# 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.

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 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.)

Visiting students - prerequisites are lifted in summer. It is in your best interest to have passed equivalent prerequisite courses.

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 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.)

Visiting students - prerequisites are lifted in summer. It is in your best interest to have passed equivalent prerequisite courses.

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 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.)

After enrolling in 11A, contact summer@ucsc.edu for an add code if you'd like to take 11B in Session 2. Visiting students - prerequisites are lifted in summer. It is in your best interest to have passed equivalent prerequisite courses.

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 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.)

If you need to take 11A in Session 1, enroll first then contact summer@ucsc.edu for an add code for 11B. Visiting students - prerequisites are lifted in summer. It is in your best interest to have passed equivalent prerequisite courses.

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 course 11A or Applied Mathematics and Statistics 11A and 15A,or Economics 11A. Prerequisite(s): course 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!After enrolling in 19A, contact summer@ucsc.edu if you need an add code for 19B. Visiting students - prerequisites are lifted in summer. It is in your best interest to have passed equivalent prerequisite courses.

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 course 11A or Applied Mathematics and Statistics 11A and 15A

,or Economics 11A. Prerequisite(s): course 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 class starts. Be sure to check your UCSC email for specific instructions!If you enroll in Math 3 in Session 1, contact summer@ucsc.edu for an add code to 19A 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 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 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.)

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 19B in Session 1, contact summer@ucsc.edu if you need an add code for 23A in Session 2. Visiting students - prerequisites are lifted in summer. It is in your best interest to have passed equivalent prerequisite courses.

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 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.)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 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.)

Visiting students - prerequisites are lifted in summer. It is in your best interest to have passed equivalent prerequisite courses.

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 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.)

Proposed Instructor - David Rubinstein

#### 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 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.)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): course 19B or 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!After enrolling in 23A in Session 1, contact summer@ucsc.edu if you need an add code for 23B 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 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): course 19B or 20B or AP calculus BC exam score of 4 or 5. (General Education Code(s): MF.)

After enrolling in 19B in Session 1, contact summer@ucsc.edu if you need an add code for 23A in Session 2. Visiting students - prerequisites are lifted in summer. It is in your best interest to have passed equivalent prerequisite courses.

Proposed Instructor - Anthony Tromba

#### MATH 23B

**Session 2**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.)After enrolling in 23A in Session 1, contact summer@ucsc.edu for an add code for 23B in Session 2. Visiting students - prerequisites are lifted in summer. It is in your best interest to have passed equivalent prerequisite courses.

Proposed Instructor - Sami Cineli

#### 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 Applied Mathematics and Statistics 20. Prerequisite(s): course 22 or 23A; course 21 is recommended as preparation.

If taking your last prerequisite in Session 1 contact summer@ucsc.edu for a permission code for this Session 2 class. Visiting students - prerequisites are lifted in summer. It is in your best interest to have passed equivalent prerequisite courses.

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. Prerequisite(s): satisfaction of the Entry Level Writing and Composition requirements; course 11A or 19A or 20A; and course 21 or Applied Mathematics and Statistics 10 or Applied Mathematics and Statistics 10A. Enrollment limited to 80. (General Education Code(s): MF.)

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. Prerequisite(s): satisfaction of the Entry Level Writing and Composition requirements; course 11A or 19A or 20A; and course 21 or Applied Mathematics and Statistics 10 or Applied Mathematics and Statistics 10A. Enrollment limited to 80. (General Education Code(s): MF.)

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): course 23B; and either course 100 or Computer Science 101.

If taking your last prerequisite in Session 1 contact summer@ucsc.edu for a permission code for this Session 2 class. Visiting students - prerequisites are lifted in summer. It is in your best interest to have passed equivalent prerequisite courses.

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): course 22 or 23B and either course 100 or Computer Science 101.

Proposed Instructor - Nathan Marianovsky

#### MATH 106

Session 2

Linear systems, exponentials of operators, existence and uniqueness, stability of equilibria, periodic attractors, and applications. (Formerly course 106A.) Prerequisite(s): courses 21 and 24 (preferred) or Applied Mathematics and Statistics 10 and 20; and either course 100 or Computer Science 101.

Proposed Instructor - Hirotaka Tamanoi

#### MATH 110

**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): course 100 or Computer Science 101.

Proposed Instructor - Yonatan Katznelson

#### 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.

If taking your last prerequisite in Session 1, contact summer@ucsc.edu for a permission code for this Session 2 class. Visiting students - prerequisites are lifted in summer. It is in your best interest to have passed equivalent prerequisite courses.

Proposed Instructor - Jianqi Lui

#### 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): course 21 or Applied Mathematics and Statistics 10 and either course 100 or Computer Science 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): course 19B or 20B. Course 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)

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

## Vector Calculus (online) (5 credits)

## Vector Calculus (online) (5 credits)

## Vector Calculus (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)

## Algebra (5 credits)

## Advanced Linear Algebra (5 credits)

## History of Mathematics (5 credits)

High Schooler? Not sure which class is right for you? Click here for more information.