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:
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
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 |