week. He needs information to be spoonfed to him, because its not his style to overthink. If you push for ...
2
votes
1answer
95 views

How to solve this Mystery with Mathematics

I read a mystery in a book but I can't solve it with Mathematics. The mystery is: "I have tripled my nephew's age, and 5 years ago I have 5 times from his twin brother age. What is my age now?" In ...
0
votes
3answers
82 views

Baloney detection kit for Math

There are folks who claim they proved Fermat's Last Theorem, Riemman Hypothesis offering no more than a half a dozen pages (sometimes one or two pages) of proof, very few if any citations of previous ...
1
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2answers
146 views

Math Riddles #10 - Car Meter Riddle

Today my car meter reads as 72927 kms. I notes that this is a palindrome. How many minimum kms I need to travel so my car meter find another palindrome?
1
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1answer
68 views

Which math software?

As a math student interested in mathematical modelling, which math software should I start with (mathematica, matlabe, octave, or what else?)?
3
votes
1answer
54 views

Figuring out deficiencies in math education.

I'm mostly self-taught and while I know (and use) many advanced mathematical topics, I often enough find holes in my understanding of lower level math. Is there an exam (or series of exams) I could ...
1
vote
1answer
99 views

What is the contribution of group theory to topology?

An answer for a question on MathOverflow.net which asked for some recommendations on textbooks for books in topology received the following comment: "It's a great book to introduce applied ...
1
vote
1answer
46 views

What are some helpful pre-requisites/hints/encouragement for going through Theodore Frankel's “Geometry of Physics” in a self-study?

I plan on working through "Geometry of Physics" by Frankel. I keep on running into little snags here and there, and I am wondering if that's just part of the process, or whether I am ill-prepared. ...
1
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0answers
57 views

Why are hyperbolic trigonometric functions avoided in (my) high school and early post-secondary school?

I remember seeing hyperbolic trigonometric functions (sinh, cosh, tanh, etc.) in my precalculus textbook back in high school and see them today in my calculus textbook. However, I have not had a ...
10
votes
2answers
166 views

How to introduce category theory to a high school audience?

I am a mathematician with background in Category Theory. I have been asked to give a 20 minute talk about my area of research to an audience of talented high school students and school mathematicians ...
-1
votes
1answer
25 views

Get sides of triangle with only angle as given?

Can someone tell me how to get the sides of triangle(opposite,adjacent and hypotenuse) if i only have an angle as given? I got the angle by getting using atan2(y-y,x-x); Now i want to get the sides ...
6
votes
1answer
276 views

What pure mathematics foundations should an applied mathematician have?

I'm studying mathematics, with some statistics also, and I've always chosen applied courses. I'm getting to the point where I'm studying 3rd year undergraduate to graduate level material. My first ...
5
votes
4answers
471 views

Why study quadrilaterals?

My niece is in the 10th grade, and they have to do lot of theorems related to quadrilaterals. And, I was surprised to know that they have to learn by rote some theorems. This has made her feel that ...
8
votes
1answer
209 views

Darboux's Integral vs. the “High School” Integral

The definition of the integral below is what I usually call the "High School definition," because that's usually where I've seen it in use. Take a partition $\Delta = \{ x_0, x_1, x_2, \ldots, ...
0
votes
1answer
84 views

Should i continue trying or am i just not good enough [closed]

You've probably seen many of these, and i'm sorry to create another one but i'm at loss. I want to be a programmer at some point in my life (just finishing highschool) I want to go to university ...
16
votes
1answer
212 views

How often should math students take day breaks and longer breaks or vacations? Any research?

John Edensor Littlewood wrote in page 197 of Littlewood's Miscellany "For a week without teaching duties - and here I think I am preaching to the converted - I believe in on afternoon and the ...
6
votes
4answers
545 views

Teaching irrational numbers?

I'm interested in teaching the irrational numbers to high-school students, and I need your ideas on how to do in an 'optimal' and innovative way. And my question is: What should the teacher know ...
2
votes
0answers
84 views

Exercises or courses to improve logical rigor and reasoning skills

There is plenty of math that is beautiful without needing much explanation of theory, such as fractals, geometric patterns and the Game of Life, that may interest beginners in mathematics. However, if ...
0
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0answers
24 views

What does typed and character mean?

Sometimes while I'm on the website I see stuff like simply typed lambda calculus, or "characters". What does this mean and where can I learn about that stuff? Thanks in advance
-1
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2answers
125 views

Is Math like a Language? [closed]

This is a sincere question, Is math like a language where after a certain period in one's life, he or she can't get good at it? I feel once someone reaches a particular age, he just loses to ability ...
0
votes
2answers
74 views

Question about secant and cosecant.

Ok so if we take a right triangle and consider an angle $\alpha$ we get the following: From here we can define the fundamental trigonometric functions sine and cosine where ...
2
votes
0answers
47 views

What is a sound curriculum for exponent rules in freshman algebra in high school?

We all know the the rules of exponents covered in freshman algebra. The question is, what is the best way to approach these topics as most 9th graders struggle in this area? I work as an after school ...
2
votes
2answers
113 views

Explaining how to simplify a quotient with negative exponents?

I work as an after school tutor at my high school. I've had kids come up to me asking how to do these types of problems: $\left(\displaystyle \frac{5xy^{-2}}{3z^{-1}} \right)^{-2}$ My approach is ...