Students are required to take three upper-division elective courses from the following list of possible electives. Note that many of these electives have lower-division prerequisites. Students should plan carefully which ones to take to ensure they are prepared for their selected upper-division electives. Also note that enrollment in the graduate courses is by permission of the instructor, who will verify adequate preparation.

All students, but especially those doing a double major or a major-minor combination, may also petition to count courses that are not already on the list as electives, subject to approval.

**Applied Mathematics (AM) Electives**

- Any 5-credit upper-division AM course that is not already a core course.
- Any 5-credit graduate AM course with the exception of AM 200, AM 211, AM 212A and AM 214.

**Computer Science and Engineering (CSE) Electives**

**Note: **Many courses require lower-division CSE courses. Lecture-lab combinations count as one course.

- CSE 101 Introduction to Data Structures and Algorithms
- CSE 102 Introduction to Analysis of Algorithms
- CSE 106 Applied Graph Theory and Algorithms
- CSE 140 Artificial Intelligence
- CSE 142 Machine Learning
- CSE 144 Applied Machine Learning
- CSE 160/L Introduction to Computer Graphics and Laboratory
- CSE 161/L Introduction to Data Visualization and Laboratory
- CSE 162/L Advanced Computer Graphics and Animation and Laboratory

**Notes:**

- Note that most of these courses require CSE 101 as a prerequisite and that enrollment restrictions vary and might apply to any of the CSE courses listed here on short notice. CSE 101, CSE 102, CSE 140, CSE 142, and CSE 144 are courses for which enrollment restrictions may apply, and that may only be appropriate for double-majors (or major-minor combinations).
- CSE 162/L is a course that has more than one upper-division prerequisite beyond those that are already part of the core requirements. This course may only be appropriate for double-majors (or major-minor combinations).

**Earth Sciences (EART) Electives**

**Note**: Many courses require lower-division PHYS or CHEM courses:

- EART 124 Modeling Earth’s Climate
- EART 160 Planetary Science
- EART 162 Planetary Interiors
- EART 125 OR EART 225 Statistics and Data Analysis in the Geosciences
- EART 172/OCEA 172 OR EART 272/OCEA 272 Geophysical Fluid Dynamics

**Electrical and Computer Engineering (ECE) Electives**

Lecture-lab combinations count as one course.

- ECE 101/L Introduction to Electronic Circuits and Laboratory
- ECE 103 Signals and Systems
- ECE 115 Introduction to Solid Mechanics
- ECE 135/L Electromagnetic Fields and Waves and Laboratory
- ECE 141 Feedback Control Systems
- ECE 153 Digital Signal Processing

**Notes**:

- Most of these courses require ECE 101/L as a prerequisite.
- ECE 141 and ECE 153 are courses that have more than one upper-division prerequisite beyond those that are already part of the core requirements. These courses may only be appropriate for double majors (or major-minor combinations).

**Economics (ECON) Electives**

**Note**: Many courses require ECON lower-division courses:

- ECON 100M Intermediate Microeconomics, Math Intensive
- ECON 100N Intermediate Macroeconomics, Math Intensive
- ECON 113 Introduction to Econometrics
- ECON 166A/CSE 166A Game Theory and Applications I

**Note**:

- ECON 166A is a course that has more than one upper-division prerequisite beyond those that are already part of the core requirements. This course may only be appropriate for double-majors (or major-minor combinations).

**Mathematics (MATH) Electives**

**Note**: Many MATH electives require MATH 100 as a prerequisite.

- MATH 105A Real Analysis
- MATH 110 Introduction to Number Theory
- MATH 111A Algebra
- MATH 111T Algebra
- MATH 115 Graph Theory
- MATH 116 Combinatorics
- MATH 117 Advanced Linear Algebra
- MATH 118 Advanced Number Theory
- MATH 120 Coding Theory
- MATH 134 Cryptography
- MATH 160 Mathematical Logic I

**Ocean Sciences (OCEA) Electives**

**Note**: Some OCEA Electives require lower-division PHYS electives, or upper-division EART electives:

- OCEA 260/EART 260 Introductory Data Analysis in the Ocean and Earth Sciences
- OCEA 286 Introduction to Ocean Modeling
- OCEA 100 OR OCEA 200 Physical Oceanography
- OCEA 111 OR OCEA 211 Climate Dynamics

**Physics (PHYS) Electives**

**Note**: Many courses require lower-division PHYS courses:

- PHYS 105 Mechanics
- PHYS 110A Electricity, Magnetism, and Optics
- PHYS 110B Electricity, Magnetism, and Optics
- PHYS 139A Quantum Mechanics I
- PHYS 139B Quantum Mechanics II
- PHYS 150 Quantum Computing
- PHYS 171/ASTR 171 General Relativity, Black Holes, and Cosmology

**Notes**:

- The prerequisites of PHYS 116A, PHYS 116B, and PHYS 116C is waived for students who have taken AM 100 and AM 112 and STAT 131(or CSE 107).
- PHYS 139A, PHYS 139B, PHYS 171 are courses that have more than one upper-division prerequisite beyond those that are already part of the core requirements. These courses may only be appropriate for double majors (or major-minor combinations).

**Statistics (STAT) Electives**

- STAT 132 Classical and Bayesian Inference