Are you a high schooler looking for an online calculus based statistics course? Yes, I know that you can easily read your book and get the answers to weekly quizzes and end of chapter questions from your teacher. But what if I told you that you could learn by solving problems yourself?

Calculus based statistics has been a part of a lot of our lives. One of the best parts is that there are many tools, which you can use to learn it from home. These tools like books, websites and even apps can be extremely helpful while learning. Just by reading one or two chapters, you will get a whole lot clearer understanding than what you have on first sight and then you will have enough information to start studying calculus based statistics and that is when you need to understand how to use it wisely.

Unable to “wait for the next academic semester”? Distance Calculus @ Roger Williams University has you covered!

### Distance Calculus Courses

- Math 213: Calculus I (4 credits)
- Math 214: Calculus II (4 credits)
- Math 351: Multivariable Calculus (4 credits)
*(same as Calculus III, Calculus IV, Vector Calculus)* - Math 317: Differential Equations (3 credits)
- Math 331: Linear Algebra (3 credits)
- Math 315: Probability Theory (3 credits)
*Calculus-Based Statistics* - Math 136: Precalculus (4 credits)
- Math 124: Basic Statistics (3 credits)
- Math 207: Applied Calculus (3 credits)
*Survey of Calculus • Liberal Arts Calculus*

### Frequently Asked Questions

- University Accreditation
- Costs
- Transferring Credits
- Flexible Enrollment
- Enroll Any Time → Finish Fast
- Asynchronous – No Meeting Times
- Course Syllabi PDFs
- How Long To Finish Course
- Introductory Videos
- Course Enrollment Form

Our Distance Calculus courses are designed to be asynchronous – a fancy term for “self-paced” – but it more than just self-paced – it is all about working on your timeline, and going either as slow as you need to, or as fast as your academic skills allow.

Many students need a Calculus course completed on the fast track – because time is critical in finishing calculus courses needed for academic prerequisites and graduate school applications.

Here is a video about earning real academic credits from Distance Calculus @ Roger Williams University:

# WHO CAN ENROLL?

The short answer: Anyone.

Revised answer: Anyone with a (decent) computer and (stable) internet connection..

## INSTITUTIONAL REQUIREMENTS

To enroll in Distance Calculus @ Roger Williams University, you will be registered as a **Non-Degree Seeking, Non-Matriculating Student** student. This category is for students who are taking just 1 or 2 (or a few) courses at Roger Williams University – University College. At other college/universities, these special admission areas are sometimes called “Extension Schools”.

Unlike regular admission to Roger Williams University, you do not have to complete SAT exams, write an entrance essay, submit high school transcripts, etc. Accordingly, you are not eligible as a “Non-Matriculating” student to pursue any degree-granting courses or obtain a Bachelor’s or Master’s or Ph.D. degree *at Roger Williams University* (without further applications).

But most likely, your academic plans are at **another college/university**, and you just need to take one or more Calculus courses to satisfy some requirements, and you wish to complete these courses via Distance Calculus for one of many reasons, including flexibility of scheduling, interest in technology-based curriculum, etc., and **transfer** these academic credits to your main academic institution.

Possibly you are not a student at another academic institution at all! We have many students who are taking Distance Calculus as a refresher course, or part of a professional development plan at their place of work, or in preparation for a graduate school application, or are retired and looking for some academic challenges.

## ACADEMIC REQUIREMENTS / PREREQUISITES

The only significant academic requirement for enrolling in Distance Calculus is meeting the prerequsities for the courses. For Calculus I, for example, the prerequisite is “a course in precalculus”.

A very common question we receive from students is: “I took precalculus 10 years ago, do I need to take it again before enrolling in Distance Calculus?”

The answer to this question is **no** in most cases. If we detect a weakness in your academic background surrounding issues in precalculus, for example, we will assign you extra modules at the precalculus level for you to strengthen your skills in that area. Due to the Mastery Learning approach of Distance Calculus, you can go as slow or as fast as you like through the material, so if you need extra time on precalculus, you take an extra few days/weeks to review that material and improve your skills.

If you have not actually taken a prerequisite course and would like to “skip it”, that, of course, is not allowed. We do require all new students to submit proof of completion of prerequisite courses via academic transcript.

## DISTANCE CALCULUS STUDENTS ARE…

In summary, “who can enroll” might best be explained via a list of the most common types of students we have in Distance Calculus:

**Working Professionals**

A working adult taking college classes at night, aiming to complete a B.A. or M.A. at a local institution, who is taking a Distance Calculus course.**Undergraduate Students**

An undergraduate student who cannot fit calculus into his/her schedule at her main academic institution, or did not like the large and impersonal classrooms, etc., and prefers to take calculus via Distance Calculus on-line.**High School Students**

High school students who are advanced, and have completed their school’s AP Calculus course, and could like to continue their calculus studies rather than wait until they start university. Or, at some high schools, AP Calculus is not offered.**Military Personnel**

We have many students who are currently in the military, sometimes in hostile areas of the world. The flexibility of Distance Calculus allows them to concentrate on their military duties, and work on their calculus studies when their tours have ended or taken a break.**Graduate School-Bound**

Students who have completed an academic degree, and are planning to return to a further academic program (i.e. graduate school), and need to bolster their graduate school application by completing some further math courses.**Life-Long Learners**

Without a degree goal or other similar plans, we have many students who are just interested in the academic challenges inherant in a student of calculus, and take our courses for pure intellectual interest.**Grammar/Middle School Teachers**

In many districts, teachers are required to continue their professional development in their general and specialization areas. Distance Calculus can provide satisfaction of these requirements in many cases.

## What is Calculus Based Statistics?

Calculus Based statistics takes the four core concepts of calculus (Continuity, Limits, Definite integral, Derivative) and applies them to statistical theory. Essentially, **non-calculus based statistics is for consumers of statistics and calculus based statistics is more suited for people who want to create statistics** (Columbia, 2021).

## Elementary Statistics vs. Calculus Based Statistics

There are many similarities and some important differences between Elementary Statistics and Calculus Based Statistics. Whichever class you take, you’re going to cover the same core concepts including ANOVA, Confidence intervals, Correlation, Regression and Statistical Inference.

The main difference is in **how these topics are approached. **For example, in a basic stats class, confidence intervals are introduced as a way to describe the distribution of parameters (i.e. how spread out your estimated results are). The focus is on how to make and interpret these intervals. With a calculus based statistics approach, functions are derived for these intervals. In a non-calc class, you might study the survival function for a certain species. In a calculus based course, you might take that same survival function and integrate it to show that the average lifetime for that species is the area under the curve.

In non-calculus statistics classes the focus is on *using* statistics. Calculus based statistics is more about creating the statistics (for others to consume). It is generally a more rigorous class that will help you to:

- Create statistics from scratch for any data type,
- Understand where many statistical rules and assumptions come from,
- Extend basic tests and procedures to non-standard situations.

## Calculus Based Statistics: Examples

## Typical Contents for Calculus Based Statistics

**Many of the following concepts are found in a calculus based statistics class.** They are either not covered at all in an elementary statistics class or are skimmed over:

- Finite and Infinite Sets,
- Increasing and decreasing functions,
- Moment-generating functions,
- Probability axioms,
- Continuity,
- Limit of functions,
- Derivatives (e.g. the chain rule and implicit differentiation),
- Summation notation,
- Integrals (e.g. Riemann integrals, improper integrals),
- Extrema of functions,
- Sequence and series (including power series, Taylor series and monotonic series),
- Tests for series convergence.

On the other hand, **you probably won’t see these advanced calculus concepts in a calculus based statistics class or an elementary statistics class. **In fact, you probably won’t come across them at all unless you dive into the realm of mathematical statistics:

- Differential forms: integrands for complicated domains.
- Essential discontinuities: discontinuities that jump wildly as they get closer to the limit.
- Exterior calculus: a high dimensional extension of calculus.
- Holomorphic Functions: functions that are infinitely differentiable.
- Non-Newtonian Calculus: a family of non-linear calculi.
- Ornstein-Uhlenbeck Process:a differential equation that models the motion of a particle under friction.
- Punctured Disks: A flat disk with a pinprick. One example of a myriad of shapes that can be integrated in calculus, but that you won’t see in statistics.
- Tangent Spaces: a generalization of a two-dimensional curve tangent line to manifolds.
- Tetration Functions: iterated exponentiation.

## Should I Take Calculus or Non-Calculus Based Statistics?

Which course you take largely depends on what your future goals are.

Few disciplines really *need* calculus based statistics. Those that do include economics, mathematical statistics and many research-heavy fields. In addition, some academic disciplines encourage (or require) a calculus background in addition to statistics. For example, statistics and calculus are highly sought after skills by research-active life scientists at the University of Arizona (Watkins, 2010).

As elementary statistics focuses more on data analysis, it’s well-suited to pre-med students, social science majors, and business majors.

For other disciplines, it’s a grey area. For example, data scientists can get away with not knowing calculus for many positions but many career opportunities will require you to use calculus to explore data.

## Definitions and How To Articles (From CalculusHowTo.com)

The following how to articles (on CalculusHowTo.com) cover the basics of calculus: the tools you will likely need to get you through an introductory calculus based statistics class.

- Area of a Bounded Region
- Area Under a Curve (Excel)
- Average Value of a Function
- Basic Operations on Functions
- Check the Continuity of a Function
- Decompose a Composite Function
- Eliminate exponents
- How to Find Intercepts
- Intersection of Two Lines
- How to Enter Data into a List TI89
- Optimization Problems
- Quadratic Formula
- Related Rates
- Relation vs Function
- Second Derivatives (Test, Finding)
- Sum of a Convergent Geometric Series
- Symbols and Equations (How to Read Them)
- Vertical Tangents