MthSc 853, Spring 2011
# MthSc 853, Spring 2011

"You see this little hole? This moth's just about to emerge. It's in
there right now, struggling. It's digging it's way through the thick
hide of the cocoon. Now, I could help it - take my knife, gently widen
the opening, and the moth would be free - but it would be too weak to
survive. Struggle is nature's way of strengthening it."

--Locke (*Lost*, 2004)

Class
Syllabus

### Lecture Notes

Section 1:
Vector spaces. (11 pages. Updated Jan 24, 2011)

Section 2:
Duality. (7 pages. Updated Jan 31, 2011)

Section 3:
Linear mappings. (14 pages. Updated Feb 14, 2011)

Section 4:
Matrices. (11 pages. Updated Feb 14, 2011)

Section 5:
Determinant and trace. (15 pages. Updated March 2, 2011)

Section 6:
Spectral theory. (22 pages. Updated March 3, 2011)

Section 7:
Euclidean structure. (18 pages. Updated March 29, 2011)

Section 8:
Self-adjoint mappings. (13 pages. Updated April 11, 2011)

Section 9:
Calculus in vector spaces. (12 pages. Updated April 21, 2011)

Section 10:
Positive definite mappings. (14 pages. Updated April 29, 2011)

### Homework

Homework 1. Due
Tuesday, January 25, 2011

Homework 2. Due
Wednesday, February 2, 2011

Homework 3. Due
Monday, February 7, 2011

Homework 4. Due
Monday, February 14, 2011

Homework 5. Due
Monday, February 21, 2011

Homework 6. Due
Wednesday, March 2, 2011

Homework 7. Due
Wednesday, March 9, 2011

Homework 8. Due
Wednesday, March 16, 2011

Homework 9. Due
Friday, April 1, 2011

Homework 10. Due
Monday, April 11, 2011

Homework 11. Due
Wedsesday, April 20, 2011