Questions related to the teaching and learning of mathematics.

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9
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3answers
137 views

Video Lessons in Complex Analysis

Does anybody have some link for good video lessons of a complete course in Complex Analysis? Grateful.
1
vote
1answer
36 views

Introduction to Newtons method

I'm supposed to come up with two ways to introduce Newtons method for the approximation of zeros for highschool students. (That is the method using tangents and with the formula $ x_{n+1} = x_{n} - ...
0
votes
0answers
52 views

Fun Lagrange multiplier problem?

Do any of you have a fun or interesting Lagrange multiplier problem that would be suitable for undergraduate calculus students? I'm planning on working through a standard Lagrange multiplier problem ...
0
votes
1answer
23 views

Systems of Inequalities question

Amy is a landscaper and has been given an assignment to modify the plans for a park in a small neighbourhood. The land she is working on is covered in trees and shrubs. Amy needs to make the park ...
2
votes
0answers
28 views

Ratio Question (Primary School)

Now, there are 6 students who are sharing 4 desks at the library. While 4 of them are using the desks, the other 2 students have to wait and watch. If they have to use the desk for the same amount of ...
8
votes
1answer
161 views

How to draw greek letters on paper / blackboard?

For $\gamma$ (gamma), I've noticed people doing a sort of $\alpha$ (alpha) rotated by ninety degrees, which seems to be the standard on-paper-or-blackboard equivalent of $\gamma$. But for letters ...
23
votes
6answers
515 views

Open source lecture notes and textbooks

This question is inspired by the popular "Best Sets of Lecture Notes and Articles". Indeed, I would like to collect a "big-list" of open source (that is, with $\LaTeX$ code available) high-quality ...
0
votes
1answer
35 views

Formula to find the sum of digits

I want to know if there is a way to find the sum of the digits of a power $a^b$ For exemple $9^{14}$ = 22876792454961 , Sum is 2 + 2 + 8 + .... + 6 + 1 Thanks in advance.
2
votes
2answers
248 views

Real numbers as decimals

I'm looking for a book that develops the theory of real numbers in a rigorous way in terms of their decimal expansions. The exposition should be concrete and preferably aimed at mathematically ...
3
votes
2answers
151 views

Why learn abstract mathematics? What is the point? [closed]

I'm a mathematics college lecturer and have an mphil degree in the subject. But I often wonder why I'm learning this senior undergrad level mathematics---analysis, topology, functional analysis, ...
1
vote
2answers
31 views

Countability - Constant Functions

I am learning about countability. I know about diagonalization and I am confused about constant functions and whether or not they are countable. A constant function in my case would be: $f(0) = 1,$ ...
0
votes
0answers
23 views

Example of caculation the cummulative probability

I have a question about probability that I am confusing. I have k bit symbols. Now, I want to calculate the successful decoding probability for k bits. It can defined by this equation ...
3
votes
1answer
158 views

Prove that the exponential function is differentiable

Imagine that you are writing a book on the foundations of analysis. You have already proved that for each $a > 1$ there is a unique function $f_a(x) = a^x$ satisfying the following: $f_a$ is an ...
2
votes
1answer
42 views

A Very Elementary Article or Webpage about Secret Sharing

I'm looking for an article or webpage about secret sharing with Latin squares, accessible to middle school students. I searched but found none. Can you help me? Thanks.
0
votes
2answers
32 views

Arithmetic Progressions Formula

I'm studying progressions in math class in Portugal, and I don't know the words/translation in english for certain things so I'll try to explain. I have this arithmetic progression: 2, 8, 18, 32 ... ...
2
votes
1answer
95 views

How can I learn to recognize the obvious questions?

I have heard and seen several references to "obvious questions", "obvious axioms" and other "obvious" things (I am not referring to obvious results!). Now, in a seminar I am taking, at the end of each ...
2
votes
0answers
64 views

First hand written draft Or LaTex typed draft; when some one want to publish? [closed]

When some one solve a math research problem and want to publish it somewhere; of course one should type it in LaTex. My Question: What should be the ideal way(time) to type it, I mean first one ...
0
votes
1answer
292 views

Taking Calculus II and Calculus III at the same time?

A little background: I'm a high school student enrolling at a local university next fall. I plan to pursue a mathematics degree, have studied this Calculus book. During the next semester, I plan to ...
1
vote
1answer
45 views

Teaching non-integer exponents

Say I'm teaching a younger student the concept of exponents. Now the basic example to begin with is say $2^3$ where it can be 'visualised' as having two blocks, then doubling the number of blocks, ...
1
vote
2answers
25 views

Large round brackets in equation

I cannot recall what the large () brackets mean - Google seems to be full of links on how to create them but not what they actually are or how to resolve them. $ ...
6
votes
2answers
71 views

Is there a way to simplify this equation

Is there a way to simplify this equation? $$ CE = 2 FD \sin \left( \arctan \left( \frac{AF}{FD} \right) - \arccos\left( \frac{AB}{\sqrt{AF^2+FD^2}}\right) \right) + \sqrt{AF^2+FD^2-AB^2} $$ Edit: ...
0
votes
2answers
42 views

Why do we need zeroes when writing some of those kinds of numbers?

I've looked up that zero is a placeholder in numbers that have this digit. I also figured out what would happen if there's no zero in 5,074 in a math journal. The number would be 5,74, which would ...
1
vote
2answers
114 views

How to find the order of a group generated by two elements?

What is the order of a group $G $ generated by two elements $x$ and $y$ subject only to the relations $x^3 = y^2 = (xy)^2 = 1$? List the subgroups of $G$. Since the above relation is the 'only' ...
2
votes
1answer
60 views

Order of a study

So i just recently had to drop two math courses, topology, math logic, because my math maturity wasn't up to the level needed to excel in them. I intend on taking them again, but not without first ...
0
votes
0answers
50 views

Appreciating the Distributive Law

I'm going to introduce my middle school students to the distributive law in arithmetic, in a meaningful way so that they understand its importance and value. I need some interesting examples and ...
0
votes
3answers
186 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. ...
32
votes
1answer
685 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 ...
3
votes
2answers
44 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 ...
1
vote
4answers
824 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 $3$ ($y\times 3 = z$) ...
0
votes
3answers
72 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
25 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 ...
2
votes
4answers
191 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
votes
1answer
63 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
0answers
151 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 ...
4
votes
0answers
87 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
93 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
vote
2answers
61 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
58 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
vote
3answers
37 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
88 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
62 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 ...
18
votes
5answers
584 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 ...
2
votes
1answer
31 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
votes
2answers
168 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 ??????
27
votes
8answers
3k 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 ...
0
votes
1answer
25 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 ...
4
votes
2answers
119 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 ...
1
vote
0answers
26 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 ...
7
votes
1answer
113 views

Is the actual learning of a course done in second reading?

I am now a graduate student. When I was an undergraduate, I would mostly study on my own directly from the books, and not concentrate much on lectures. Also, since I was a pretty good student, I would ...
1
vote
1answer
141 views

What does mean the exact value of derivative

i'm starting my calculus's journey and i have a question. What does mean the exact value of a derivative Take an easy example we have a derivative of $f(x)=x^2$, that is $f'(x)=2x$. Someone would ...