Introduction To Mathematical Thinking: And, Or, & Not

mathematical thinking

Well well, I am now on week two of:  Introduction To Mathematical Thinking, a free and open course offered online via, which is taught by Dr. Keith Devlin of Stanford University.

The course is geared to teach you how to think mathematically, and more to the point, I think what is meant by that is how to problem solve and communicate with precision, excluding ambiguity from your processes and statements. Which makes sense, in math the answer is either wrong or right, true or false, so communicating in a precise manner would be essential to correctness.

So far, I have understood parts of the assignments and quizzes, and failed miserably at other parts. Example, never before have I seen the symbols for And, Or, & Not in mathematics:

Screenshot of Assignment 2, of the Stanford online course Mathematical Thinking.

As you can see from these math problems, the symbols are a capital V for “Or”, and an inverted or upside down capital ^ for “And” and a negative sign with a hook on the end, which means “Not”. Also new to me were the symbols for Phi, and Psi:


The Greek letters Phi and Psi.

I believe we are simply using these Greek letters as variables, but I am honestly not 100% sure of this, which in hindsight is a question I should of asked by now on the Discussion Forum. After all, peer review and group study is the core concept of this online course, or MOOC, which seems to be the new buzzword for these types of classes offered online to masses of people around the world.

I need to do more “dirty work” and get down to writing out the problems and figuring them out repeatedly. This first week I did not devote enough time to actually doing the material myself, which I am humbled to report has manifested itself in my first test score on Problem Set 1, in which I scored a total of 10 out of 21 correct, and was then deducted 2 points for completing the test a day late.

So, I dismal score of 8/21 on the first test. This convinced me to pay more attention to the lectures, spend more time on the forums and Facebook study groups, and most importantly, I need to actually do the problems multiple times and practice the new concepts for I have clearly failed to firmly grasp them this first week.

Now, I never made it to Pre-Calculus in high school, so I am not well versed in mathematics anyways, especially since this is the first math course I have taken in 8 years, but it is supposed to be a transitional course from high school mathematics to university mathematics.

Clearly, this is a course I need if I am to accomplish my goal of becoming capable of high level mathematics and I am grateful to, Stanford, and Dr. Devlin and his team for the opportunity to take this course and to learn as much as possible from it.

Whether or not I receive a passing grade is inconsequential to me, for learning the material is all that matters and which is the most important to me, though, a certificate of completion from Stanford University would put a smile on my face, for sure.

I am still progressing in my other areas of self-improvement, and I will try to update everyone on those soon, I just have been so busy with all this work and courses and life, that I have admittedly been neglecting this blog.

Take care, and remember, it is never too late to learn something new, never.


Tomorrow I Start Mathematical Thinking by Dr. Keith Devlin, Stanford (Coursera)

university of stanford


Hello there!
Been really busy with all the areas of study and I have another part-time job now on top of that, so I’ve been neglecting this blog but that should change soon as I begin posting more often for anyone who is interested.

Tomorrow I start an online course offered by Stanford professor Dr. Keith Devlin, it’s called Introduction to Mathematical Thinking and is offered via It is a transitional course that teaches you how to go from high school math to college math. You can read about it here, as it was featured today in a story on USA Today:

There are currently over 50,000 people registered for the course! Awesome!

So Much To Do, So Little Time!!!

cute asian girl


Hey everyone!

Well I am currently on Unit three of the Castilian Spanish language course from Rosetta Stone and progressing decently, at least in my opinion! I have also started Japanese, and am still early on in the first unit of Japanese language pack. Wow, what a difference! Spanish and English have a few similarities, but Japanese is from a whole another planet! It’s fun though, especially because it is so amazingly different from what I’ve been used to my whole life.

I am currently up to Algebra, Geometry and a few other things on Khan Academy.

Right now for the programming languages I am focusing on C, Python, and Java. But I am also working PHP, JavaScript, and a couple others in when I have time.

My first online course that I am actually registered for, begins in approx 15 days. It is a Greek and Roman Mythology course offered online by The University of Pennsylvania. I also start a Mathematical Thinking course soon, offered by Prof. Devlin of Stanford University.

I am of course still working on CS50 Fall 2011, and am registered for the online class CS50x, starting on October 15th, offered by and Prof. David J Malan.

Look for more updates soon and I will try to be more detailed next time, I just don’t have much time today.

Have a good one!

There Are 10 Types of People In This World…

base-2 math

… those who understand binary, and those who don’t! Today I thought I would share a video link with everyone that explains how binary works. If you don’t know, binary is how computers know what to do. At some level, everything the computer does is because of the binary base-2 number system. One and zero, on and off, true and false. This is because electricity is either flowing or it isn’t, so base-2 math of binary is logical and an essential part of computer science. Check out this fun video by Sal Khan of Khan Academy as he explains how binary mathematics works:

What The Frak, Part Deux

my khan academy energy points and stats

Chillen with Magellan! (awarded for achieving proficiency in 100 different skills)

Finally! Yesterday I finally finished the Khan Academy module on Fractions. It seemed to take forever but I achieved proficiency in the 35 skills that make up the module. I am now working on Exponents and Radicals, Statistics, Probability, and a dozen other little odds and ends (like stem & leaf trees, graphs, bars, charts, perimeter, etc) in the Arithmetic and Pre-Algebra section.

I now have over 400,000 Energy Points.

As John Chrichton would say… “What The Frak!”

what the frak!

Just a simple update today on my progression in mathematics. I have now been going through the Khan Academy mathematics modules for 19 days. I started at the very beginning with simple addition and subtraction and have now worked my way up to the  fractions modules. I have two months until my online classes on edX start (offered by MIT and Havard), so I have a couple months to get through algebra and hopefully trig so I can be ready for the computer science and programming courses.
Current Energy Points (KhanAcademy): 291,195

Have a great day and thanks for reading.

Who Needs Math In The Real World Anyways?

The Khan Academy by Salman Khan

… Me apparently!

Being a lot better at the maths would really help me in my goals to further my own education and especially with computer science and programming.

As part of my independent learning journey I have started reviewing mathematics from the ground up. I started on Khan Academy about 13 days ago (at the very first level with basic addition and subtraction) and have quickly progressed through the arithmetic stage. What has startled me, is just how much basic math skills I have forgotten in the 8+ years since I used math and probably 15+ years since I did math without a calculator. Reviewing math from the bottom up I can confirm my own thoughts that it would be vital to get back into the swing of things mathematically. I have progressed up to the factors, fractions, and exponents modules and will be moving on to the geometry & algebra modules within a week I predict.

I have a new thirst for knowledge and have given myself a goal of becoming proficient at math and progressing all the way to the higher level maths that I never achieved before. The furthest I went in math was what my high school, Kent-Meridian in Kent, Washington, called “Algebra 3 with Trig”. It was the class right after Geometry and before Precalculus. I was always good at geometry but never desired to go very far with math; but that has all changed and I am looking forward to, and even excited about, becoming highly educated on mathematics.

My very generic planned course of progression for learning mathematics:

Arithmetic — > Geometry / Algebra –> Algebra II –> Probability / Statistics –> Precalculus / Trigonometry –> Differential and Integral Calculus –> Multi-variable Calculus –> Differential Equations –> Linear Algebra –> Proofs –>

… and then in no particular order I intend to at least get familiar with the following topics:

* Graph Theory * Real Analysis (Key) * Number Theory * Complex Analysis * Abstract Algebra (Key) * Topology * Discrete Mathematics *

So to end this post I will give an update on my progress thus far in math at KA:

Current Khan Academy “Energy Points”: 227, 247.