Prerequisites: This course has as a prerequisite credit of MATH 234 or cons inst.
Lecture Meetings (3 Credits): Lectures will meet MWF 7:45-8:35AM in 6102 Sewell Social Sciences. Attendance is encouraged.
Contact: Aaron Goldsmith, Dept. of Mathematics.
Email: asgoldsmith@math.wisc.edu
Office Hours: on T 9:30-11:00, 2:00-3:30
Course Description: This is an honors course and is meant to provide instruction on how to write and understand proofs, while covering similar topics as Math 340. After completing Math 341, students should be prepared to take proof-based courses at the 5XX level. This course is designated a "writing-intensive" course. Alternatives: Math 340 for less theoretical students, Math 375 for Honors students as part of the calculus sequence.
Text: Linear Algebra, 4th edition, by S.H. Friedberg, A. J. Insel, and L. E. Spence.
Syllabus: We will cover most of Chapters 1-6.
Course Learning Objectives:
- Give precise definitions of linear algebraic concepts such as the trace of a square matrix, the definition of a symmetric matrix.
- Prove that a given set is a basis for a vector space.
- Prove or disprove that a given subset is a subspace of a vector space.
- Use properties of a linear transformation in proofs.
- Find a change of basis matrix.
- Solve systems of linear equations.
- Find the basis for the nullspace and range of a linear transformation.
- Use theorems about the number of solutions of a system of linear equations.
- Give precise definitions of minors and cofactors of a matrix.
- Compute the determinant of a matrix using various methods such as a formula, row operations, and cofactor expansion.
- Give precise definitions of eigenvalues/eigenvectors.
- Find eigenvalues/eigenvectors.
- Give precise definition of T-invariant subspaces.
- Prove that given subspaces are T-invariant.
- Give precise definition of an inner product.
- Use Gram-Schmidt process to find an orthonormal basis.
- Prove properties of finite-dimensional inner product spaces.
- Use the rank-nullity theorem to compute dimensions and to prove theorems.
- Give precise definitions of one-to-one and onto transformations.
- Know properties of diagonalizable matrices.
- Diagonalize matrices.
Grading: A numerical score for this course will be determined from the following components.
- Midterm exams(16% each). There will be two in-class midterms on the Wednesday before Spring break (03/21) and before the final (05/02). More information will appear on the Exams page as it becomes available.
- Final exam(34%). The final exam will be on 5/8/2018 at 10:05 (room TBD). More information about the final exam will be posted in the Exams page as it becomes available.
- Homework(34%). Each Friday, I will post homework which will be due on the next Friday in class. If you want, you can turn them in to my mailbox early in the hallway of Van Vleck 2nd floor.
Grades will be kept as up to date as possible and posted online through Canvas.
Policies and other practical matters:
- Placement, Enrollment, Waitlist, &c: For assistance in these matters after please visit https://www.math.wisc.edu/placement. Note that this page also includes a link to contact information.
- Attendance: Attendance will not be recorded, but is encouraged. Students are responsible for all material covered in a missed lecture.
- Missed Exams: Make ups for missed exams will be offered only in exceptional circumstances. Students with a valid conflict which would prevent them from sitting for an exam should contact me WELL BEFORE the exam date.
- Academic Honesty: Your integrity is your own. Do not squander it. Information regarding academic honesty is available here.
- Academic Assistance: Information about various academic assistance programs can be found in the math department.