Wolfram Alpha: A Personal Tutor for Math Students…..Or Anyone!!!


Have you ever wanted to know not only what the solution to a question is but also why it is that solution? This problem will pop up from time to time in everyday life whether you’re at work, school, meetings, or just feeling curious. Luckily, there is a program that can answer (provided you ask correctly) nearly any question that you can give it. It is called WolframAlpha and it is branded as a “computation knowledge engine”. A means to provide the full knowledge of collective humanity at the cost of a few keystrokes.

When I first heard about this site (Fall 2010) I could not believe the talk. I was in a Calculus class with a terrible teacher; the kind who sit behind a podium and merely read you the textbook for an hour. We were discussing the behavior of Limits at Infinity and all was not well with my learning of the topic. I struggled to wade through the -then new- language of a Calculus curriculum and still could not seem to grasp the concept until….

When you pull up the site for use you will basically see a semi austere search engine interface. This was a bit un-nerving at first as it gives no boundary to what needs to be typed into the text box to get a desired result.  And I thought “How the hell do you input Calculus data and get a sensible result?”, I was at a loss. I then simply (and quite intuitively) typed into the dialog box the relevant information as best as  could logically deduce, pressed enter and waited for an error to be replied but that was not to be. I had asked the interface to show me the answer to a limit problem and it had quite easily returned a sensible and correct result WITH the steps and thoughts required to solve the problem! I was truly impressed to say the least.

So I asked it some other questions;

  • What aircraft are overhead? It gave me a factual answer of which aircraft (Carriers and flights!!) that were passing overhead of my computer’s IP location at that time.
  • How far am I(Ocala, FL)  from the Statute of Liberty? Answer: 916.1 miles, 1174 Kilometers, 796.1 Nautical miles, as a sound wave: 1 hour and 12 minutes, etc.
  • How many licks to get to the center of a Tootsie pop? Answer: 3481 (according to The Univ. of Cambridge)

These are simply amazing results for a knowledge engine. For fun, ask “what is the secret to life?” and you’ll receive an answer or type “hello” to the SE, and you’ll receive an intelligible response. My point is that to become familiar with this tool and make wide-spread use of this technology could have a great and positive impact on the ease and quickness of how information comes to light.

Since that day when I first discovered the value that this site presents to life, I have tried to evangelize its worth to anyone that will listen. Unfortunately, many of you do not. If you one day find yourself just wasting time one day droning at Facebook, twitter, or some blowhard’s blog then you have time to test drive this site.   I promise it will be worth your while and may even come in handy more than a few times (especially you college / high school students).

I will leave you with a thought that I had about my time in the Marine Corps in reference to this subject. When you are asked a questioned by a superior ranked Marine during an inspection, casually, or during a technical evaluation and you do not know the answer to said question. The correct reply is acknowledge your short coming and a EXPEDITIOUSLY seek that correct answer. with WolframAlpha its as good as done.



Pt. 6(a) Vectors: Vector Applications

Here I solve a Resultant Vector problem where there are 2 forces acting on an object. This is part 1 of a 2 part lecture on popular uses for vectors in problem solving and to show how to calculate the combined force exerted on an object under ideal conditions.

Pt. 5 Vectors: Unit vectors, Standard Vectors, and Linear Combinations

Here we will explore the concept of a Unit vector and some related thoughts. We will go deeper into what a vector is made of and practice an example of both creating a Unit vector and also a linear combination of i and j. As always, enjoy and feel free to give some feedback!

05/2012 Update

Well, As I stated in the preceding entry for “Current Happenings”,  I will be moving towards a more academic based content.  This is true as I will be promoting more Math and Physics posts to hopefully help anyone interested in learning either OR to help someone who is currently learning these topics but may want an alternative source for explanation. I am desperately trying to get back into the habit of being consistent with writing up these pencasts and trying to upload them in a timely manner. I have plenty of great and exciting topics to discuss and look forward to sending them out.

As a final request, If you happen to come across my blog and view any of my material, would you be so kind as to leave some feedback about your time spent. I want to collect some user data and analyze what I could be doing that will produce greater user results. I am currently using a software/hardware known as Livescribe which allows me to sync what I say and write while displaying the result on a piece of white “paper”. These lectures are a bit tougher for me to do because they involve some extemporaneous speaking skills but I think the result is better understood. I am really interested in the user accessibility experience of these lectures because they appear as a link to click on my blog (Livescribe is not fully supported on WordPress yet). I want to make sure I am not losing exposure due to a convoluted presentation style.

Lastly, any help in this matter would be greatly appreciated by me as I am deciding if I should use another host to present this information or just keep it as it is. Thanks again for reading.

-Keith C.

Pt. 3 Working Backwards: Finding a Vector Given Magnitude and Direction Angle


In the third part of this lecture, we will be culminating our new-found knowledge to  derive a 2d Vector given only the magnitude and direction in word problem form. To be able to answer these style of questions there will be some instruction provided that goes “in detail” about the component make up of a Vector. I will explain the component parts (x,y) and their associated meanings. This will give a clear and intuitive understanding of how to provide a logical answer when faced with a similar question (usually in a Physics setting).


Pt. 2 How to plot a Vector, Find Magnitude, and Direction Angle


Here we will continue deeper into Vectors and actually plot one and discuss the formulas needed reveal the length (magnitude) and Theta (direction angle). I will solve a question by providing a 2d Vector from the given plots and also using the new found Vector to discover it’s length and angle.  It is a very straight forward lecture in this series but none the less important before moving on. If there are any questions please feel free to contact me.

Pt. 1 Vectors and Their Basic Properties

Hello all,

In this “continuous-form” lecture I will be discussing Vectors and their associated operations. At first we will explore what a vector is and what components are necessary to actual make it a vector. We will cover scalars, Magnitude, Direction Angle, and learn some useful formulas for manipulating vectors to achieve a goal. As I have written, this will be a continuous form lecture in that it will consist of numerous chronological parts. I am trying this approach for a few reasons but mainly because it can keep these Livescribe files short enough to easily view and it will serve to “compartmental-ize” the data so that any un-clear areas or topics can be easily found/viewed without much trouble. as always I hope you enjoy this lecture and invite you to feel free with any questions or comments you may have.