All Questions

OK so this is really old school. Back in the 1980s, as a latchkey kid, I played on the computers in the library in elementary and middle school. There was this one bizarre educational game that I'd ...

I am going to teach an undergraduate statistics course next year. My plan is to spend less time on theory and a more time on teaching students to doing some statistics on computer. However, this ...

Does the row space contains everything orthogonal to the nullspace in linear algebra? In chapter3 of Gilbert Strang's linear algebra and its applications (4th edition) ，about orthogonal vectors and ...

There's a nice example of why people dislike proof by exhaustion on the Wikipedia page. The problem statement is "prove that all years in which the Modern Olympics are held are divisible by 4&...

Teaching discrete mathematics, we pose (from the textbook) questions on finding compositions of relations, notably, relations on very small finite sets with only 3 or 4 elements (as an introductory ...

Ok so I have this equation ((M % a) % b)=((M % b) % a) where M is some positive integer. Now I need a equation something like <...

I want to learn probability theory and discrete math. However, I also need to brush up on computational calculus and linear algebra. Would you recommend only studying one subject at a more intense ...

Preparing for a class I teach this summer and stumbled upon a technology problem. I want to show my students a graph, ask students to annotate it privately (eg mark mean on a histogram) and then ...

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

So, I realize this can be a broad question, so I'll narrow it down. I have lived in Spain and own several Math textbooks from that country (the equivalent of 8th grade and high school Math). Has ...

Suppose you have a carton that has the form of a square with sides of length a. If we want to produce a box out of it whose height is x we might deduce the following formula: $$V_a(x)= x(a-2x)^2=a^2 x ...

I am going to teach 2nd-year undergraduate students in applied math or computer science a course called "Discrete Mathematics for Computer Science". Most students who take this course plan ...

tl;dr: Why do so many students have poor intuition of numbers, and what can be done about it? $$$$ I've always been good with numbers. As a maths tutor, one of the things I notice is how poor the ...

I am currently student teaching for an Integrated Math 1 class (which is similar to Algebra 1) that consists of 9th graders. I have been teaching my students how to solve linear systems using ...

As I wrap up my Spring semester online courses, I'm starting to think about next Fall when (hopefully) our university will return to full in-person classes. Because of COVID, over the last year I have ...

I'm trying to explain some basic concept to my kid (he just started learning basic algebra following Discovering Algebra: An Investigative Approach by Jerald Murdock ). For example homeomorphism means ...

So I'm wrapping up my second year teaching high school calculus, and my first as an AP course. In addition to review, I'd like to end the year by giving the students a taste of the kinds of real-...

Look at the following example: Which picture has four apples? A B C D B is the expected answer but should not the correct answer be BCD? Technically if a set has exactly $m$ elements, then it ...

Whether we are preparing undergraduates for research in industry or academia effective collaboration is an important higher skill. I think there are two aspects to this in mathematics - thinking ...

I have always wondered whether it is necessary or not. For me, it seems that it is enough to teach them the intuitive idea, that is, limit is just an approximation of a certain process. what do you ...

I just read an interesting article that helps to understand completing the square, and prove the quadratic equation from a geomterical perspective. My question is how do I understand the graphical ...

I've taken Calculus 1 and it's time to relearn because I've forgotten some of it. But it's been a couple months since I've done any solid mathematics. I was hoping for a book that would include ...

I'm teaching a physics class that has a year of calculus as a prerequisite, but as so often happens, many of my students have forgotten a lot of the much more basic math from earlier classes. In ...

I am going to teach this probability and statistics course in a couple of weeks. The probability part can be made very interesting, in my opinion, easily. But I am a little worried that I might make ...

Let us assume that I want to graph any of the functions below. A) A can of soda costs $\$1$. Draw a graph depicting the total cost as a function of the number of cans you buy. Comment: One cannot ...

Background The students in my country are supposed to be able to work with and answer questions about functions at the age of around 15. This is asserted in the standard mathematics curriculum for ...

Case: Exam Problem given to student at university: Give a problem/context illustrating the operation $\frac{4}{5} + \frac{2}{3}$ Answer by student: Anna and Beatrice buy flowers for grandpa for his ...

Wikipedia shows that in 1886 John Milton Gregory outlined his "The Seven Laws of Teaching"; asserting that a teacher should: Know thoroughly and familiarly the lesson you wish to teach; ...

Background Hello, I am an undergraduate in CS. I would like to study Graph Theory on my own (self-study) for a competitive examination (named GATE). It is an examination for undergraduates and as such,...

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 ...

A math student may write very long and detailed answers, just because he or she does not know what to look for, for example in Geometry proofs. Or - a student may just write an arbitrary step without ...

[cross posted from mse] the class of all finite groups is not closed under produtcs - example: the product over all finite cyclic groups - thus it is not a variety of algebras, ie, it's not ...

I am teaching 12-16 year olds. How should I write down the Pythagorean theorem equation? Some alternatives: $a^2 + b^2 = c^2$ $\text{leg}^2 + \text{leg}^2 = \text{hypotenuse}^2$ $\text{leg}_1^2 + \...

Say I have the problem: I roll a die three times and I am interested in the probability of ending up with two 1's. My impression is that a single roll is called a trial. What is the full 3-roll action ...

I want to start by sharing my teaching philosophy: I believe in teaching in a way that is primarily student-centered. That is, I prefer to do less talking to give the student(s) more time to practice ...

Like the title says. I am self studying intro to proofs(How to prove it by velleman) so I can start an introduction to analysis. I am wondering if I should complete all the exercises in the textbook(...

I want to stress to my students that we should be careful with how we treat the equals sign and that we should always make sure that the units match. However, sometimes I write $ 11:40 - 15 \text{ min}...

Learning mathematics and learning parkour seem to have a lot in common. Both can be done on varying levels, but to progress in either one needs to overlearn and build basic skills so that these skills ...

Evidence suggests that even instructional approaches that produce conceptual gains may leave students reliant and expecting to be reliant on guidance from instructors (Redish et al., 1998). Students ...

TL;DR version: It seems to me that high school curricula no longer distinguish between "horizontal shift" and "phase shift", or between "frequency" and "angular ...

I was reading this book: "Dynamics of Particles and Rigid Bodies: A Self-Learning Approach" by Mohammed F. Daqaq In the preface, the author explains of his "flipped classroom ...

I just looked at matriculation exams from Finland. They have both basic and advanced level exams. Most US high school seniors could not pass the basic exam. If each US state were to create its own ...

I have been looking at questions on Math Stack Exchange and I am frequently coming across topics that sound as if they could have been optional chapters in a high school geometry class, but I have ...

Tom Lehrer claims and the audience seems to agree with him that the 'old way', before new math to do subtraction was to say, for example, 'three from two is nine carry the one'. I never heard of this ...

I am thinking of taking up a position at a liberal art college. I have taught mathematics at large public universities but I have no idea what is it like to work at a liberal art colleges. So what are ...

Why are higher level math textbooks almost completely black and white? I can't think of any math textbooks on a subject more advanced than calculus that uses colors. Edited to add that the comments by ...

Many definitions in mathematics are "fully crystalized". Sometimes the form of these definitions might be somewhat baffling to the uninitiated. For example, the definition of a relation ...

Some students are prone to making small calculation errors. Not errors in understanding, but errors like adding or multiplying integers incorrectly, or dropping a negative sign. Unsystematic errors in ...

In an Advanced Calculus course, students were asked to prove $$|a_1 +a_2+...+a_n| \le |a_1|+|a_2|+... +|a_n|$$ for $n$ real numbers $a_1,a_2,...a_n$ I am teaching assistant for this course, and one of ...

Mathematics Educators. I'm having a difficult time understanding modular arithmetic (particularly its applications for proof writing). I understand very well the basics. I know that $a\equiv b \pmod n$...