Math & Statistics Courses

Many students admitted to the College of Letters and Science (L&S) as freshmen have met the Quantitative Reasoning (QR) requirement. If you have not, you are encouraged to satisfy it by the end of your freshman year.

Fall Program for Freshmen (FPF) Math & Statistics courses meet UC Berkeley's QR requirement. In addition, we offer some Math courses that may be applied toward your undergraduate major requirements.

You may also satisfy the QR requirement through scores on SAT I, SAT II, ACT, or Advanced Placement (AP) math exams or through equivalent coursework.

>> Review L&S QR Requirement

Note: If you have satisfied the QR requirement and math is not required by your intended major, you are not required to select a math course.

Selecting a Math Course

It's up to you to select the appropriate math course. FPF math courses are UC Berkeley-equivalent and more challenging than students expect. Many students with Advanced Placement (AP) math credit find the same level of course work at UC Berkeley much more difficult.

The UC Berkeley Math Department has determined that scoring a 3 or 4 on the AP Math exam indicates readiness for college-level calculus. However, scores are not an indicator of how a student will perform in a college calculus course. Both the Math Department and FPF strongly suggest that you do not choose your math course based on AP test scores alone.

When deciding on an FPF math course, consider the following:

Read our course descriptions carefully and take the FPF Math Diagnostic Test. This exam, designed by FPF instructors, helps you determine your mathematical skill level.

>> Take FPF Math Diagnostic Test

Things to Consider

Which math course you choose depends on your math background and your intended major.

Note: UC Berkeley Extension FPF does not offer Math 53 or Math 54. If you have met the prerequisites for Math 53 or 54 (scoring a 5 on your AP Calculus BC Exam, or completing Math 1A and 1B or their equivalent), and you are required to take either of these courses in the fall semester as a math or engineering student, please e-mail our staff at fallfrosh@unex.berkeley.edu.

Math & Statistics Course Descriptions

Mathematics 32-Precalculus

(4 units)

Examples of Intended Majors: Any major that requires Math 16A or Math 1A

Prerequisite: Three years of high school mathematics

Satisfies: Quantitative Reasoning requirement if completed with a grade of C- or higher. Some majors have specific grade requirements.

Course Overview: This course is designed for students who wish to prepare for calculus. It covers exponential and logarithmic functions, trigonometry, complex numbers, binomial theorem, conics and analytic geometry. Three hours of lecture and two hours of discussion per week.

Topics Covered: Factoring polynomials. Quadratic equations. Equations of lines. Symmetry and graphs. One dimensional inequalities. Definition and graph of a function. Techniques of graphing. Composition of functions. Inverse of a function. Linear functions. Quadratic functions. Polynomial functions. Rational functions. Quadratic optimization problems. Exponential and logarithmic functions. Properties of logarithms. Equations and inequalities with logarithms. Compound interest. Exponential growth and decay. Trigonometric functions. Right triangle applications. Trigonometric identities. Radian measure of angles. Graphs of the six trigonometric functions. Addition formula for trigonometric functions. Double angle formulas. Product-to-sum and sum-to-product formulas. Trigonometric equations. Inverse trigonometric functions. Law of sines. Law of cosines. Vectors. Parametric equations. Polar coordinates.

Skills Needed

Statistics 2-Introduction to Statistics

(4 units)

Examples of Intended Majors: Psychology, Political Economy, Development Studies, Legal Studies, Nutritional Sciences & Toxicology

Prerequisite: High school algebra

Satisfies: Quantitative Reasoning requirement if completed with a grade of C- or higher. Some majors have specific grade requirements.

Course Overview: This course introduces basic concepts of probability and statistical inference and covers standard methods for making inferences about populations from information contained in sample data – the methods used in ample surveys, opinion polls, research studies, and industry. Three hours of lecture and two hours of discussion per week.

Topics Covered: Populations, statistics, variables, observational studies versus experiments, graphs of data, descriptive measures of location and spread, normal approximation, correlation, the regression line, Simpson’s paradox, probability, binomial and normal distributions, the behavior of the average of samples, and such inference methods as estimation, confidence intervals, hypothesis tests for averages and percentages, and the chi-square test.

Skills Needed

Mathematics 16A-Analytic Geometry and Calculus

(3 units)

Examples of Intended Majors: Integrative Biology, Life Sciences, Business Administration, Architecture, Economics

Prerequisites: Three years of high school mathematics, including trigonometry; we strongly recommend that you have taken precalculus before taking 16A.

Satisfies: Quantitative Reasoning requirement if completed with a grade of C- or higher. A minimum grade of C- is required for students to continue in Math 16B. Some majors have specific grade requirements.

Course Overview Math 16A begins with a review of functions and then introduces the derivatives of simple functions, logarithms, and exponentials, as well as applications of the derivative, including rate of change, techniques of graphing, optimization problems, related rates, and differentials. It introduces integration, the fundamental theorem of calculus, areas in the plane, and other applications of the definite integral. This course is intended for students in the social and biological sciences or whose programs require only one year of calculus. Three hours of lecture and one hour of discussion per week.

Skills Needed

Mathematics 1A-Calculus

(4 units)

Examples of Intended Majors: Physical Sciences, Engineering, Mathematics, Computer Sciences, Molecular and Cell Biology, Economics, Astronomy, Chemistry, Geology, Statistics

Prerequisite: Three and a half years of high school mathematics, including trigonometry and analytic geometry; we strongly recommend that you have taken precalculus before taking Math 1A.

Satisfies: Quantitative Reasoning requirement if completed with a grade of C- or higher. Some majors have specific grade requirements. Students taking 1A after 16A receive only 2 units of credit for 1A. A minimum grade of C- or better is required for students to continue in Math 1B.

Course Overview: Math 1A covers the topics of calculus of one variable, mainly with derivatives, and such applications as graphing and optimization. It introduces the idea of integration and such applications as volumes of revolution. Students are expected to understand some theorems and their proofs. This rigorous course emphasizes conceptual understanding and is intended for students in engineering and physical sciences. Three hours of lecture and two to three hours of discussion per week at the discretion of the instructor.

Topics Covered: Intuitive and precise limit definitions. Continuity. Definition of the derivative. Shortcut rules for finding derivatives. Product rule, quotient rule, chain rule, implicit differentiation. Related Rates. Linear Approximations and Differentials. Mean Value Theorem. L’Hopital’s rule. Curve Sketching. Optimization. Newton ’s Method. Definition of Riemann integral. Fundamental Theorem of Calculus (Parts 1 and 2.) Natural Logarithm defined as an integral. Area between two curves. Volumes of solids of revolution.

Skills Needed

Mathematics 1B-Calculus

(4 units)

Examples of Intended Majors: Physical Sciences, Engineering, Mathematics, Computer Sciences, Molecular and Cell Biology, Economics, Astronomy, Chemistry, Geology, Statistics

Prerequisites: Math 1A or equivalent coursework; please check assist.org or the Office of Undergraduate Admissions to make sure your coursework is equivalent to UC Berkeley's Math 1A.

Satisfies: Quantitative Reasoning requirement if completed with a grade of C- or higher. Some majors have specific grade requirements. Students taking 1B after 16B receive only 2 units for 1B.

Course Overview: Math 1B is a continuation of Math 1A. It involves integration techniques and applications and introduces infinite series and first- and second-order differential equations and their uses. It is intended for students with majors in engineering, math, and some sciences. Three hours of lecture and two hours of discussion per week.

Topics Covered: Integration by parts. Trigonometric integrals. Trigonometric Substitution. Partial Fractions. Midpoint, Trapezoid and Simpson’s Rules. Improper Integrals. Arc Length. Area of a surface of revolution. Sequences and series. Integral Test. Comparison Tests. Alternating series. Ratio test. Root test. Power series. Taylor series. Binomial Series. Modeling with differential equations. Direction fields. Euler’s method. Separable equations. Exponential growth and decay. Logistic equation. Linear differential equations. Homogeneous and nonhomogeneous second-order linear differential equations and their applications. Series solutions for second-order differential equations.

Skills Needed