A01: Wednesday 6:00--6:50 pm, AP&M B412 with Scott Fernandez
A02: Wednesday 7:00--7:50 pm, AP&M B412 with Scott Fernandez
A03: Wednesday 4:00--4:50 pm, TM102 1 with Brian Preskitt
A04: Wednesday 5:00--5:50 pm, TM102 1 with Brian Preskitt
Credit Hours: 4 units
Prerequisite: Math 20F or Math 31AH
Catalog Description:Second course in linear algebra from a computational yet geometric point of view. Elementary Hermitian matrices, Schurís theorem, normal matrices, and quadratic forms. Moore-Penrose generalized inverse and least square problems. Vector and matrix norms. Characteristic and singular values. Canonical forms. Determinants and multilinear algebra.
Textbook: Linear Algebra and its Applications, fourth edition, by Strang. International edition shouldn't matter: just make sure you are doing the same problems as everyone else. We will cover most of Chapers 1-6. (See calendar for specific details.)
Course Outcomes: By the end of the course, you should be able to show understanding and mastery of the subject material
- by performing calculations, including knowing which tools to use for which jobs.
- by clearly explaining concepts, definitions and theorems.
- by proving results related to the material.
For this course, the main subject material is
- Vector spaces (defintion, examples, bases, matrices as maps between vector spaces and their subspaces, linear transformations, normed/inner product vector spaces, orthogonality, projections, Gram-Schmidt process)
- Least squares problems (connections to projections, matrix decompositions, generalized inverse/pseudoinverse)
- Determinants (definition, properties, formulas, applications)
- Eigenvalues and eigenvectors (and their connections to the other topics)
- Matrix decompositions (LDU, Schur's theorem, Jordan form/diagonalization and singular value decomposition)
I will focus my teaching, homework and tests on these subjects and outcomes.
Reading: Reading the assigned material in advance of each lecture is expected. This will keep the reading interesting and give the lectures more clarity. Reading the sections of the textbook corresponding to the assigned homework exercises is considered part of the homework assignment. You are responsible for material in the assigned reading whether or not it is discussed in the lecture.
Lecture: Attending the lecture is a fundamental part of the course. You are responsible for material presented in the lecture whether or not it is discussed in the textbook. You should expect questions on the exams to test your understanding of concepts discussed in the lecture and in the homework assignments.
Calculators: A calculator is not particularly needed or expected for this class. If you want, a TI-83 or TI-84 (or similar model) suffices for this course, as would any more powerful calculator (such as a TI-89). The calculator should be used only as an aid in learning concepts, not just as a means of computation. Note: The use of calculators will not be permitted during exams.
Gradescope: All assignments will be turned in via Gradescope.com.
- Your login is your university email, and your password can be changed here. The same link can be used if you need to originally set your password.
- Assignments should be in a single pdf file before being uploaded, or as a picture for each question.
- Hand written files can be scanned to be uploaded. High resolution is not required. However, make sure your files are legible before submitting.
- Most word processors can save files as a pdf.
- There are many tools to combine pdfs, such as here.
- All grading, including the midterms and final, will be done on Gradescope. Regrade requests can be sent via Gradescope.
- If you have not yet been added to the course, the Gradescope entry code is M4JBVM.
Homework: Homework exercises will be assigned on Wednesdays on the course homework page and they are due on the subsequent Wednesday by midnight. There will be about three problems that you will turn in each week. In addition, I will give more suggested problems. These will not be turned in, but you should to do them if you want to succeed in the class. In particular, the graded problems will likely not be enough practice to be able to do the required calculations quickly enough for a test.
Midterm Exams: There will be two midterm exams, one given on Friday, Jan 29 and the other on Friday, Feb 19 during class (see the course calendar). No calculators will be allowed during the midterm exams. One 3x5 notecard can be brought with as many notes as you can fit. Students will not be allowed to take makeup midterm exams. If you will miss an exam for an excellent reason, contact me as soon as possible so that we can make arangements. If you get hit by a bus on your way to the exam, let me know as soon as you can.
Final Examination: The final examination will be held at the following time:
- 8:00am--10:59am Wednesday, March 16 (See the course calendar.)
No calculators or notes will be allowed during the midterms or druing the final examination.
Grading: Assignment grades will be posted on Gradescope. Your term grade will be based on the scores of the homework, two midterms, and one final exam with the lowest homework grade dropped. It will calculated as follows:
- (20% HW) + (20% Midterm) + (20% Midterm) + (40% Final)
I will not determine a curve until after the final exams have been graded. However, I generally curve the exams so that the class average for each is somewhere in the range of 75 to 85%.
Academic Dishonesty: Academic dishonesty is considered a serious offense at UCSD. Students caught cheating will face an administrative sanction which may include suspension or expulsion from the university. It is in your best interest to maintain your academic integrity.
Students with special needs or disabilities must provide an Authorization for Accommodation
(AFA) letter issued by the Office for Students with Disabilities (OSD) as soon as possible.
Please call OSD at 858-534-4382 or visit http://disabilities.ucsd.edu for more information