# MAT202 Linear Algebra with Applications

Announcement:

This summer, Princeton  will be offering a small suite of  STEM courses this summer (MAT 103, 104, 201, 202 and PHY 110) for students who need these specific courses for degree or concentration progress. Students accepted to the program will not be charged tuition for the courses; students on financial aid will also receive an allotted living expense budget.Please visit: https://forms.gle/52iszwnhbMGLXmCe7 for more information and to apply. The deadline for application is April 7, 2021.

Schedule: MW at 8:30 AM, at 11 AM, at 1:30 PM, and at 3:00 PM (Spring only), Friday precepts; Fall and Spring. Optional review sessions are very helpful, but they are scheduled only after classes begin.

Brief Course Description: More abstract than calculus, this course aims to develop basic algebraic tools for work with problems involving many variables. Starting from systems of linear equations and vectors in 2-space and 3-space, this course develops ideas about length, angles and resolving a general vector into useful components, identifying features of linear systems or processes in order to choose a basis that is well-adapted to studying a particular phenomenon and move between different points of view to reveal the essential underlying structure.  Companion course to 201 (Multivariable Calculus). Discusses matrices and linear transformations, linear independence and dimension, bases and coordinates, determinants, orthogonal projection, least squares, eigenvalues and their applications to quadratic forms and dynamical systems.

Why take this course? Along with 201, it builds vocabulary and algebraic tools to describe and understand phenomena in the natural world, and improves analytic and problem solving skills which are valuable in many disciplines.

Prerequisites & Placement Info:  Although it does not rely on the mathematical topics taught in the calculus sequence, this course does rely on the independent problem solving skills whose development are a main focus of 104 in particular. Prior experience with vectors and functions of two or three variables is very helpful but not required, and so taking 201 before 202 is a good idea if you need both.

Who takes this course? Most students in this course are first- or second-year students who consider majoring in one of the sciences or engineering.   More mathematically inclined economics majors will take this course along with 201.

### FAQ:

• You already took a linear algebra course in high school or at a local college, and so you want to place out of MAT202.  Many students in 201/202 have had prior experience with some multivariable calculus and/or linear algebra, 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 may want to consider 203/204 instead, which requires an intense commitment and interest in deeper understanding of the subject and its applications.
• How much work is this course? We expect that the weekly problem sets will take at least 3 hours to complete, although this can vary quite a lot for individual students, and this is only the beginning! The exams often include more challenging problems which require complex analytic skills. Learning to think independently and creatively in a mathematical setting takes time and lots of practice.  To do well on math exams, you need to work through a lot of extra problems from past exams and quizzes. All in all, you should be ready to spend at least 10 hours per week working outside of class.
• You think MAT202 is too hard after looking at the sample problems or attending the first couple classes.  This class is quite abstract and algebraic, so it is a big change from calculus. It takes time to digest the new ideas and methods and you can feel quite lost in the meantime. Go to office hours, work with others, attend the review sessions. The abstract ideas get clearer as you work with them longer and apply them in more concrete scenarios. The background you get in 201/202 is essential for any quantitative field.
• You think MAT202 is not challenging enough.  Wait till you have had a quiz, which usually occurs in the 3rd week.  Homework problems are often quite routine compared to exam questions.  Try some old quiz problems 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 204 or 217 instead (these are offered only in spring).
• You want to take both MAT201 and MAT202 in the same semester to get your engineering prerequisites over with. Is this possible? It is not impossible but this is not a good idea for most students. The work load and pace of 201 is particularly overwhelming for many students, and adjusting to the abstraction in 202 is also a big step. Doing both these demanding courses in a single semester should not be undertaken lightly. We would not recommend it for anyone, but it is especially inadvisable for anyone who got less than an A in 104
• Which is harder? MAT201 or MAT202? They are challenging in different ways. MAT201 is calculus and therefore relatively familiar, and up to the last few weeks of the course the difficulties are mostly technical rather than conceptual. Its problems routinely use everything students learned in single-variable calculus along with all the ideas and technical tricks from high school algebra and precalculus. The course culminates with Stokes's theorem, Green's theorem and the Divergence theorem which are especially challenging, both technically and conceptually. By contrast, because 202 is more algebraic and abstract compared to calculus, many students find it difficult in a new way that can be rather disconcerting. The calculations are relatively simple once you understand what you need to compute, but it can take time to master the abstract concepts well enough to understand what that might be. The challenge in 201 is usually how to finish a problem as the technical complications mount, whereas in 202 the challenge is often in seeing how to start the problem.
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