# Core Requirements

Effective September 1, 2020

The Core defines the required program of courses that all students in the major must complete, and is distinguished from a student's Concentration. Core requirements are on average completed earlier than a student's Concentration, but the only requirements that impose explicit restrictions on when a course can be completed during a student's undergraduate career are the Gateway and Capstone requirements. The presentation of Core requirements below is meant to convey information about the conceptual precedence and preferred sequencing of courses in the Core. Course instructors may, additionally, restrict entry to certain courses to students who have completed listed prerequisites, See the information specific to each course in ExploreCourses and consult with course instructors for more information on the expected or required preparation for each course.

NOTE: All Core courses must be passed for 3 units or more, with a letter grade of C- or better, or with an S grade, or an equivalent no-option passing grade, except as modified by the Covid-19 policies in effect during 2020-2021. See the Minimum Units Policy, Grading Basis Policy and Minimum Grade Policy under Major Policies for more details. See also the procedures for Course Nominations and Replacement Petitions.

In order to graduate with a B.S. in Symbolic Systems, a student must complete the following core courses, plus a five-course Concentration.

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Preparations: These courses should be completed early in the major

### Gateway Course

Must be taken before a major declaration can be approved.

- SYMSYS 1: Minds and Machines (CS 24, LINGUIST 35, PHIL 99, PSYCH 35)

### Single Variable Calculus

One of the following:

- MATH 19, 20, and 21 (or 21A): Calculus
- 10 units of Advanced Placement Calculus credit
- Placement by the Mathematics Placement Diagnostic into MATH 20 or 21 and completion of the rest of the series, or into MATH 51

### Multivariate Systems

One of the following:

- MATH 51: Linear Algebra, Multivariable Calculus, and Modern Applications
- MATH 51A: Linear Algebra, Multivariable Calculus, and Modern Applications, ACE
- MATH 61CM: Modern Mathematics: Continuous Methods
- MATH 61DM: Modern Mathematics: Discrete Methods
- CME 100: Vector Calculus for Engineers (ENGR 154)
- CME 100A: Vector Calculus for Engineers, ACE

### Further Study in Multivariate Systems

(Optional, but recommended, and may count within some Concentrations)

One or more of the following courses, which may be needed as preparation for some Core options and other advanced courses in the major:

- MATH 52: Integral Calculus of Several Variables, and/or MATH 53: Ordinary Differential Equations with Linear Algebra
- MATH 63CM and (optionally) MATH 62CM: Modern Mathematics: Continuous Methods
- MATH 62DM and/or MATH 63DM: Modern Mathematics Discrete Methods [Note: MATH 63DM counts for the Probability Theory and Statistics Core requirement]
- MATH 113: Linear Algebra and Matrix Theory
- MATH 104: Applied Matrix Theory [prerequisite: CS 106A]
- CME 102: Ordinary Differential Equations for Engineers (ENGR 155A) and (optionally) CME 104: Linear Algebra and Partial Differential Equations for Engineers (ENGR 155B)
- CME 102A: Ordinary Differential Equations for Engineers, ACE, and (optionally) CME 104A: Linear Algebra and Partial Differential Equations for Engineers, ACE
- CME 103: Introduction to Matrix Methods (EE 103) [prerequisite: CS 106A or programming experience]

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Breadth Requirements: One three-quarter sequence of training in each of four methodological areas, plus a Cross-Area Requirement

### Philosophical Analysis

Courses that focus on critical, deep questioning, careful reasoning, introspection, and argumentation, and the meaning of intuitions, scenarios, and evidence. Each of the following:

- An introductory course in the Philosophy Department or a Thinking Matters course taught by a Philosophy Department faculty member. One of the following:
- Any course of 3 units or more listed with a PHIL course number (with the exception of PHIL 99/SYMSYS 1)
- THINK 69: Emotion

- Writing in the Major (WIM) Course.
- PHIL 80: Mind, Matter, and Meaning

- An advanced undergraduate Philosophy course that lists PHIL 80 as a prerequisite. One of the following:
- PHIL 107B: Plato's Later Metaphysics and Epistemology
- PHIL 167D: Philosophy of Neuroscience (PHIL 267D, SYMSYS 206A)
- PHIL 172: History of Modern Moral Philosophy
- PHIL 173B: Metaethics
- PHIL 175: Philosophy of Law
- PHIL 180: Metaphysics (PHIL 280)
- PHIL 180A: Realism, Anti-Realism, Irrealism, Quasi-Realism (PHIL 280A)
- PHIL 181: Philosophy of Language (PHIL 281)
- PHIL 182: Advanced Philosophy of Language (PHIL 282)
- PHIL 182A: Naturalizing Representation (PHIL 282A)
- PHIL 182H: Truth (PHIL 282H)
- PHIL 184: Formal and Informal Epistemology (PHIL 284)
- PHIL 186: Philosophy of Mind (PHIL 286)
- PHIL 187: Philosophy of Action (PHIL 287)
- PHIL 189G: Fine-Tuning Arguments for God's Existence

### Formal Methods

Courses that focus on rigorous definitions, axioms, theorems, and proofs, and their use in developing mathematical theories and meta-theories. Each of the following:

- Formal Logic. One of the following:
- Theory of Computation. One of the following:
- CS 103: Mathematical Foundations of Computing
*[corequisite: CS 106B or X]* - CS 154: Introduction to Automata and Complexity Theory
*[prerequisite: CS103 or significant proof-writing experience (see the**course description for CS 103**)]*

- CS 103: Mathematical Foundations of Computing
- Probability Theory and Statistics. A course that covers the theory of probability and is grounded in multivariable calculus. One of the following:
- CS 109: Introduction to Probability for Computer Scientists
- STATS 116: Theory of Probability
- STATS 110: Statistical Methods in Engineering and the Physical Sciences
- MS&E 120: Probabilistic Analysis
- MS&E 220: Probabilistic Analysis
- EE 178: Probabilistic Systems Analysis (same as EE 278A)
- CME 106: Introduction to Probability and Statistics for Engineers (ENGR 155C)
- MATH 151: Introduction to Probability Theory
- MATH 63DM: Modern Mathematics: Discrete Methods

### Computational Methods

Courses that focus on software design, data structures, algorithms, development, applications, evaluation, and simulation. Each of the following:

- Programming I. One of the following:
- CS 106A: Programming Methodology
- Equivalent preparation, as evidenced by successful completion of CS 106B or 106X

- Programming II. One of the following:
- A post-CS 106B course covering one or more broad computational methods with a substantial programming component. One of the following:
- CS 107: Computer Organization and Systems
- CS 107E: Computer Systems from the Ground Up
- CS 129. Applied Machine Learning
- CS 147: Introduction to Human-Computer Interaction Design,
*plus*one of the following: - CS 221: Artificial Intelligence: Principles and Techniques
- CS 229: Machine Learning (STATS 229)
- CS 230: Deep Learning

### Empirical Cognitive Science

Courses that focus on questions, hypotheses, models, predictions, and explanations that are derived from or testable in neural and behavioral data. Each of the following:

- Overview of psychology.
- PSYCH 1: Introduction to Psychology

- An introductory area course in cognition, language, and neuroscience. One of the following:
- BIO 150: Human Behavioral Biology (HUMBIO 160)
- LINGUIST 145: Introduction to Psycholinguistics (LINGUIST 245A, PSYCH 140)
- LINGUIST 150: Language and Society
- PSYCH 30: Introduction to Perception
- PSYCH 45: Introduction to Learning and Memory
- PSYCH 50: Introduction to Cognitive Neuroscience
- PSYCH 60: Introduction to Developmental Psychology
- PSYCH 70: Self and Society: Introduction to Social Psychology (SOC 2)
- PSYCH 75: Introduction to Cultural Psychology
- PSYCH 141: Cognitive Development
- PSYCH 154: Judgment and Decision-Making

- Linguistic Theory. A course introducing a core area of theoretical inquiry in linguistics. One of the following:
- LINGUIST 105: Phonetics (LINGUIST 205A)
- LINGUIST 110: Introduction to Phonology
- LINGUIST 120: Introduction to Syntax
- LINGUIST 130A: Introduction to Semantics and Pragmatics (LINGUIST 230A)
- LINGUIST 130B: Introduction to Lexical Semantics
- Additional approved undergraduate courses offered on a semi-regular basis:
- LINGUIST 21N: Linguistic Diversity and Universals: The Principles of Language Structure
- LINGUIST 30N: Linguistic Meaning and the Law
- LINGUIST 121A: The Syntax of English
- LINGUIST 121B: Crosslinguistic Syntax
- LINGUIST 134A: The Structure of Discourse: Theory and Applications (LINGUIST 234)
- LINGUIST 160: Introduction to Language Change

### Cross-Area Requirement

A non-introductory course, which has as a prerequisite at least one Core course (or equivalent), and which combines methods and subject matter from at least two Breadth areas in the Core.

- Suggested courses for most students. Any of those listed below:
- CS 147: Introduction to Human-Computer Interaction Design
- CS 229: Machine Learning (STATS 229)
- LINGUIST 130A: Introduction to Semantics and Pragmatics (LINGUIST 230A)
- LINGUIST 180: From Languages to Information (CS 124, LINGUIST 280)
- PHIL 152: Computability and Logic (PHIL 152)
- PHIL 154: Modal Logic (PHIL 254)
- PHIL 167D: Philosophy of Neuroscience
- PHIL 181: Philosophy of Language (PHIL 281)
- PSYCH 204. Computation and Cognition: the Probabilistic Approach
- PSYCH 209: Neural Network Models of Cognition

- Any other course on the full list of approved Cross-Area Requirement courses

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Experiential Requirements: Courses that should be taken later in the major

### Advanced Small Seminar Requirement*

- An approved course which
- Builds on the Core Preparations and Breadth Requirements
- Enrolls no more than 20 students
- Is an interactive, discussion-based seminar

*May be double-counted for an applicable Concentration requirement, but not for a Core requirement.

Current Year Advanced Small Seminar Course Options

### Capstone

A two-course requirement consisting of the following components, chosen in consultation with, and approved by, a student's Concentration Adviser (3 or more units each):

#### Practicum

A project or internship-accompanying course. One of the following:

- SYMSYS 190: Senior Honors Tutorial (taken under a student's Honors Adviser)
- An approved project course with a SYMSYS listing in the 195-series
- Supervised research with a faculty member on an approved symbolic-systems related project, taken as SYMSYS 196: Independent Study, or a department-based directed research course
- SYMSYS 192: Symbolic Systems in Practice (must be taken in conjunction with an approved internship or service project)

#### Integrative Requirement*

Either an additional research project course (e.g., the second course of an Honors Project) or a Concentration-Specific Integrative Course, which ** must be completed no earlier than the Junior Year**.

One of the following (the first three bulleted options are the *Standard Options* available across all Concentrations):

- SYMSYS 190: Senior Honors Tutorial (continuation of the course taken for the Practicum requirement)
- An approved project course with a SYMSYS listing in the 195-series (may be either the second quarter of a 2-quarter course, or a one-quarter course)
- Supervised research with a faculty member on an approved symbolic-systems related project, taken as SYMSYS 196: Independent Study, or a department-based directed research course (may be either the second quarter of a 2-quarter course or a one-quarter course)
- An approved Concentration-Specific Integrative Course taken within a Concentration.

*Units must be applied to a student's Concentration

Students who have sophomore standing as of Fall 2020, or have declared a SymSys major prior to Fall 2020, have the option to continue under the previous requirements.