# Electives & Tracks

Within the MCS program, students expand their expertise by taking three higher-level courses from the approved list below. Each course must be at least 3 units, and the courses should be selected from the offerings of at least two different departments.

Additional Notes:

- Students who wish to take another course as a technical elective may submit a petition, which must be approved by the program director. Courses must provide skills relevant to the MCS degree and not overlap with other courses in the student's program.
- Examples of courses that would NOT count as technical electives because of significant overlap with other required major courses or content too far removed from MCS are ECON 102A, ENGR 108, MS&E 120, and MS&E 140.
- Students can use research units from a 199 course for a maximum of three units toward the MCS electives if the research is related to MCS/ data science and approved by the program director.

##
Computational & Mathematical Engineering (CME)

- Approved courses:
- Any CME course numbered 200 or above

- Recommended courses:
- Introduction to Numerical Methods for Engineering (CME 206)
- Software Development for Scientists and Engineers (CME 211)
- Numerical Linear Algebra (CME 302)

##
Computer Science (CS)

- Approved courses:
- Any CS course numbered 110 or above

- Recommended courses:
- From Languages to Information (CS 124)
- Computer Vision: Foundations and Applications (CS 131)
- Web Applications (CS 142)
- Data Management and Data Systems (CS 145)
- Introduction to the Theory of Computation (CS 154)
- Design and Analysis of Algorithms (CS 161)
- Artificial Intelligence: Principles and Techniques (CS 221)
- Introduction to Robotics (CS 223A)
- Natural Language Processing with Deep Learning (CS 224N)
- Probabilistic Graphical Models: Principles and Techniques (CS 228)
- Machine Learning (CS 229)
- Deep Learning for Computer Vision (CS 231N)
- Mining Massive Data Sets (CS 246)
- Introduction to Cryptography (CS255)

##
Data Science (DATASCI)

- Approved courses:
- Any DATASCI course numbered 100 or above

##
Economics (ECON)

- Approved Courses:
- Advanced Topics in Econometrics (ECON 102C)
*Note: ECON 102A and ECON 102B overlap significantly with other courses in the major and are not accepted.* - Foundations of Finance (ECON 135)
- Market Design (ECON 136)
- Decision Modeling and Information (ECON 137)
- Introduction to Financial Economics (ECON 140)
- Financial Markets (ECON 141)
- Imperfect Competition (ECON 157)
- Game Theory and Economic Applications (ECON 160)
- Empirical Environmental Economics (ECON 177)
- Experimental Economics (ECON 179)
- Data Science for Environmental Business (ECON 185)
- Machine Learning and Causal Inference (ECON 293)

- Advanced Topics in Econometrics (ECON 102C)

##
Electrical Engineering (EE)

- Approved courses:
- Any EE course numbered 200 or above

- Recommended courses:
- The Fourier Transform and Its Applications (EE 261)
- Introduction to Linear Dynamical Systems (EE 263)
- Probability and Statistical Inference (EE 278)
- Convex Optimization I (EE 364A)
- Convex Optimization II (EE 364B)

##
Management Science & Engineering (MS&E)

- Approved courses:
- Introduction to Finance and Investment (MS&E 145)
- Any MS&E course numbered 200 or above

- Recommended courses:
- Mathematical Programming and Combinatorial Optimization (MS&E 212)
- Introduction to Optimization Theory (MS&E 213)
- Simulation (MS&E 223)
- Fundamentals of Data Science: Prediction, Inference, Causality (MS&E 226)
- Applied Causal Inference with Machine Learning and AI (MS&E 228)
- Market Design for Engineers (MS&E 230)
- Introduction to Computational Social Science (MS&E 231)
- Introduction to Game Theory (MS&E 232)
- Game Theory, Data Science and AI (MS&E 233)
- Data Privacy and Ethics (MS&E 234)
- Machine Learning for Discrete Optimization (MS&E 236)
- Investment Science (MS&E 245A)
- Advanced Investment Science (MS&E 245B)
- Introduction to Stochastic Control with Applications (MS&E 251)

##
Math

- Approved courses:
- MATH 56
- Any MATH course numbered 100 or above

- Recommended courses:
- Functions of a Complex Variable (MATH 106)
- Graph Theory (MATH 107)
- Introduction to Combinatorics and its Applications (MATH 108)
- Groups and Symmetry (MATH 109)
- Number Theory for Cryptography (MATH 110)
- Linear Algebra and Matrix Theory (MATH 113)
- Functions of a Real Variable (MATH 115)
- Partial Differential Equations I (MATH 131P)

##
Statistics (STATS)

- Approved courses:
- STATS 100
- STATS 101
- Any STATS course numbered 200 or above

- Recommended courses:
- Data Mining and Analysis (STATS 202)
- Sampling (STATS 204)
- Introduction to Nonparametric Statistics (STATS 205)
- Applied Multivariate Analysis (STATS 206)
- Introduction to Time Series Analysis (STATS 207)
- Introduction to the Bootstrap (STATS 208)
- Statistical Methods for Group Comparisons and Causal Inference (STATS 209)
- Statistical Methods in Biology (STATS 215)
- Introduction to Statistical Learning (STATS 216)
- Introduction to Stochastic Processes II (STATS 218)
- Machine Learning Methods for Neural Data Analysis (STATS 220)
- Design of Experiments (STATS 263)

##
Other Departments

- Archaeological Geographical Information Systems (ARCHLGY 198A)
- Fundamentals of Geographic Information Science (EARTHSYS 144)
- Metalogic (PHIL 151)
- Computability and Logic (PHIL 152)
- Causal Inference for Social Science (POLISCI 150C)
*Note: POLISCI 150A and POLISCI 150B overlap significantly with other courses in the major and are not accepted.*

##
MCS Track Option

The MCS program has designed three tracks to allow majors to pursue their interests in fields where applied mathematics and statistical analysis is utilized. Some students may choose to pursue a track in place of their MCS electives. Declared MCS majors are not required to choose a track.

##
Biology Track

The biology path is intended for students interested in pursuing a graduate degree in the bioinformatics and biostatistics related fields.

Take three courses from the Biology core:

- BIO 82
- BIO 83
- BIO 84
- BIO 85
- BIO 86

OR Take **two classes from the above** biology core and take **one **of the following:

- BIO 104
- BIO 118
- BIO 133
- BIO 144
- BIO 183
- BIO 187
- BIO 230

Other Notes:

- Honors students should take BIO 113, BIO 114, and STATS 155.
- Bio/Stats 141 can replace STATS 191 (Introduction to Applied Statistics) or STATS 203 (Introduction to Regression Models and Analysis of Variance).

##
Engineering Track

Take one course from the following:

- Math 106
- Math 108
- Math 116
- Math 118
- Math 132
- Math 174
- Phil 151

Take two courses from the following:

- ENGR 15
- ENGR 20
- ENGR 25B
- ENGR 30
- ENGR 40
- ENGR 50
- ENGR 105

##
Statistics Track

Take the core courses in Math, CS, MS&E, and Stats in addition to the following courses:

- Stats 217 (3 units)
- An advanced CS course, such as CS 246 (3 units)
- An advanced MS&E course, such as MS&E 220 or 223 (3 units)

Choose three statistics path electives (below), which replace the major electives (9 units):

- Stats 202
- Stats 206
- Stats 207
- Stats 208
- Stats 216
- Stats 219
- Stats 270