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A learner’s journey to uncover math’s hidden structure

The Complex Plane
The Complex Pl…
Set Closure Under Operations
Set Closure Unde…
Standard Form and Basic Ops.
Standard Form an…
Geometric Closure and Felix Klein
Geometric Closure…
Mobius Transforms and Matrices
Mobius Transforms…
Complex Numbers vs. Vectors
Complex Numbers…
Complex Functions
Complex Functio…
Power Series Symmetry
Power Series Sym…
Calculus
Calculus
Euler’s Formula: A Visual Guide
Euler’s Formula: A…
Complex Algebra Applications
Complex Algebra A…
Divergence, Curl, and Maxwell
Divergence, Curl,…
Gauge Symmetry
Gauge Symmetry
Geometric Derivatives
Geometric Derivati…
…
…
Infinitesimals vs.  Limits
Infinitesimals vs….Text is not SVG – cannot display

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Recent Posts

Potentials and Gauge Symmetry in Electromagnetism

Potentials and Gauge Symmetry in Electromagnetism

August 20, 2023
Finally wrapping up our dive into the different representations of Maxwell's equations, we arrive at the vector potential forms. Unlike...
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Maxwell’s Equations: Differential and Integral Forms

Maxwell’s Equations: Differential and Integral Forms

May 2, 2023
What are the big ideas behind Maxwell's equations? In this post, we uncover the Vector Calculus that gives their two...
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Convergence and Complex Taylor Series

Convergence and Complex Taylor Series

March 25, 2023
Infinite series are up there with some of the coolest functions in math. They're at the heart of Calculus with...
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Vectors vs. Complex Numbers: Intro to Complex Differentiation

Vectors vs. Complex Numbers: Intro to Complex Differentiation

January 16, 2023
An example of a linear transformation, the angle with which we'll be looking at complex numbers and vectors alike.Credit: All...
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Infinitesimals Vs. Limits In Calculus

Infinitesimals Vs. Limits In Calculus

December 11, 2022
Credit: [Contemporarycalculus.com] When I was learning Calculus on my own, I decided to skip limits. Sounds stupid, I know, but...
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Algebra Needs Complex Numbers

Algebra Needs Complex Numbers

September 10, 2022
If you've been following along with my earlier posts on the complex number system then you've gotten a taste of...
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Imaginary Numbers and Real Math

Imaginary Numbers and Real Math

August 29, 2022
All math is connected. But as mathematicians go deeper and deeper into the weeds the results they find grow increasingly...
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Imaginary Apples and Oranges

Imaginary Apples and Oranges

August 17, 2022 2 Replies
What is the sum of 3 apples and 4 oranges? This classic statement highlights the difficulties in comparing the incomparable....
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The Mystery of the Complex Plane

The Mystery of the Complex Plane

August 14, 2022
Think about when you learned algebra for the first time. On that seemingly uneventful day of middle school, the letter...
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My Mission

One of the hardest things I find about learning math is finding continuity. Bridging the gap between Algebra 1 and Geometry and Calculus is one that is largely left to the student, and the goal of this blog is to lay as much of its foundation as possible for those willing to start that journey. By documenting my own meandering road to that goal through weekly posts, I hope this map through the forest of numbers can be a stepping stone for others to start their own dive down the rabbit hole. The clickable MathMaps are a reflection of my personal views about the various topics I’m exploring and the intricate connections they possess. I post 1-2 times a week and continually update my map of the mathematical wilderness, so be sure to stick around for the journey!