Math 12a --- Fall 2003
Linear Algebra & Discrete Dynamical Systems, Part I

Professor: Weiqing Gu, Olin 1279, x18929, gu@math.hmc.edu

Office Hours:
MON 2:45-3:45 PM, FRI 5:00-6:00 PM
Each of these times is open to students of both sections

Problem Session:
SUN 8-9 PM, Beckman B134.

Course Tutoring time and location:
Linde Activities Center (upstairs) SUN/TUE/THU 9-11pm.

Course Content: This course is an introduction to linear algebra and discrete dynamical systems. Linear algebra is the study of linear functions of several variables. Matrices and matrix algebra are used to study and model them. Many real-world phenomena are modeled by functions of several variables, and it is often interesting and important to understand the long-term behavior of the "dynamics" of repeatedly iterating such functions. Discrete dynamical systems is the study of the dynamics of both linear and non-linear functions. We will study the dynamics of linear maps of several variables, as well as the non-linear maps of just one variable, whose dynamics are already quite interesting. You will see connections to calculus (Math 11) as well as see common themes with your later study of differential equations (Math 13) and multivariable calculus (Math 14).

Text: David Poole, Linear Algebra, A Modern Introduction, 1st edition. (Note that the entire book has changed from last year.)
Doing the reading will be essential for success in this course.

Course Schedule: Please click here to find what the upcomming lecture topics will be about.

Homeworks, Exams, and Grading:

Honor Code: Though cooperation on homework assignments is fine, students are expected to write up their own solutions individually. (That is, no copying.) Comprehension is the goal, so even with cooperation, you should understand solutions well enough to write them up yourself. It is appropriate to acknowledge the assistance of others when given. The Harvey Mudd College honor code applies in all matters of conduct concerning this course.

HW Assignments
HW #1 (due WED 09/03)
  • READ Chapter 1 Section 1.0 - 1.3 and Chapter 2 Section 2.0-2.1
  • DO 1.1 (3a)c), 12, 19) 1.2 (9, 17, 27,39, 40, 50)

  • Please WRITE your HW number and section # on your HW!
    [Gu 10am = Sec 1, Gu 11am = Sec 2]
  • If you just recently added the class, or are a high school student, please subscribe to the course lists if you are not already on them, by sending an e-mail to listkeeper@hmc.edu, with "subscribe math-12-X-l@hmc.edu" in the body of the message. (Replace X by your section number.)
  • HW #2 (due FRI 09/05)
  • READ Section 2.2
  • DO 1.3 (6, 8, 13, 18, 23) 2.1 ( 21, 30, 32, 40 )
  • HW #3 (due MON 09/08)
  • READ Sections 3.0-3.2
  • DO 2.2 ( 2, 5, 13, 26, 33, 36, 40, 43, 45)
  • HW #4 (due WEN 09/10)
  • READ Sections 3.3 and 2.3
  • DO 3.1 ( 2, 13, 16, 31, 38) 3.2 (4, 24, 36, 44)
  • HW #5 (due FRI 09/12)
  • READ Section 2.3 (again), Section 3.4
  • DO 3.3 (7, 17, 45, 53) 2.3 (3, 7, 19, 21, 47))
  • HW #6 (due MON 09/15)
  • READ Sections 3.4 (again)
  • DO 2.3(25, 26, 27, 28, 30, 42, 43, 44, 46)
  • HW #7 (due WEN 09/17)
  • READ Sections 3.5
  • DO 3.4(3, 6, 7, 11, 15, 24, 35, 37, 39, 41, 51)
  • HW #8 (due FRI 09/19)
  • READ Sections 4.0-4.3
  • DO 3.5(2, 4, 7, 12, 15, 21, 25, 36, 40, 44)
  • HW #9 (due MON 09/22) MON
  • READ Section 4.3 (again) Section 4.4
  • DO4.2(8, 10, 17, 27, 29, 32, 46, 49, 53, 58, 65, 66)
  • HW #10 (due WED 09/24)
  • READ Section 4.4 (again)
  • DO 4.1(1, 11, 13) 4.3(3, 8, 12, 16, 19, 22, 25, 40)
  • Remember the midterm will be handed out this coming Friday.
    HW #11 (due FRI 09/26)
  • READ all the handouts and your class notes, all the materials covered so on the book
  • DO 4.4(13, 15, 21, 23, 44) and turn in a summary of materials covered based on your review
    IN CLASS REVEIW SESSION THIS FRIDAY. Pick up your exams and turn in your HW's in class.
  • MON 09/29 EXAMS DUE IN CLASS. We'll start discussing discrete dynamical systems today. Be sure to take notes... there is no textbook for this part of the course, since most schools do not teach a freshman course on this material!
    HW #12 (due WED 10/01)
  • READ your class notes!
  • DO this handout for HW#12.
  • If you are a high school student, or a student at another college, then we need to get you access to the software! Please write your professor an e-mail ASAP with your e-mail address and school info, thanks!
  • If you need an extension on this assignment to this Friday, you may have it if you need it.
  • for Friday 10/03
  • READ your class notes!
  • to be decided
  • HW #13 (due Monday 10/06)
  • READ your class notes!
  • DO this handout for HW#13. Write the HW number (13) on it!
  • HW #14 (due Wed 10/08)
  • READ your class notes!
  • DO this handout for HW#14. Write the HW number (14) on it!
  • HW #15 (due Fri 10/10)
  • READ your class notes!
  • DO this handout for HW#15. Write the HW number (15) on it!
  • HW #16 (due MON 1)10/13
  • READ your class notes
  • DO this handout for HW#16. Write the HW number (16) on it!
  • HW #17 (due WED 1)10/15
  • READ all handouts and your class notes
  • DO making a list of the problems you have for the review session on Wednesday; a summary for the materials after midterm I; and one suggested problem for final exam
  • IN CLASS REVEIW SESSION. Pick up your exams and turn in your HW on summary and suggested problem in class.