Online Mathematics Diagnostic Examination Project

Success in Lower Division Mathematics courses at UC Berkeley requires a solid understanding of foundational mathematical concepts. As you progress into more advanced courses, you will be expected to have a strong command of sophisticated mathematical techniques and how to use them to analyze complex problems. In order to be successful, you'll need to understand both how to apply such techniques and the underlying reasons why they work.

Taking a calculus or linear algebra class at UC Berkeley with serious gaps in your foundational knowledge, will make your learning experience much, much more challenging. There are likely to be key concepts that are almost impossible to understand fully, as well as computational techniques that you frequently struggle to apply without errors. As such, careful selection of your first math course will help prepare you for future success. It's not uncommon for students in their first semester to be stunned by the enormous jump in difficulty from highschool to Berkeley Mathematics; it is not to be underestimated. This brief diagnostic test has been designed to help you gauge how prepared you are, and recommend the best path for future success.

Before selecting your first math course, it's important to be realistic about your range of knowledge and level of comfort with Mathematics. Even if you are eligible to skip over lower division courses (via highschool examination scores), it may be worthwhile to start from the beginning (Math 3/10A/16A/51). Here are some of the key differences between highschool and UC-level math:

• More Conceptual. The material will emphasize conceptual understanding rather than rote computation. While each course will build a toolkit of essential computational techniques, why and how they work is what really matters. You'll need to understand why specific methods are effective under certain conditions and how to adapt them when assumptions change. Some concepts may require weeks of concentrated thought to fully internalize.
• Much Faster Pace. Nearly every lecture introduces a new concept or technique, assuming a solid grasp of previously covered foundational material. If you fall behind it can be really difficult to catch up. With this in mind, it's important for students to attend every lecture and discussion section.
• More In-Depth Computations. Examples and problems often involve multiple parts that combine various techniques. Developing a strong intuition is crucial for progressing from point A to point B through a sequence of logical steps.
• Serious Applications. Real-world problems frequently present complexities that necessitate sophisticated mathematical techniques for accurate modeling. Lower-division math courses are structured to swiftly bring students up to speed, balancing thoroughness with practicality.

1. Have a pencil and paper at hand.
2. Take the test in a distraction-free environment.
3. You will not be timed. Take your time to think about each question thoroughly.

The original project was a joint effort by Professors James A. Sethian, Theodore A. Slaman, and W. Hugh Woodin of the Department of Mathematics at the University of California, Berkeley. The project was revived and updated by Sean Gonzales (PhD Mathematics 2026).