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
More Details
- How Our Courses Work
- About the Mastery Learning Format
- Asynchronous & Self-Paced
- Computer & Software Requirements
- Maximum Course Time (1 Year)
- Completion Time Estimates
- Academics
- Course Prerequisites
- Course Syllabi
- Grading Policy
- University Accreditation (NECHE)
- Course Articulation/Transfer
- How Exams Work
- Explore
- Honors Course Track
- Student Reviews
- Introductory Videos
- Who Can Enroll?
Frequent Questions
- Enrollment
- When Can I Enroll?
- When Can I Start My Course?
- Term Dates: Enroll Anytime!
- Costs & Tuition
- Credits & Transcripts
- Will My Credits Transfer?
- Letters of Recommendation
- Is My College On Your Transfer List?
- Other Questions
- Frequently Asked Questions
- Is This the Same as AP Calculus?
- Are These Computer-Based Courses?
- Are These Online Courses?
- Financial Aid?
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).








