# 2020 Mathematics Summer Courses

#### MATH 2

**Session 1**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.

UCSC students - If this class is a prerequisite for a Session 2 course you want to take, email summer@ucsc.edu for a permission code anytime after you enroll.

Visiting students - prerequisites are lifted in summer. It is in your best interest to take equivalent prerequisite courses. Contact summer@ucsc.edu for a permission code to enroll.

Proposed Instructor - Maryam Nashed

#### MATH 3-01

**Session 1**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 MATH 3 and AM 3. AM 3 can substitute for MATH 3. Prerequisite(s): MATH 2 or mathematics placement (MP) score of 200 or higher. (General Education Code(s): MF.)

UCSC students - If this class is a prerequisite for a Session 2 course you want to take, email summer@ucsc.edu for a permission code anytime after you enroll.

Visiting students - prerequisites are lifted in summer. It is in your best interest to take equivalent prerequisite courses. Contact summer@ucsc.edu for a permission code to enroll.

Proposed Instructor - Deewang Bhamidipati

#### MATH 3-02

**Session 2**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 MATH 3 and AM 3. AM 3 can substitute for MATH 3. Prerequisite(s): MATH 2 or mathematics placement (MP) score of 200 or higher. (General Education Code(s): MF.)

UCSC students - If you need to take the prerequisite in Session 1, enroll in that course first, then email summer@ucsc.edu for a permission code to enroll in this course.n code to enroll.

Visiting students - prerequisites are lifted in summer. It is in your best interest to take equivalent prerequisite courses. Contact summer@ucsc.edu for a permission code to enroll.

Proposed Instructor - Maryam Nashed

#### MATH 11A

**Session 1**A modern course stressing conceptual understanding, relevance, and problem solving. The derivative of polynomial, 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 MATH 19A, or AM 11A, or AM 15A, or ECON 11A. Prerequisite(s): MATH 3 or AM 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.)

UCSC students - If this class is a prerequisite for a Session 2 course you want to take, email summer@ucsc.edu for a permission code anytime after you enroll.

Proposed Instructor - Ryan Pugh

#### MATH 11B

**Session 2**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 MATH 19B, or AM 11B, or AM 15B, or ECON 11B. Prerequisite(s): MATH 11A or MATH 19A or AM 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.)

UCSC students - If you need to take the prerequisite in Session 1, enroll in that course first, then email summer@ucsc.edu for a permission code to enroll in this course.

Proposed Instructor - Sami Cineli

#### MATH 19A-01

**Session 1**Online only class.

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 MATH 11A, or AM 11A, or AM 15A, or ECON 11A. Prerequisite(s): MATH 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.)

Note: Course includes additional fee for online exam proctoring.This course will be hosted online at login.uconline.edu. It will be available the Friday before the class starts. Be sure to check your UCSC email for specific instructions!Proposed Instructor - Anthony Tromba

#### MATH 19A-02

**Session 2**Online only class.

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 MATH 11A, or AM 11A, or AM 15A, or ECON 11A. Prerequisite(s): MATH 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.)

UCSC students - If you need to take the prerequisite in Session 1, enroll in that course first, then email summer@ucsc.edu for a permission code to enroll in this course.

Note: Course includes additional fee for online exam proctoring. This course will be hosted online at /login.uconline.edu. It will be available the Friday before class starts. Be sure to check your UCSC email for specific instructions!Proposed Instructor - Frank Bauerle

#### MATH 19B-01

**Session 1**Online only class.

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 MATH 11B, or AM 11B, or AM 15B, or ECON 11B. Prerequisite(s): MATH 19A or MATH 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.)

Note: Course includes additional fee for online exam proctoring. This course will be hosted online at /login.uconline.edu. It will be available the Friday before class starts. Be sure to check your UCSC email for specific instructions!Proposed Instructor - Anthony Tromba

#### MATH 19B-02

**Session 2**Online only class.

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 MATH 11B, or AM 11B, or AM 15B, or ECON 11B. Prerequisite(s): MATH 19A or MATH 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.)

UCSC students - If you need to take the prerequisite in Session 1, enroll in that course first, then email summer@ucsc.edu for a permission code to enroll in this course.

Note: Course includes additional fee for online exam proctoring. This course will be hosted online at/login.uconline.edu. It will be available the Friday before class starts. Be sure to check your UCSC email for specific instructions!After enrolling in 19A in Session 1, contact summer@ucsc.edu if you need an add code for 19B in Session 2. Visiting students - prerequisites are lifted in summer. It is in your best interest to have passed equivalent prerequisite courses.

Proposed Instructor - Frank Bauerle

#### MATH 21-01

**Session 1**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 AM 10. Prerequisite(s): MATH 11A or MATH 19A or MATH 20A or AM 11A or AM 15A. (General Education Code(s): MF.)

Proposed Instructor - Cisil Karaguzel

#### MATH 21-02

**Session 2**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 AM 10. Prerequisite(s): MATH 11A or MATH 19A or MATH 20A or AM 11A or AM 15A. (General Education Code(s): MF.)

Proposed Instructor - David Rubinstein

#### MATH 21-03

**Session 2**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 AM 10. Prerequisite(s): MATH 11A or MATH 19A or MATH 20A or AM 11A or AM 15A. (General Education Code(s): MF.)

Proposed Instructor - Cisil Karaguzel

#### MATH 22

**Session 1**Functions of several variables. Continuity and partial derivatives. The chain rule, gradient and directional derivative. Maxima and minima, including Lagrange multipliers. The double and triple integral 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): MATH 11B or MATH 19B or MATH 20B or AM 15B or AP calculus BC exam score of 4 or 5. (General Education Code(s): MF.)

UCSC students - If you are completing the prerequisites in Session 1 for a Session 2 course, email summer@ucsc.edu for a permission code for the Session 2 class anytime after you enroll in the Session 1 class(es).

Proposed Instructor - Andres Perico

#### MATH 23A-01

**Session 1**Online only class.

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): MATH 19B or MATH 20B or AP calculus BC exam score of 4 or 5. (General Education Code(s): MF.)

Note: Course includes additional fee for online exam proctoring. This course will be hosted online at /login.uconline.edu. It will be available the Friday before class starts. Be sure to check your UCSC email for specific instructions!Proposed Instructor - Frank Bauerle

#### MATH 23A -02

**Session 2**Online only class.

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): MATH 19B or MATH 20B or AP calculus BC exam score of 4 or 5. (General Education Code(s): MF.)

Proposed Instructor - Anthony Tromba

#### MATH 23B-02

**Session 1**Online only class.

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): MATH 23A.(General Education Code(s): MF.)

Proposed Instructor - Longzhi Lin

#### MATH 23B-01

**Session 2**Online only class.

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): MATH 23A.(General Education Code(s): MF.)

Proposed Instructor - Longzhi Lin

#### MATH 24

**Session 1**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 AM 20. Prerequisite(s): MATH 22 or MATH 23A; MATH 21 is recommended as preparation.

Proposed Instructor - Hirotaka Tamanoi

#### MATH 100-01

**Session 1**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. (General Education Code(s): MF.)

Prerequisite(s): satisfaction of the Entry Level Writing and Composition requirements; MATH 11A or MATH 19A or MATH 20A; and MATH 21 or AM 10 or AMS 10A.

Proposed Instructor - John McHugh

#### MATH 100-02

**Session 2**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. (General Education Code(s): MF.)

Prerequisite(s): satisfaction of the Entry Level Writing and Composition requirements; MATH 11A or MATH 19A or MATH 20A; and MATH 21 or AM 10 or AMS 10A.

Proposed Instructor - Nathan Marianovsky

#### MATH 103A

**Session 2**Complex numbers, analytic and harmonic functions, complex integration, the Cauchy integral formula, Laurent series, singularities and residues, conformal mappings. (Formerly course 103.) Prerequisite(s): MATH 23B; and either MATH 100 or CMPS 101.

UCSC students - f you need to take the prerequisite in Session 1, enroll in that course first, then email summer@ucsc.edu for a permission code to enroll in this course.

Proposed Instructor - Hirotaka Tamanoi

#### MATH 105A

**Session 1**The basic concepts of one-variable calculus are treated rigorously. Set theory, the real number system, numerical sequences and series, continuity, differentiation. Prerequisite(s):MATH 22 or MATH 23B and either MATH 100 or CMPS 101.

Proposed Instructor - Nathan Marianovsky

#### MATH 106

**Session 2**Linear systems, exponentials of operators, existence and uniqueness, stability of equilibria, periodic attractors, and applications. Prerequisite(s): MATH 21 or AM 10; and either MATH 24 or AM 20; and either MATH 100 or CSE 101.

Proposed Instructor - Hirotaka Tamanoi

#### MATH 110 (5 credits)

**Session 1**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): MATH 100 or CSE 101.

Proposed Instructor - Jianqi Lui

#### MATH 110-02

**Session 2**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): MATH 100 or CSE 101.

Proposed Instructor - Jianqi Liu

#### MATH 111T

**Session 2**Introduction to groups, rings and fields; integers and polynomial rings; divisibility and factorization; homomorphisms and quotients; roots and permutation groups; and plane symmetry groups. Also includes an introduction to algebraic numbers, constructible numbers, and Galois theory. Focuses on topics most relevant to future K-12 teachers. Students cannot receive credit for this course and course 111A. Prerequisite(s): MATH 100.

Proposed Instructor - Yonatan Katznelson

#### MATH 117

**Session 1**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. Prerequisite(s): MATH 21 or AM 10 and either MATH 100 or CSE 101.

Proposed Instructor - Yiyi Zhu

#### 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): MATH 19B or MATH 20B. MATH 100 is strongly recommended for preparation. (General Education Code(s): TA.)

Proposed Instructor - John Pelias

## College Algebra for Calculus (5 credits)

## Precalculus (5 credits)

## Precalculus (5 credits)

## Calculus with Applications (5 credits)

## Calculus with Applications (5 credits)

## Calculus for Science, Engineering, and Mathematics (online) (5 credits)

## Calculus for Science, Engineering, and Mathematics (online) (5 credits)

## Calculus for Science, Engineering, and Mathematics (online) (5 credits)

## Calculus for Science, Engineering, and Mathematics (online) (5 credits)

## Linear Algebra (5 credits)

## Linear Algebra (5 credits)

## Linear Algebra (5 credits)

## Introduction to Calculus of Several Variables (5 credits)

## Vector Calculus (online) (5 credits)

## Vector Calculus (online) (5 credits)

## Vector Calculus (online) (5 credits)

## Vector Calculus (online) (5 credits)

## Ordinary Differential Equations (5 credits)

## Introduction to Proof and Problem Solving (5 credits)

## Introduction to Proof and Problem Solving (5 credits)

## Complex Analysis (5 credits)

## Real Analysis (5 credits)

## Systems of Ordinary Differential Equations (5 credits)

## Introduction to Number Theory (5 credits)

## MATH 110 (5 credits)

## Algebra (5 credits)

## Advanced Linear Algebra (5 credits)

## History of Mathematics (5 credits)

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