Stanfd University MATHEMATICAL AND COMPUTATIONAL SCIENCE Courses offered by Mathematical and Computational Science program are listed under the subject code MCS on the Stanfd Bulletin's ExpleCourses (http://explecourses.stanfd.edu) website. This interdisciplinary undergraduate degree program in MCS is sponsed by Stanfd's departments of Mathematics, Computer Science, Management Science & Engineering, and Statistics, providing students with a ce 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. Utilizing the faculty and courses of the departments listed above, this maj prepares students f graduate study employment in the mathematical and computational sciences 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 f students interested in applications of mathematics, statistics, and computer science to the biological sciences (bioinfmatics, computational biology, statistical genetics, neurosciences); and in a similar spirit, an engineering and statistics option. Undergraduate Mission Statement f Mathematical and Computational Science The mission of the Mathematical and Computational Science Program is to provide students with a ce 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 wk in mathematics, computer science, statistics, and management science and engineering. A computational biology track is available f students interested in biomedical applications. The program prepares students f careers in academic, financial and government settings as well as f study in graduate professional schools. Learning Outcomes The program expects undergraduate majs 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:. 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. Bachel of Science in Mathematical and Computational Science Suggested Preparation f the Maj Students dinarily would have taken two of the required Math courses (MATH 5 Linear Algebra and Differential of Several Variables/MATH 52 Integral of Several Variables/MATH 53 Ordinary Differential Equations with Linear Algebra) and one of the required Statistics courses (STATS 6 They of Probability, ) befe declaring MCS during their freshman sophome year. How to Declare To declare the maj, a student must submit the Declaration of Maj in Axess. Following a review of the student's transcript, a department adviser is assigned to the student upon declaration approval. It is recommended that students meet with their adviser at least once per quarter to discuss progress towards degree completion. Course Requirements f the MCS Bachel's Degree (78-84 units) Mathematics (MATH) 28 Single-variable calculus AP credit. 0 MATH 9 MATH 20 MATH 2 Students may choose one of the following sequences: 5 Multivariable and Linear Algebra MATH 5 MATH 52 MATH 53 Linear Algebra and Differential of Several Variables Integral of Several Variables Ordinary Differential Equations with Linear Algebra (a proof-iented sequence) MATH 6CM MATH 62CM MATH 63CM (a proof-iented sequence) MATH 6DM MATH 62DM MATH 63DM Select one of the following: 3 MATH 3 Linear Algebra and Matrix They Computer Science (CS) 22-24 CS 03 Mathematical Foundations of Computing 5 CS 06A Programming Methodology 5 CS 06B Programming Abstractions 5 CS 06X Programming Abstractions (Accelerated) Select two of the following: 7-9 CME 08 CS 07 CS 54 CS 6 CS 8W Computer Organization and Systems Introduction to Automata and Complexity They Design and Analysis of Algithms Computers, Ethics, and Public Policy Management Science and Engineering (MS&E) 7-4 3 Or select three of the following: MS&E MS&E 2 MS&E 23 Introduction to They
2 Mathematical and Computational Science Statistics (STATS) -2 STATS 6 They of Probability 5 STATS 200 Introduction to Statistical Inference 3 STATS 203 Introduction to Regression Models and Analysis of Variance Students who sced a 5 on both the AB and BC advanced placement exams (total of 0 units) can be waived out of MATH 9, MATH 20, MATH 2 ; See also the Registrar's Advanced Placement (https://registrar.stanfd.edu/ students/transfer-credit/advanced-placement) web site (AP (https:// registrar.stanfd.edu/students/transfer-credit-and-advancedplacement/advanced-placement/ap-credit-chart) IB (https:// registrar.stanfd.edu/students/transfer-credit-and-advancedplacement/advanced-placement/ib-credit-chart) exams). Writing in the Maj Requirement The University requires students to complete at least one approved writing-intensive course in each of their majs. See the Hume Center f Writing and Speaking (https://undergrad.stanfd.edu/tuting-suppt/ hume-center/writing/writing-maj) web site f a full description of the WIM (https://undergrad.stanfd.edu/tuting-suppt/hume-center/ writing/writing-maj/overview-wim-requirement) requirement. Choose one from the MCS-designated WIM courses to fulfill the Writing in the Maj requirement: MATH 09 MATH 0 MATH 20 CS 8W STATS 55 Applied Group They Applied Number They and Field They Groups and Rings Computers, Ethics, and Public Policy Statistical Methods in Computational Genetics WIM courses offered by other majs may be used in cases of specific concentrations (e.g. biology, decision they). Adviser approval required. Mathematical and Computational Science Approved Electives Choose three courses in Mathematical and Computational Science 00- level above, at least 3 units each from two different departments. At least one must be from following list: 3-4 units Choose three courses from the following: 9 units ECON 02C ECON 40 ECON 60 ECON 79 EE 26 EE 263 EE 278 EE 282 EE 364A EE 364B MS&E 220 MS&E 223 MS&E 226 Advanced Topics in Econometrics Introduction to Financial Economics Game They and Economic Applications Experimental Economics The Fourier Transfm and Its Applications Introduction to Linear Dynamical Systems Introduction to Statistical Signal Processing Computer Systems Architecture Convex Optimization I Convex Optimization II Probabilistic Analysis Simulation "Small" Data MS&E 334 MCS 00 MATH 07 MATH 3 MATH 4 MATH 5 MATH 6 MATH 3P MATH 36 MATH 58 MATH 59 MATH 72 STATS 206 STATS 207 STATS 208 STATS 25 STATS 26 STATS 28 STATS 29 STATS 240 STATS 270 Topics in Social Data Mathematics of Spts Graph They Introduction to Combinatics and Its Applications Linear Algebra and Matrix They Functions of a Real Variable Complex Analysis Partial Differential Equations Basic Probability and with Engineering Applications Discrete Probabilistic Methods Lebesgue Integration and Fourier Analysis Applied Multivariate Analysis Introduction to Time Series Analysis Introduction to the Bootstrap Statistical Models in Biology Introduction to Statistical Learning Introduction to I Introduction to II Statistical Methods in Finance Bayesian Statistics I F Computer Science (CS), electives can include courses not taken as units under the CS list above and the following: CME 206 CME 2 CME 302 CS 08 CS 0 CS 40 CS 43 CS 57 CS 6 CS 94 CS 22 CS 223A CS 225A CS 228 CS 229 CS 243 CS 246 CS 248 Introduction to Numerical Methods f Engineering Software Development f 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 Algithms 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 Electives that are not offered this year, but may be offered in subsequent years, are eligible f credit toward the maj.
Stanfd University 3 With the adviser's approval, courses other than those offered by the sponsing 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 maj. Grade and Course Requirements: All courses used to fulfill maj requirements must be taken f a letter grade with the exception of courses offered satisfacty/no credit only. The student must have a grade point average (GPA) of 3.0 better in all course wk used to fulfill the maj requirement. Students who earn less than a 'B-' in STATS 6 They of Probability STATS 200 Introduction to Statistical Inference must repeat the course. Only one MCS ce course can be substituted by filing a petition with their adviser (with the exception of STATS 200 Introduction to Statistical Inference which cannot be substituted). The Course Substitution Fm (https://mcs.stanfd.edu/sites/default/files/mcscourse-substitution_fm_0.pdf) must be submitted the quarter pri 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 f MCS required course may establish placement in a higher-level course. Transfer requests must first be submitted to Student Services Center pri to being evaluated by your adviser. Submit the MCS Program Transfer Credit Fm (https://mcs.stanfd.edu/sites/default/files/ mcs_ug_course_equiv_petition_.pdf) to the student services office. At least three quarters befe graduation, majs must file with their adviser a plan f completing degree requirements. Mathematical and Computational Science Biology Track (Option) Students in the Biology track take the introducty courses f the Mathematics and Computational Science maj with the following allowable substitutions as electives. STATS/BIO 4 Biostatistics 3-5 Allowable Elective Course Substitutions: Take three courses from Foundational Biology Ce: 0 BIO 82 BIO 83 BIO 84 BIO 85 BIO 86 Genetics Biochemistry & Molecular Biology Physiology Evolution Cell Biology Or take two courses from the Biology ce and one of the following: 3-4 BIO 04 BIO 8 BIO 33 BIO 44 BIO 83 BIO 230 Advanced Molecular Biology Genetic Analysis of Biological Processes Netwk analysis f community ecology and conservation research Conservation Biology: A Latin American Perspective Theetical Population Genetics (offered alternate years) Molecular and Cellular Immunology Hons students select the following three courses: -4 STATS 55 BIO 3 Statistical Methods in Computational Genetics Fundamentals of Molecular Evolution BIO 46 Population Studies The following courses are no longer offered, but may be used by students who completed them in fulfillment of this requirement: BIO02, 60A & 60B Can replace STATS 203 Introduction to Regression Models and Analysis of Variance from the maj's Statistics ce requirement. Mathematical and Computational Science Engineering Track (Option) Students in the Engineering track take the introducty courses f the Mathematics and Computational Sciences maj with the following allowable substitutions. With consent of an MCS adviser, MATH 5, MATH 52, MATH 53 series may be substituted f CME 00, CME 02, CME 04. Depending on the exact material taught in relevant years, an additional math course may be necessary CME 00 CME 02 CME 04/ ENGR 55B Vect f Engineers Ordinary Differential Equations f Engineers Linear Algebra and Partial Differential Equations f Engineers STATS 6 may be replaced by: 3-5 STATS 0 Statistical Methods in Engineering and the Physical Sciences /STATS 203 may be replaced by: 3-4 Allowable Elective Course Substitutions: 9 MATH 6 Introduction to Combinatics and Its Applications Complex Analysis Select two of the following: 3-5 ENGR 5 ENGR 20 ENGR 25B ENGR 30 ENGR 40 ENGR 50 ENGR 05 Dynamics Introduction to Chemical Engineering Biotechnology Introducty Electronics Introduction to Materials Science, Nanotechnology Emphasis Feedback Control Design Only M&CS majs pursuing the engineering track may petition their adviser to substitute the required Math series f CME courses listed above. Mathematical and Computational Science Statistics Track (Option) Students in the Statistics track take the introducty courses f the Mathematics and Computational Sciences maj with the following additional courses - (87 units total) Required: Additional Courses f the Statistics Track: 9 Introduction to I Advanced CS, such as: 3 CS 246 Mining Massive Data Sets 5
4 Mathematical and Computational Science Advanced MS&E, such as: 3 MS&E 220 MS&E 223 Probabilistic Analysis Simulation Allowable Elective Course Substitutions: 9 Select three of the following: STATS 206 STATS 207 STATS 208 STATS 26 STATS 29 STATS 270 Applied Multivariate Analysis Introduction to Time Series Analysis Introduction to the Bootstrap Introduction to Statistical Learning Bayesian Statistics I Hons Program The hons program is designed to encourage a me intensive study of mathematical sciences than the B.S. program. Students interested in hons should consult with their adviser no later than winter quarter of their juni year to prepare their program of study. Hons wk may be concentrated in fields such as biological sciences, environment, physics, etc. Students are required to submit an outline describing the concentration f hons wk, including the courses they intend to use two quarters pri to expected degree conferral. An MCS Hons Proposal Fm is due no later than the Preliminary Study List deadline of the quarter in which the degree is expected to be conferred. In addition to meeting all requirements f the B.S., the student must:. Maintain an average letter grade equivalent to at least a 3.5 in all academic wk. 2. Complete at least 5 units in mathematical sciences in addition to the requirements f the maj listed above. Include in these 5 units at least one of the following: a. An approved upper-level graduate course b. Participation in a small group seminar c. At least 3 units of directed reading 3. Prepare a statement describing maj area of concentration f hons wk. 4. Describe how each course selected added to the student's knowledge and understanding in area chosen f concentration. 5. Hons statement should be submitted to the adviser by the late application deadline of the student's graduation quarter using the MCS Hons Approval fm (https://mcs.stanfd.edu/academics/ hons). Suggested electives f students pursuing Hons: CME 206 Introduction to Numerical Methods f Engineering 3 CS/STATS 229 Machine Learning 3-4 CS 248 Interactive Computer Graphics 3-4 EE 364A Convex Optimization I 3 3 MATH 72 Lebesgue Integration and Fourier Analysis 3 MATH 205A Real Analysis 3 3 STATS 26 Introduction to Statistical Learning 3 Introduction to I 2-3 Min in Mathematical and Computational Science The min 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: 3-5 MATH 5 Linear Algebra and Differential of Several Variables Select two of the followning: 0 CS 06A CS 06B CS 06X Programming Methodology Programming Abstractions Programming Abstractions (Accelerated) Select two of the following: 8 STATS 6 They of Probability 5 STATS 200 Introduction to Statistical Inference In addition to the above, the min requires three courses from the following, two of which must be in different departments: Select three of the following: 9 CME 08 CS 03 CS 07 CS 54 CS 6 ECON 60 EE 26 MS&E 22 MATH 09 MATH 0 MATH 5 MATH 3P STATS 200 STATS 203 Mathematical Foundations of Computing Computer Organization and Systems Introduction to Automata and Complexity They Design and Analysis of Algithms Game They and Economic Applications The Fourier Transfm and Its Applications Mathematical Programming and Combinatial Optimization Introduction to Combinatics and Its Applications Applied Group They Applied Number They and Field They Functions of a Real Variable Partial Differential Equations Introduction to Statistical Inference Introduction to Regression Models and Analysis of Variance Introduction to I
Stanfd University 5 Other upper-division courses appropriate to the program maj may be substituted with consent of MCS program direct. Undergraduate majs in the constituent programs may not count courses in their own departments. Faculty Direct: Bradley Efron Faculty Advisers: Assistant Profess John Duchi, Profess Bradley Efron, Associate Profess Ramesh Johari, Associate Profess David Rogosa, Profess Chiara Sabatti Steering Committee: Takeshi Amemiya (Economics, emeritus), Emmanuel Candès (Mathematics, Statistics), Brian Conrad (Mathematics), Richard Cottle (Management Science and Engineering, emeritus), John Duchi (Electrical Engineering & Statistics), Darrel Duffie (Economics & GSB), Bradley Efron (Statistics), Peter Glynn (Management Science and Engineering), Ramesh Johari (Management Science and Engineering), Percy Liang (Computer Science & Statistics), Parviz Moin (Mechanical Engineering), Gege Papanicolaou (Mathematics), Eric Roberts (Computer Science, emeritus), David Rogosa (Education & Statistics), Tim Roughgarden (Computer Science), Chiara Sabatti (Biomedical Data Science & Statistics), David Siegmund (Statistics), Jonathan Tayl (Statistics), Brian White (Mathematics)