Questions related to the teaching and learning of mathematics.

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15
votes
7answers
298 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 ...
42
votes
8answers
6k views

When to learn category theory?

I'm a undergraduate who wishes to learn category theory but I only have basic knowledge of linear algebra and set theory, I've also had a short course on number theory which used some basic concepts ...
8
votes
0answers
397 views

Is it possible to learn mathematics right from the source instead of reading textbooks. By studying the masters and not their pupils

I was wondering if mathematics learning process require the use of textbooks. When I was a high school student, I read as a preparation for university, Legendre book on Elements of geometry and ...
2
votes
0answers
37 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
70 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
73 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
869 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 ...
0
votes
1answer
411 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 ...
0
votes
2answers
86 views

Pure Mathematics to Actuarial Science.

I did my undergraduate in pure mathematics and recently after a three year break I decided to get a master's degree in Actuarial Science. I am in the second week of classes and I feel completely lost. ...
14
votes
7answers
3k views

How to study for analysis?

I am currently a first year undergraduate majoring in mathematics. I'm taking an introductory analysis course and find it very hard compared to other math couses. I know that the topics covered in the ...
1
vote
1answer
27 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} - ...
465
votes
141answers
29k 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 ...
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 ...
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 ...
2
votes
2answers
226 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 ...
6
votes
0answers
64 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 ...
-2
votes
0answers
21 views

How do I understand differentiation and integration? [closed]

Whats a good generalized perspective to understand derivatives and integrals?
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 ...
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. ...
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, ...
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, ...
2
votes
3answers
1k 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 : ...
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
57 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 ...
1
vote
1answer
435 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 ...
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
73 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
3answers
93 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 ...
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 ...
32
votes
13answers
2k views

How To Present Algebraic Topology To Non-Mathematicians?

I am writing my master thesis in algebraic topology (fundamental groups) and as a system in my school students must write about one page about their theses explaining for non mathematicians the ...
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 ...
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 ...
10
votes
9answers
989 views

A Poster About Prime Numbers [closed]

We're going to design a poster about prime numbers, which will appear in a mathematics magazine for middle school students. The poster should be both visually attractive and mathematically rich. Do ...
-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
1answer
412 views

Line Drawing Using Bresenham Algorithm

Indicate which raster locations would be chosen by Bersenham’s algorithm when scan converting a line from screen co-ordinates (1,1) to (8,5). First the straight values (initial values) must be found ...
1
vote
6answers
3k 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.
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: ...