Questions related to the teaching and learning of mathematics.

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3
votes
11answers
332 views

Interesting piece of math for high school students?

I'm giving an hour long lecture to high school math students with a fairly high aptitude in math. I want to present something a little advanced for them (undergrad level) that they have to struggle ...
2
votes
0answers
40 views

How to decide which theorems from textbook to prove

I've noticed that theorems in textbooks roughly come in two varieties: those that are worth trying to prove yourself, and those that aren't. I'm not going to try and give criteria for "worth trying" ...
3
votes
1answer
71 views

Advice for Math Majors -What to do if you come into college with a lot of college credit? [on hold]

In high school I was a good maths student and took AP Calculus BC my freshman year and got a 5 and then took Multivariable Calculus, Linear Algebra, Differential Equations, Introduction to ...
4
votes
2answers
75 views

where to start if you lack basics? [on hold]

I've joined this forum for few weeks now and it amazes me that so many people are good at math. For me, I'm more of a history person rather than math person, so I hated math since I was young, not ...
3
votes
0answers
29 views

On contemporary mathematics education [on hold]

In the olden days, when a professor assigns a problem, the students did not have much resources. They had to struggle alone or possibly with another person for a long time and get to the solution. The ...
6
votes
3answers
64 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
28 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
32 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
19 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 ...
5
votes
0answers
65 views

What do math graduate school look for in prospective student? [closed]

I am a professor at a liberal arts college, and I have thus never been on an admissions committee for math graduate school. I can remember some of the things in my graduate school application that ...
2
votes
0answers
23 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
112 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 ...
15
votes
7answers
300 views
+100

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
20 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.
1
vote
1answer
31 views

Why can we square both sides when LHS and RHS is square rooted?

When we have something in this form: $\sqrt{x + a} = \sqrt{y + b}$ A common technique to solve is to square both side so that: $(\sqrt{x + a})^2 = (\sqrt{y + b})^2 \implies x + a = y + b$ I'm an ...
2
votes
2answers
227 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 ...
4
votes
2answers
98 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, ...
0
votes
0answers
29 views

Motivation for an undergraduate major in statement of purpose [migrated]

Is it okay to mention in my statement of purpose for admission to grad school in math, that my undergraduate major is engineering because my parents wanted me to do it? I was initially wrote my ...
1
vote
2answers
28 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: $f(0) = 1,$ ...
-2
votes
1answer
58 views

Mathematical thinking

I was curious to know some books that would lead to more mature development of mathematical thinking? I know mathematics is not just the computation, but the science of developing patterns and ...
0
votes
0answers
15 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
86 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
35 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
20 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
74 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
60 views

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

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
0answers
18 views

Find Dot Product of two points in latitude and longitude.

Let's say we have two points $P1 = (\text{lat}1, \text{long}1) , P2 = (\text{lat}2,\text{long}2)$. How do i find the cross product of this two points?
0
votes
1answer
56 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 ...
0
votes
0answers
24 views

Is there a way to follow a question? [migrated]

I often see questions on math.stackexchange.com that I would like to follow. That is, I would be notified if there is any activity on the question so that I can see the answers that are provided. Is ...
1
vote
1answer
36 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, ...
0
votes
1answer
58 views

An arbitrary guy needs some advice! [closed]

I am doing Mechanical Engineering (2nd year) and it's already becoming clear that I am no more interested in this course.I am very much motivated to study Theoretical Physics and Pure Mathematics(I ...
1
vote
2answers
21 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. $ ...
1
vote
0answers
62 views

Good community colleges for mathematics in US

Which community colleges in the US have the strongest mathematics programs ? After searching a bit on my own, I found North Seattle Community College - it seems to have a little stronger program ...
6
votes
2answers
70 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
40 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
58 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
53 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
37 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 ...
-1
votes
1answer
101 views

How can I retrieve all the results in one go? [closed]

Please excuse me for posting this question here, but I'm just not sure where this question properly belongs; moreover, as I'm in search of a funded Masters or PhD in Mathematics abroad, perhaps this ...
0
votes
3answers
85 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. ...
30
votes
1answer
450 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
votes
2answers
87 views

Logical order to understand math? [closed]

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 ...
3
votes
2answers
36 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
818 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
37 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
21 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
1answer
40 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 ...
2
votes
4answers
175 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
37 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
132 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 ...