# Mathematics Summer Courses

#### MATH 2

**Session 2**Prerequisites lifted in summer for visiting students.

Operations on real numbers, complex numbers, polynomials, and rational expressions; exponents and radicals; solving linear and quadratic equations and inequalities; functions, algebra of functions, graphs; conic sections; mathematical models; sequences and series. Prerequisite(s): mathematics placement (MP) score of 100 or higher.

Instructor: Suzana Milea

#### MATH 3-01

**Session 1**Prerequisites lifted in summer for visiting students.

Inverse functions and graphs; exponential and logarithmic functions, their graphs, and use in mathematical models of the real world; rates of change; trigonometry, trigonometric functions, and their graphs; and geometric series. Students cannot receive credit for both course 3 and Applied Mathematics and Statistics 3. Applied Mathematics and Statistics 3 can substitute for course 3. Prerequisite(s): course 2 or mathematics placement (MP) score of 200 or higher. (General Education Code(s): MF, Q.)

Instructor: Charles Petersen

#### MATH 3-02

**Session 2**Prerequisites lifted in summer for visiting students.

Inverse functions and graphs; exponential and logarithmic functions, their graphs, and use in mathematical models of the real world; rates of change; trigonometry, trigonometric functions, and their graphs; and geometric series. Students cannot receive credit for both course 3 and Applied Mathematics and Statistics 3. Applied Mathematics and Statistics 3 can substitute for course 3. Prerequisite(s): course 2 or mathematics placement (MP) score of 200 or higher. (General Education Code(s): MF, Q.)

Instructor: Matthew Grace

#### MATH 11A

**Session 1**Prerequisites lifted in summer for visiting students.

A modern course stressing conceptual understanding, relevance, and

problem solving . The derivative ofpolynomial , exponential, and trigonometric functions of a single variable is developed and applied to a wide range of problems involving graphing, approximation, and optimization. Students cannot receive credit for both this course and course 19A or Applied Mathematics and Statistics 11A and 15A, or Economics 11A. Prerequisite(s): course 3 or Applied Mathematics and Statistics 3; or mathematics placement (MP) score of 300 or higher; or AP Calculus AB exam score of 3 or higher. (General Education Code(s): MF, IN, Q.)Instructor: Yucheng Lu

#### MATH 11B

**Session 2**Prerequisites lifted in summer for visiting students.

Starting with the fundamental theorem of calculus and related techniques, the integral of functions of a single variable is developed and applied to problems in geometry, probability, physics, and differential equations. Polynomial approximations, Taylor series, and their applications conclude the course. Students cannot receive credit for this course and course 19B, or Applied Mathematics and Statistics 11B and 15B, or Economics 11B. Prerequisite(s): course 11A or 19A or Applied Mathematics and Statistics 15A or AP Calculus AB exam score of 4 or 5, or BC exam score of 3 or higher, or IB Mathematics Higher Level exam score of 5 or higher. (General Education Code(s): MF, IN, Q.)

Instructor: Sami Erman

Cineli #### MATH 19A-01

**Session 1**Online only class. Prerequisites lifted in summer for visiting students.

The limit of a function, calculating limits, continuity, tangents, velocities, and other instantaneous rates of change. Derivatives, the chain rule, implicit differentiation, higher derivatives. Exponential functions, inverse functions, and their derivatives. The mean value theorem, monotonic functions, concavity, and points of inflection. Applied maximum and minimum problems. Students cannot receive credit for both this course and course 11A or Applied Mathematics and Statistics 11A and 15A,or Economics 11A. Prerequisite(s): course 3 or Applied Mathematics and Statistics 3; or mathematics placement (MP) score of 400 or higher; or AP Calculus AB exam score of 3 or higher. (General Education Code(s): MF, IN, Q.)

Instructor: Tony Tromba & Frank Bauerle

2017 Syllabi (for class expectations reference)

#### MATH 19A-02

**Session 2**Online only class. Prerequisites lifted in summer for visiting students.

The limit of a function, calculating limits, continuity, tangents, velocities, and other instantaneous rates of change. Derivatives, the chain rule, implicit differentiation, higher derivatives. Exponential functions, inverse functions, and their derivatives. The mean value theorem, monotonic functions, concavity, and points of inflection. Applied maximum and minimum problems. Students cannot receive credit for both this course and course 11A or Applied Mathematics and Statistics 11A and 15A

,or Economics 11A. Prerequisite(s): course 3 or Applied Mathematics and Statistics 3; or mathematics placement (MP) score of 400 or higher; or AP Calculus AB exam score of 3 or higher. (General Education Code(s): MF, IN, Q.)Instructor: Tony Tromba & Frank Bauerle

2017 Syllabi (for class expectations reference)

#### MATH 19B-01

**Session 1**Online only class. Prerequisites lifted in summer for visiting students.

The definite integral and the fundamental theorem of calculus. Areas, volumes. Integration by parts, trigonometric substitution, and partial fractions methods. Improper integrals. Sequences, series, absolute convergence and convergence tests. Power series, Taylor and Maclaurin series. Students cannot receive credit for both this course and course 11B, Applied Math and Statistics 11B and 15B, or Economics 11B. Prerequisite(s): course 19A or 20A or AP Calculus AB exam score of 4 or 5, or BC exam score of 3 or higher, or IB Mathematics Higher Level exam score of 5

of higher. (General Education Code(s): MF, IN, Q.)Instructor: Tony Tromba & Frank Bauerle

2017 Summer and 2018 Spring syllabi (for class expectations reference)

#### MATH 19B-02

**Session 2**Online only class. Prerequisites lifted in summer for visiting students.

The definite integral and the fundamental theorem of calculus. Areas, volumes. Integration by parts, trigonometric substitution, and partial fractions methods. Improper integrals. Sequences, series, absolute convergence and convergence tests. Power series, Taylor and Maclaurin series. Students cannot receive credit for both this course and course 11B, Applied Math and Statistics 11B and 15B, or Economics 11B. Prerequisite(s): course 19A or 20A or AP Calculus AB exam score of 4 or 5, or BC exam score of 3 or higher, or IB Mathematics Higher Level exam score of 5

of higher. (General Education Code(s): MF, IN, Q.)Instructor: Tony Tromba & Frank Bauerle

2017 Summer and 2018 Spring syllabi (for class expectations reference)

#### MATH 21

**Session 1**Prerequisites lifted in summer for visiting students.

Systems of linear equations matrices, determinants. Introduces abstract vector spaces, linear transformation, inner products, the geometry of Euclidean space, and eigenvalues. Students cannot receive credit for this course and Applied Mathematics and Statistics 10 or 10A. Prerequisite(s): Mathematics 11A or 19A or 20A or Applied Mathematics and Statistics 11A or 15A. (General Education Code(s): MF, Q.)

Instructor: Natalya Jackson

#### MATH 21

**Session 2**Prerequisites lifted in summer for visiting students.

Systems of linear equations matrices, determinants. Introduces abstract vector spaces, linear transformation, inner products, the geometry of Euclidean space, and eigenvalues. Students cannot receive credit for this course and Applied Mathematics and Statistics 10 or 10A. Prerequisite(s): Mathematics 11A or 19A or 20A or Applied Mathematics and Statistics 11A or 15A. (General Education Code(s): MF, Q.)

Instructor: Andres Perico

#### MATH 22

**Session 1**Prerequisites lifted in summer for visiting students.

Functions of several variables. Continuity and partial derivatives. The chain rule, gradient

and directional derivative. Maxima and minima, including Lagrange multipliers. The double and tripleintegral and change of variables. Surface area and volumes. Applications from biology, chemistry, earth sciences, engineering, and physics. Students cannot receive credit for this course and course 23A. Prerequisite(s): course 11B or 19B or 20B or Applied Mathematics and Statistics 15B or AP calculus BC exam score of 4 or 5. (General Education Code(s): MF.)Instructor: Patrick Allmann

#### MATH 23A-01

**Session 1**Online only class. Prerequisites lifted in summer for visiting students.

Vectors in n-dimensional Euclidean space. The inner and cross products. The derivative of functions from n-dimensional to m-dimensional Euclidean space is studied as a linear transformation having matrix representation. Paths in 3-dimensions, arc length, vector differential calculus, Taylor's theorem in several variables, extrema of real-valued functions, constrained extrema and Lagrange multipliers, the implicit function theorem, some applications. Students cannot receive credit for this course and course 22. (Formerly Multivariable Calculus.) Prerequisite(s): course 19B or 20B or AP calculus BC exam score of 4 or 5. (General Education Code(s): MF.)

Instructor: Tony Tromba & Frank Bauerle

2017 Summer and 2018 Spring syllabi (for class expectations reference)

#### MATH 23A -02

**Session 2**Online only class. Prerequisites lifted in summer for visiting students.

Vectors in n-dimensional Euclidean space. The inner and cross products. The derivative of functions from n-dimensional to m-dimensional Euclidean space is studied as a linear transformation having matrix representation. Paths in 3-dimensions, arc length, vector differential calculus, Taylor's theorem in several variables, extrema of real-valued functions, constrained extrema and Lagrange multipliers, the implicit function theorem, some applications. Students cannot receive credit for this course and course 22. (Formerly Multivariable Calculus.) Prerequisite(s): course 19B or 20B or AP calculus BC exam score of 4 or 5. (General Education Code(s): MF.)

Instructor: Tony Tromba & Frank Bauerle

2017 Summer and 2018 Spring syllabi (for class expectations reference)

#### MATH 23B

**Session 2**Prerequisites lifted in summer for visiting students.

Double integral, changing the order of integration. Triple integrals, maps of the plane, change of variables theorem, improper double integrals. Path integrals, line integrals, parametrized surfaces,

area of a surface, surface integrals. Green's theorem, Stokes' theorem, conservative fields, Gauss' theorem. Applications to physics and differential equations, differential forms. (Formerly Multivariable Calculus.) Prerequisite(s): course 23A. (General Education Code(s): MF.)Instructor: Sami Erman

Cineli #### MATH 24

**Session 2**Prerequisites lifted in summer for visiting students.

First and

second order ordinary differential equations, with emphasis on the linear case. Methods of integrating factors, undetermined coefficients,variation of parameters, power series, numerical computation. Students cannot receive credit for this course and Applied Mathematics and Statistics 20. Prerequisite(s): course 22 or 23A; course 21 is recommended as preparation.Instructor: Victor Bermudez

#### MATH 100-01

**Session 1**Prerequisites lifted in summer for visiting students.

Students learn the basic concepts and ideas necessary for upper-division mathematics and techniques of mathematical proof. Introduction to sets, relations, elementary mathematical logic, proof by contradiction, mathematical induction, and counting arguments. Prerequisite(s): satisfaction of the Entry Level Writing and Composition requirements and course 21 and course 11A or 19A or 20A. (General Education Code(s): MF.)

Instructor: Salvador Guerrero

#### MATH 100-02

**Session 2**Prerequisites lifted in summer for visiting students.

Students learn the basic concepts and ideas necessary for upper-division mathematics and techniques of mathematical proof. Introduction to sets, relations, elementary mathematical logic, proof by contradiction, mathematical induction, and counting arguments. Prerequisite(s): satisfaction of the Entry Level Writing and Composition requirements and course 21 and course 11A or 19A or 20A. (General Education Code(s): MF.)

Instructor: Salvador Guerrero

#### MATH 103A

**Session 2**Prerequisites lifted in summer for visiting students.

Complex numbers, analytic and harmonic functions, complex integration, the Cauchy integral formula, Laurent series, singularities and residues, conformal mappings. (Formerly course 103.) Prerequisite(s): course 23B; and either course 100 or Computer Science 101.

Instructor: Hirotaka Tamanoi

#### MATH 105A

**Session 1**Prerequisites lifted in summer for visiting students.

The basic concepts of one-variable calculus are treated rigorously. Set theory, the real number system, numerical sequences and series, continuity, differentiation. Prerequisite(s): course 22 or 23B and either course 100 or Computer Science 101.

Instructor: Steven Flynn

#### MATH 110

**Session 1**Prerequisites lifted in summer for visiting students.

Prime numbers, unique factorization, congruences with applications (e.g., to magic squares). Rational and irrational numbers. Continued fractions. Introduction to Diophantine equations. An introduction to some of the ideas and outstanding problems of modern mathematics. Prerequisite(s): course 100 or Computer Science 101. (General Education Code(s): Q.)

Instructor: Yonatan Katznelson

#### MATH 111A

**Session 2**Prerequisites lifted in summer for visiting students.

Group theory including the Sylow theorem, the structure of abelian groups, and permutation groups. Prerequisite(s): course 21 or Applied Mathematics and Statistics 10 and either course 100 or Computer Science 101.

Instructor: Elijah Fender

#### MATH 117

**Session 1**Prerequisites lifted in summer for visiting students.

Review of abstract vector spaces. Dual spaces, bilinear forms, and the associated geometry. Normal forms of linear mappings. Introduction to tensor products and exterior algebras.

Instructor: Suzana Milea

#### MATH 181

**Session 2**A survey from a historical point of view of various developments in mathematics. Specific topics and periods to vary yearly. Prerequisite(s): course 19B or 20B. Course 100 is strongly recommended for preparation. (General Education Code(s): TA.)

Instructor: Hirotaka Tamanoi

## College Algebra for Calculus

## Precalculus

## Precalculus

## Calculus with Applications

## Calculus with Applications

## Calculus for Science, Engineering, and Mathematics (online)

## Calculus for Science, Engineering, and Mathematics (online)

## Calculus for Science, Engineering, and Mathematics (online)

## Calculus for Science, Engineering, and Mathematics (online)

## Linear Algebra

## Linear Algebra

## Introduction to Calculus of Several Variables

## Vector Calculus (online)

## Vector Calculus (online)

## Vector Calculus

## Ordinary Differential Equations

## Introduction to Proof and Problem Solving

## Introduction to Proof and Problem Solving

## Complex Analysis

## Real Analysis

## Introduction to Number Theory

## Algebra

## Advanced Linear Algebra

## History of Mathematics

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