MAT204 Advanced Linear Algebra with Applications

Schedule: MWF at 11AM or at 1:30PM, Spring Only. 

Brief Course Description: A more abstract treatment than 202, but more concrete than 217. Topics include linear systems of equations, linear independence and dimension, linear transformations, determinants, real and complex eigenvectors and eigenvalues, orthogonality, spectral theorem, singular value decomposition, Jordan normal forms. The course will present various applications of linear algebra in graph and network theory, cryptography, image compression, probability and statistics, machine learning, principal component analysis, linear, constrained, and regularized least-square optimization, ranking algorithms (least-squares, Google page rank), and SVD-based recommendation engine (Netflix). Compared to 202 the course requires more curiosity and greater independence as well as thorough conceptual understanding and computational fluency. 

Why take this course?  204 is more in-depth and abstract than 202; It will be a first introduction to mathematical proofs for most students. Many interesting applications are illustrated in weekly problem sets and optional MATLAB exercises. Its homework and exam problems often require greater fluency in mathematical computations and sophistication in mathematical thinking. For most students, MAT202 is an excellent course that provides enough challenge and the background needed for upper division quantitative work. 

Who takes this course? Most students in this course will be continuing from 203 in the Fall, and some are first-year students who took 215 or 216 in the Fall. Very strong students from 104 and 201 have also been successful in MAT204. Most students in this course have strong mathematical interest and maturity and intend to major in physics or engineering with a strong interest in applied math.   

Prerequisites & Placement Info:  While calculus is not a strictly required in this course, you will need to have the mathematical maturity and independence that most students acquire by studying calculus in courses like 203. The course moves rapidly and will require a serious amount of time and effort. Because the course is more algebraic and abstract compared to calculus, many students find it difficult in a new way. It is quite difficult to judge how much time you will need to master the more abstract aspects of the course. For many students, this is a big adjustment, and quite unlike the math courses you have taken before. So be prepared to invest a lot of time early on to learn how to think about proofs and counterexamples. Because of its greater abstraction, 204 will give you a better sense of what it is like to be a math major than 203.

Work Load: MAT204 covers a few more topics and many more applications than MAT202 and it has a significantly higher work load. Weekly precepts will cover more sophisticated examples and interesting applications. Each weekly problem set comprise three parts: a selection of standard exercises, supplementary application problems, and optional MATLAB exercises. Students are expected to read the textbook before each class and review lecture notes after each class. Homework will most likely take at least 6 hours, although this can vary quite a lot depending on your background and goals.  There will be organized homework sessions with guidance from undergraduate course assistants before each problem set is due, but students should first work independently before seeking help from course assistants during homework sessions.  To do well on math exams, you need to work through a lot of extra problems from old exams and quizzes. All in all, you should be ready to spend at least 10 hours per week working outside of class.

Grading: MAT204 is graded with a more generous curve than MAT202 in order to remove considerations of grades as a deciding factor between the two courses. 

FAQ: 

• You already took linear algebra in high school or at a local college, so you want to place out of MAT202/204.  Some students in MAT202/204 have had linear algebra before, but very rarely with the same depth and thoroughness.  Most students will find that the sample problems are much more sophisticated than problems they have encountered in high school. 

• You think MAT204 is too hard after looking at the sample problems or attending the first couple classes.  There is a lot of overlap between MAT202 and MAT204, so it is quite easy to switch between the two courses in the first few weeks.  You may prefer the pace and style of MAT202.  For most engineering majors, MAT202 is an equally good choice of linear algebra course and will give you all the background you need for upper division courses in other quantitative disciplines.

• You think MAT204 is not challenging enough.  Wait till you have had a quiz, which usually occurs in the 3rd week.  Try some old quizzes for this course, but don’t just read the questions and solutions. Instead see if you can produce correct solutions to most of the problems in the allotted time.  If you can do well on old exams, then you may consider taking MAT217, but first check out MAT215.  You should have some solid experience writing proofs to do well in MAT217.