Choosing Courses

Serious gaps in your foundational knowledge will make calculus or linear algebra classes at UC Berkeley much more challenging, and make it difficult to fully understand key concepts, as well as the workings of advanced computational techniques. Key differences between high school and UC-level math include:

• More Conceptual. Berkeley math courses emphasize both computational and conceptual understanding of the material. 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. In particular, exam questions often require students to apply their conceptual understanding to unfamiliar problems, and not just rely on mechanical problem solving skills. Furthermore, 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 lecture to lecture. 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 in person.
  
  

• More In-Depth Computations. Examples and problems often involve multiple parts that combine various techniques. Developing a strong mathematical 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.

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 high school examination scores), it may be worthwhile to start from some of our first course offerings (Math 3/10A/16A/51). 

It’s important to keep in mind that you are not just completing coursework, you are developing a mathematical intuition. Developing strong mathematical instincts requires experience and time with the material; skipping ahead or advancing as early as possible may be a disservice to your growth and will not necessarily bring a competitive advantage. 

Math 1 - Foundations of Lower Division Mathematics, is a 2-unit course designed for students who are relatively prepared for calculus and do not need a full precalculus course, but would greatly benefit from targeted study of select foundational topics. It can be taken alongside other lower division math courses or prior to your first math course. The course covers algebraic operations, laws of exponents and logarithms, inequalities and absolute values, single-variable function properties, polynomials, power and exponential functions, logarithmic functions, trigonometric functions, coordinate geometry in two and three dimensions, complex numbers, and functions of several variables.

Math 3 - Precalculus, is designed to prepare students for Mathematics 10A/16A/51. Prerequisites for Math 3 is 3 years of high school mathematics, or if you have taken the SAT: at least a score of 560 on the SAT I: Math or at least a score of 570 on the SAT II: Math Level I, or at least a score of 520 on the SAT II: Math Level II/IIC. Importantly, you may feel that starting with Math 3 will put you behind your peers or is a form of remediation. In fact, the opposite is true: Math 3 will provide a solid foundation on which to build. Starting at the beginning to build a strong command of introductory material will be more beneficial to you in the long run, rather than skipping over the fundamentals to “keep up” with other students.

Math 16A/B - Analytic Geometry and Calculus, covers much of the same basic topics as Math 51/52, with less emphasis on theory so is generally thought to be less rigorous and demanding. The 16 series is referred to as our “terminal one-year calculus sequence” because it does not prepare you to continue in advanced Math courses. If there is a possibility that your academic/career goals will require more advanced math (multivariable calculus, linear algebra, real analysis, complex algebra, etc.), consider preparing yourself to begin with Math 51/52.

Math 10A/B - Methods of Mathematics, Calculus, Statistics, and Combinatorics, covers calculus and discrete topics that are particularly appropriate for intended life science majors. The 10 series covers the calculus in the 51/52 series, but at a faster pace, since it also covers combinatorics and probability. The 10 series serves as a prerequisite for Math 54 - Linear Algebra and Differential Equations, but no other more advanced courses. If there is a possibility that your academic/career goals will require more advanced math (multivariable calculus, real analysis, complex algebra, etc.), consider preparing yourself to begin with Math 51/52.

Math 51/52 - Calculus I/II, is the calculus series intended for STEM majors. It prepares students to continue on to more advanced mathematical study, including multivariable calculus, linear algebra, complex algebra, analysis, etc. The course provides an introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

With regards to High School Exam Credits, the Math Department accepts:

• AP Calculus AB with a score of 3, 4, or 5 for Math 51.
• AP Calculus BC with a score of 3 or 4 for Math 51.
• AP Calculus BC with a score of 5 for Math 51 and Math 52.

Please note: Other Departments and Colleges may use their own scales to determine AP subject credit for mathematics. Please check with them directly and plan accordingly. Information on international baccalaureate exams is listed in more detail on our website.

A chart summarizing common majors and their first Math requirement is included below.

Students do not need to take a placement exam to enroll in their first math courses. Please note that for Math 3, you should also have received:

• at least a score of 560 on the SAT I: Math or
• at least a score of 570 on the SAT II: Math Level I, or
• at least a score of 520 on the SAT II: Math Level II/IIC.

That depends on your math background and your intended major (see below). Math 16A-16B covers much of the same basic topics as Math 51-52 (formerly 1A-1B), but lacks in-depth calculus and so is less rigorous and demanding. Math 10A-10B covers calculus and discrete topics that are particularly appropriate for intended life science majors. Mathematics 3 (formerly 32), Precalculus, is designed to prepare students for Mathematics 51 or 16A. Prerequisites for Math 3 is 3 years of high school mathematics.

On a side note, Math 16A-16B are referred to as a “terminal one-year calculus sequence,” because they do not prepare you to continue in math. In order to take Math 53 or 54, you must pass Math 51-52 (or equivalent) with a letter grade of C- or better. The Math 10 series covers the calculus in the 51-52 series, but at a faster pace, since it also covers combinatorics and probability.

The Math Department does not enforce prerequisites so you may go ahead and enroll. It's important to note that if your intended Major requires Math 51 or an equivalent course, you will want to consult with them before skipping Math 51 for 51. It's possible the Major will still require Math 51, or will require a credit by examination - taking a more advanced course does not equate to waiving a major requirement. We also recommend that you look at course materials early in order to determine whether you will need to drop back into Math 51.