625.633.81 - Monte Carlo Methods

Applied and Computational Mathematics
Spring 2024


This course is an introduction to fundamental tools in designing, conducting, and interpreting Monte Carlo simulations. Emphasis is on generic principles that are widely applicable in simulation, as opposed to detailed discussion of specific applications and/or software packages. At the completion of this course, it is expected that students will have the insight and understanding to critically evaluate or use many state-of-the-art methods in simulation. Topics covered include random number generation, simulation of Brownian motion and stochastic differential equations, output analysis for Monte Carlo simulations, variance reduction, Markov chain Monte Carlo, simulation-based estimation for dynamical (state-space) models, and, time permitting, sensitivity analysis and simulation-based optimization. Course Note(s): This course serves as a complement to the 700-level course EN.625.744 Modeling, Simulation, and Monte Carlo. EN.625.633 Monte Carlo Methods and EN.625.744 emphasize different topics, and EN.625.744 is taught at a slightly more advanced level. EN.625.633 includes topics not covered in EN.625.744 such as simulation of Brownian motion and stochastic differential equations, general output analysis for Monte Carlo simulations, and general variance reduction. EN.625.744 includes greater emphasis on generic modeling issues (bias-variance tradeoff, etc.), simulation-based optimization of real-world processes, and optimal input selection.


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Carsten Botts


Course Structure

The course materials are divided into modules which can be accessed by clicking Course Modules on the left menu. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview allsections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline.

Course Topics

Please see course description.

Course Goals

The goal of this course is for students to understand the applications, theoretical properties, and limitations of Monte Carlo methods.To understand these features of Monte Carlo methods, students will be asked to do some theoretical calculations related to Monte Carlo methods, and they will also be asked to write their own Monte Carlo methods using R.

Course Learning Outcomes (CLOs)



Robert, C. and Casella, G. (2010). Introducing Monte Carlo Methods with R (2010 ed.). New York, NY: Springer.

ISBN-13: 978-1441915764

Note: Please get the latest edition of the textbook.

Textbook information for this course is available online through the appropriate bookstore website: For online courses, search the MBS website at http://ep.jhu.edu/bookstore.

Required Software


You will need to access/download the most recent version of R.

Student Coursework Requirements

It is expected that each module will take approximately 7–10 hours per week to complete. There will be one module/week, and there will be fourteen modules. An assignment will be given with each module. Each module is made available on a Monday and the corresponding homework will be due the following Sunday. There will be no module during the week of March 18th. The first exam will be given during the seventh module (Mon 3/4 - Sun 3/10), and the second exam will be given during the fourteenth module (Mon 4/29 - 5/5).

This course will consist of the following basic student requirements:

Assignments (50% of Final Grade Calculation)

Assignments will be problem sets which include a mix of theoretical and numerical calculations (many of the numerical calculations will require programming).

All assignments are due according to the dates in the Calendar. Late submissions will not be accepted.

Exams (50% of Final Grade Calculation, combined from 25% for Midterm and 25% for Final)

The midterm exam will be available in Module 7 and the final exam will be available in Module 14. You will have one week to complete the exams and they will be due by 12AM exactly one week from their release. You are forbidden from using your notes, the text, or any other outside material on these exams.

Grading Policy

Assignments are due according to the dates posted in your Canvas course site. You may check these due dates in the Course Calendar or the Assignments in the corresponding modules. I will post grades approximately one week after assignment due dates. 

There will be two exams in this course. Homework will be assigned on a regular basis. All of the exams will be take-home. Each exam will comprise 25% of your total grade, and the average of your homework grades will comprise 50% of your total grade.

Below is the lowest letter grade you will get if your final average is within a given numerical range. If the instructor believes a curve is necessary, one will be given.

Score RangeLetter Grade
100-98= A+
97-94= A
93-90= A−
89-87= B+
86-83= B
82-80= B−
79-70= C
<70= F

Final grades will be determined by the following weighting:




% of Grade






Exams (Midterm + Final)


50% (25% + 25%)

Important Dates

Exam I: given with Module 7.
Exam II: given with Module 14.

Course Policies

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.