Math 3110, Spring 2014

"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)

Resources

• Class Syllabus

• Text: Introduction to Linear Algebra, 4th edition, by Gilbert Strang.

• The author, Professor Gilbert Strang of MIT taught Linear Algebra in the Fall of 2011 out of his textbook. The lectures were videotaped and are part of the MIT OpenCourseWare (OCW) project.

• Course structure: This will be a "half-flipped" course. Students will be required to watch roughly one video lecture a week on their own time. To make up for this, roughly one in-class period a week will be allocated as an interactive problem solving session, with a special focus on homework problems.

• A wonderful video lecture on the Overview of the key ideas of linear algebra by Gil Strang.

• Math 3110 course schedule.

Homework

Homework 1: pdf | tex. Due Friday, January 17th.
Homework 2: pdf | tex. Due Friday, January 24th.
Homework 3: pdf | tex. Due Friday, January 31st.
Homework 4: pdf | tex. Due Friday, February 7th.
Homework 5: pdf | tex. Due Friday, February 14th.
Homework 6: pdf | tex. Due Friday, February 21st.
Homework 7: pdf | tex. Due Friday, February 28th.
Homework 8: pdf | tex. Due Friday, March 7th.
Homework 9: pdf | tex. Due Friday, March 14th.
Homework 10: pdf | tex. Due Friday, March 28th.
Homework 11: pdf | tex. Due Friday, April 4th.
Homework 12: pdf | tex. Due Friday, April 11th.
Homework 13: pdf | tex. Due Friday, April 18th.
Homework 14: pdf | tex. Due Friday, April 25th.

Exams

• Practice Midterm 1 (Fall 2012).
• Practice Midterm 2 (Fall 2012).
• Midterm 1
• Midterm 2

Lecture notes

Part I: Solutions of linear equations and vector spaces

1. Geometry of linear equations. Strang: Lecture 1, Sections 1.1, 1.2, 2.1.
2. Elimination with matrices . Strang: Lecture 2, Sections 2.2, 2.3.
3. Multiplication and inverse matrices. Strang: Lecture 3, Sections 2.4, 2.5.
4. LU-factorization. Strang: Lectures 4 & 5 (1st half), Sections 2.6, 2.7.
5. Vector spaces, column space, and row space. Strang: Lectures 5 (2nd half) & 6, Sections 3.1, 3.2.
6. Solving Ax=0: Pivot and free variables. Strang: Lecture 7, Section 3.2.
7. Solving Ax=b: Homogeneous and particular solutions. Strang: Lecture 8, Sections 3.3, 3.4.
8. Linear independence, spanning sets, and bases. Strang: Lecture 9, Section 3.5.
9. The four fundamental subspaces. Strang: Lecture 10, Section 3.6.
10. Other vector spaces. Strang: Lecture 11, Section 3.2.
11. Application: Graphs and networks. Strang: Lecture 12, Section 8.2.

Part II: Orthogonality, determinants, and eigenvectors

1. Orthogonality. Strang: Lecture 14, Section 4.1.
2. Projections. Strang: Lecture 15, Section 4.2.
3. Least squares. Strang: Lecture 16, Section 4.3.
4. Orthogonal bases and Gram-Schmidt. Strang: Lecture 17, Section 4.4.
5. Determinants. Strang: Lecture 18, Section 5.1.
6. Formulas for determinants. Strang: Lecture 19, Section 5.2.
7. Applications of determinants. Strang: Lecture 20, Section 5.3.
8. Eigenvalues and eigenvectors. Strang: Lecture 21, Section 6.1.
9. Diagonalization. Strang: Lecture 22, Section 6.2.
10. Application: Markov chains. Strang: Lecture 24 (1st part), Section 8.3.
11. Application: Fourier series. Strang: Lecture 24 (2nd part), Section 8.5.

Part III: Positive definite matrices and applications

1. Symmetric matrices. Strang: Lecture 25 (1st part), Section 6.4.
2. Positive definite matrices Strang: Lectures 25 (2nd part) & 27, Section 6.5.
3. Complex matrices. Strang: Lecture 26, Section 10.1, 10.2, 10.3.
4. Similar matrices and Jordan canonical form. Strang: Lecture 28, Section 6.6.
5. Singular value decomposition. Strang: Lecture 29, Section 6.7.
6. Linear transformations. Strang: Lecture 30, Section 7.1, 7.2.
7. Change of basis. Strang: Lecture 31, Section 7.2, 7.3.
8. Left, right, and pseudoinverses. Strang: Lecture 32, Section 7.2, 7.3.