Math 54: Honors Linear Algebra

First Day Handout

Links to textbooks:

Linear Algebra Done Wrong (W)

Linear Algebra Done Right (R)

NEW: Course Reserves

NEWER: Math Resource Center

Syllabus/Reading/Assignments:

Date Read ahead: Homework due: Topics covered or to be covered (approx.)
9/2   Math interests survey Vector spaces & subspaces def. and examples
9/7

R: p. 1-14; W: p. 6-11

 W: p5 (1.2 &1.4); R: p19 (5-9) Linear independence, span, bases, dimension
9/9 R: p. 37-41   Bases cont., definition of linear map
9/14 R: p. 41-47, W: 12-22

W: p11 (2.2 c,d,e & prove a)
R: p35 (4, 8, 9); lec: Prop. 3a

 Linear maps as matrices, composition and matrix multiplication
9/16 W: 22-30, Sec. 8 highly recmd.   Linear map properties, fundamental subspaces
9/21 W: 39-45

W: p16-17 (3.1c, 3.3a,b,c,d)
W: p23 (5.1a, 5.5, 5.7)
R: p59 (2, 5, 7); handout

 Linear systems & Gaussian elimination
9/23 W: 46-52   Gaussian elimination
9/28 W: 52-59 W: p46 (2.1, 2.2),
p51 (3.1, 3.2, 3.8, 3.9)		 Fundamental subspaces & rank theorem
9/30 W: 59-68   Inverses, change of bases
10/5     Mini-midterm (solutions)
10/7     Invariant subspaces, eigenvalues & eigenvectors
10/12 R: Chapter 5 (76-91)   Upper-triangular & diagonal matrices
10/14 R: Chapter 5 (91-93) R: Ch. 1 (1, 2-optional, 15);
Ch 2 (12); Ch. 3 (8);
Ch. 5 (3, 5, 9, 10)		 Upper-triangular & diagonal matrices
10/19     Upper-triangular & diagonal matrices
10/21 Notes shared by Joy Ko
W: 99-103		   Determinants & finding eigenvalues
10/26     Midterm review
10/28     Midterm (solutions)
11/2  

 

 Determinants & finding eigenvalues
11/4 W: 115-122 W: p85 (3.1, 3.3 (any method), 3.5, 3.6, 3.7); p103 (1.2); p112 (2.3, 2.9) Determinants & finding eigenvalues
11/9 W: 115-122   Inner products and norms
11/11 W: 123-132   Gram-Schmidt orthogonalization
11/16 W: 133-138 (rec: R Ch. 6)

W: p122 (1.2, 1.6, 1.7, 1.9);
W: p132 (3.4); R: Ch. 6 (1)

Least squares approximation
11/18 W: 138-144 (rec: R Ch. 6)   Adjoint
11/23 W: 144-148 W: p132 (3.2, 3.6); p138 (4.2, 4.3); R: Ch. 6 (10) Isometries & rigid motions
11/25     HOLIDAY
11/30 W: 157-159   Schur representation
12/2 W: 159-162 (rec: R 128-137) (Due Friday) R: Ch 6 (2, 18); W: p141 (5.1, 5.3);
p147 (6.5,6.8,6.9); p149 (7.1)		 Spectral theorem
12/7     Flexible
12/10     Final exam: 2:00 - 5:00 PM
       
       
       

 

 

l>