Degree Requirements

The student must have a grade point average (GPA) of 3.0 or better in all course work used to fulfill the major requirement.
At least three quarters before graduation, majors must file with their advisor a plan for completing degree requirements.

All courses used to fulfill major requirements must be taken for a letter grade with the exception of courses offered satisfactory/no credit only.
Students who earn less than a 'C+' in course Theory of Probability or course Introduction to Statistical Inference must repeat the course.
Only one MCS core course can be substituted by filing a petition with their advisor (with the exception of course Introduction to Statistical Inference which cannot be substituted). The Course Substitution Form must be submitted the quarter prior to enrolling in the course.
Course transfer credit is subject to department evaluation and to the Office of the Registrar's external credit evaluation. These courses may result in a replacement course for MCS required course or may establish placement in a higher-level course. Transfer requests must first be submitted to Student Services Center prior to being evaluated by your advisor. Submit the MCS Program Transfer Credit Form to the student services office.
Students may take their three electives courses for credit (CR).
Students may be granted a one-time exception to take a core course for credit (CR) with the exception of course and course.
The University requires students to complete at least one approved writing-intensive course in each of their majors. See the Hume Center for Writing and Speaking web site for a full description of the WIM requirement.

Course Requirements

		Units
		Course List
Mathematics (MATH)		28
Single-variable calculus or AP credit. 1
course	Calculus	3
course	Calculus	3
course	Calculus	4
Students may choose one of the following sequences:		15
Multivariable Calculus and Linear Algebra
course	Linear Algebra, Multivariable Calculus, and Modern Applications
course	Integral Calculus of Several Variables
course	Ordinary Differential Equations with Linear Algebra
Modern Mathematics: Continuous Methods (a proof-oriented sequence)
course	Modern Mathematics: Continuous Methods
course	Modern Mathematics: Continuous Methods
course	Modern Mathematics: Continuous Methods
Modern Mathematics: Discrete Methods (a proof-oriented sequence)
course	Modern Mathematics: Discrete Methods
course	Modern Mathematics: Discrete Methods
course	Modern Mathematics: Discrete Methods
Select one of the following:		3
course	Applied Matrix Theory
course	Linear Algebra and Matrix Theory
Computer Science (CS)		22-25
course	Mathematical Foundations of Computing	5
course	Programming Methodology	5
and either
course	Programming Abstractions	5
or course	Programming Abstractions
Select two of the following:		7-10
course	Introduction to Scientific Computing
course	Computer Organization and Systems
course	Introduction to the Theory of Computation
course	Design and Analysis of Algorithms
course	Computers, Ethics, and Public Policy
course	Ethics, Public Policy, and Technological Change
Management Science and Engineering (MS&E)		7-11
course	Introduction to Optimization (Accelerated)	3-4
course	Stochastic Modeling	3
Or select three of the following:		9-11
course	Introduction to Optimization
course	Introduction to Stochastic Modeling
course	Introduction to Optimization
course	Introduction to Optimization Theory
course	Stochastic Modeling
course	Introduction to Stochastic Control with Applications
Statistics (STATS)		10-11
course	Theory of Probability	3-4
or course	Introduction to Probability Theory
course	Introduction to Statistical Inference	4
Select one of the following:		3
course	Introduction to Applied Statistics
course	Introduction to Regression Models and Analysis of Variance
Writing in the Major (WIM)		3-5
Choose one from the MCS-designated WIM courses to fulfill the Writing in the Major requirement:
course	Applied Group Theory
course	Applied Number Theory and Field Theory
course	Groups and Rings
course	Fundamental Concepts of Analysis
course	Computers, Ethics, and Public Policy
course	Ethics, Public Policy, and Technological Change
course	Modern Statistics for Modern Biology
WIM courses offered by other majors may be used in cases of specific concentrations (e.g. biology, decision theory). Advisor approval required.
Mathematical and Computational Science Approved Electives		9
Choose three courses in Mathematical and Computational Science 100-level or above, at least 3 units each from two different departments.
Choose three electives:
course	Advanced Topics in Econometrics
course	Introduction to Financial Economics
course	Game Theory and Economic Applications
course	Experimental Economics
	The Fourier Transform and Its Applications
course	Introduction to Linear Dynamical Systems
course	Introduction to Statistical Signal Processing
course	Computer Systems Architecture
course	Convex Optimization I
course	Convex Optimization II
course	Probabilistic Analysis
course	Simulation
course	Fundamentals of Data Science: Prediction, Inference, Causality
course	Introduction to Stochastic Control with Applications
course	Topics in Social Data
course	Applied Matrix Theory
course	Functions of a Complex Variable
course	Graph Theory
course	Introduction to Combinatorics and Its Applications
course	Linear Algebra and Matrix Theory
course	Introduction to Scientific Computing
course	Functions of a Real Variable
course	Complex Analysis
course	Partial Differential Equations
course	Stochastic Processes
course	Basic Probability and Stochastic Processes with Engineering Applications
course	Discrete Probabilistic Methods
course	Fundamental Concepts of Analysis
course	Lebesgue Integration and Fourier Analysis
course	Metalogic
course	Mathematics of Sports
course	Data Science 101
course	Data Mining and Analysis
course	Applied Multivariate Analysis
course	Introduction to Time Series Analysis
course	Bootstrap, Cross-Validation, and Sample Re-use
course	Statistical Models in Biology
course	Introduction to Statistical Learning
course	Introduction to Stochastic Processes I
course	Introduction to Stochastic Processes II
course	Stochastic Processes
course	Statistical Methods in Finance
course	A Course in Bayesian Statistics
For Computer Science (CS), electives can include courses not taken as units under the CS list above and the following:
course	Introduction to Numerical Methods for Engineering
course	Software Development for Scientists and Engineers
course	Numerical Linear Algebra
course	Object-Oriented Systems Design
course	Principles of Computer Systems
course	Operating Systems and Systems Programming
course	Compilers
course	Computational Logic
course	Design and Analysis of Algorithms
course	Software Project
course	Artificial Intelligence: Principles and Techniques
course	Introduction to Robotics
course	Experimental Robotics
course	Probabilistic Graphical Models: Principles and Techniques
course	Machine Learning
course	Program Analysis and Optimizations
course	Mining Massive Data Sets
course	Interactive Computer Graphics
Electives that are not offered this year, but may be offered in subsequent years, are eligible for credit toward the major.
With the advisor's approval, courses other than those listed or offered by the sponsoring departments may be used to fulfill part of the elective requirement. Courses must provide skills relevant to the MCS degree and do not overlap courses in the student's program. Depending on student’s interests, these may be in fields such as, biology, economics, electrical engineering, industrial engineering, and medicine, are otherwise relevant to a mathematical sciences major.
Total Units		76-89

1

Students who scored a 5 on both the Calculus AB and BC advanced placement exams (total of 10 units) can be waived out of courseCalculus, course Calculus, course Calculus; See also the Registrar's Advanced Placement web site (AP or IB exams). Students who place out of MATH 19, 20, and 21 are required to take additional Math classes as discussed with MCS student services and the student's faculty advisor.

Mathematical and Computational Science Tracks

MCS program has designed three tracks to allow majors to pursue their interests in fields where applied mathematics and statistical analysis is utilized. Declared MCS majors are not required to choose a track. These tracks are not declared in Axess and are not printed on the transcript or diploma.

Biology Track

Students in the Biology track take the introductory courses for the Mathematics and Computational Science major with the following allowable substitutions as electives.

		Units
		Course List
STATS/course	Biostatistics 1	5
Allowable Elective Course Substitutions:
Take three courses from Foundational Biology Core:		10
course	Genetics
course	Biochemistry & Molecular Biology
course	Physiology
course	Evolution
course	Cell Biology
Or take two courses from the Biology core and one of the following:		3-4
course	Advance Molecular Biology: Epigenetics and Proteostasis
BIO 133	(no longer offered)
course	Conservation Biology: A Latin American Perspective
course	Theoretical Population Genetics (offered alternate years)
course	Molecular and Cellular Immunology
Honors students select the following three courses:		1-4
course	Modern Statistics for Modern Biology
course	Fundamentals of Molecular Evolution
course	Genes and Disease (no longer offered)
The following courses are no longer offered, but may be used by students who completed them in fulfillment of this requirement: BIO102, 160A & 160B

1	course: Biostatistics (BIO 141) can replace course Introduction to Applied Statistics or course Introduction to Regression Models and Analysis of Variance from the major's Statistics core requirement.

Engineering Track

Students in the Engineering track take the introductory courses for the Mathematics and Computational Sciences major with the following allowable substitutions.

		Units
		Course List
With consent of an MCS advisor, course, course, course series may be substituted for course, course, course. Depending on the exact material taught in relevant years, an additional math course may be necessary 1		15
course	Vector Calculus for Engineers
course	Ordinary Differential Equations for Engineers
course /course	Linear Algebra and Partial Differential Equations for Engineers
course may be replaced by:		3-5
course	Statistical Methods in Engineering and the Physical Sciences
course/course may be replaced by:		3-4
course	Data Mining and Analysis
Allowable Elective Course Substitutions:		9
Select one of the following:		3-4
course	Functions of a Complex Variable
course	Introduction to Combinatorics and Its Applications
course	Complex Analysis
course	Metalogic
Select two of the following:		3-5
course	Dynamics
course	Introduction to Chemical Engineering
ENGR 25B
ENGR 40	(no longer offered)
course	Introduction to Materials Science, Nanotechnology Emphasis
course	Feedback Control Design

1	Only MCS majors pursuing the engineering track may petition their advisor to substitute the required Math series for CME courses listed above.

Statistics Track

Students in the Statistics track take the introductory courses for the Mathematics and Computational Sciences major with the following additional courses - (87 units total)

Required:

		Units
		Course List
Additional Courses for the Statistics Track:		9
course	Introduction to Stochastic Processes I
Advanced CS, such as:		3
course	Mining Massive Data Sets
Advanced MS&E, such as:		3
course	Probabilistic Analysis
or
course	Simulation
Allowable Elective Course Substitutions:		9
Select three of the following:
course	Data Mining and Analysis
course	Applied Multivariate Analysis
course	Introduction to Time Series Analysis
course	Bootstrap, Cross-Validation, and Sample Re-use
course	Introduction to Statistical Learning
course	Stochastic Processes
course	A Course in Bayesian Statistics

Honors Program

The honors program is designed to encourage a more intensive study of mathematical sciences than the B.S. program. Students interested in honors should consult with their faculty advisor as soon as possible to allow more opportunities in course planning and concentration area. The honors program allows for a capstone experience, building upon the student’s current academic knowledge and strengthening their understanding in a specific field of study/concentration. Honors work may be concentrated in fields such as biological sciences and medicine, environment, physics, sports analytics, investment science, AI/machine learning, etc.

Students are required to submit an MCS Honors Proposal Form describing the concentration for honors work, including the courses they intend to use, by the final study list deadline two quarters prior to the expected degree conferral quarter. The honors final report is due no later than the last day of classes of the quarter the student expects to graduate. More information can be found on the MCS Honors Website.

In addition to meeting all requirements for the B.S., the student must:

Maintain a GPA of at least 3.5 in all major coursework.
Students should complete 15 units of graduate level coursework. Included in these 15 units can be any of the following:
1. Related research from a 199 course
2. Participation for credit in a small group seminar
3. Directed reading
Complete a final report which should:
1. Include their name, degree and the title of their work.
2. Be typed with 12pt font, single-spaced, minimum 1 page (no longer than 2 pages) with a one-inch margin at the top and bottom of each page.
3. Explain a theme between the student’s coursework, their interests, and how they relate to MCS.
4. Describe how each course selected added to the student's knowledge and understanding in the chosen area of concentration.
5. The student's work must demonstrate in-depth learning of a topic or shared idea in the breadth of the MCS major (examples are on MCS webpage), and all students are held to Stanford’s Honor Code.

		Units
Course List
Suggested electives for students pursuing honors:
course	Introduction to Numerical Methods for Engineering	3
CS/course	Machine Learning	3-4
course	Interactive Computer Graphics	3-4
course	Convex Optimization I	3
course	Fundamental Concepts of Analysis	3
course	Lebesgue Integration and Fourier Analysis	3
course	Real Analysis	3
course	Data Mining and Analysis	3
course	Introduction to Statistical Learning	3
course	Introduction to Stochastic Processes I

Department: Mathematical and Computational Science