0
votes
0answers
22 views

Is this correct? A snail climbs up a 20 metre wall. [duplicate]

A snail climbs up a 20 metre wall. Every hour it climbs up 5 metres then slides back 3 metres. How long does it take the snail to climb up the wall. My solution: By 16 m, the snail would have taken 8 ...
1
vote
1answer
45 views

Matrices of the form $A^p=(a_{ij}^p)$

I am wondering if there is a name for these kind of matrices and if they are interesting or not? Do they even exist? Let $A$ be a $n\times n$ matrix with elements $a_{ij}$. $A= (a_{ij})_{i,j\in\{1, ...
0
votes
0answers
15 views

Classroom enhancement resources for linear algebra

My university offers small grants (in the \$100 - \$300 range) for classroom enhancement resources. In the past, I've applied for and received a grant to purchase a Zometools kit used for ...
13
votes
6answers
2k views

Why teach linear algebra before abstract algebra?

Is there a reason why most undergraduate curriculums put linear algebra before abstract algebra? I'm asking this because personally it seems to be much easier to understand the architecture behind ...
0
votes
1answer
46 views

Pre requisites of linear algebra

I want to learn abstract linear algebra. Do I require the knowledge of discrete mathematics before I start? I have the impression that abstract maths and their proofs can be understood easily by the ...
7
votes
6answers
483 views

Thinking of mathematics in terms of analogs

I think the way that I've come to think about mathematics is becoming problematic and I'm wondering if I should abandon it. When I study mathematics, I find myself trying to compare the mathematical ...
1
vote
3answers
255 views

Roadway and book recommendations to math study.

I had some calculus, linear algebra and complex analysis courses back in college. But it is not comprehensive. And I felt that my college math was not taught in a logical sequence (maybe because my ...
0
votes
1answer
101 views

What is the rank of the differentiation operator on Pn? What is the kernel?

For this question I was thinking of saying Pn(x)=Ax^n+Ax^(n-1)+...+Ax^2+Ax^1+1 and finding the first derivative P'n(x)=n.Ax^(n-1)+(n-1)Ax^(n-2)+...+2Ax^1+A+0 so in matrix form would get a n by 1 ...
2
votes
3answers
64 views

Why do I see i and k as the indices of summation?

I'm working on linear algebra and just wanted to clear up an uncertainty regarding whether there is a difference in the use of i and k as the dummy variables for the index of summation? ...
3
votes
2answers
371 views

What is the distance between the line and plane if it is parallel?

So far, I've gotten that the line is parallel to the plane $x = 2 + t$, $y = -3 + 2t$, $z = 1 + 4t$ With the vector of that being $U$ is $(1,2,4)$ and the plane $2y-z = 1$ with the vector $V$ being ...
2
votes
1answer
204 views

4 big ideas in algebra that have rich connections to other fields? [closed]

In his controversial post criticizing high school algebra, Grant Wiggins issued a challenge to his readers: Can you identify 4 big ideas in algebra, ideas that not only provide a powerful set of ...
5
votes
4answers
7k views

“Tricks” for solving the determinant of a matrix

I've got an exam coming up, and I'm worried that (as I usually tend to do) I will mess up with some minor algebraic calculation in a large problem like finding the determinant of a 4x4 or larger ...
8
votes
3answers
1k views

Reviews/comparison of Python vs Matlab for teaching Linear Algebra

I am wondering about advantages of using Python for teaching introductory linear algebra. I have been using Matlab and I became interested in Python mainly because of several resources, e.g., ...
0
votes
1answer
120 views

Graphical Demonstration of Linear Transformations on $\mathbb{R}^2$

I'm looking for some applet, program, software, demonstration etc. to use it in a class while teaching linear transformation in $\mathbb{R}^2$, so that the students can graphically understand the ...
10
votes
4answers
664 views

Best way of introducing determinants in a linear algebra course

What is the best way of introducing determinants in a linear algebra course? I want to give real life examples of where the determinant is applied. It should have a real impact.
0
votes
3answers
85 views

Why change a given basis?

Why would we want to transform a vector in our normal basis (xyz axes) to another basis? The only situation I can recall is when we are looking at a force applied on an inclined plane. Are there any ...
5
votes
4answers
1k views

When is linear algebra usually taught

Just curious, when should I learn linear algebra in college? And when is linear algebra usually taught? What precedes linear algebra and what usually goes after linear algebra courses?
3
votes
1answer
226 views

Functions that generate “easy” matrices of full rank

While explaining how to invert matrices I once used this ill-fated example $A=\begin{pmatrix} 1&2&3\\4&5&6 \\7&8&9 \end{pmatrix}$ which can not be inverted ($\det(A)=0$). That ...
1
vote
3answers
208 views

How to introduce basis vectors

What is attractive way to introduce basis vectors? I am looking for a hook that students will find motivating. It needs to have an impact. I have normally introduced it by just stating independent ...
3
votes
3answers
2k views

What is the importance of determinants in linear algebra?

In some literature on linear algebra determinants play a critical role and are emphasized in the earlier chapters. (See books by Anton & Rorres, and Lay). However in other literature it is totally ...
10
votes
5answers
2k views

Motivating linear algebra for economics students?

I'm a tutor for the introductory linear algebra course at my school; this course is required for most upper division economics classes, so a lot of my tutees are economics majors. This is a typical ...
10
votes
7answers
8k views

practical uses of matrix multiplication

The use of matrix multiplication is usually given with graphics initially (scalings, translations, rotations, etc). Then there are more in-depth examples such as counting the number of walks between ...