# Core Requirements

Effective September 1, 2023 - version G4.1

(students who declared in prior years may use requirements in effect during that year or later. See the Bulletin Archive for past versions of the requirements.)

*Updated December 5, 2023 - additional text added next to asterisk for Single Variable Calculus requirement, clarifying options for Replacement Petitions; December 1, 2023 - CS 147L now counts as a stand-alone option for fulfilling the post-CS 106B Computational Methods Breadth Requirement, without needing to be paired with CS 147 (note that the CS 147 + selected 193x courses option will be eliminated for that requirement for majors declaring after Spring 2024); September 26, 2023 - new options added for the formal logic requirement and Capstone Standard Options*

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. The Course Plan form for the Bachelor of Science degree summarizes the structure of both the Core and the Concentrations, as well as how they interact.

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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 either 21: Calculus or 21A: Calculus, ACE
- Note: Effective Autumn 2023-24, Credit for MATH 21 is an enforced prerequisite for enrolling in MATH 51 or CME 100. Please read the Math Department's rationale for requiring MATH 21 prior to a course in multivariable calculus.

- 10 units of Stanford credit duplicating MATH 19, 20, and 21, achieved through Advanced Placement or other international exams
- Both of the following:
- 6 units of Stanford credit duplicating MATH 19 and 20, achieved through Advanced Placement or other international exams
- Either MATH 21: Calculus or MATH 21A: Calculus, ACE

*At the request of the Mathematics Department, the Mathematics Placement Diagnostic option that was previously available for fulfilling all or part of the Single-Variable Calculus requirement may only be utilized by students who were declared and approved as Symbolic Systems majors before the end of the Academic Year 2022-23. See the previous Bulletin from 2022-23 for the G4.0 requirements if you are eligible to complete them. Students who were not declared SymSys majors prior to September 1, 2023 but who (a) completed the Multivariate Systems requirement (see below) prior to the 2023-24 academic year and (b) placed into MATH 51 on the Mathamatics Placement Diagnostic may submit a Replacement Petition under the Requirement Versions Transition category, to use their Placement Diagnostic result to fulfill the Single Variable Calculus requirement. This option is not available to students who had not fulfilled the Multivariate Systems requirement prior to 2023-24. Any student in the major may submit a Replacement Petition under the Up-Level Replacement category to replace units in the MATH 19-20-21 series. All Replacement Petitions are subject to approval by the Symbolic Systems Program and must meet the criteria described under the submitted category.

### 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

* NOTE: The Symbolic Systems Program recommends these courses as preferred ways for most students to fulfill the Multivariate Systems requirement, because of their more extensive coverage of linear algebra methods used in many higher level courses which are options for the major.

### 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 56: Proofs and Modern Mathematics
*(may be paired with MATH 51; may also be useful as preparation for entry into PHIL 151, CS 154, or CS 157 -- see "Formal Methods" under "Breadth Requirements")* - 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 177K: On Domination (ETHICSOC 177K, ETHICSOC 277K, PHIL 277K)
- 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 184B: Formal Epistemology
- PHIL 184M: Topics in the Theory of Justification
- PHIL 186: Philosophy of Mind (PHIL 286)
- PHIL 187: Philosophy of Action (PHIL 287)
- PHIL 189G: Fine-Tuning Arguments for God's Existence
- SYMSYS 205: The Philosophy and Science of Perception
- SYMSYS 207: Conceptual Issues in Cognitive Science

### 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**)]* - PHIL 152: Computability and Logic (PHIL 252)
*[prerequisite: PHIL 151]*

- 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 147L: Cross-platform Mobile App Development
- 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 introduction to an area. A course with no prerequisites beyond PSYCH 1 and/or SYMSYS 1, covering a disciplinary division or subdivision in cognition, language, and neuroscience. One of the following:
- BIO 150: Human Behavioral Biology (HUMBIO 160)
- LINGUIST 105: Phonetics (LINGUIST 205A)
- LINGUIST 130A: Introduction to Semantics and Pragmatics (LINGUIST 230A)
- LINGUIST 130B: Introduction to Lexical Semantics
- 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 applying formal methods to language and communication. One of the following:
- LINGUIST 110: Introduction to Phonology
- LINGUIST 116A: Introduction to Word Formation
- LINGUIST 121A: The Syntax of English
- LINGUIST 121B: Crosslinguistic Syntax
- LINGUIST 130A: Introduction to Semantics and Pragmatics (LINGUIST 230A)
- LINGUIST 130B: Introduction to Lexical Semantics
- LINGUIST 145: Introduction to Psycholinguistics (LINGUIST 245A, PSYCH 140)
- LINGUIST 160: Historical Linguistics

### 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: These should be completed 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

An experiential requirement consisting of the following components, planned in consultation with, and approved by, a student's Concentration Adviser (3 or more units each). To obtain approval for your Capstone plan, please submit the Capstone Approval Form. Note, this form must be submitted in addition to your Symsys Course Plan. Additionally, your Capstone plan is subject to final approval by the Symbolic Systems Program office.

#### 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 or CS 177: Human-Centered Project Management
- 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)
- One of the following courses, taken in conjunction with section leading in a SymSys Core course:
- SYMSYS 197: Practicum in Teaching SYMSYS 1
- PSYCH 182: Practicum in Teaching PSYCH 1
- CS 198: Teaching Computer Science

#### Integrative Requirement*

Either an additional research project course (e.g., the second course of an Honors Project) or a Concentration-Specific Integrative Course. The Integrative Requirement * 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) or CS 177: Human-Centered Project Management
- 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 (CSIC) taken within a Concentration. CSICs are courses that integrate the themes of the Concentration with the Core requirements, i.e. Breadth Requirements other than in the area of the Concentration itself

*Units must be applied to a student's Concentration

#### Presentation Requirement (not a course requirement, check-off only)

A public presentation of the student's work at one of the following annual events:

- Symbolic Systems Autumn Poster Fair for Summer interns and Capstone Projects
- Symbolic Systems Spring Graduation Fair for Capstone and Master's Projects
- Symbolic Systems Senior Honors Forum at the end of Spring Quarter

The above Core is part of the G4 requirements (with later variations noted in each year's Bulletin), which took effect on September 1, 2020. Students who had sophomore standing as of Fall 2020, or have declared a SymSys major prior to Fall 2020, have the option to continue under the G3 requirements.