MATH257
MATH257 (Linear Algebra with Computational Applications) is a 3-credit-hour class that is one of the math courses required for both EE and CE majors as part of the ECE core curriculum. It is offered in the fall, spring, and summer.
Who Should Take the Exam
Though this class is only 3 credit hours, it is thought through many students that the course load reflects more of a 4 credit hour class. And with this class typically taken in parallel with PHYS 211/212/213/214 ECE210/220 and so on... taking this class for a full semester can easily start to creep up on you for coursework hours and extra unneeded stress. In recent years, students have also been complaining that the course itself, if taken in its entirety, is very disorganized.
A student can take this class to "get it out of the way", effectively gaining the credit without needed to go through the entire semester class. In fact, only a select few classes for higher ECE level classes need MATH257 as a prerequisite, so unless planning on taking that class in the future, it is proved unecessary to need to take the entire class.
Even if Linear Algebra is fundamentally found in all aspects of engineering, many computers are able to handle these calculations for us, so a mental grasp of the concepts and general algorithms and theorums are all typically enough.
Content Covered
- Linear equations, linear systems
- Matrix operations, LU decomposition
- Vector spaces, subspaces
- Basis and dimension
- Linear transformations
- Eigenvalues, eigenvectors
- Inner products and norms
- Orthogonality, orthogonal projections, linear regression
- Equilibrium, linear dynamical systems
- Gram-Schmidt method, QR decomposition
- Principle Component Analysis
- Singular value decomposition, pseudo-inverse
Prerequisites
MATH221 is the only official prerequisite for this course. It is important to be familiar with calculus before taking MATH257, as it is used in the course.
Exam Format
As of 2024, the math proficiency exams have been moved to the CBTF. The exam consists of a combination of MCQ and FRQ, with about a 70/30 split. This exam has been reported to change every offered session, whether being only 2 hours long and 7 question to 3 hours long and almost 30 questions long. It is best to prepare with the longer in mind and grasp an understanding of all content.
How to Prepare
You can find all helpful lecture videos in the Illinois Media Space for Mathematics. Following these notes will give you a very strong foundation into all the necessary concepts needed to pass the proficiency exam. Doing countless practice problems, both computational and conceptual are pertinent to pass the test.
Life After
After passing MATH257, ECE students are required to take ECE313, which delves into probability theory. For many, this is a course similar to MATH257, except many typically hold off on taking ECE313 until later, due to ECE313 also being deemed a very bad class to take. Many also just choose to take it over the summer.