Probability Theory - Calculus-Based Statistics - Online Course for Academic Credit
Often referred to as the "higher Probability & Statistics course", or even "Calculus-based Statistics", our Probability Theory course is actually an introduction to the study of statistics and probability, but based upon the usage of Calculus to study both discrete and continuous aspects of the subject. Accordingly, there is no prerequisite of a previous study of statistics, but rather a prerequisite of having completed Calculus II (having completed or concurrently enrolled in Multivariable Calculus is recommended). The Probability Theory course is an essential part of the mathematical training for those wishing to study Data Science.
Completion of DMAT 311 - Computational Probability Theory earns 3 academic credit semester hours with an official academic transcript from Roger Williams University, in Providence, Rhode Island, USA, which is regionally accredited by the New England Commission of Higher Education (NECHE), facilitating transfer of credits nationwide to other colleges and universities.
Probability Theory Introductory Videos
Probability Theory Course Introduction
The curriculum for the course, Prob/Stat&Mathematica by Carpenter/Davis/Raschke/Uhl, is a thorough and advanced investigation of the subject matter, fascinating and challenging at the same time. The usage of the powerful computer algebra and graphing system Mathematicaâ„¢ allows for a unique exploration of distributions - both discrete and continuous - and their application to the cornerstone of the subject - the data set from a real-world situation.
Probability Theory differs from the "lower" Statistics course significantly in both approach and difficulty level. Compare the prerequisites:
DMAT 311 - Learning Outcomes
- To understand the core concepts of Probability, Sampling, Distributions, and Density
- To understand and compute Monte-Carlo method for integration
- To understand and compute Expected Value, Variance, Mean, Mode, Median
- To understand and compute Probability and Conditional Probability
- To understand and compute Markov's and Chebyshev's Theorems
- To understand and compute normally and exponentially distributions
- To understand and compute calculus-based formulas and relationships between Cumulative Distribution Functions and Probability Density Functions
- To understand and compute the Central Limit Theorem
- To understand the core concepts of discrete and random variables
- To understand and compute Joint Distributions, Correlations, and Covariance
- To understand the Law of Total Probability
- To understand and compute the classic statistics measures of Confidence Intervals and Hypothesis testing.
DMAT 311 - Syllabus of Topics
In 2023, Distance Calculus introduced a new catalog of courses. New DMAT 311 = Old DMAT 315 = Old MATH 315
Time commitments are important for success in an online Probability Theory course for college credit from Distance Calculus. There are no fixed due dates in the Distance Calculus online courses, so it is important that students instead set their schedules for a dedicated amount of time towards the coursework.
It is also very important to consider that going faster through a course is DIRECTLY DEPENDENT upon your math skill level, and your successful engagement of the course. We require that you complete the course in a Mastery Learning format. If you are struggling with the course content, or trying to go too fast where the quality of your submitted work is suffering, then the instructors will force a slow-down of your progress through the course, even if you have fixed deadlines.
Probability Theory Examples of the Curriculum
Below are some PDF "print outs" of a few of the Mathematicaâ„¢ notebooks from Prob/Stat&Mathematica by Carpenter/Davis/Raschke/Uhl. Included as well is an example homework notebook completed by a student in the course, demonstrating how the homework notebooks become the "common blackboards" that the students and instructor both write on in their "conversation" about the notebook.
- Basics Notebook Example: 7.01.T1 - Tutorials - Monte Carlo estimation of integrals and other area measurements
- Homework Notebook Example: 7.03.G3 - Probability calculations in context: Series wiring versus parallel wiring
Distance Calculus Referenced Colleges & Universities (29 Years - 393+ Institutions)
Distance Calculus students have transferred course credits to these colleges and universities:
Distance Calculus - Student Reviews
Probability Theory is required for me to apply to Master's programs in Statistics, so I was glad when I found Distance Calculus. While the course was slightly less difficult than I originally expected, there were parts that definitely slowed me down and made me think. (Also, although calculus is not everywhere in the course, it is everywhere in normal and exponential variables and beyond, so make sure to review derivatives and integrals (single and double)!) I used Mathematica for my software, and it helped speed along calculations and proved to be the perfect stage and tool for this material. I think visual learners will absolutely revel in how the material is presented in this course. (I know I did!) As there is plenty of writing and calculation to do, you have many opportunities to develop and strengthen your voice as a mathematician. The modern format of 80% electronic notebook work and 20% handwritten work is an excellent mixture for studying probability theory and grasping its core ideas. Dr. Curtis is clear in his answers to any questions and concerns you may have and is highly responsive to email and chat, and to responses you leave in your notebooks. He truly wants to help you and to see you succeed, and he is always on your side.
I highly recommend Probability Theory with Distance Calculus!
First, this course uses software called LiveMath. This software can be a little bit challenging to get the hang of, but once you do get the hang of it, it's super easy. Remember that for all new things, it takes a bit to get used to it. Overall, I was highly satisfied with this course. I thought that the instructions were extremely detailed, including a video and a textbook explaining every different concept. In addition, this course offered exposure to a lot of different aspects of finite math. I think that many would agree with me on the following, that, you know, when a teacher is passionate about what they are teaching, it is so much more enjoyable, and you can definitely see that in this course. This course can be challenging at times. Maybe it'll be easy for you, maybe it'll be hard, but I think it's important to remember that the things that challenge us are, you know, the things that make us learn and the things that make us better. There's also a math chat option for if you need help or if you have any questions. Overall, I would recommend this course. I actually initially went into this course looking for an easy course to just help me get the credit requirements, but it ended up being an amazing learning experience and completely shifted my perspective on math overall. And another thing that I thought was great in this course is throughout so many different lectures, the professor would explain how each different thing can be applicable in life. And I think that, you know, that is a lot of what people think about when they are learning something. They're like, will I ever use this? Do I need to learn this? And a lot of this actually is really applicable. And I think that even if, you know, you may not be doing these math equations in your future, I think that, you know, the psychology behind these and the rules can be applied to so many different fuacets of life.
The only problem with the course is the lack of pen and paper work. This shouldn't come as a crazy surprise with an online course, but there is not much emphasis on symbolic computation. Mathematica or other software does most of the heavy computation for you. The lectures usually show how to solve the problems through paper, but those skills are rarely put into practice. Literacy Sheets act as a way to do some of that (especially with the Calculus II & III course).
All in all, this isn't a huge issue. I just memorize and practice things like double integration, Laplace, ODE solving, matrix diagonalized form, row operations, etc. With a little outside work, this resolves itself. Without Roger WIlliams, I probably would not have been able to take any of these math courses in highschool.
So overall, a great choice for highschool advanced math, especially with transferrable credits.
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Frequently Asked Questions
Do I Need To Take Statistics Before Probability Theory?
No. The actual topic coverage of Statistics and Probability are very close to one another. The Probability Theory course does everything with the machinery of Calculus, while the Statistics course stays away from Calculus and just concentrates on observing the patterns in the data.
Is Probability Theory The Same As Calculus-Based Statistics?
Yes. Probability Theory is exactly a first course in calculus-based Statistics.
Is Probability Theory Good for Data Science?
Yes. It is mandatory that any Data Science student will have taken Probability Theory (and more advanced courses after Probability Theory as well) prior to starting a Data Science certificate or degree.
Can I Take Probability Theory Without Calculus II?
No. Calculus II is very much a prerequisite for Probability Theory, and not a nominal prerequisite. Probability Theory relies very strongly on the mastery of the Calculus II content.
Is Probability Theory from Distance Calculus Accredited?
Yes, All Distance Calculus courses are offered through Roger Williams University in Providence, Rhode Island, USA, which is regionally accredited (the highest accreditation) through New England Commission of Higher Education (NECHE).








