# Calculus-Based Statistics - Probability Theory

Probability Theory - also called Calculus-Based Statistics - is the "upper level" statistics course that uses Calculus to explore the topics of elementary statistics.This course is a gateway course for Data Science, Economics, and any discipline that utilizes data - that really means ALL JOBS these days!!

The curriculum for our Probability Theory course is absolutely wonderful, exploring the topics of beginning statistics with a fresh approach, devoid of the "here's the next formula and here's what it means" commonly found in traditional textbook courses.

Our Distance Calculus Probabality Theory course is highly experimentation-based, so you will run simulations in either LiveMath or Mathematica, and look at the topics empirically, trying to determine what is going on with the mathematics like a good scientist would - using observation and deductive reasoning.

Probability Theory covers the all of the topics in a basic non-major Statistics course. You do not need to have taken "baby" Statistics prior to taking Probability Theory - but you will need Calculus II under your belt.

Below are some videos on our Probability Theory Course:

## Probability Theory Course

## Preparing for Data Science

## Distance Calculus - Student Reviews

*Date Posted: Feb 19, 2020*

Review by: Rebecca Johnson

Courses Completed: Applied Calculus

Review: I took the Business Calculus course from Distance Calculus in 2013. I was admitted to my MBA program, but then they told me I needed to take Calculus before starting the program. I finished the Business Calculus course in about 3 weeks in August before my program started. Not the most fun thing to do over the summer, but at least I got it done. Thanks Diane and Distance Calculus team!

Transferred Credits to: Kellogg MBA Program

*Date Posted: Apr 10, 2020*

Review by: Benjamin T.

Courses Completed: Calculus I

Review: This course provided an excellent chance to learn about Calculus...again. I took calculus in high school, but I learned so much more with this course! It does take a good amount of time to do all the lessons, so definitely keep on top of them, but all the exercises helped me to really understand the material. And the nice thing is you can do it on your own time at home.

Transferred Credits to: Western University of Health Sciences: College of Optometry

*Date Posted: Jan 13, 2020*

Review by: Daniel Marasco

Courses Completed: Multivariable Calculus

Review: This course was more affordable than many, and the flexible format was terrific for me, as I am inclined to work very diligently on tasks on my own. It could be dangerous for a person who requires external discipline more, but it works well for self-starters, allowing you to prioritize when you have other pressing work. I was a full time teacher adding a math certification, and this course allowed me to master the math while working around my teaching schedule and fitting work into moments here and there when I had time. I was able to transfer the credits to Montana State University, Bozeman for my teaching internship program without a hitch. The instructors were all very helpful and patient, even when I failed to see a ridiculously simple solution on one problem after 20 emails back and forth. Overall, I was more pleased with my experience in this class than I was with any of my other 9 courses.

Transferred Credits to: Montana State University, Bozeman

## Distance Calculus - Curriculum Exploration

### Functions

- P2: Functions:
- P2.1: What is a Function?
- P2.1.a: Notation
- P2.1.b: Data Sets & Functional Notation
- P2.1.c: More Data Sets
- P2.1.d: When is a Data Set NOT a Function?
- P2.1.e: Algebraic Formulae
- P2.1.f: Massachusetts Lunatics
- P2.1.g: Hurricane Katrina Data
- P2.1.h: Formal Definition of Function
- P2.1.i: Homework Problems
- P2.2: Graphing Data Functions
- P2.2.a: Input vs. Output
- P2.2.b: Graphing Data in LiveMath Manually
- P2.2.c: Graphing Multiple Data Sets
- P2.2.d: Graphing 3D Data
- P2.2.e: Not a Function?
- P2.3: Functions from Algebraic Formulae
- P2.3.a: Generating Data
- P2.3.b: Graphing Generated Data
- P2.3.c: Increasing Resolution
- P2.3.d: Smooth Curves
- P2.3.e: Graphing Without Data
- P2.3.f: Graph Multiple Functions Together
- P2.3.g: Functions in 3D
- P2.4: Bad Inputs?
- P2.4.a: Undefined Input Values
- P2.4.b: All Good Input Values = Domain
- P2.4.c: All Realized Output Values = Range
- P2.5: Combinations of Functions
- P2.5.a: Add, Subtract Functions
- P2.5.b: Multiply Functions
- P2.5.c: Divide Functions
- P2.5.d: Abstract Substitution
- P2.5.e: Composition of Functions
- P2.6: Functions Without Algebraic Formulae