Abstract
A course on nonlinear dynamics is taught for freshmen in Shanghai University. Focusing on the scientific concepts of chaos, fractals and bifurcation, the course helps students to understand diversity, uncertainty and unpredictability in the real world. The paper surveys the technical contents of the course and highlights its pedagogical features. Student feedback is also reported.
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References
1.
Smith
L. A.
, Chaos: A Very Short Introduction (Oxford University Press , Oxford , 2007 ).
2.
Gleick
J.
, Chaos: Making a New Science (Viking Press , New York , 1987 ).
3.
Lorenz
E. N.
, The Essence of Chaos (University of Washington Press , Seattle, WA , 1993 ).
4.
Ruelle
D.
, Chance and Chaos (Princeton University Press , Princeton, MA , 1991 ).
5.
Stewart
I.
, Does God Play Dice? The New Mathematics of Chaos (Blackwell Publishing , Oxford , 1989 ).
6.
Smith
P.
, Explaining Chaos (Cambridge University Press , Cambridge , 1998 ).
7.
Lorenz
E. N.
, ‘Deterministic nonperiodic flow’ , J. Atmos. Sci. , 20 (1963 ), 130 –141 .
8.
May
R. M.
, ‘Biological populations with nonoverlapping generations: Stable points, stable cycles, and chaos’ , Science , 186 (1974 ), 645 –647 .
9.
Li
T.-Y.
Yorke
J.
, ‘Period there implies chaos’ , Amer. Math. Monthly , 82 (1975 ), 985 –992 .
10.
Hénon
M.
, ‘A two-dimensional mapping with a strange attractor’ , Commun. Math. Phys. , 50 (1976 ), 69 –79 .
11.
May
R. M.
, ‘Simple mathematical models with very complicated dynamics’ , Nature , 261 (1976 ), 459 –467 .
12.
Smale
S.
, ‘Finding a horseshoe on the beaches of Bio’ , Math. Intel. , 20 (1998 ), 39 –44 .