Stochastic calculus is a dynamic field of study that has wide applicability across careers. An understanding of stochastic processes is vital to get started. The following are five of the best online foundational courses, as well as a buyer’s guide to help you search on your own.
How We Chose Our Ratings
The ratings are on a five-star scale, with five stars being the best. The following factors were weighed to come up with the ratings.
Most of the courses on this list are free or close to it. Affordability positively affected a course’s rating.
The materials provided played a large factor in the rankings. We analyzed the quality, breadth and accessibility of the materials for the final list.
Courses that offered general overviews of stochastic processes were generally rated higher than more niche classes. Classes that were more narrowly focused, or on the other hand, covered topics outside of stochastic processes, were ranked lower.
All the courses on the list have positive user reviews. However, the rating was positively affected for courses with particularly good reviews or high volume of positive reviews.
Top 5 Best Online Courses for Stochastic Calculus
Here is a look at our favorite online courses, along with general information and links to their sites.
This course made the top of the list because Coursera’s platform allows easy access to a high-quality class that is affordable and fairly flexible.
The National Research University Higher School of Economics is a top research university based in Russia. While this is a foundational course, its focus is undergraduate students in their third or fourth year, or first-year master’s students. It’s recommended to have some familiarity with probability theory, but not required.
Feedback from students is positive. The course has a rating of 4.4 out of 5 stars on Coursera.
This is a structured course. It’s eight weeks long and requires six to eight hours of commitment each week. There are graded assignments, which you must complete in order to pass the course. Upon completion, you receive a certificate that you can list on your resume and LinkedIn.
While this is a formal class, there is still quite a bit of flexibility. There are enrollment and assignment deadlines, but as long as you earn your certificate within 180 days, you are able to go at your own pace and still pass. The assignment deadlines are suggestions to keep you going at a steady rate, so this course offers a nice balance between structure and flexibility.
The lectures appear in online videos, all of which you can access from the start. There is also an interactive textbook and quizzes. You are able to discuss ideas with your classmates online. Everything you need is included in the low tuition rate.
Overall, this is a solid course that is flexible and affordable, which makes it the favorite on this list. You can find more information here on Coursera’s website.
who should try it:
Someone who has completed two to three years of undergraduate studies and is looking for a very affordable, flexible & thorough foundational course that provides a certificate of completion.
When it comes to mathematics, you can’t do much better than the Massachusetts Institute of Technology. MIT’s Open Courseware platform allows anyone to access materials from their courses for free.
Although there are not lectures, you have access to all the lecture slides. Once you purchase the textbook, you’ll be able to do the assignments, the answers for which are on the site.
The reason this is not on the top of our list, is the textbook costs about the same as the Coursera course, but the Coursera class is structured and has lectures, graded assignments, human interaction and a certificate of completion. So overall, Coursera is a better deal. However, this course is a close second due to its complete flexibility and the high-quality materials. The cost of a textbook is a small price to pay for MIT content.
Although this is an introductory course to stochastic concepts, it’s graduate level, so it’s not for beginners. You’ll need a basic familiarity with probability theory and linear algebra. This is a great course for someone who wants an introduction to stochastic processes but does not have a lot of time for a structured class with deadlines. This one is completely at your own pace, and nothing is graded.
You can take a look for yourself here on MIT’s open courseware site.
who should try it:
An independent learner who wants high-quality material with complete flexibility, and is not interested in graded assignments,interaction with an instructor and peers or having a formal record of completion.
NPTEL is the National Programme on Technology Enhanced Learning, which is a collaboration between seven Indian technology institutes to make technological education accessible. This is another free, open course along the same lines of MIT’s concept.
The content and lectures are downloadable. No textbook is required. There are some courses recommended as prerequisites to understand the material, such as probability theory, calculus and matrix algebra. These are recommendations, but not required, as the content is all openly accessible.
There are around 40 lectures in the series, including a two-hour probability theory refresher. There are no assignments or grades, so this is another course for independent learners. There is no formal certificate of completion. You set your own pace for getting through the material.
The website can be a bit cumbersome at times, and the English has some quirks to it, but overall the site has good reviews, and this can be an excellent choice for someone wanting a thorough look at stochastic processes for free.
To browse the materials and see if this is a good fit, check out the NPTEL website.
who should try it:
A self-motivated learner who wants a high volume of free, thorough material and a completely flexible schedule without graded assignments or exams.
This is another free courseware option on the MIT open platform. Again, you have access to content from excellent MIT instructors without paying anything. Unlike the other MIT class on this list, this course does not even require the purchase of a textbook.
The class provides you with video lectures, course notes, assignments and solutions, exams with answers, and an online, free PDF textbook. All the material is provided at once for you to review at your own pace. You do not have access to faculty or student interaction. There are neither graded exams nor a certificate of completion. This is another learning method that is great for someone who wants to learn the material, is an independent learner and is not concerned with an official record of completion.
The course focuses on discrete stochastic processes, which are in the realm of probability. It examines systems that evolve over time due to random changes within intervals. There is a strong math focus in the course, but this is more niche than the other MIT course on the list, so it isn’t ranked as high. Still, discrete processes are typically considered easier to study, so this may be a nice introduction on which to build an understanding of stochastic calculus down the road.
It’s recommended to have taken an introductory probability course. The site provides a link to buy the textbook that MIT uses in its own introductory probability course, in case you would like to review it.
Visit here to check out the free materials on MIT’s site.
who should try it:
An independent learner who would like a gentle introduction to stochastic processes comprehensive free materials provided by a top quality instructor.
This is supposed to be a prep course for UCLA Anderson’s Masters of Financial Engineering (MFE) degree, but it can be taken as a stand-alone class as well. Stochastic calculus is one of many topics covered, so this is a good choice if you want more than just one math topic and are interested in the quantitative finance applications of stochastic calculus.
This class, while offered online, is a traditional format. It includes three hours of lecture weekly. You will have homework, and there is a mid-term and final exam. Lectures are accessible at any time during the week, but there are scheduled online office hours with faculty. Enrollment is on a schedule, so you must pay attention to those deadlines. While the course covers stochastic processes, it includes many other topics as well. This contributed to the lower rating, but depending on your purposes, its general curriculum may be a positive factor for you.
You will need some prior knowledge of algebra, calculus, statistics and probability, but there is some refresher material in the curriculum. A textbook is not required, but the tuition cost is quite a bit higher than others on this list. This is a pass/fail course that is based on the midterm and final scores. Upon completion, you will receive a certificate. This class is rated lower than the others due to the price and time commitment, but if you are looking for a more traditional route, this may be at the top of your own list.
UCLA School of Management is a highly reputable tech-oriented school with a reputation for friendliness. If you have the resources and time to dedicate, this may be a great option for you.
All the information you need is on UCLA Anderson’s site.
who should try it:
Someone looking for a traditional class format and certificate of completion and has the resources to devote to a graduate-level quantitative and finance-oriented approach to a variety of math topics.
While the above list is a good starting point, you may want to explore other options. The following is a guide to help you focus your search. When deciding on a course, it’s helpful to look at several factors to determine which is best for you.
Determine Your Goals
Before setting out to find a class, it’s helpful to explore your goals. Do you want the course solely to expand your personal knowledge as a hobby in your spare time, or do you want something that will help you enter a particular career or gain a promotion? Do you want a course that will help you down the road if you pursue a degree in the field?
Your goal will play a huge role in which course(s) will be best for you. If you simply want to expand your knowledge, there are a lot of options for you in the form of free or inexpensive materials. If you want something for your resume, you may prioritize a traditional course with a certificate. If you are looking to prep yourself for a degree, you may want to look at universities and colleges to enroll in a formal course that may count as credits or fulfill prerequisites down the line.
Look at Your Budget
You don’t want to get your heart set on a course, only to find it is outside your budget. Set your budget ahead of time, and try your best to stick to it. Price should be one of the first factors you look at during your search to ensure a course is a good fit.
Review the Syllabus
Review a course’s syllabus early on. Some classes will have more emphasis on certain topics than others. Especially in the realm of stochastic calculus, there are many different routes to take for the curriculum. You do not want to spend the majority of the course on topics of little interest or applicability to you, so it’s worth your time to check out the syllabus ahead of time.
Tying It All Together
With the right knowledge and some patience, you can find a course to give you a good foundation for stochastic calculus. Keep in mind your goals, budget and the course syllabus, and you will find a quality educational experience that will meet your specific needs and goals.