# 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: Apr 5, 2020*

Review by: Catherine M.

Courses Completed: Calculus I

Review: Calculus I from Distance Calculus was wonderful! I took AB Calculus in high school, but I didn't take the AP Calc exam. Instead I took Calculus I with Distance Calculus, and it was so much better! It was a little review of topics, but not really. I really understood calculus when I finished!

Transferred Credits to: University of Chicago

*Date Posted: Jan 19, 2020*

Review by: William Williams

Student Email: wf.williamster@gmail.com

Courses Completed: Linear Algebra, Probability Theory

Review: I have difficulty learning calculus based math, akin to dyslexia when examining the symbolic forms, equations, definitions, and problems. Mathematica based calculus courses allowed me to continue with my studies because of the option of seeing the math expressed as a programming language for which I have no difficulty in interpreting visually and the immediate feedback of graphical representations of functions, equations, or data makes a huge impact on understanding. Mathematica based calculus courses should be the default method of teaching Calculus everywhere.

Transferred Credits to: Thomas Edison State College

*Date Posted: Jan 12, 2020*

Review by: Anonymous

Courses Completed: Calculus I

Review: This course is amazing! I took it as a requirement for admission to an MBA program, and couldn't have been happier with the quality and rigor of the course. I previously took calculus two times (at a public high school and then a large public university commonly cited as a "public ivy"), this course was by far the best and *finally* made the concepts click. Previously I had no idea what was going on because terrible PhD students were teaching the course and saying stuff like "a derivative is the slope of a tangent line" - ??? but what does that mean ???, but the instructors in the Shorter University course explain everything in ways where it FINALLY made sense (e.g., "imagine a roller coaster hitting the top of a hill, there's a moment where it shifts momentum and you're not accelerating or decelerating, that's what a 0 rate of change is - that's when the derivative would be zero"). They explain everything in multiple ways and relate it to other concepts. It all made perfect sense when I finally had a good instructor. Really recommend this class

Transferred Credits to: The Wharton School, UPenn

## 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