Chaos and Calculus syllabus

CC MATHEMATICS MATHEMATICAL EXPLORATIONS

Course Syllabus
Block 1 of
Mathematical Explorations

Professors:

Jane McDougall	jmcdougall@coloradocollege.edu
	Tutt Science Center 206D x6275
	Office Hours: M-F 1:30-2:30 (Friday by appointment)
Marlow Anderson	manderson@coloradocollege.edu (Block 2)

Paraprofessional:
      Rahbar Virk: Tutt Science Center, x6727, rvirk@coloradocollege.edu

Student Mentor:
     Rachel Feder: Phone (310) 818 3861 mailto:r_feder@coloradocollege.edu

Class time:
     9:00 AM each morning, with occasional additional meetings in the afternoon.

Texts and Readings:
    Excerpts from Calculus Gems (Course Packet Available from the Bookstore), by George F. Simmons
    Calculus (Schaum's Outline), by Ayres and Mendelson
    Arcadia, by Tom Stoppard
    Borges Short Stories

Grades:
    During Block 1, you will undertake three formal writing assignments. In addition, you will have four quizzes over the material and regular homework problems, due within a day or two of when they are assigned. These problems will sometimes be group and sometimes individual assignments. You will receive a grade for each block of this course. The evaluation for the first block will be based as follows:
    15% each for the first and last essays,
    10% for the group library project,
    15% for homework,
    20% for the quizzes,
    15% for the final,
    10% for class participation.

Honor Code:
    Each assignment will have specific instructions about how much collaboration is allowed with your classmates. No collaboration will be allowed on quizzes. On all assignments, you must give complete bibliographical references for all sources you consult, including online resources. Honor Code convictions will result in an automatic grade of No Credit for the course. For more information about the Colorado College Honor Code, see http://www.coloradocollege.edu/academics/honorcode.asp

Schedule:

WEEK 1
Monday, Sept 5	10:30 AM: Introduction. Video Feedback and the Pixel Lighting Game 1:30 PM - 3 PM: Video: The Strange New Science of Chaos. Discussion.
Tuesday, Sept 6	Peak and Frame Handout: Chapter 4 pp 122-145: The tent map Calculus Chapters 3,6, and parts of 16,26, 28: Pre-calculus review
Weds., Sept 7	Peak and Frame Handout: Chapter 4 pp 146-160: The Butterfly Effect and Bifurcation Diagrams Calculus Chapter 7 and 8. Limits and Continuity. Homework One is due at 3 p.m.
Thursday, Sept 8	Peak and Frame Handout: Chapter 5 pp 161-170: The logistic map Calculus Chapter 9: Definition of derivative Quiz One is available after class and due at 3 p.m.
Friday, Sept 9	Peak and Frame Handout: Chapter 5 pp 170-175: Logistic Map and Bifurcation Diagram. Writing Center visit at 9:30 AM Geometric Series. Calculus Gems Course Packet pp 96 – 105: Fermat and his secants. Calculus Chapter 10, 17, 26, 28. Computing the Derivative for various functions. Product Rule, Quotient Rule, Chain Rule.
WEEK 2
Monday, Sept 12	Homework Two is due at 4 p.m. Try to complete as much as possible on this homework by Friday. Calculus Chapter 14,15. Absolute and Relative Maxima and Minima. Quiz Two is available after class and due at 3 p.m.
Tuesday, Sept 13	First Essay due 3:00 PM: The Butterfly Effect Calculus Chapter 11, 15, 17, 25, 26: Implicit Derivatives. Derivatives of inverse trig functions. Calculus Chapter 21: Newton's Method. Fermat's Theorem. Derivative Tests. Curve Sketching.
Weds., Sept 14	Theorems from Calculus (Mean Value Theorem, Intermediate Value Theorem) Calculus Chapter 15: Optimization Peak and Frame Handout: Chapter 5 pp 176-186: Universality
Thursday, Sept 15	Calculus Gems Course Packet pp 35 – 46: Archimedes Calculus Gems Course Packet pp 223 – 236: Archimedes finds the area of a parabola Homework Three is due at 4 p.m. Quiz Three is available after class and due at 3 p.m.
Friday, Sept 16	Calculus Gems Course Packet pp 240 – 241: Fermat's trick for power functions Calculus Gems Course Packet pp 131 – 140: Newton. Arcadia. Read and Discuss Act I Scene I &2
WEEK 3
Monday Sept 19	Arcadia. Act I Scene 3&4 Calculus Gems Course Packet pp 141 – 157: Leibniz Free will and Determinism Homework Four is due at 4 p.m.
Tuesday, Sept 20	Arcadia. Act II Scene 5&6 Calculus Chapter 23: Riemann Sums Iterated Function Systems Second Essay: Library Group Project. Due by 3:00 p.m.
Weds., Sept 21	Arcadia. Act II Scene 6&7 Leibniz Video Feedback Final Attempt! Calculus Chapter 24. Fundamental Theorem of Calculus. Entropy and Thermodynamics Quiz Four is available after class and due at 3 p.m.
Thursday, Sept 22	Cabin Trip: Depart 9 a.m. Calculus Chapter 22. Method of substitution. Laplace and Fourier - Reading pp 171-174 of handout. The Chaos Game.
Friday, Sept 23	Calculus Chapter 29. Volumes of Revolution. Calculus Chapter 29. Areas between curves. Return to campus, departing the cabin at 11 a.m.
WEEK 4
Monday, Sept 26	The Mandelbrot Set and the logisitic Bifurcation Diagram. Experimenting with Iterated Function Systems (i.e. fern pictures etc.) Peer Review is Due at 1:30 pm (pick up your reviewed work at 2:30 pm) 2:30 - 3:30 review of u-substitution and optimization
Tuesday, Sept 27	11am Third Writing Assignment: Essay on Arcadia is due. Review Homework Five is due at 1 p.m. 6pm - 7:30 pm Review Session in Math Lounge
Weds., Sept 28	Final Test (Quiz 5).
Monday, Oct 3	Second Block begins!