Textbook: Axler, Sheldon, Linear Algebra done right, 2nd Edition, Springer ISBN
... Structure: This course is primarily aimed at math majors and students ...
Elementary Linear Algebra (Math 515) Class meeting times: TU 1:05‐2:30, Cardwell 130 Instructor: Ricardo Castano‐Bernard, e‐mail:
[email protected] Office Hours: CW 46C, TU by appointment Textbook: Axler, Sheldon, Linear Algebra done right, 2nd Edition, Springer ISBN 0‐387‐98258‐2 Structure: This course is primarily aimed at math majors and students interested in the theoretical foundations of Linear Algebra. In particular, the material will be introduced from an abstract perspective. Students should expect to be exposed to the structure of mathematical reasoning in the form of definitions, theorems and proofs. Homework and exam problems will often require students to write mathematically coherent statements, often substantiated by proofs. Students wanting to have a more computational introduction to Linear Algebra are encouraged to take, eg, Applied Matrix Theory (Math 551) instead. Course Prerequisites: Calculus III (Math 222) Grading: There will be 3 midterm exams: 100 points each. Weekly homework: 10 point each. Homework will be assigned on Thursday each week and will be due on the following Thursday (during class). In addition, students will occasionally be required to post solutions to homework problems on the board; meaningful oral presentations may be regarded as extra credit. Tentative grading scale: 90, 80, 70, 60, 50% corresponds to letter grades A, B, C, D, F respectively. Exam makeups and late homework: there will be no make‐up exams and late homework will not be accepted. If you expect to miss an exam, please notify me. If you miss an exam due to an emergency and you provide documented evidence justifying your absence (e.g. due to medical emergency, provide an MD signed note), your missed exam score will be the average score of the other two. Boiler plate: Statement Regarding Academic Honesty: Kansas State University has an Honor System based on personal integrity, which is presumed to be sufficient assurance that, in academic matters, one's work is performed honestly and without unauthorized assistance. Undergraduate and graduate students, by registration, acknowledge the jurisdiction of the Honor System. The policies and procedures of the Honor System apply to all full and part‐time students enrolled in undergraduate and graduate courses on‐campus, off‐campus, and via distance learning. The honor system website can be reached at http://www.ksu.edu/honor. A component vital to the Honor System is the inclusion of the Honor Pledge which applies to all assignments, examinations, or other course work undertaken by students. The Honor Pledge is implied, whether or not it is stated: "On my honor, as a student, I have neither given nor received unauthorized aid on this academic work." A grade of XF can result from a breach of academic honesty. The F indicates failure in the course; the X indicates the reason is an Honor Pledge violation.
In this class, you are authorized to work together on homework, as you see fit unless otherwise instructed on that particular assignment. You will be asked to sign the honor pledge on assignments where you are required to work alone, such as exams. Statements for Academic Accommodations for Students with Disabilities: Any student with a disability who needs a classroom accommodation, access to technology or other academic assistance in this course should contact Disability Support Services (dss@k‐state.edu) and/or the instructor. DSS serves students with a wide range of disabilities including, but not limited to, physical disabilities, sensory impairments, learning disabilities, attention deficit disorder, depression, and anxiety." Statement Defining Expectations for Classroom Conduct: All student activities in the University, including this course, are governed by the Student Judicial Conduct Code as outlined in the Student Governing Association By Laws, Article VI, Section 3, number 2. Students who engage in behavior that disrupts the learning environment may be asked to leave the class. Statement for Copyright Notification: This syllabus and all lectures and class materials are copyrighted. During this course students are prohibited from selling notes to or being paid for taking notes by any person or commercial firm without the express written permission of the professor teaching this course. Campus Safety Statement: Kansas State University is committed to providing a safe teaching and learning environment for student and faculty members. In order to enhance your safety in the unlikely case of a campus emergency make sure that you know where and how to quickly exit your classroom and how to follow any emergency directives. To view additional campus emergency information go to the University's main page, http://www.k‐state.edu, and click on the Emergency Information button.
Elementary Linear Algebra (Math 515) Tentative Lecture Schedule: Week 1: Vector spaces; properties; Week 2: Subspaces; sums and direct sums. Week 3: Span and linear independence; bases; dimension. Week 4: Linear maps; examples; null spaces and ranges; Week 5: The matrix of a linear map; invertibility. Exam 1: Thursday February 21, 1:052:20 CW 130 Week 6: Polynomials. Week 7: Invariant subspaces; eigenvalues and eigenvectors; polynomials applied to operators. Week 8: Triangular matrices; diagonal matrices Spring Break Week Week 9: Inner products, norms, orthonormal basis, projections; optimization problems Week 10: Linear functionals and adjoints. Exam 2: Thursday April 4, 1:052:20 CW 130 Week 11: Self‐adjoint and normal operators Week 12: The Spectral Theorem Week 13: Operators on complex vector spaces Week 14: Characteristic polynomial; decomposition of an operator Week 15: Jordan form. Exam 3: Thursday May 9, 1:052:20 CW 130 This schedule is subject to change
