Textbook: Linear Algebra and Its Applications, by David C. Lay
Topics to be covered:
Finite-dimensional vector spaces over R (real numbers) and C (complex numbers) presented from two view points: axiomatically and with coordinate calculations.
Linear transformations, matrices, rank, determinant, eigenvalues, eigenspaces.
Systems of linear equations.
Examples and applications.
Schedule and Homework assignments
Grading policy:
Attendance 20%
Homework 30% (Weekly homework will be due Thirsday of each week)
Midterm 20% (July 27)
Final 30% (August 13)
Instructor: Maria Voloshina
Office: Hylan 805
Office hours: M 16:00-17:30, W 11:30-13:00 and by appointment
Email: voloshin@math.rochester.edu
Webpage: http://www.math.rochester.edu/u/voloshin/
Webpage for Math 235: http://www.math.rochester.edu/u/voloshin/math235.html
July 6-8, 12
Chapter 1. Linear Equations in Linear Algebra
(Systems of linear equations. Row reduction and echelon forms. Vector equations. The matrix equation Ax=b. Solution set of linear systems. Linear independence. Introduction to linear transformations. The matrix of a linear transformation)
July 13-15
Chapter 2. Matrix Algebra
(Matrix Operations. The inverse of a Matrix. Characterizations of invertible matrices. Partitioned Matrices. Subspaces of R^n)
Review
July 19-20
Chapter 3. Determinants
(Introduction to determinants. Properties of determinants. Cramer's Rule, Volume, and Linear transformations)
Exercises. Practice midterm.
July 21-22, 26-27
Chapter 4. Vector Spaces
(Vector spaces and subspaces. Null spaces, Column spaces, and Linear transformations. Linearly independent sets. Bases. Coordinate systems. The dimention of a vector space. Rank. Change of basis)
Midterm (July 27)
July 28-29, August 2
Chapter 5. Eigenvalues and Eigenvectors
(Eigenvectors and eigenvalues. The characteristic equation. Diagonalization. Eigenvectors and linear transformations. Complex eigenvalues)
Review
August 3-5
Chapter 6. Orthogonality and Least-Squares
(Inner product, length, and orthogonality. Orthogonal sets. Orthogonal projections. The Gram-Schmidt process. Least-Squares problems. Inner product spaces)
August 9-12
Chapter 7. Symmetric Matrices and Quadratic Forms
(Diagonalization of symmetric matrices. Quadratic forms)
Exercises. Review. Applications. Practice Final.
August 13
Final examination
Assignment 1, due July 15
1.1 (p.10) #1; 1.2 (p.25) #5a, 7, 17; 1.3 (p.37) #5, 11; 1.4 (p.46) #3, 17;
1.5 (p.55) #1; 1.6 (p.64) # 5, 13; 1.7 (p.74) #11, 17; 1.8 (p.83) #1
Assignment 2, due July 22
2.1 (p.107-108) #1, 10; 2.2 (p.117) #4, 33; 2.3 (p.123) #2, 4, 23; 2.4 (p.130) #3;
2.9 (p.174) #5, 16; 3.1 (p.185) #6, 18; 3.2 (p.193) #5, 21
Assignment 3, due July 29
3.3 (p.204) #2, 22; 4.1 (p.217) #8, 11; 4.2 (p.228) #3; 4.3 (p.237) #3, 33;
4.4 (p.248) #6, 9; 4.5 (p.255) #11; 4.6 (p.263) #6, 13
Assignment 4, due August 5
4.7 (p.270) #6, 9; 5.1 (p.303) #7, 12; 5.2 (p.311) #5, 10, 21;
5.3 (p.319) #1, 7; 5.4 (p.327) #2, 6, 11; 5.5 (p.335) #3, 22
Assignment 5, due August 12
6.1 (p.376) #9, 24; 6.2 (p.387) #10, 13; 6.3 (p.395) #4, 15; 6.4 (p.403) #7, 14;
6.5 (p.411) #2; 6.7 (p.430) #1, 4, 16; 7.1 (p.448) #27; 7.2 (p.457) #3