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Mathematical and Computational Science

Contacts

Office: Sequoia Hall, 390 Serra Mall
Mail Code: 94305-4065
Phone: (650) 723-2620
Email: helnnn@stanford.edu
Web Site: http://stanford.edu/group/mathcompsci

Courses offered by Mathematical and Computational Science program are listed under the subject code MCS on the Stanford Bulletin's ExploreCourses website.

This interdisciplinary undergraduate degree program in MCS is administrated by the departments of Mathematics, Computer Science, and Statistics. It provides a core of mathematics basic to all the mathematical sciences and an introduction to concepts and techniques of computation, optimal decision making, probabilistic modeling, and statistical inference.

Using the faculty and courses of the departments listed above, this major prepares students for graduate study or employment in the mathematical and computational sciences or in those areas of applied mathematics which center around the use of computers and are concerned with the problems of the social and management sciences. A biology option is offered for students interested in applications of mathematics, statistics, and computer science to the biological sciences (bioinformatics, computational biology, statistical genetics, neurosciences); and in a similar spirit, an engineering and statistics option.

Undergraduate Mission Statement for Mathematical and Computational Science

The mission of the Mathematical and Computational Science Program is to provide students with a core of mathematics basic to all the mathematical sciences and an introduction to concepts and techniques of computation, optimal decision making, probabilistic modeling and statistical inference. The program is interdisciplinary in its focus, and students are required to complete course work in mathematics, computer science, statistics, and management science and engineering. A computational biology track is available for students interested in biomedical applications. The program prepares students for careers in academic, financial and government settings as well as for study in graduate or professional schools.

Learning Outcomes

The program expects undergraduate majors to be able to demonstrate the following learning outcomes. These learning outcomes are used in evaluating students and the department's undergraduate program. Students are expected to be able to demonstrate:

  1. understanding of principles and tools of statistics.
  2. command of optimization and its applications and the ability to analyze and interpret problems from various disciplines.
  3. an understanding of computer applications emphasizing modern software engineering principles.
  4. an understanding of multivariate calculus, linear algebra, and algebraic and geometric proofs.

Bachelor of Science in Mathematical and Computational Science

The requirement for the bachelor's degree, beyond the University's basic requirements, is an approved course program of 75-77 units, distributed as follows:

Mathematics (MATH)
MATH 41Calculus *5
MATH 42Calculus *5
Select one of the following:5
Linear Algebra and Differential Calculus of Several Variables
Honors Multivariable Mathematics
Select one of the following:5
Integral Calculus of Several Variables
Honors Multivariable Mathematics
Select one of the following:5
Ordinary Differential Equations with Linear Algebra
Honors Multivariable Mathematics
Select one of the following:3
Applied Matrix Theory
Linear Algebra and Matrix Theory
Computer Science (CS)
CS 103Mathematical Foundations of Computing5
Select one of the following:5-10
Programming Abstractions (Accelerated)
or both
Programming Methodology
Programming Abstractions
Select two of the following:7-9
Introduction to Scientific Computing
Computer Organization and Systems
Introduction to Automata and Complexity Theory
Design and Analysis of Algorithms
Computers, Ethics, and Public Policy
Management Science and Engineering (MS&E)
Linear and Nonlinear Optimization
Stochastic Modeling
Or select three of the following:7-11
Introduction to Optimization
Introduction to Stochastic Modeling
Linear and Nonlinear Optimization
Stochastic Modeling
Stochastic Control
Statistics (STATS)
STATS 116Theory of Probability5
STATS 200Introduction to Statistical Inference3
Select one of the following:3
Introduction to Applied Statistics
Introduction to Regression Models and Analysis of Variance
*

Students who scored a 5 on both the Calculus AB and BC advanced placement exams (total of 10 units) can be waived out of MATH 41 and MATH 42. See also the Registrar's Advanced Placement web site.

Writing in the Major Requirement (3-4 units)

The University requires students to complete at least one approved writing-intensive course in each of their majors. See the Hume Center for Writing ad Speaking web site for a full description of the WIM requirement.

Choose one from the following to fulfill the WIM requirement:3-4 units
Applied Group Theory
Applied Number Theory and Field Theory
Groups and Rings
Fundamental Concepts of Analysis
Computers, Ethics, and Public Policy
Statistical Methods in Computational Genetics

Mathematical and Computational Science Electives (9 Units)

Choose three courses in Mathematical and Computational Science 100-level or above, at least 3 units each from two different departments. At least one must be from following list:

Choose three courses from the following:9-15
Advanced Topics in Econometrics
Causal Inference and Program Evaluation
Introduction to Financial Economics
Game Theory and Economic Applications
The Fourier Transform and Its Applications
Introduction to Linear Dynamical Systems
Computer Systems Architecture
Convex Optimization I
Convex Optimization II
Mathematics of Sports
Probabilistic Analysis
Simulation
Stochastic Control
Applied Matrix Theory
Functions of a Complex Variable
Introduction to Combinatorics and Its Applications
Linear Algebra and Matrix Theory
Functions of a Real Variable
Complex Analysis
Partial Differential Equations I
Fundamental Concepts of Analysis
Lebesgue Integration and Fourier Analysis
Calculus of Variations
First-Order Logic (Winte)
Data Mining and Analysis
Applied Multivariate Analysis
Introduction to Time Series Analysis
Introduction to the Bootstrap
Introduction to Statistical Learning
Introduction to Stochastic Processes
Introduction to Stochastic Processes
Stochastic Processes
Statistical Methods in Finance
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:
Introduction to Numerical Methods for Engineering
Introduction to Programming for Scientists and Engineers
Numerical Linear Algebra
Object-Oriented Systems Design
Principles of Computer Systems
Operating Systems and Systems Programming
Compilers
Logic and Automated Reasoning
Design and Analysis of Algorithms
Computing with Physical Objects: Algorithms for Shape and Motion
Software Project
Artificial Intelligence: Principles and Techniques
Introduction to Robotics
Experimental Robotics
Probabilistic Graphical Models: Principles and Techniques
Machine Learning
Program Analysis and Optimizations
Mining Massive Data Sets
Interactive Computer Graphics

With the adviser's approval, courses other than those offered by the sponsoring departments may be used to fulfill part of the elective requirement. These may be in fields such as biology, economics, electrical engineering, industrial engineering, and medicine, etc., that might be relevant to a mathematical sciences major, depending on a student's interests.

  • At least three quarters before graduation, majors must file with their advisers 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.
  • The student must have a grade point average (GPA) of 2.0 or better in all course work used to fulfill the major requirement.
  • ¬†Electives that are not offered this year, but may be offered in subsequent years, are eligible for credit toward the major: CME 311, Econ 179, EE 278B, STATS 215.

Mathematical and Computational Science Biology Track (Option)

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

STATS/BIO 141Biostatistics 13-5
Take three courses from the Biology Core:10
Genetics, Biochemistry, and Molecular Biology
Cell Biology and Animal Physiology
Plant Biology, Evolution, and Ecology
Or take two courses from the core and one of the following:3-4
Demography: Health, Development, Environment
Evolutionary Paleobiology
Evolution
Conservation Biology: A Latin American Perspective
Developmental Biology I
Developmental Biology II
Theoretical Population Genetics
Molecular and Cellular Immunology
Honors students select the following three courses:1-4
Statistical Methods in Computational Genetics
Fundamentals of Molecular Evolution
Population Studies
1

Can replace STATS 191 Introduction to Applied Statistics or STATS 203 Introduction to Regression Models and Analysis of Variance

Mathematical and Computational Science Engineering Track (Option)

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

With consent of advisor, courses of the CME 100-102-104 series can substitute courses of the MATH 51-52-53 series. Depending on the exact material taught in relevant years, an additional math course might be necessary
Vector Calculus for Engineers
Ordinary Differential Equations for Engineers
Linear Algebra and Partial Differential Equations for Engineers
STATS 116 may be replaced by:3-5
Statistical Methods in Engineering and the Physical Sciences
STATS 191/STATS 203 may be replaced by:3-4
Data Mining and Analysis
Engineering Track Electives:
Select one of the following:3-4
Functions of a Complex Variable
Introduction to Combinatorics and Its Applications
Complex Analysis
Mathematics of Computation
Partial Differential Equations II
Calculus of Variations
First-Order Logic
Select two of the following:3-5
Dynamics
Introduction to Chemical Engineering
Biotechnology
Engineering Thermodynamics
Introductory Electronics
Introduction to Materials Science, Nanotechnology Emphasis
Feedback Control Design

Mathematical and Computational Science Statistics Track (Option)

Students in the Statistics track take the introductory courses for the Mathematics and Computational Sciences major with the following additional courses - (85 units total)

Required:
STATS 217Introduction to Stochastic Processes3
Advanced CS, such as:
CS 246Mining Massive Data Sets3-4
Advanced MS&E, such as:
MS&E 220Probabilistic Analysis3-4
or
Simulation
Statistics Track Electives:
Select three of the following:9
Data Mining and Analysis
Applied Multivariate Analysis
Introduction to Time Series Analysis
Introduction to the Bootstrap
Introduction to Statistical Learning
Stochastic Processes
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. In addition to meeting all requirements for the B.S., the student must:

  1. Maintain an average letter grade equivalent to at least a 3.5 in all academic work.
  2. Complete at least 15 units in mathematical sciences in addition to the requirements for the major listed above. Include in these 15 units at least one of the following:
    1. An approved higher-level graduate course
    2. Participation in a small group seminar
    3. At least 3 units of directed reading
  3. Prepare a statement describing major area of concentration for honors work.
  4. Describe how each course selected added to the student's knowledge and understanding in area chosen for concentration.
  5. Students interested in honors should consult with their adviser by last quarter of their junior year to prepare their program of study. Honors work may be concentrated in fields such as biological sciences, environment, physics, etc.
  6. Suggested electives for students pursuing Honors: EE 364, CME 206, CS 229, CS 248, MATH 171, MATH 172, STATS 202, STATS 216, STATS 217.

Minor in Mathematical and Computational Science

The minor in Mathematical and Computational Science is intended to provide an experience of the four constituent areas: Computer Science, Mathematics, Management Science and Engineering, and Statistics. Five basic courses are required:

Select one of the following:3
CS 106XProgramming Abstractions (Accelerated)3-5
or
Programming Methodology
   and Programming Abstractions
MATH 51Linear Algebra and Differential Calculus of Several Variables5
or
Applied Matrix Theory
MS&E 211Linear and Nonlinear Optimization3-4
or
Stochastic Modeling
STATS 116Theory of Probability3-5
and either
Introduction to Applied Statistics
or
Introduction to Statistical Inference

In addition to the above, the minor requires three courses from the following, two of which must be in different departments:

Select three of the following:9
Introduction to Scientific Computing
Mathematical Foundations of Computing
Computer Organization and Systems
Introduction to Automata and Complexity Theory
Design and Analysis of Algorithms
The Fourier Transform and Its Applications
Game Theory and Economic Applications
Stochastic Control
Applied Matrix Theory
Functions of a Complex Variable
Introduction to Combinatorics and Its Applications
Applied Group Theory
Applied Number Theory and Field Theory
Functions of a Real Variable
Partial Differential Equations I
Fundamental Concepts of Analysis
Calculus of Variations
First-Order Logic
Introduction to Applied Statistics
Introduction to Statistical Inference
Data Mining and Analysis
Introduction to Regression Models and Analysis of Variance
Introduction to Stochastic Processes

Other upper-division courses appropriate to the program major may be substituted with consent of the program director. Undergraduate majors in the constituent programs may not count courses in their own departments.

Co-Directors: Bradley Efron, Susan Holmes

Committee in Charge: Takeshi Amemiya (Economics, emeritus), Emmanuel Candes (Mathematics, Statistics), Gunnar Carlsson (Mathematics), Richard Cottle (Management Science and Engineering, emeritus), Bradley Efron (Statistics), Margot Gerritsen (ICME), Peter Glynn (Management Science and Engineering), Susan Holmes (Statistics), Parviz Moin (Engineering), George Papanicolaou (Mathematics), Eric Roberts (Computer Science), David Rogosa (Education), Tim Roughgarden (Computer Science), Chiara Sabatti (Statistics), Amin Saberi (Management Science and Engineering), David Siegmund (Statistics), Jonathan Taylor (Statistics), Brian White (Mathematics).