# 2021 Remote 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 - Ryan Pugh

#### 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. General Education Code MF

Prerequisite(s): MATH 2 or mathematics placement (MP) score of 200 or higher. Students may not enroll in or receive credit for MATH 3 after receiving credit with a 'C' or better in AM 11A, MATH 11A, MATH 19A, MATH 20A or equivalents.

Proposed Instructor - Maryam Nashed

#### 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. General Education Code MF

Prerequisite(s): MATH 2 or mathematics placement (MP) score of 200 or higher. Students may not enroll in or receive credit for MATH 3 after receiving credit with a 'C' or better in AM 11A, MATH 11A, MATH 19A, MATH 20A or equivalents.

Proposed Instructor - Maryam Nashed

#### MATH 11A-01

**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. General Education Code MF

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.

Proposed Instructor - Cisil Karaguzel

#### MATH 11A-02

**Session 2**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. General Education Code MF

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.

Proposed Instructor - Amethyst Price

#### MATH 11B-01

**Session 1**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. General Education Code MF

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.

Proposed Instructor - Alonso Sanchez

#### MATH 11B-02

**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. General Education Code MF

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.

Proposed Instructor - Cheyenne Dowd

#### MATH 19A-01

**Session 1**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. General Education Code MF

Prerequisite(s): MATH 3; or mathematics placement (MP) score of 400 or higher; or AP Calculus AB exam score of 3 or higher.

Proposed Instructor - Frank Bauerle

#### MATH 19A-02

**Session 2**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. General Education Code MF

Prerequisite(s): MATH 3; or mathematics placement (MP) score of 400 or higher; or AP Calculus AB exam score of 3 or higher.

Proposed Instructor - Frank Bauerle

#### MATH 19B-01

**Session 1**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. General Education Code MF

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.

Proposed Instructor - Anthony Tromba

#### MATH 19B-02

**Session 2**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. General Education Code MF

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.

Proposed Instructor - Anthony Tromba

#### 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. General Education Code MF

Prerequisite(s): MATH 11A or MATH 19A or MATH 20A or AM 11A or AM 15A.

Proposed Instructor - Mita Banik

#### 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. General Education Code MF

Prerequisite(s): MATH 11A or MATH 19A or MATH 20A or AM 11A or AM 15A.

Proposed Instructor - John McHugh

#### 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. General Education Code MF

Prerequisite(s): MATH 11A or MATH 19A or MATH 20A or AM 11A or AM 15A.

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 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 MATH 23A. General Education Code MF

Prerequisite(s): MATH 11B or MATH 19B or MATH 20B or AM 15B or AP calculus BC exam score of 4 or 5.

Proposed Instructor - Jadyn Breland

#### MATH 23A-01

**Session 1**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 MATH 22 or AM 30. General Education Code MF

Prerequisite(s): MATH 19B or MATH 20B or AP calculus BC exam score of 4 or 5.

Proposed Instructor - Anthony Tromba

#### MATH 23A -02

**Session 2**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 MATH 22 or AM 30. General Education Code MF

Prerequisite(s): MATH 19B or MATH 20B or AP calculus BC exam score of 4 or 5.

Proposed Instructor - Frank Bauerle

#### MATH 23B-01

**Session 1**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. General Education Code MF

Prerequisite(s): MATH 23A.

Proposed Instructor - Longzhi Lin

#### MATH 23B-02

**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. General Education Code MF

Prerequisite(s): MATH 23A.

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 - Cheyenne Dowd

#### 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 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 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 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 - Sam Miller

#### MATH 103A

**Session 2**Complex numbers, analytic and harmonic functions, complex integration, the Cauchy integral formula, Laurent series, singularities and residues, conformal mappings.

Prerequisite(s): MATH 23B; and either MATH 100 or CSE 101.

Proposed Instructor - Hirotaka Tamanoi

#### MATH 105A

**Session 2**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 CSE 101.

Proposed Instructor - John McHugh

#### 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 110-01

**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 - Deewang Bhamidipati

#### 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 117-01

**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 - Yufei Zhang

#### MATH 117-02

**Session 2**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 - Nathan Marianovsky

#### MATH 124

**Session 1**Topics include introduction to point set topology (topological spaces, continuous maps, connectedness, compactness), homotopy relation, definition and calculation of fundamental groups and homology groups, Euler characteristic, classification of orientable and nonorientable surfaces, degree of maps, and Lefschetz fixed-point theorem.#### MATH 134

**Session 1**Introduces different methods in cryptography (shift cipher, affine cipher, Vigenere cipher, Hill cipher, RSA cipher, ElGamal cipher, knapsack cipher). The necessary material from number theory and probability theory is developed in the course. Common methods to attack ciphers discussed.

Prerequisite(s): MATH 100 or CSE 101; MATH 110 is recommended as preparation.

Proposed Instructor - Philip Barron

#### MATH 181

**Session 2**A survey from a historical point of view of various developments in mathematics. Specific topics and periods to vary yearly. General Education Code TA

Prerequisite(s): MATH 19B or MATH 20B. MATH 100 is strongly recommended for preparation.

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 with Applications (5 credits)

## Calculus with Applications (5 credits)

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

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

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

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

## Linear Algebra (5 credits)

## Linear Algebra (5 credits)

## Linear Algebra (5 credits)

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

## Vector Calculus (5 credits)

## Vector Calculus (online) (5 credits)

## Vector Calculus (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)

## MATH 110 (5 credits)

## Advanced Linear Algebra (5 credits)

## Advanced Linear Algebra (5 credits)

## Introduction to Topology (5 credits)

## Cryptography (5 credits)

## History of Mathematics (5 credits)

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