**The Story of Math Academy’s Eurisko Sequence **

2023 May | During its operation from 2020 to 2023, Eurisko was the most advanced high school math/CS sequence in the USA.

Blog

An assortment of writings that are more than scratch work but not cohesive enough to form a booklet.

## Top Selected

**But WHERE do the Taylor Series and Lagrange Error Bound even come from?! **

2019 Dec | An intuitive derivation.

## Other Selected

**Business Lessons from Science Fair **

2023 Jun | The most important things I learned from competing in science fairs had nothing to do with physics or even academics. My main takeaways were actually related to business -- in particular, sales and marketing.

**My Experience with Teacher Credentialing and Professional Development **

2023 Apr | It's centered around political ideology rather than the science of learning.

**Minimalist Strength Training, Phase 1: Getting Ripped **

2022 Oct | Daily 20-30 minute bedroom workout with gymnastic rings hanging from pull-up bar -- just as much challenge as weights, but inexpensive and easily portable.

**Tips for Developing Valuable Models **

2022 Oct | Stuff you don't find in math textbooks.

## Other

**How to Remember Type I, II, and III Regions in Multivariable Calculus **

2023 May | Type I pairs with the variable that runs vertically in the usual representation of the coordinate system. The remaining types are paired with the rest of the variables in ascending order.

**Minimalist Strength Training, Phase 2: Gaining Mass **

2023 Apr | Minor changes to increase workout intensity and caloric surplus.

**Why I Don’t Worship at the Altar of Neural Nets **

2023 Jan | In order to justify using a more complex model, the increase in performance has to be worth the cost of integrating and maintaining the complexity.

**Selecting a Good Problem to Work On **

2023 Jan | Good problem = intersection between your own interests/talents, the realm of what's feasible, and the desires of the external world.

**Quants vs Systems Coders **

2022 Oct | Two subtypes of coders that I watched students grow into.

**The 5 Breeds of Quants **

2022 Aug | ... are summarized in the following table.

**From Procedures to Objects **

2022 Aug | An aha moment with object-oriented programming.

**The Ultimate High School Computer Science Sequence: 9 Months In **

2021 Feb | In 9 months, these students went from initially not knowing how to write helper functions to building a machine learning library from scratch.

**Tips for LaTeX Math Formatting **

2020 Sep | How to avoid some of the most common pitfalls leading to ugly LaTeX.

**Path Dependency in Multivariable Limits **

2019 Dec | The behavior of a multivariable function can be highly specific to the path taken.

**Thales’ Theorem **

2019 Dec | Every inscribed triangle whose hypotenuse is a diameter is a right triangle.

**Trick to Apply the Chain Rule FAST - Peeling the Onion **

2019 Dec | A simple mnemonic trick for quickly differentiating complicated functions.

**Trick to Apply the Chain Rule FAST - Peeling the Onion **

2019 Dec | A simple mnemonic trick for quickly differentiating complicated functions.

**CheckMySteps: A Web App to Help Students Fix their Algebraic Mistakes **

2019 May | A prototype web app to automatically assist students in self-correcting small errors and minor misconceptions.

**Solving Tower of Hanoi with General Problem Solver **

2019 May | A walkthrough of solving Tower of Hanoi using the approach of one of the earliest AI systems.

**New Food Vignette: A First Account of Pesto **

2017 Sep | If only I could forget the first bite, so that I might live it again.

**Can Imago Dei be Present in Transhumans or a Future Species that Humans Evolve Into? **

2017 Sep | Yes, provided that the corresponding evolutionary enhancements do not remove our freedom nor our opportunities for relationship, the two components to the choice to partake in relationship with God (i.e., the collective universe) and His Creation (i.e., the constituents of the collective universe).

**The Data Scientist’s Guide to Topological Data Analysis: Preamble **

2017 Sep | Bridging the communication gap between academia and industry in the field of TDA.

**A Game-Theoretic Analysis of Social Distancing During Epidemics **

2016 May | In a simplified problem framing, we investigate the (game-theoretical) usefulness of limiting the number of social connections per person.

**Making Indirect Interactions Explicit in Networks **

2016 Mar | Category theory provides a language for explicitly describing indirect relationships in graphs.

**Book Summary: Memory Evolutive Systems **

2016 Mar | Framing complex systems in the language of category theory.

**Introduction to Computers **

2015 Nov | The main ideas behind computers can be understood by anyone.

**The Brain in One Sentence **

2015 Nov | The brain is a neuronal network integrating specialized subsystems that use local competition and thresholding to sparsify input, spike-timing dependent plasticity to learn inference, and layering to implement hierarchical predictive learning.

**Shaping STDP Neural Networks with Periodic Stimulation: a Theoretical Analysis for the Case of Tree Networks **

2015 Aug | We solve a special case of how to periodically stimulate a biological neural network to obtain a desired connectivity (in theory).

**On the Contrasting Educations and Outcomes of Ben Franklin and Montaigne **

2015 May | Montaigne's education, strictly dictated by his parents and university studies, resulted in an isolative work with scholarly impact but limited public reach. Conversely, Benjamin Franklin's goal-oriented self-teaching led to influential creations and roles benefiting his community and nation.

**A Brief Overview of Spike-Timing Dependent Plasticity (STDP) Learning During Neural Simulation **

2015 Feb | Implementation notes for STDP learning in a network of Hodgkin-Huxley simulated neurons.

**A Visual, Inductive Proof of Sharkovsky’s Theorem **

2015 Jan | Many existing proofs are not accessible to young mathematicians or those without experience in the realm of dynamic systems.

**Building an Iron Man Suit: A Physics Workbook **

2014 Jul | A workbook I created to explain the math and physics behind an Iron Man suit to a student who was interested in the comics / movies.

**The Physics Behind an Egg Drop: A Lively Story **

2014 Jul | A workbook I created to explain the math and physics behind an egg drop experiment to a student who was interested in Lord of the Rings and Star Wars.

**A Formula for the Partial Fractions Decomposition of $x^n/(x+a)^k$ **

2013 Aug | And a proof via double induction.

**Call of the Wild: An Insight into the Life of Jack London **

2013 May | In his book The Call of the Wild, Jack London conveys the fleetingness of luxury and the constant hardship in his life by chronicling Buck's transition from an affluent lifestyle to a constant struggle for mastery.

**Sound Waves **

2012 Dec | A brief overview of sound waves and how they interact with things.

**Detecting Dark Matter **

2012 Dec | A brief overview of the experimental search for dark matter (XENON, CDMS, PICASSO, COUPP).

**Evidence for the Existence of Dark Matter **

2012 Dec | Mass discrepancies in galaxies and clusters, cosmic background radiation, the structure of the universe, and big bang nucleosynthesis's impact on baryon density.