## AMS 210.03 - APPLIED LINEAR ALGEBRA

### Spring 2020

Instructor: Yan Yu
Office: Math Tower Room 1-104
Lecture: Tu/Th 8:30am-9:50am; Humanities 1006
Office Hours: Tu/Th 11:00am-12:00pm Math Tower 1-104
Email: yan.yu@stonybrook.edu
Course Info: An introduction to the theory and use of vectors and matrices. Matrix theory including systems of linear equations. Theory of Euclidean and abstract vector spaces. Eigenvalues and eigenvectors. Linear tranformations.
Textbook: Introduction to Linear Algebra: Models, Methods, and Theory ; Alan Tucker
Course Outline:
Ch Topics
1 Introductory Models
2 Matrices
3 Solving Systems of Linear Equations
4 Applications
5 Theory of Systems of Linear Equations
Learning Outcomes:
• Become familiar with a diverse set of linear models and use them to interpret theory and techniques throughout the course:
• a system of 3 linear equations in 3 unknowns;
• a Markov chain model;
• a dynamic (iterative) linear systems of equations;
• a general equilibrium model.
• Compute and apply basic matrix-vector operations:
• scalar products;
• matrix-vector products;
• matrix multiplication.
• Demonstrate diverse uses of scalar and vector measures of a matrix
• matrix norms;
• dominant eigenvalue and dominant eigenvector.
• Solve a system of linear equations using:
• Gaussian elimination;
• determinants;
• matrix inverses;
• iterative methods;
• least squared approximate solutions using pseudo-inverses.
• Demonstrate how Gaussian elimination determines if a system of linear equations is:
• overdetermined;
• underdetermined and how to determine the family of solutions;
• uniquely determined and find the solution.
• Apply basic ideas of numerical linear algebra:
• computational complexity of matrix operations;
• LU decomposition;
• using partitioning to simplify matrix operations;
• ill-conditioned matrices and the condition number of a matrix.
• Learn and use basic theory about the vector spaces associated with a linear transformation:
• linear independence;
• the null space;
• the range space;
• orthonormal spaces.
• Examine a sampling of linear models, chosen from linear regression, computer graphics, markov chains, and linear programming.
• Strengthen ability in communicating and translating of mathematical concepts, models to real world settings:
• present solutions to problems in a clear, well-laid out fashion;
• explain key concepts from the class in written English;
• convert problems described in written English into an appropriate mathematical form;
• convert the mathematical solutions into a written answer.
Exams: Midterm-1 Tuesday, 3/3/2020
Midterm-2 Tuesday, 4/14/2020
Final Tuesday, 5/12/2020, 11:15am - 1:45pm
E-mail: darya.stepanenko@stonybrook.edu
Office Hours: W 4-6pm
Office Hours Room: Harriman Hall 132

Joanna Siemion
E-mail: joanna.siemion@stonybrook.edu
Office Hours: Th 4-6pm
Office Hours Room: Harriman Hall 132

Yizhou Yu
E-mail: yizhou.yu@stonybrook.edu
Office Hours: Tu 2-4pm
Office Hours Room: Harriman Hall 132

Michael Fink
E-mail: michael.fink@stonybrook.edu
Office Hours: M 4-6pm
Office Hours Room: Harriman Hall 132

Policies
• Homework assignments given regularly on Blackboard; due at the beginning of class on the due date. For full credit, please write down all intermediate steps needed, not just final answers.
• Late homework is an automatic zero.
• All exams are closed book and closed notes. No phones are allowed.
• Exams will start at the beginning of class; come early so you are prepared.
• All exams will be held in regular classroom, unless stated otherwise.
• 20% Homework - The lowest homework grade will be dropped
• 25% Midterm-1
• 25% Midterm-2
• 30% Final
Lower Division Upper Division
A's 25% 30%
B's 30% 35%
C's 25% 25%
D's 10% 5%
F's 10% 5%
Academic Integrity Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Any suspected instance of academic dishonesty will be reported to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/
Disability Act: If you have a physical, psychological, medical or learning disability that may impact on your ability to carry out assigned course work, I would urge that you contact the staff in the Disabled Student Services office(DSS), Room 133, Humanities, 632-6748/TDD. DSS will review your concerns and determine with you what accommodations are necessary and approciate. All information and documentation of disability are confidential.
Critical Incident Management: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures.
Homework Homework # 1 - Due: 2/11/2020
1.1: 9, 14, 22 (integer solutions only)
1.2: 4, 6a
1.3: 3cd, 5ac, 8 (rat doesn't stay in the room)

Homework # 2 - Due: 2/18/2020
2.1: 2, 12bd
2.2: 10, 18, 22
2.3: 1c, 2e, 3e

Homework # 3 - Due: 2/25/2020
2.4: 1, 2, 6ac, 10cd
2.5: 2d, 10ab, 26c, 28c

Homework # 4 - Due: 3/12/2020
2.6: 6b, 7, 9
3.1: 2b, 23(for (i), (iii), (v))

Homework # 5 - Due: 3/31/2020
3.2: 2, 3d, 5 (for 3d), 6 (for 3d)
3.3: 5a, 7d, 18

Homework # 5 - Due: 4/7/2020
3.3: 33ac, 34 (for 33ac)
3.4: 8a, 11(i)
3.5: 18, 19cd, 22ab

Homework # 7 - Due: 4/23/2020
4.2: 2, 5
4.4: 1, 8, 18, 22