Magic Maple

As a transfer student, I got a lot benefit from the experience of transfer. I have the chance of taking the same course in two languages in two countries and I learn a lot from the comparisons.

I took Advanced Math I and II in my freshman year in China. The contents of them are almost equivalent to calculus courses here in America, which are the sum of Math115, 116, 215 and 216 here in the UM. My credits for Advanced Math I and II were transferred to credits for Math 115 and 116, thus, I took 215 and 216 last fall and this summer, respectively. Since I have already learned the same content and they are easy as well, I had an easy time in solving the problems. Although these two courses somehow are like reviewing my Advanced Math II, I learn a lot from them, especially utilizing mathematical software.

For Chinese college math courses, we rarely use calculators or software for solving problems. On one hand, we are able to deal with addition, subtraction, multiplication and division, even solving equations since our primary school. On the other hand, the objective of the college math courses is teaching us the methods of solving complicated mathematical problems by hand. However, there are labs, purposes of which are introducing mathematical software to students for either Math215 or 216 here in the UM. The knowledge for software is entirely new knowledge for me and they are really interesting. Not only math courses, I also learned to use professional software, ChemDraw from Chem216.

In my opinion, western education pays more attention to teaching the use of software; however, Chinese colleges are focus more on practicing by hands.

I learn to use Maple and Matlab on Math215 and 216. They are professional mathematical software. I’m going to show some simple and famous curves drew by Maple14 following. The Maple commands are behind the corresponding figures. You can try them yourselves by copy and paste into a Maple program.  


(1) Folium of Descartes

with(plots):a:=1:
curve:=implicitplot(x^3+y^3=3*a*x*y,x=-2..2,y=-2..2,thickness=3,grid=[100,100]):
display(curve,scaling=constrained,title="folium of Descartes",tickmarks=[0,0]);

Folium of Descartes and its asymptote

with(plots):with(plottools):
tuxing:=implicitplot(x^3+y^3=6*x*y,x=-5..8,y=-5..8,thickness=3,color=red,grid=[100,100]):
zhixian:=line([-5,3],[3,-5],color=blue,thickness=3):
display(tuxing,zhixian,scaling=constrained);


(2) Devil's curve

with(plots):a:=5:b:=5.3:
curve:=implicitplot(y^2*(y^2-a^2)=x^2*(x^2-b^2),x=-a-1..a+1,y=-b-1..b+1,thickness=3,grid=[100,100]):
display(curve,scaling=constrained,title="Devil's Curve",tickmarks=[0,0]);


The reason of its name is given by Devil can be found at: Devil's curve.


(3) Fat circle

with(plots):a:=2:
curve:=implicitplot(x^4+y^4=a^4,x=-a..a,y=-a..a,thickness=3):
display(curve,scaling=constrained,title="fat circle",tickmarks=[4,4]);


(4) Lemniscate

with(plots):
tuxing:=implicitplot(2*(x^2+y^2)^2=25*(x^2-y^2),x=-5..5,y=-3..3,thickness=3,color=red,numpoints=10000):
display(tuxing,scaling=constrained,title="Lemniscate");


(5) Cardioid

with(plots):
tuxing:=implicitplot(x^2+y^2=(2*x^2+2*y^2-x)^2,x=-1..2,y=-1..1,thickness=3,color=red,numpoints=7000):
display(tuxing,scaling=constrained,title="Cardioid");

The logo is Maple is a piece of maple.

This logo can also be drew with Maple.