Between free variables, wronskians, orthogonal projections and complex roots Math 54 often leaves students wondering how any of their previous math classes prepared them for this class. Since this course does not build off of Math 1A, 1B or 53 it introduces students to a whole new world of concepts - both exciting and overwhelming. It’s essentially the first “real” math class students will typically take at Cal, and often the hardest. Math 54, however, is also the class most math majors will cite as the reason for their chosen course of study.
“ Math 54, however, is also the class most math majors will cite as the reason for their chosen course of study”
The Truth About Math54
This course challenges its students in that they are required to think critically and often far beyond the theorems given. Exams often begin with a long series of true and false questions that really test a student's knowledge of minor theorem exceptions, and of course the central invertible matrix theorem. That’s why the first few weeks of the course are absolutely essential. A lot of the preliminary information will seem trivial and almost redundant, but hidden within those seemingly redundant theorems are slight exceptions, discrepancies, and tricks that will come up and prove to be confusing on later exams.
Talk Your Reasoning Out Loud
After the first midterm, the course picks up very quickly. Familiar concepts are introduced in new ways and with new confounding variables and it’s often hard for students to keep track of all the information thrown their way. The best advice I could give a student is to talk through all of their reasoning OUT LOUD! When presented with a true and false, talk yourself through why you chose false. More often than not students will ask me whether their answer is right or wrong and when I ask them to explain their reasoning, they catch their own mistake.
“Write down everything you know, write down where you need to end up, and oftentimes the logic is made self-evident before your eyes”
This same tip applies to proofs. As one of the more proof-heavy lower division math classes at Berkeley, students often ask me how to first approach proofs. Write down everything you know, write down where you need to end up, and oftentimes the logic is made self-evident before your eyes. Take your time and remember your basic theorems.
Practice Makes Perfect
The next tip is relatively straightforward, but often the hardest: practice, practice, practice. Doing midterm level practice problems throughout the semester rather than just the few days before the exam is instrumental in doing well in the class. Learning the tricks of the problems and recognizing patterns only comes with consistent practice and the incorporation of more varied and difficult problems. SLC Adjunct courses receive study guides and extra practice problems straight from professors, and Tau Beta Pi has an exam database online you can tap to make sure you’re getting the practice you need.
Find Your Crew
Finally it is super important to build a community. Tackling Math 54, or any class, alone, is a much harder and less fun endeavor than it needs to be. Solving problems in a group, getting your questions answered by your peers and enjoying the studying process are only a few of the many benefits to working within a larger community. Everyone approaches proofs and problems differently, and oftentimes you can learn a lot from the thought process of one of your peers. Between pointing out flaws in their logic, and having to explain comments to someone else, group studying requires you to have an understanding of the material that is much deeper than what you would get alone.
Math 54 is a gateway to many more complex math, engineering statistics, and physics upper division classes. By having the right strategy and community in place, it can be a successful and fulfilling experience.