math Archives - Jacob N Calvert

Calculus Made Simple

May 22, 2020

To many, integral and differential calculus may as well be a foreign language from an alien planet. Many people don’t grasp the fundamental concepts which drive the calculus, and consequently fail to derive the value they otherwise could from that knowledge. I’ve always found the key to making use of some bit of knowledge is to internalize it, to restate the concepts in terms that are familiar and comfortable to you, but to compare this restatement and internalization to the…

Neural Networks and How They Work

April 9, 2018

Jacob

Math

AI or Artificial Intelligence has been making headlines the world over the past few months. It’s time we all learn a little about how AI began and what role neural networks plays. Artificial intelligence, also sometimes referred to as machine intelligence (MI), is a burgeoning field of Computer Science which has ties to many, many other fields. AI is the application of neural networks in various forms to allow a machine to imitate or give the impression of natural…

Reliably identifying discrete colors from an RGB color sensor

April 16, 2016

Jacob

Math

For my Capstone Design project, one of my many tasks was to identify discrete colors on painted blocks (red, green, blue, yellow) using a the TCS34725 color sensor. I configured the color sensor to pass back four 16-bit integers representing the RGB and Clear color values of the reflected object that the sensor is “looking” at. Initially, I tried a simple linear matrix equation to map the input RGBC values to RGBy output numbers. I then took the highest output value…

It’s been a while again!

April 16, 2016

Jacob

General

I have been very busy with Capstone Design again this semester so I’ve not had any time to myself. However, I have quite a lot to write about! School I am wrapping up my final few classes and getting ready for graduation! This semester I have taken several rather applicable classes to my upcoming work situation. My favorite class has absolutely been Embedded Systems. This class goes from the question What is an embedded system? through What are the considerations when designing an embedded…

It’s Been a While!

December 18, 2015

Jacob

General

I’ve not posted in a few months, mainly because I’ve been extremely busy! Here’s what I’ve been up to recently. School I just finished up the semester and finals were rough, but I came out with great success. I really enjoyed a few of my classes. Namely, Computer Architecture, where I studied how the MIPS32 ISA was designed, and then implemented several hardware versions of it. The second best class was Digital Systems Design where I was introduced to VHDL and was able…

Interesting Numbers

October 3, 2014

Jacob

Math

The Fibonacci sequence is one of the most widely used sequences when introducing the concept of sequences. The sequence is defined as the following: FN = FN – 1 + FN – 2 So, starting with F0 = 0 and F1 = 1, the first few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … and so on. An interesting thing to note about the Fibonacci sequence is that the ratio of one Fib number to its predecessor…

Be An Engineer

September 30, 2014

Jacob

General

Tonight while taking a study break from cramming for a Data Structures and Algorithms exam, I ran across this exceptionally interesting site called BeAnEngineer.com. The movement is funded by ExxonMobil and supported by an array of various engineering associations and institutions that are pushing for expanded engineering education. The site contains all sorts of information on multiple engineering fields as well as the stories of some of the most famous innovators of our time. I agree wholeheartedly with this mission of advancing the…

Toom-k Polynomial Multiplication

September 10, 2014

Jacob

Math

I’ve been pretty busy with classes the past two weeks, but I’ve learned a few neat things and I’d like to share one of them. Multiplying big numbers is a problem when the numbers are really, really big. How big is really, really big? Depends on the hardware your using. But to multiply really big numbers, we represent the two multiplicands as polynomials where each term is in the form cxn, where x is the base in the number system, c is its coefficent modifier…

Look and Say Numbers Sequence

August 14, 2014

Jacob

Math

The very famous John Conway (Conway’s Game of Life) discusses a silly ‘look-and-say’ math trick that I’ve been playing on people since middle school. Who would have guessed such interesting characteristics could come of this sequence? I am inspired by John Conway’s insight into things as simple as this basic sequence. See the video below: