MATH 114/214: Introduction to Computational Stochastics
Spring quarter, 2025

Course Description This is an introductory course on stochastic simulations. %%computational stochastic processes. Topics include sampling random variables and variance reduction, Markov chain Monte Carlo simulations, and numerical methods for stochastic differential equations. If time permits, some selected advanced topics, such as simulation of rare events, simulation of chemical reactions, and algorithms of stochastic optimization, will be covered.
        The course is co-listed as Math 114 (for undergraduate students) and Math 214 (for graduate students). A course project is part of Math 214.
Prerequisites The prerequisite for Math 114 is Math 180A. In addition, students are strongly recommended to have completed a computer programming course before enrolling in Math 114. Examples of such a course include: CSE 5A, CSE 8A, CSE 11, or ECE 15.
Lectures 3:00 pm - 3:50 pm, Mondays, Wednesdays, and Fridays, Peterson Hall 103.
Instructor Bo Li (Office: AP&M 5723. Email: bli@math.ucsd.edu)
Office hours: 12:30 - 1:00 Wednesdays and 4:00 pm - 5:00 pm, Fridays, AP&M 5723.
Discussion Sessions Session A01, 7:00 pm - 7:50 pm, Thursdays, Center Hall 217A.
Session A02, 8:00 pm - 8:50 pm, Thursdays, Center Hall 217A.
Teaching Assistant Silvia Liu (Office: HSS 4056. Email: mil094@ucsd.edu)
Office hours: 1:00 - 2:00 Wednesdays and 10:00 - 11:00 Thursdays and Fridays.
Canvas and Gradescope Canvas will be used to manage our course (e.g., class announcement, homework assignments, etc.). Gradescope will be used to collect and grade homework and exams, and manage the grading.
Textbooks We will use the following two books. UCSD has the full access to these eBooks.
  • E. Gobet, Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear, Chapman and Hall/CRC, 2020.
  • R. Y. Rubinstein and D. P. Kroese, Simulation and the Monte Carlo Method, 3rd ed., John Wiley & Sons, 2017.
Lecture Notes When completed, lecture notes will be posted in Canvas.
Homework Homework is assigned, collected, and partially graded regularly. A large portion of homework is computationally oriented, and Matlab is the preferred mathematical software.
Please note:
  • No late homework will be accepted unless a written verification of a valid excuse (such as hospitalization, family emergency, religious observance, court appearance, etc.) is provided.
  • While discussions are allowed, students must complete their homework assignments independently. Copying homework (entirely or partially) is absolutely prohibited.
Exams and Projects Math 114: There will be one 50-minute midterm and one 3-hour final exam. Both exams will be close-book and close-note exams. The final exam will be cumulative.
      Midterm Exam: 3:00 pm - 3:50 pm, Friday, May 2, 2025, Peterson Hall 103 (same as the lecture room).
      Final Exam: 3:00 am - 5:59 pm, Wednesday, June 11, 2025 (place to be announced).
Math 214: There will be a 50-minute, close-book and close-note, midterm exam and a final course project.
      Midterm Exam: 3:00 pm - 3:50 pm, Friday, May 2, 2025, Peterson Hall 103 (same as the lecture room).
      The final course project is due 3:00 pm, Wednesday, June 11, 2025.
Please note:
  • Neither rescheduled nor make-up exams will be allowed unless a written verification of a valid excuse (such as hospitalization, family emergency, religious observance, court appearance, etc.) is provided.
  • No previous research project or course project from a different course will be accepted as a final course project.
Project Guidelines This is only for Math 214. A set of guidelines for course projects (requirement, some suggested topics, etc.) will be provided later.
Assessment Versioning Following UCSD (and common) practice recommended by the Academic Integrity Office, assessments, especially those given at non-overlapping times, will be comparable, but may not be identical. This practice is meant to maintain course integrity, avoiding non-allowed collaboration (either intentional or accidental).
Grading Math 114: The final course grade will be determined based on the homework (40%), midterm exam (20%), and final exam (40%). The final course grade will be curved within Math 114.
Math 214: The final course grade will be determined based on the homework (40%), midterm exam (20%), and final course project (40%). The final course grade will be curved within Math 214.
Academic Integrity All students are expected to conduct themselves with academic integrity. Violations of academic integrity will be treated seriously. Please see
Disability Accomodation Students requesting accommodations for this course due to a disability must provide a current Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities. Students are required to discuss accommodation arrangements with instructors and OSD liaisons in the department in advance of any exams or assignments.
Topics to be covered Here is a tentative list of topics to be covered in the course.
  • Introduction
    • Four examples
    • Outline of the course
  • Sampling random variables
    • The inversion method and the transformation method
    • The acceptance-rejection method
    • Sampling Bernoulli, bionomial, geometrical, and Poisson variables
  • Variance reduction
    • Controlling variables
    • Importance sampling
    • Stratified sampleing
  • Markov chain Monte Carlo (MCMC)
    • Concept, examples, and basic properties of Markov chains
    • The Metropolis-Hastings algorithm
    • The simulated annealing algorithm
    • The Gibbs sampler
  • Numerical stochastic differential equations (SDE)
    • A brief introduction to Brownian motion
    • Simulations of Brownian motion and its variants
    • A brief introduction to Ito calculus and SDE
    • Euler-Maruyama and Milstein's methods
    • Stability and convergence
  • Additional topics
    • Simulation of rare events
    • Simulation of chemical reaction
    • Algorithms for stochastic optimization
References Here is a list of reference books; UCSD has the electronic access to many of these books.
  • G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, Oxford University Press, 3rd ed., 2001.
  • G. F. Lawler, Introduction to Stochastic Processes, 2nd ed., Chapman & Hall/CRC, 2006.
  • M. A. Pinsky and S. Karlin, An Introduction to Stochastic Modeling, 4th ed., Acdemic Press, 2010. (UCSD has access to the ebook.)
  • S. Asmussen and P. W. Glynn, Stochastic Simulation, Springer, 2007. (UCSD has access to the ebook.)
  • D. P. Kroese, T. Taimre, and Z. I. Botev, Handbook of Monte Carlo Methods, John Wiley & Sons, 2011. (UCSD has access to the ebook.)
  • J. S. Liu, Monte Carlo Strategies in Scientific Computing, Springer, 2004. (UCSD has access to the ebook.)
  • C. P. Robert and G. Casella, Monte Carlo Statistical Methods, 2nd ed., Springer, 2004. (UCSD has access to the ebook.)
  • N. Madras, Lectures on Monte Carlo Methods, Amer. Math. Soc., 2002.
  • C. Graham and D. Talay, Stochastic Simulation and Monte Carlo Methods, Springer, 2013. (UCSD has access to the ebook.)
  • P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, 1992. (UCSD has access to the ebook.)
Last updated by Bo Li on March 31, 2025.