You may have already fulfilled the L&S Quantitative Reasoning requirement, but your intended major(s) may require math courses.

## Mathematics 32—Precalculus (4 units)

**Department Abbreviation:** XMATH 32

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

**Prerequisite:** Three years of high school mathematics and at least a score of 560 on the SAT I Math portion. Email fpf@berkeley.edu if you need to take math but have scored below a 560 on the SAT I.

**Satisfies:** Quantitative Reasoning requirement if completed with a grade of C− or better. Some majors have specific grade requirements.

**Course Description:** 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.*

## Mathematics 16A—Analytic Geometry and Calculus (3 units)

**Department Abbreviation:** XMATH 16A

**Examples of Intended Majors:** Business Administration (Haas), Architecture, Economics, Public Health, Environmental Sciences

**Prerequisite:** Three years of high school mathematics, including trigonometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic exam or Math 32. It is strongly recommended that you take 16A only if you have already completed precalculus. Students will not receive credit for 16A after taking 1A. Two units of Math 16A may be used to remove a deficient grade in Math 1A.

**Satisfies:** Quantitative Reasoning requirement if completed with a grade of C− or better. Some majors have specific grade requirements. Math 16A (or equivalent) is required to continue on to Math 16B.

**Course Description:** Math 16A covers much of the same basic topics as Math 1A, but does not include in-depth calculus and does not prepare you to continue on to Match 53 or 54. Math 16A 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 life and social sciences whose programs require only one year of calculus.

## Mathematics 1A—Calculus (4 units)

**Department Abbreviation:** XMATH 1A

**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, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test or Math 32. It is strongly recommended that you take 1A only if you have already completed precalculus.

**Satisfies:** Quantitative Reasoning requirement if completed with a grade of C- or better. Some majors have specific grade requirements. Math 1A (or equivalent) is required to continue on to Math 1B.

**Course Description:** Math 1A covers the topics of calculus of one variable, mainly with derivatives, and applications such as graphing and optimization. It introduces the idea of integration and applications such 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.

**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:**

- Facility with a scientific calculator or graphing calculator may be required
- Ability to determine the value of a complicated expression using a scientific or graphing calculator

- Facility with fractions
- Ability to simplify rational expressions and solve rational equations

- Facility with algebra
- Ability to solve linear equations
- Ability to solve quadratic equations by factoring, completing the square and using the quadratic formula
- Ability to solve a linear system of equations

- Facility with graphing
- Ability to identify and plot points on the Cartesian plane
- Ability to graph lines

- Facility with exponential and logarithmic functions
- Familiarity with e and natural logarithms
- Ability to simplify expressions containing logarithms
- Ability to solve logarithmic equations
- Ability to graph exponential and logarithmic functions

- Facility with trigonometry
- Familiarity with radian measure
- Ability to compute trigonometric functions of simple angles
- Ability to use the Pythagorean Theorem
- Ability to solve triangle using the Law of Sines or the Law of Cosines
- Knowledge of addition formula for sine and cosine

## Mathematics 1B—Calculus (4 units)

**Department Abbreviation:** XMATH 1B

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

**Prerequisite:** Math 1A or equivalent coursework; please check Assist.org or with 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 better. Some majors have specific grade requirements. Math 1B is required to continue on to Math 53 or 54, and is recommended to continue on to Math 55.

**Course Description:** 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.

## Statistics 2—Introduction to Statistics (4 units)

**Department Abbreviation:** XSTAT 2

**Examples of Intended Majors:** Psychology, Political Economy, Development Studies, Legal Studies, Nutritional Science: Dietetics, Nutritional Science: Physiology and Metabolism

**Prerequisite:** None

**Satisfies:** Quantitative Reasoning requirement if completed with a grade of C− or better. Some majors have specific grade requirements. Stat 2 does NOT fulfill prerequisites for the economics major, statistics major or the Haas Undergraduate Business Program.

**Course Description:** 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 sample surveys, opinion polls, research studies and industry.

## Mathematics 10A—Methods of Mathematics: Calculus, Statistics, and Combinatorics (4 units)

**Department Abbreviation:** XMATH 10A

**Examples of Intended Majors:** Integrative Biology, Molecular and Cell Biology, other life sciences

**Prerequisite:** Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test or Math 32. It is strongly recommended that you take 1A only if you have already completed precalculus.

**Satisfies:** Quantitative Reasoning requirement if completed with a grade of C- or better. Some majors have specific grade requirements. Math 10A is required to continue on to Math 10B.

**Course Description:** Intended for majors in the life sciences. Introduction to differential and integral calculus of functions of one variable, ordinary differential equations, and matrix algebra and systems of linear equations.

**Class Description:** The first of a two-semester sequence of introductory college-level mathematics, covering topics in calculus, statistics and combinatorics. Primarily intended for life science majors, with many examples and applications from this context. Topics covered include mathematical modeling with functions, differential and integral calculus of functions of one variable, ordinary differential equations, matrix algebra, and systems of linear equations.