# Mathematics Summer Courses

#### MATH 2 [In Person]

**Session 2**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. Students may not enroll in or receive credit for MATH 2 after receiving credit with a 'C' or better in AM 3, MATH 3, AM 11A, MATH 11A, MATH 19A, MATH 20A or equivalents.

Proposed Instructor: Divya Maneesha Ampagouni

#### MATH 3-01 [Online]*

**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. 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.

General Education Code: MF

Proposed Instructor: Malachi Alexander*Pending CCI Approval

#### MATH 3-02 [Online]*

**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.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.

General Education Code: MF

Proposed Instructor: Malachi Alexander*Pending CCI Approval

#### MATH 11A [Online]*

**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: MF

Proposed Instructor: Sophie Aiken*Pending CCI Approval

#### MATH 11A [Online]*

**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. 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: MF

Proposed Instructor: Sophie Aiken*Pending CCI Approval

#### MATH 11B [Online]*

**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: MF

Proposed Instructor: Deewang Bhamidipati*Pending CCI Approval

#### Math 16A [In Person]*

**Session 2**Introduction to mathematical modeling of systems in biology and the environment. Mathematical topics include functions, sequences, conceptual calculus and differential equations, taught through examples, computation, and visualization. Computational tools include interactive graphing software, spreadsheets, and a high-level programming language (e.g., Python). Modeling systems in the environment, ecology, evolution, cell, and molecular biology. Representing systems in state space, and studying change through derivatives. Analyzing equilibria in one- and two-dimensional systems.

General Education Code: MF

Proposed Instructor: Marty Weissman*Pending CCI Approval

#### MATH 19A-01 [Online]

**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. 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: MF

Proposed Instructor: Frank Bauerle#### MATH 19A-02 [Online]

**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. 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: MF

Proposed Instructor: Tony Tromba#### MATH 19B-01 [Online]

**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. 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: MF

Proposed Instructor: Longzhi Lin#### MATH 19B-02 [Online]

**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

Proposed Instructor: Frank Bauerle#### MATH 21-01 [Online]*

**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

Proposed Instructor: Cheyenne Dowd*Pending CCI Approval

#### MATH 21-02 [Online]*

**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

Proposed Instructor: Cheyenne Dowd*Pending CCI Approval

#### MATH 22 [In Person]

**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. 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: MF

Proposed Instructor: Jadyn Breland#### MATH 23A-01 [Online]

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

General Education Code: MF

Proposed Instructor: Tony Tromba#### MATH 23A-02 [Online]

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

General Education Code: MF

Proposed Instructor: Longzhi Lin#### MATH 23B-01 [Online]

**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. Prerequisite(s): MATH 23A.

General Education Code: MF

Proposed Instructor: Frank Bauerle#### MATH 23B-02 [Online]

**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. Prerequisite(s): MATH 23A.

General Education Code: MF

Proposed Instructor: Tony Tromba#### MATH 24 [In Person]

**Session 2**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 [In Person]

**10-Week**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; MATH 11A or MATH 19A or MATH 20A; and MATH 21 or AM 10 or AMS 10A.

General Education Code: MF

Proposed Instructor: John Pelias#### MATH 100-02 [In Person]

**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; MATH 11A or MATH 19A or MATH 20A; and MATH 21 or AM 10 or AMS 10A.

General Education Code: MF

Proposed Instructor: Suzana Șerboi#### MATH 103A [In Person]

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.**10-WeeK**Proposed Instructor: Hirotaka Tamanoi

#### MATH 105A [In Person]

#### MATH 106 [In Person]

**Session 1**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: Fulya Tastan

#### MATH 110 [In Person]

**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: Amethyst Price

#### MATH 111A [In Person]

**10-Week**Group theory including the Sylow theorem, the structure of abelian groups, and permutation groups. Students cannot receive credit for this course and MATH 111T. Prerequisite(s): MATH 21 or AM 10 and either MATH 100 or CSE 101.

Proposed Instructor: Albert Zhang

#### MATH 115 [In Person]

**Session 1**Graph theory, trees, vertex and edge colorings, Hamilton cycles, Eulerian circuits, decompositions into isomorphic subgraphs, extremal problems, cages, Ramsey theory, Cayley's spanning tree formula, planar graphs, Euler's formula, crossing numbers, thickness, splitting numbers, magic graphs, graceful trees, rotations, and genus of graphs. Prerequisite(s): MATH 21 or AM 10 and either MATH 100 or CSE 101.

Proposed Instructor: Suzana Șerboi

#### MATH 117 [In Person]

#### MATH 181 [In Person]

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.**Session 1**

General Education Code: TA

Proposed Instructor: Deewang Bhamidipati#### MATH 194 [In Person]

**Session 1**Designed to expose the student to topics not normally covered in the standard courses. The format varies from year to year. In recent years each student has written a paper and presented a lecture on it to the class. Prerequisite(s): satisfaction of the Entry Level Writing and Composition requirements; MATH 103A or MATH 105A or MATH 110 or MATH 111A or MATH 111T or MATH 117. Enrollment priority is given to seniors; juniors may request permission from the undergraduate vice chair.

Proposed Instructor: Viktor Ginzburg