Overview This is an introductory course to proof-based mathematics. We will be interested in understanding the rigorous foundations of the theory of systems of linear equations, vector spaces, matrices, eigenvalues, and determinants.
Office My office is 446 in the Mathematical Sciences building.
Office hours M 2:30-3:30, W 10:00-11:00, R 4:30-5:30, or by appointment
Text The textbook for this class is Linear Algebra: Ideas and Applications (4th Edition) by Richard C. Penney. The third edition of the book should also suffice.
Academic calendar For ease of reference, here is a link to the academic calendar detailing all breaks, add/drop deadlines, etc.
Accommodations In this mathematics course accommodations are managed between the instructor, student, and DRC Testing Center. Students should see instructors outside class hours, before or after class or during office hours, to share your Accommodation Memorandum for the current semester and discuss your accommodations as soon as possible.
Exams There will be four exams, three in-class exams and one taken during the scheduled final exam period. (See below for schedule and further details.) One exam will be dropped. Please contact me as soon as possible when you become aware of any exam conflicts or if you have missed an exam. All material discussed in lecture or assigned as homework as well as relevant sections of the textbook is fair game for testing.
Homework There will be weekly homework sets. (See below for details and due dates.) Students are encouraged to collaborate on homeworks as long as: 1) all collaborators are listed on the cover sheet of each student's assignment; 2) each student turns in their own, individual work. Rote copying of solutions from peers, or plagiarism of any kind, will not be tolerated.
Homework formatting Homeworks must be typed or neatly written on loose leaf paper (no fringes!). There should be no significant cross-outs, rewrites, scratchwork, scribbling, etc. Problems should be clearly indicated and pages must be securely fastened together. Homework should have a cover sheet attached with your name, course section (either 11 or 21), the homework set number, and the names of your collaborators, in that order.
Late homework Late homework will only be accepted if turned in to me in person during office hours. As part of the conditions of acceptance, you may be asked to present your solution of a problem of my choosing. No penalty will be assessed for assignments which are not excessively late (less than one week past due).
Quizzes There will be several quizzes throughout the semester. Quizzes will be announced at least one class period in advance. One quiz will be dropped, maybe more depending on the total number of quizzes.
Grades After drops, each item in a given category receives equal weighting. Your percentage of points earned in each category will be combined into a single score with weighting 63% on exams, 32% on homeworks, and 5% on quizzes. Grades will be assigned based on rank among all students in both sections. For marginal cases, there will be some discretionary leeway in final grade assignment to account for course participation/engagement or extraordinary effort. The following is a sample cutoff distribution which is fairly typical for courses I have previously taught. The final grade cut-offs may differ slightly. A >92, A- >88, B+ >84, B >77, B- >73, C+>69, C> 64, C- >60.
LaTeX is the language for mathematical typesetting. If you are a CS, Math, or Stats major, I would strongly recommend becoming proficient in LaTeX. Here is the link to A.J. Hildebrand's excellent collection of beginner LaTeX resources. Another great place to start is Jon Peterson's advice and resources for new researchers. You will probably also frequently need to consult the LaTeX Wiki.
Open Source Textbooks in Linear Algebra: A First Course in Linear Algebra by Robert A. Beezer and Linear Algebra by Jim Hefferon. Feel free to peruse and let me know your feedback.
The following is a tentative outline of topics covered and is subject to change. If you are absent from class it is your responsibility to find out what material was covered and to obtain notes from classmates.
Week 1 Linear Systems (1.2); Gaussian Elimination (1.3)
Week 2 Complex Numbers (5.3); Vector Spaces (1.1); Column and Null Spaces (1.4)
Week 3 LABOR DAY; Linear Transformations (3.1); Composition, Kernels, and Images
Week 4 Matrix Multiplication (3.2); Inverses and Isomorphisms (3.3); Linear Dependence (2.1)
Week 5 Linear Dependence (2.1); TEST 1; LU Factorization (3.4)
Week 6 Dimension and Bases (2.2); Rank-Nullity Theorem (2.3)
Week 7 Rank-Nullity Theorem (2.3); Eigenvectors (5.1, 5.3)
Week 8 FALL BREAK; Diagonalization (5.2); Inner Products (6.1)
Week 9 Orthogonality (6.1); TEST 2; Gram-Schmidt (6.2)
Week 10 Gram-Schmidt (6.2); Quadratic Forms (6.6)
Week 11 Quadratic Forms (6.6); Orthogonal Matrices (6.4)
Week 12 Least Squares (6.5); Computing Eigenvalues (8.2)
Week 13 Computing Eigenvalues (8.2); Determinants (4.1); TEST 3
Week 14 Determinants (4.1), THANKSGIVING BREAK
Week 15 Determinants (4.2, 4.3)
Week 16 LEEWAY/REVIEW
Assignment 1, Due: Friday, September 1, in class
Assignment 2, Due: Friday, Sept. 8, in class
Assignment 3, Due: Friday, Sept. 15, in class.
Here is the source file, if you want to type up the homework. Happy TeX'ing!
Assignment 4, Due: Friday, Sept. 29, in class. Source.
Assignment 5, Due: Friday, October 6, in class. Source.
Assignment 6, Due: Wednesday October 18 , in class. Source.
Assignment 7, Due: Friday, October 27, in class. Source.
Assignment 8, Due: Friday, , in class
Assignment 9, Due: Friday, , in class
Assignment 10, Due: Friday, , in class
Assignment 11, Due: Friday, , in class
Assignment 12, Due: Friday, , in class
Quiz 1 , September 6, Solution.
Quiz 2, October 13, Solution.
Wednesday, September 20
Topics: Sections 1.1-1.4, 3.1 in the text as well as related lectures and homeworks.
Wednesday, October 18
Topics: Sections 3.2, 3.3, 3.5, 2.1-2.3, 5.1, 5.3 in the text as well as related lectures and homeworks.
Friday, November 17