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!!

TIM and Math

Vesa Lappalainen / Faculty of Information Technology

Go to: r.jyu.fi/tmath

or show this to mobile

What is TIM?

The Interactive Material

  • TIM is an open source cloud-based platform to make interactive documents like

    • lecture notes / eBooks
    • weekly exercises
    • exams
    • manuals
    • workbook
    • discussions
    • write together and share

  • For:

    • normal lectures
    • peer instruction
    • self studying
    • MOOC
    • Flipped Classroom
    • whatever

Properties

  • mark as read (red for unread, click away, yellow for changed block)
  • lecture mode (real time questions, lecture wall)
  • correction phrases
  • comments (public/private)
  • see all answers from the user, not just the last one
  • group answering
  • automatic assessment for some task types
  • keep original and translated document in sync
  • gamification

Examples

Examples of interactions

This is examples for slow devices. One must take cursor over the task to get it open.

1. Videos

The Brachistochrone

2. Textual answers

# text1

Write what you found out about different curves when watching previous videos



 

        

        





                
3. Textual answers with automatic assessment

        

        




                
                    #
                
                number3
            

                
52 - 25 = 


        

        





                
4. Return image

        

        





                
In a math assignment, it may be reasonable to write things to paper and return an image of that

        

        




                
                    #
                
                image2
            

                


 

        

        





                
5. Multiple choices

        

        




                
                    #
                
                mcq31
            

                
        

        




                
                    #
                
                Howmany
            

                How many boxes
Open plugin

        

        




                
                    #
                
                Vaaka
            

                Weight
Open plugin

        

        






                
6. Write the problem


More than asking the final result, ask the formula and let computer to do the calculations:

        

        




                
                    #
                
                sageV
            

                
Repair the calculation


 Count mass of the aluminium piece that has density of \(2.7 \, \mathrm{g/cm^3}\)


V = 2 * 3 * 4 * 5


 

        

        





                
7. Image dragging

        

        




                
                    #
                
                prosessit3
            

                
Drag processes to correct places

        

        





                




        

        




                
                    #
                
                imagex172
            

                
Drag words to correct positions over the graph

        

        





                




        

        




                
                    #
                
                Plugin2
            

                
What forces affect the cyclist?

        

        





                




        

        




                
                    #
                
                vapaa1
            

                
Draw an example of a discontinuous function

        

        





                
8. TeX writing

        

        





                
One can write math by TeX:

        

        




                
                    #
                
                mp1
            

                
Task: Pythagorean theorem


Write a Pythagorean theorem using TeX syntax


$$
x = \frac {-b \pm \sqrt{b^2 - 4ac}}{2a}
$$


 

        

        





                
.

        

        




                
                    #
                
                writemath2
            

                
Write LaTeX-formula here




 

        

        





                
9. GeoGebra

        

        





                
        

        







                
10. Octave

        

        





                
                    #
                
                esim5_6
            

                
Example 5-6


num = [0 0 1]
den = [1 0.8 1]
G = tf(num,den)
nyquist(G);



 

        

        





                
11. Maxima


        

        




                
                    #
                
                maxima1
            

                
Maxima


integrate (1/(1+x^3), x);


 

        

        




                
                    #
                
                maxima2
            

                
Maxima and TeX-output


Use tex-function to output as TeX.


tex(integrate (1/(1+x^3), x))$


 

        

        




                
                    #
                
                maxima3
            

                
Maxima and display2d


display2d: true$
linel: 80$
1/(1+x^3);
integrate (%, x);


 

        

        





                
        

        





                
12. MathCheck by Antti Valmari

        

        




                
                    #
                
                seq1
            

                
Solve `2|x| - |x-1| = x/2 +2`


x = -2 \/ x = 2


 

        

        





                
        

        





                
13. Sage math

        

        




                
                    #
                
                sageP1
            

                
Example of derivative and integral


f = x^2+3*x-5
df = diff(f,x)
F = integrate(f,x)


 

        

        




                
                    #
                
                sageP11
            

                
Example of solution


x, a, b, c = var('x a b c')
r = solve([a*x^2 + b*x + c == 0],x)


 

        

        




                
                    #
                
                sage1
            

                
Write a function to draw


f = sin(x)
plot(f,-3,3)


 

        

        




                
                    #
                
                sage2
            

                
Press Save and drag the slider


f = sin(1/x)
@interact
def _(x2=slider(0.0001,2,default=1.0)):
    p = plot(f, (x, 0, x2))
    pretty_print(html('$f(x)\;=\;%s$'%latex(f)))
    show(p)


 

        

        





                
14. Embedded pages

        

        





                
    

  • TODO: This should be faund a new eaxmple.
    • 


        

        








                
15. JavaScript

        

        




                
                    #
                
                jsLumiukkoUusi
            

                
Task: Snowman


Try to change the position of the snowman's head.


//
  var x1 = 100;
  var y1 = 200;
  circle(ctx, x1, y1, 50);

  var x2 = x1;
  var y2 = y1 - 50 - 30;
  circle(ctx, x2, y2, 30);

  var x3 = x2 + 10;  // Change this value
  var y3 = y2 - 30 - 20;
  ctx.fillStyle = "yellow";
  circle(ctx, x3, y3, 20);


 

        

        




                
                    #
                
                vpython2
            

                
3D-grafiikka


sphere(pos=vector(4,7,3),radius=2,color=color.green)
box(pos=vector(4,2,3),size=vector(8,4,6),color=color.red)


 

        

        




                
                    #
                
                jsIntegraali
            

                
Definite Integral




 

        

        





                
Linear

        

        




                
                    #
                
                jsMokki1
            

                
Linear map




 

        

        






                
16. For smaller children

        

        




                
                    #
                
                lauseke
            

                
        

        




                
                    #
                
                jsLauseke
            

                
Try to remove parentheses and look how the result changes




 

        

        





                
17. Statistics

        

        




                
                    #
                
                rData1
            

                
Save data


1.28 -1.84 1.47 6.1 10.36 6.68 1.49 -1.54 4.49 3.35 -0.1 2.33
-0.92 1.75 4.48 1.99 4.73 0.88 -0.78 -0.93 -2.46 -1.18 -0.45 4.71
-1.09 1.08 4.61 1.1 6.16 1.8 -2.94 -1.95 2.17 -2.89 3.4 -0.85
-0.74 1.63 -5.28 1.56 2.24 0.77 6.66 3.69 4.4 5.26 0.4 6.35 1.49
2.62 0.3 -3.3 4.19 5.44 1.61 0.18 2.64 4.46 0.77 6.53 -4.02 4.14
-0.89 2.84 3.12 4.09 3.14 6.99 -0.44 1.64 -2.84 5.28 0.5 -1.27
-3.81 3.91 4.47 6.7 5.17 1.44 7.18 1.33 6.05 -3.36 0.45 5.49 2.21
1.48 -2.18 3.54 -2.5 3.77 1.29 0.17 5.4 2.01 8.19 2.91 1.38 1.92
-0.53 2.64 4.13 2.31 3.28 2.75 0.11 6.15


 

        

        




                
                    #
                
                sageP02
            

                
//
y <- scan("data1.dat")


 

        

        





                

        

        




                
                    #
                
                sageP05
            

                
//
mean(y)
var(y)


 

        

        




                
                    #
                
                sageP07
            

                
//
png()
hist(y)


 

        

        





                
18. GlowScript

        

        





                
                    #
                
                vpython14
            

                
3D-surface


def f(x, y):
    # Return the value of the function of x and y:
    return 0.7+0.2*cos(2*t)*sin(10*x)*cos(10*y)

p = plot3D(f, 0, 1, 0, 1, 0, 1) # function, xmin, xmax, ymin, ymax (defaults 0, 1, 0, 1, 0, 1)


 

        

        




                
                    #
                
                vpython4
            

                
A "hard-sphere" gas at 300 K


Natoms = 100  # change this to have more or fewer atoms


 

        

        





                
19. Java

        

        




                
                    #
                
                javagra3D
            

                
Java/Graphics 3D surface


        window.add((x,y)->sin(x)*cos(y),-2*PI,-2*PI,2*PI,2*PI);
        window.rotate(Axis.X, 50);
        window.rotate(Axis.Y, 20);


 

        

        





                
20. Math.js

        

        





                
See Math.js.

        

        




                
                    #
                
                css1
            

                
Write function to draw


1 * sin(x) + 2 * cos(x/2)


 

        

        





                
21. Stack


        

        




                
                    #
                
                jsxsin
            

                
        

        





                
                    #
                
                visjs3D
            

                
3D surface


    for (var x = 0; x < axisMax; x+=axisStep) {
        for (var y = 0; y < axisMax; y+=axisStep) {
            var value = (Math.sin(x/50) * Math.cos(y/50) * 50 + 50);
            data.add({id:counter++,x:x,y:y,z:value,style:value});
        }
    }


 

        

        





                
                    #
                
                jsx1
            

                
Sin(x)


 var f = 'sin(x)+1';


 

        

        




                
                    #
                
                jsx2
            

                
Oletetaan, että \(A\) on piste suoralla \(L\) ja että \(\bar v\) on suoran \(L\) suuntavektori. Yhtälö \[\overline {OP} = \overline {OA} + t \bar v\] on suoran \(L\) vektorimuotoinen parametriesitys. Tässä esiintyvä kerroin \(t\) on parametri ja vektori \(\overline {OP}\) on paikkavektori liikkuvalle pisteelle \(P\) suoralla. Alla voit kokeilla, miten \(A\):n, \(\bar v\):n ja \(t\):n muuttaminen vaikuttaa suoraan.


 //


 

        

        




                
                    #
                
                jsx3
            

                
O(n)


Säädä alla olevilla "liukureilla" x- ja y-skaalausta.


let xmax = 10;
let ymax = 10;
functions = [
{ f:(x) => x                  , c: 'red'},
{ f:(x) => 6*x                , c: 'orange'},
{ f:(x) => Math.log2(x)       , c: 'blue'},
{ f:(x) => x * Math.log2(x)   , c: 'gray'},
{ f:(x) => x * x              , c: 'blue'},
{ f:(x) => x * x * x          , c: 'green'},
{ f:(x) => Math.pow(2, x)     , c: 'red'},
];


 

        

        




                
                    #
                
                py10-4
            

                
xs = [0]*n
ys = [0]*n

for i in range(n):
    r     = x[i]**2 + y[i]**2
    xs[i] = x[i]/r
    ys[i] = y[i]/r



 

        

        





                
                    #
                
                Plugin1
            

                
Desmos x2


Open GeoGebra


 

        

        





                
25. Write Math

        

        

        

            
        

    

    
    
    


    
    
        
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