Fall-2015. Math H110 (ccn 54227): Linear Algebra

Instructor: Alexander Givental
Lectures: TuTh 11-12:30, 3 Evans
Office hours: W 4:30-6 and Th 2-3:30, in 701 Evans
Textbook: Linear Algebra by Alexander Givental
This is an unpublished (and yet unfinished) textbook, which will be made freely available online. The previous version (which is to evolve during the semester) can be found here.

Grading policies:

Homework 30%, Quizzes 30%, Final 40%
The general idea is that you don't compete with each other. Your goal should be to learn the material as well as you can, and if all of you do really well, all will get an "A". What exactly it means to learn well will become more clear during the semester (probably after some quizzes).

THE TEXT

Chapter 1. Introduction
Chapter 2. Dramatis Personae
Chapter 3. Simple Problems
Chapter 4. Eigenvalues
Epilogue: Quivers
Supplements A and B
Supplements C and D
Supplement E
Supplement G
Backmatter

HOMEWORK (due weekly on Th in class), topics of QUIZZES (usually given on Tu), and READING assignments:

QZ 1, Sep 1 (Tu): Supplement B: Complex Numbers.
Read: Supplement B (by Tu), and from Ch1. Sections 1 and 2 by Th.
HW1, due Th, Sep 3: Solve exercises of Section 1 of Ch. 1; write down solutions to the exercises 7,11,14,16,20, and submit them for grading.

Read: Sections 1-3 of Ch. 1, Supplement A (Vectors in Geometry). Over the Labor Day weekend, try to solve all exercises from Supplement A.
On Tue, Sep. 8 we will have a problem-solving session where I may ask you to present your solutions at the blackboard.
QZ 2. Sep. 8: In the spirit of exercises from Section 2, i.e. on classification of quadratic curves and quadratic forms on the plane.
HW 2, due Th, Sep.10: 33, 35, 46, 47, 49.

Read: Section 1 of Ch. 2, Supplements C and D.
QZ 3, Tu, Sep. 15: Definition and examples of vector spaces (and fields).
HW3, due Th, Sep. 17: 65, 71, 77, 402, 413.

Read: Pages 33-41 (Section 2 from Chapter 2).
QZ 4, Tu, Sep. 22: "Matrices" (pages 33-39) and corresponding exercises.
HW4, due Th, Sep. 24: 88, 93, 105, 106, 107.

Read: Section 3 (Determinants).
QZ 5, Tu, Sep. 29: Properties of permutations.
HW5, due Th, Oct. 1: 117, 135, 136, 137, 138.

Read: Supplement E (Quaternions) SEction 3 (Determinats)
QZ 6, Tu, Oct. 6: The three "cool formulas"
HW6, Th, Oct. 8: 145, 152, 153, 154, 156

Read: Sections 1,2 (Rank, Gaussian elimination) of Chapter 3.
QZ 7, Tu, Oct. 13: Dimension counting.
HW7, due Th, Oct. 15: 162, 164, 167, 172, 175.

Read: pp. 79--89.
QZ 8, Tu, Oct. 20: LPU-factorization.
HW8, due Th, Oct. 22: 174 (the last system), 176 (b), 177(b), 184, 185.

Read: pp. 87-96.
QZ 9, Tu, Oct. 27: Classification of quadratic forms and conics over complex numbers.
HW9, due Th, Oct. 29: 186, 189, 190, 198, 208.

Read: Supplement G; Ch.4: pages 99-102.
QZ 10, Tu, Nov.3: (Anti-)hermitian quadratic forms, their classification, and inertia indices.
HW10, due Th, Nov. 5: 196, 209, 210, 213, 425 (from Supplement G).

Read: pp. 99-112.
QZ 11, Tu, Nov. 10: Hermitian spaces.
HW11, due Tu, Nov. 17: 228, 231, 241, 242, 250.

Read: pp. 111-119.
QZ 12, Tu, Nov. 17: The complex and real spectral theorems, and their applications to Hermitian, anti-Hermitian, unitary, symmetric , anti-symmetric and orthogonal transformations.
HW12, due Tu, Nov. 24: 252, 264, 267, 276, 283.

Read: pp. 117-123 (by Tu, Nov. 24) pp. 127-137 (by Tu, Dec. 1)
QZ 13, Tu, Nov. 24: Courant-Fisher minimax principle
HW13, due Th, Dec. 3: 291, 292, 295bc, 299, 303

Read: pp. 139-148.
QZ 14, Th , Dec. 3: Nilpotent operators.
HW14, due Th, Dec. 10: 305, 308, 310, 313, 314(g)
Past final exams in Math 110
Read: Quivers
QZ 15, Tu , Dec. 8: High order linear ODEs.
Solutions to the final exam