# All Questions

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### What books teach the formula for the # of k-permutations of n objects, with x types, and $r_1,⋯,r_x$ = the number of each type of object?

Some of my 16 year old students hanker after the formula for the # of k-permutations of n objects, with x types, where $r_1, ⋯, r_x$ = the number of each type of object. This is more generalized than ...
60 views

### From primary school to higher mathematics all mathematical abstract concept summary

is there any books or articles for summary abstract concepts from primary school to higher mathematics? we know such as mathmatical operations ...
76 views

### Code for Urn (containing colored balls) generator? [duplicate]

I am interested in code that generates an urn with various colored balls for an economics experiment. I came across this thread: Urn (containing colored balls) generator? However, the server that the ...
243 views

### Distance from the wall when reading a sign? A Calc I/II problem

Here is a question on a test I asked recently in a Calculus I class I teach on Saturdays. These are students who are planning to major in Math, and they are already taking AP Calculus BC in their high ...
79 views

### Is the AC Method of Factoring polynomials more popular and used by teachers than others methods of factoring polynomials?

This is an example of the AC Method: $x^2 + 16x +63$ (1) $x² + 7x$ (2) $9x + 63$ (1) $x(x + 7)$ (2) $9(x + 7)$ so we have: $x(x + 7)+ 9(x + 7)$ (1) with (2) The Result is: $(x+9)(x+7)$ I have more ...
95 views

### Which resource(s) to use to learn the following syllabus of discrete structures?

(YES) - included; (NO) - explicitly excluded; as stated from the IOI syllabus(2019); 5.2 Discrete Structures (DS) DS1. Functions, relations, and sets (YES)Functions (surjections, injections, inverses, ...
100 views

### Best Touchscreen Laptop for Tutoring During COVID Pandemic

I run a small tutoring company, and I specialize in math and science. During the pandemic, I began tutoring online using our 3 year old HP Pavilion touchscreen laptop. It has served me well using just ...
126 views

### Have you ever completely covered every topic in a textbook, and if so, which text?

Over the years of being a student or of being a teacher, it's occurred to me that I've never done every topic in a textbook. If it's a workbook that has a few introductory theory pages and then a few ...
186 views

### Prerequisites to study Laplace Transform completely?

Hello to all the professors who read this. I'm an electrical engineering undergrad student. I wanted to ask for advice on what I should learn beforehand to fully grasp the Laplace transform. I also ...
108 views

### What should the time limit for this high school math competition topology round be?

When I participated in the 2019 John Hopkins Math Tournament, the team round consisted of two separate topics, 40 minutes per round, and 3 people per team. My team suffered on the topology round. Only ...
141 views

### How can I introduce the idea of eigenvectors and matrix decompositions to a general audience in an engaging manner?

So I'm doing a freelance writing job, writing a script for a YouTube video about eigenvectors/values. It took me a while to decide what the focus was going to be, but I finally settled on focusing on ...
78 views

### Better instruction for an identity equation worksheet

I would like to construct a good worksheet for my students. I am thinking of creating an instruction that will cover all problems related to identity equations. Here is how I initially constructed ...
106 views

### How to teach year 3 undergraduate courses to high school students?

I see on the webpage of a high school math summer program, SuMac, that they will cover some algebraic topology in a period of several weeks. And they covered every aspect of this subject, including ...
125 views

### What is the best term for "probability measure" in an undergrad introduction to probability course?

The function $P$ that takes an event $A$ as input and returns the probability $P(A)$ as output is called a "probability measure" when we are developing probability using measure theory. I have also ...
70 views

### Can I do a PhD after many years I've graduated and can I get funding? [closed]

I'm in my second year of Mathematics. I would like to take a PhD and if possible also a master. However, I was thinking to take a master in Machine Learning, work for a bit in that industry (5-10 ...
200 views

### manual solutions to graduate textbooks [closed]

Where can I find manual solution for textbooks like Advanced Linear Algebra by Rotman or Introduction to Smooth manifolds by Lee? any help would be appreciated
286 views

### As it is appears here, how many constants do you see in $2x^3 + y^4 = \sqrt 5$?

My original phrasing was "how many constants are there in...". I am trying to determine if this is more clear. This is not intended for an exam, just a basic question to get intro-level algebra ...
169 views

### What research has been done on the effects of requiring students to learn to count in an alternative number base such a binary or base eight? [closed]

What research has been done on the effects of requiring students to learn to count and do some easy arithmetic in an alternative number base, for example binary, base four, base six, base eight, base ...
319 views

### Good textbooks for a college Basic Geometry course?

I will be teaching geometry for the first time ever this summer. I teach at a community college, and we only offer this course in the summer. (Mostly high school students take it, but it is a college ...
206 views

### Duodecimal by Stealth

It is widely recognised that the Duodecimal number system is superior to the decimal system. However, it is plainly obvious that trying to introduce such a system would be difficult, especially in a ...
195 views

### Which book has functions and their respective graphs? [closed]

I am looking for a book, which has different many different types of functions and their graphs (like, Weierstrass function, Takagi function).
113 views

### How to start tackling a 200 page big script? [closed]

I am really not sure how to tackle a 200 page huge script with a lot of information about the topic linear algebra. Writing down the definitions would not make sense in my opinion, because if I want ...
159 views

### Questions about the calculus AP [closed]

I'm not sure if this is the proper place to ask this question, but I figured I'll try anyway. If I have the option of taking a Calculus AP class, and am thinking of pursuing a career in either ...
653 views

### Is AP Calculus AB really necessary?

High school student here... This coming school year I'm scheduled to start AP Calculus AB and then my school is looking into taking Multivariable Calculus at a local university. The school's calculus ...
213 views

### What is "subtract 4 from 3 times X" and why?

I saw this phrase/sentence in a worksheet, "subtract 4 from 3 times X" The question asks the students to write the statement using numbers and symbols. I think the correct answer is 3X - 4, but ...
80 views

### Can anyone help give pointers of Mathematics Story Telling Animated Videos for Age Group 10 - 15?

Ideally, these videos should talk about a real life problem which student can relate to and then showing logically how the problem can be solved. Later bringing in the right mathematical tool to solve ...
105 views

### Math elementary textbooks [closed]

I’m a master student in Turkey. I’m researching math textbooks from different counties to compare them for my thesis. However, it is really difficult to find them. I need your suggestions. Or is there ...
143 views

### How helpful are university subject rankings when choosing a place to study math?

There are many university ranking consultancies trying to compare one leading maths department with another and to conclude which one is better. Although this doesn't seem to be a very reasonable ...
434 views

### Integrated math curriculum in different countries

One of the selling points of re-hashed American 1990s high school math programs is that they are "integrated", that is, combine algebra, geometry, statistics, trigonometry just like the European ...
111 views

### books of mathematics [closed]

a)I am trying to get a book that would give describe all the coordinate systems and their transformations(e.g. cartesian,polar,spherical,homogeneous,curvilinear,generalized,etc). b) And I need to ...
180 views

### Can I motivate kids to do math by giving them candies? [closed]

I am talking about literally asking for kids' time/attention by offering them candies: not giving them tasks about summing real candies, etc. I try to teach math from time to time to my relatives of ...
157 views

### What textbook is this chapter from? [closed]

I was looking for a good explanation text on single-variable calculus, especially limits, introduction and examples. I found this pdf and I really like it and would like to read the whole book. I was ...
85 views

### How should I solve this geometrical problem [closed]

One of my students found this problem and gave it to me in order to help him but I cannot really think of something that will help for the solution. So, this is the problem: ABC is a random triangle. ...
473 views

### Why's math more complicated to understand than philosophy? [closed]

Why's math more abstruse, perplexing than philosophy? This feels true, as intelligent laypeople can understand unsolved philosophy problems and competing possible solutions, but can't understand or ...
169 views

### A linear equation -- my approach

Here is an example of a lesson I did on linear equations where my objective was to show that they are equations of first degree. The reason I do it this way is because I tend to find that students ...
312 views

### Why are math test scores dropping in America? Lack of student responsibility movement [closed]

Someone asked me this question today. Why do you honestly believe that high school math test scores in America (particularly the United States) are low compared to other countries? I thought about ...
108 views

### Math questions for math game

I am building a math game, the Problem I am not a math teacher. :) So I am trying to find the best way to create questions for different ages and different levels, I tried to google it but no luck. In ...
120 views

### Should the limits of one system of elementary set theory be the limits of a student's mathematical world? [closed]

In teaching elementary set theory, suppose we refrain from emphasizing historical decisions that were made in theory construction. Is there a danger that students may see the mathematical language ...
204 views

### Kid, 8 years old, developed a new calculation algorithm [closed]

I have a kid, 8 years old. The boy has phenomenal math skills. When he was 6 he was solving fractions with roots, writing Fibonacci series and much more. Now he developed a new calculation algorithm ...
355 views

### Proving basic Theorems and properties in high school [closed]

Why high school teachers do not emphasize knowing the proofs of properties and theorems in math. In my 40 years of teaching prospective high school teachers, I rarely found students who can derive ...
113 views

### Finding an error in a partial integration [closed]

There must be an error in this partial integration but I do not see it. Do you see it?
91 views

### Where can I find the partial order relation of prerequisites of undergraduate courses in the United States?

Let $A$ be the set of all undergraduate mathematical courses in the US and define a binary relation $\leq$ on $A$ such that for elements $a,b\in A$ (that is, $a$, $b$ are undergraduate mathematical ...
162 views

### Could students be taught the concept of rational numbers the same way as in the Formal construction section of the Wikipedia article rational number?

Link to article cited in title, Wikipedia rational number. According to this answer, some students 14-18 are still struggling to understand fractions. Maybe some students know how to perform the ...
125 views

### When a geometrical figure a special case of another [closed]

Squares are special types of rectangles. Are circles special types of ellipses/ovals? Are cones special types of pyramids? I guess the answer is no because of the 2D basis: circles are not special ...
127 views

### symmetry of a square - is it possible pure geometric approach in didactics? [closed]

Consider a square : four points in a plane constructed with classical means (compass and straightedge). Since no point is different from others (no coordinates, no labels...) it seems that we can not ...
120 views

### How to solve the simple elementary school math issue--calculate increase rate [closed]

A company report its net profit 1,000,000 in 2000,and earned 1,100,000 in 2001,so the earning increase rate from 2000 to 2001 is as below: ...
111 views

### What are the uses of calculus in every day life? [closed]

Can anybody say me what is differentiation and integration and what is the use of these ?
84 views

### How do I solve this ratio problem? [closed]

Here is the problem: If Bill takes 3 hours to paint a room and James takes 5 hours to paint a room, how long will it take to paint a room if they work together? Show your working. Thank You.
I see many teachers use slow methods to solve a given problem where there's another faster methods that doesn't demand much more effort. I'm not looking for mistakes like saying that $a$ is the slope ...