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.