Math 20F: Linear Algebra     Winter 2010

Instructor:   Wee Teck Gan     wgan@math.ucsd.edu

Lectures: MWF 10 am-10:50am in WLH 2005

Office Hours: Wed 2-3pm and Fri 3-4pm in AP&M 7240

Teaching Assistants:    

Neal Harris: rnharris@math.ucsd.edu  
Office Hours: Weeks with Matlab assignments due: Tues. 11 - 1 in AP&M B432
Every week: Thurs. 11 - 1 in AP&M 6341

Nelson Townsend: ntownsen@ucsd.edu,  
Office Hours: Thursdays 1-2pm in AP&M 6414

Section:

  • B01: Tu 2-2:50 pm at AP&M 2301
  • B02: Tu 3-3:50 pm at AP&M 2301
  • B03: Tu 4-4:50 pm at WLH 2209
  • B04: Tu 5-5:50 pm at WLH 2209
  • B05: Tu 7-7:50 pm at WLH 2207
  • B06: Tu 8-8:50 pm at WLH 2207



    Text: Linear Algebra and its applications, 3rd Edition (Addison-Wesley), by David Lay.

    Syllabus: Math 20F is a semi-rigorous introduction to linear algebra, with an emphasis on computational techniques and some applications. Linear algebra is basically the axiomatic study of ``vectors" and ``matices". You have probably encountered and seen the usefulness of vectors and matrices in 20C (Multivariable Calculus) and 20D (Differential Equations). This course gives a systematic introduction (sometimes with proofs) of the basic constructs, concepts and results regarding these objects. Topics include:

    Matrix algebra, Gaussian elimination, determinants. Linear and affine subspaces, linear independence, bases of Euclidean spaces. Eigenvalues and eigenvectors, diagonalization of symmetric matrices. Applications. Computing symbolic and graphical solutions using Matlab.

    Prerequisites: MATH 20C.

    MathLab:   Part of the course involves using the computer package MATLAB to investigate concepts and topics introduced in lectures. For Mathlab information and assignments, click here

    MathLab Quiz:  

    There is a MathLab Quiz scheduled on March 4 (Thursday). It is held in the computer lab in AP&M B432 and is open book/notes. The quiz is held at the same time as your section (but on Thurs instead of Tues). So, if your section time is 4pm, you should go to AP&M B432 at 4pm on March 4. If you cannot make it at that time, you have the option of rescheduling the MAtLAb quiz: please see here asap for how to do this and for more information about the quiz.



    Homework:   Homework is due on Fridays, 5pm, in your TA's dropbox (in AP&M, 6th floor). Late homeworks will not be accepted. It is OK, even encouraged, to discuss homework problems with your classmates, but you are required to write up your own solutions. Please write legibly and in coherent sentences. Each week, 3 of the hoemwork problems will be selected for grading, one of which is the one marked with a * below. The problem marked with a * will not be discussed in sections or during office hours.

    HW 1 (Due 1/8): Sect 1.1: 7, 11, 18*, 20, 25; Sect 1.2: 1b, 2b, 11, 16, 19

    HW 2 (Due 1/15): Sect 1.2: 29, 30, 31; Sect 1.3: 5, 10, 12, 17*, 22, 24, Sect 1.4: 2, 5, 15, 21, 26

    HW 3 (Due 1/22): Sect 1.5: 14, 18, 23, 29, 30; Sect 1.6: 7; Sect 1.7: 6, 14*, 21, 28, 39; Sect 1.8: 5, 11, 15, 16, 19

    HW 4 (Due 1/29): Sect. 1.8: 21, 24, 25, 31, 34; Sect 1.9: 4, 10, 19, 23, 27*, 35, 36; Sect 2.1: 9, 10, 12

    HW 5 (Due 2/5): Sect 2.1: 16, 17*, 21, 22; Sect 2.2: 4, 13, 15, 19, 32; Sect 2.3: 4, 13, 18, 27

    HW 6 (Due 2/12): Sect 3.1: 4, 10, 21, 24; Sect 3.2: 5, 9, 16*, 18, 33, 35; Sect 3.3: 6, 12, 20, 24

    HW 7 (Due 2/19): Sect 4.1: 2, 8*, 12, 20, 22, 26, 32; Sect 4.2: 6, 16, 24, 31, 33; Sect 4.3: 4, 8, 14, 16, 23, 34

    HW 8 (Due 2/26): Sect 4.4: 4, 8, 10, 11, 14, 22, 32; Sect 4.5: 6, 14*, 21, 23, 32; Sect 4.6: 3, 6, 8, 14, 24, 25

    HW 9 (Due 3/5): Sect 4.7: 2, 4, 8; Sect 5.1: 12, 18, 24, 25, 26, 27; Sect 5.2: 6, 10, 20; Sect 5.3: 4, 6 16*; Sect 5.4: 4, 6, 19, 20, 23

    HW 10 (Due 3/12): Sect 6.1: 10, 24, 28, 30; Sect. 6.2: 10, 14, 16, 20; Sect. 6.3: 4, 8, 12*, 16; Sect. 6.4: 4, 10.
    Exams:
    Midterm 1:  Feb 1, Mon in class. Covers Section 1.1-1.5, 1.7-1.9 and 2.1-2.3. No cheat sheets or calculators allowed.   

    Here is the Midterm I Solutions.    Here is the grade distribution for Midterm 1. Mean: 32/50, Median: 33/50.

    Grades: A+: >47, A: 41-47, A-: 40, B+ 38-39, B: 33 - 37, B-: 30-32, C+: 28-29, C:25-27, C-: 23-24, D: 18-22, F: < 18

    Sample Miterm 1 and Solutions      

    Midterm 2:  March 1, Mon in class. Covers Sections 3.1-3.3 and 4.1-4.7.    Here is a Sample Midterm 2 and Solutions   

    Here is the Midterm 2 Solutions. Here is the grade distribution for Midterm 2. Mean = 25.5/50, Median: 26/50

    A+ : > 44, A: 37-44, A-: 35-36, B+: 32-34, B: 26-31, B-: 24-25, C+: 23, C: 20-22, C-: 18-20, D: 13-17, F: < 13


    Final: March 19, Fri, 8-11am. Covers Sections 1.1-1.9 (excluding 1.6), 2.1-2.3, 3.1-3.3, 4.1-4.7, 5.1-5.4 and 6.1-6.4.     

    Here is a sample final and the Solutions   

    Grading: Homework: 15%,   2 midterm exams: 15% each,   Mathlab: 10%   final exam: 45%. (The lowest homework score will not be counted. Missed exams will count zero.)

    Approximate Lecture Schedule (may be updated during the course):

     wk  date  Monday  Wednesday  Friday
      1  1/4   Sect 1.1: Linear Equations   Sect 1.2: Row Reduction   Sect 1.3: Vector Equations
      2  1/11   Sect 1.4: Matrx Equation   Sect. 1.5: Solutions of linear Equations   Sect. 1.7: Linear Independence
      3  1/18   MLK Day   Linear transformations   Matrix of linear transfromation
      4  1/25   Sect 2.1: Matrix operations   Sect 2.2 and 2.3: Invertible matrices   Sect 3.1: Determinants
      5  2/1   Exam   Sect 3.2: Properties of determinants   Sect 3.3: Volume and linear transformation
      6  2/8   Sect 4.1: Vector spaces   Sect 4.2: Nullspace, Column space and linear maps   Sect 4.3 and 4.5: Linear independence, bases and dimensions
      7  2/15   President's Day   Sect 4.6: Rank   Sect 4.4 and 4.7: Coordinate systems and change of basis
      8  2/22   Sect 5.1: Eigenvalues and eigenvectors   Sect 5.2: Characteristic equation   Sect. 5.3 and 5.4: Diagonalization and Linear maps
      9  3/1   Exam   Sect 6.1: Inner products and Lengths   Sect 6.2 and 6.3 Orthogonality and projections
     10  3/8   Sect 6.4: Gram-Schmidt   Sect 6.5: Least Squares   Sect 7.1: Symmetric matrices
     11  3/15      3/19  Final Exam