Math 115A:  Linear Algebra

Tentative Class Schedule


Date  Topic Homework
3/30 (Mon) Sets and functions
Prove that the complex numbers satisfy the axioms of a field.
3/31 (Tues)
Quiz 0

4/1 (Wed) Section 1.2: Vector spaces
Please note that I use the problem numbering from Friedberg, 4th Edition.
Section 1.2: 1,4,8,9,10,11,13,16,20
In Problems 13 and 16, if V is a vector space, then verify all the axioms of a vector space.
4/3 (Fri)  Section 1.3: Subspaces
Section 1.3: 1,6,8,11,15,20,23,24,30
 

4/6
Section 1.4: Linear combinations
Section 1.4: 1,2(a)(c)(e),3(a)(c)(e),7,8,13,14
4/7 (Tues)
Quiz 1
Go to Gradescope to take the quiz between 12:01 am and 11:59 pm Pacific Time on Tues 4/7.  The only things you're allowed to use are: the Friedberg textbook, the class notes/videos, and your completed HW.  You may not discuss the test with anyone and you may not give or solicit help.  Besides the class materials on CCLE, the internet is off limits.  This time you're allowed 50 minutes - about 30 minutes to do the quiz and another 20 minutes to upload your solutions.  Important: Please handwrite your solutions!!!
4/8
Section 1.5: Linear dependence/independence Section 1.5: 1,2(a)(c)(e),4,5,9,15,18
4/10
Section 1.6: Bases and dimension
Section 1.6: 2(a)(c)(e),3(a),6,14,15,17  (We may not get to the definition of dimension until next week; simply take it to be the number of elements of the basis you constructed.)



4/13
Section 1.6: Bases and dimension
Section 1.6: 12,20,24,26,28,33,34
4/14 (Tues)
Quiz 2
Go to Gradescope to take the quiz between 12:01 am and 11:59 pm Pacific Time.
4/15
Section 2.1: Linear transformations
Section 2.1: 7,8,9,14(b),15
4/17
Section 2.1: Linear transformations
Section 2.1: 1,2,5,6,17,24,26,28
 

4/20
Section 2.2: Matrix representation of a linear transformation
Section 2.1: 11,13
Section 2.2: 1,2(a)(c)(f),3,4
4/21 (Tues)
Quiz 3
Go to Gradescope to take the quiz between 12:01 am and 11:59 pm Pacific Time.
4/22
Section 2.2: More on matrix representations
Section 2.3: Composition of linear transformations
Section 2.2: 5,8,10,11
Section 2.3: 2,3
4/24
Section 2.3: More on compositions of linear transformations
Section 2.3: 1,3,4,12,17
 

4/27
Section 2.4: Invertibility and isomorphisms
Section 2.4: 1, 2(a)(c)(e),3,7,14,15,16,17
4/28
(Tues)
No quiz this week

4/29
Section 2.5: Change of coordinates
Section 2.5: 1,2(a)(c),3(a)(c),5,7,10,13
5/1
Midterm Exam

 

5/4
Quotient spaces
1. Complete the proof that the quotient space V/W is a vector space.  Namely, verify the axioms (VS1)-(VS8) that were not verified in class.
2. Complete the proof that if f: V->W is a linear map, then V/Ker f is isomorphic to Im f.
5/5 (Tues)
Quiz 4

5/6
Section 4.4: Review of determinants
Section 4.4: 1,2,3(a)(c)(g),4(a),5,6
5/8
Section 5.1: Eigenvalues and eigenvectors
Section 5.1: 3(a)(b)(c)(d),4(a)(b)(e)
 

5/11
Factoring polynomials
Section 5.1: 7,8,14,15(a),16(a),17,22,23
5/12 (Tues)
Quiz 5

5/13
Section 5.2: Diagonalizability Section 5.2: 1(a)-(g),3(a)(d)(e),8
5/15
Section 5.2: Some applications
Section 5.2: 9(a),10,11,12,19



5/18
Section 5.2: Direct sum decompositions
Section 5.2: 1(h)(i),14,15,20,22
5/19 (Tues)
Quiz 6

5/20
Section 6.1: Inner products
Section 6.1: 1,2,3,4,6,8,9
5/22
Section 6.1: Inner products
Section 6.2: Gram-Schmidt orthogonalization
Section 6.1: 12,16,17,23
Section 6.2: 1(a)(b)(f)(g),2(b)(c)(g)(i)



5/25
University Holiday (Memorial Day)
5/26 (Tues)
Quiz 7

5/27
Section 6.2: Gram-Schmidt orthogonalization
Section 6.2: 4,5,6,7,9,13,19(c),21
5/29
Section 6.3: Adjoints
Section 6.3: 1,2(a)(c),3(a)(c),4,14



6/1
Section 6.4: Self-adjoint and normal operators
Section 6.4: 1,2(a)(c)(d),4,5,9,12,16,20  (Note that we'll discuss normal operators next time)
6/2 (Tues)
Quiz 8

6/3
Section 6.4: Self-adjoint and normal operators
Start doing sample problems for final exam
6/5
Review/summary (we'll do some sample problems)

 

6/9 (Tues)  Final Exam



Last modified: May 31, 2020.