Books

The Math Academy WayMath TextbooksIntroduction to Algorithms and Machine Learning Linear AlgebraCalculusAlgebraBooklets

The Math Academy Way

Using the Power of Science to Supercharge Student Learning
(350-page working draft)   doc, pdf
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  • 1. Preliminaries - The Two-Sigma Solution; The Science of Learning; Core Science: How the Brain Works; Core Technology: the Knowledge Graph; The Importance of Accountability and Incentives.
  • 2. Addressing Critical Misconceptions - The Persistence of Neuromyths; Myths & Realities about Individual Differences; Myths & Realities about Effective Practice; Myths & Realities about Mathematical Acceleration.
  • 3. Cognitive Learning Strategies - Active Learning; Deliberate Practice; Mastery Learning; Minimizing Cognitive Load; Developing Automaticity; Layering; Non-Interference; Spaced Repetition (Distributed Practice); Interleaving (Mixed Practice); The Testing Effect (Retrieval Practice); Targeted Remediation; Gamification; Leveraging Cognitive Learning Strategies Requires Technology.
  • 4. Technical Deep Dives - Technical Deep Dive on Spaced Repetition; Technical Deep Dive on Diagnostic Exams; Technical Deep Dive on Learning Efficiency; Technical Deep Dive on Prioritizing Core Topics.


Math Textbooks


During my teaching years shortly after college, I simultaneously wrote math textbooks for fun as a way to consolidate and clarify my quantitative intuition. The goal was to provide deep intuition for the core concepts and connections, along with plenty of examples and exercises, while remaining as concise as possible.

My teaching years and math textbook writing culminated in Introduction to Algorithms and Machine Learning: from Sorting to Strategic Agents. This book was written to support what was, during its operation from 2020-23, the most advanced high school math/CS sequence in the USA. It culminated in high school students doing masters/PhD-level coursework (reproducing academic research papers in artificial intelligence, building everything from scratch in Python).

Despite no intentional search optimization, this content ranks in the top results for many common search queries across various subfields of math. Some example queries are provided below:
A special thanks to Sanjana Kulkarni for her thoughtful suggestions and diligent proofreading of these books.

Print copies are available on Amazon for the minimum price possible (printing cost plus Amazon's fees).

There's also a (hacky, but functioning) knowledge graph explorer tool for the content in these textbooks, plus some related content from booklets and blog posts:

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Introduction to Algorithms and Machine Learning

from Sorting to Strategic Agents
(2022)   pdf, print, school program

This book was written to support what was, during its operation from 2020-23, the most advanced high school math/CS sequence in the USA. It culminated in high school students doing masters/PhD-level coursework (reproducing academic research papers in artificial intelligence, building everything from scratch in Python).

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Linear Algebra

(2019)   pdf, print
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Calculus

(2019)   pdf, print
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Algebra

(2018)   pdf, print
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Booklets

Below are some shorter manuscripts that I feel are interesting enough to share.


Graphing Calculator Drawing Exercises (2019)
pdf, print, course page
A Primer on Artificial Intelligence (2019)
What is AI; The First Wave: Reasoning as Search; The Second Wave: Expert Systems; The Third Wave: Computation Power and Neural Networks; Cutting Through the Hype.

Introduction to Python Programming (2019)
Getting Started in Colab; Strings, Ints, Floats, and Booleans; Lists, Dictionaries, and Arrays; If, While, and For; Functions.

Intuiting Predictive Algorithms (2018)
Naive Bayes; MAP and MLE; Linear Regression; Support Vector Machines; Neural Networks; Decision Trees; Ensemble Models.

The Data Scientist's Guide to Topological Data Analysis (2017)
Connecting Calculus to the Real World (2017)
An Intuitive Primer on Calculus (2017)
Functions; Limits; Derivatives; Integrals; Sequences; Series.

The Physics Behind an Egg Drop: A Lively Story (2014)
Velocity; Momentum; Changes in Momentum; Force; Pressure; Troll Egg Drop.