CV

Experience

I've applied math in many contexts including working as a data scientist, modeling biological neural networks, and improving particle detectors. I also tutored & taught math for a decade, culminating in (currently) developing and teaching one of the most advanced high school applied math/CS sequences in the country.

## Algorithm Developer & Domain Expert

Involved in all aspects of production of an intelligent tutoring system that seeks to become the ultimate online math learning platform. As the third member of the core team, my primary role involves developing algorithms and encoding domain-expert knowledge so that the system can behave like an experienced tutor.

Most notably, I created the Fractional Implicit Repetition (FIRe) model, which generalizes discrete spaced repetition on independent tasks to fractional implicit spaced repetition on highly connected knowledge graphs and is orders of magnitude more computationally efficient than conventional algorithms on knowledge spaces. Math Academy uses the FIRe model to estimate student knowledge profiles and select personalized tasks that optimize knowledge persistence over time, striking an optimal balance between learning new topics (maximizing knowledge gain) and reviewing already-seen topics (minimizing knowledge loss).

Additional noteworthy contributions include the following:

## Data Scientist - Analytics, R&D

Worked full time while simultaneously an undergraduate (transitioned to full-time after interning during sophomore year).

## Instructor - Computation & Modeling, Machine Learning, Intelligent Systems

Math Academy supports a highly accelerated math program (by the same name) within the Pasadena Unified School District. The program is the most advanced in the country; students take AP Calculus BC in 8th grade and study a full undergraduate math curriculum in high school.

In collaboration with Jason Roberts (founder of Math Academy), I developed and taught a special three-course math/CS sequence within the Math Academy program called Eurisko (eurisko.us). Eurisko is one of the most advanced high school math/CS sequences in the country.

## Math Educator / Content Developer

Tutored, taught, and developed math content both independently and for a variety of organizations.

## Math Instructor

Tutored ~250 students in grades K-12 over the course of 5 years, working primarily with middle/high school students taking algebra through calculus. (Evenings & weekends, 20h/week)

## Theoretical Neuroscience

Simulated cyclic Hodgkin-Huxley neural networks with spike-timing dependent plasticity and later proved results under simplifying assumptions in the special case of tree networks. Project was a self-directed investigation advised by Prof. Dervis Can Vural of the Many-Body Physics group.

## Computational Neuroscience / Deep Learning

Implemented spiking neurons in a deep neural network in attempt to create an emergent phenomenon of brain oscillations during an image classification task. Worked in the synthetic cognition group, affiliated with Los Alamos National Lab.

## Experimental Particle Physics

Improved data transmission in Fermilab and CERN particle detectors by reducing signal loss at the detector surface. Finalist in Intel's International Science/Engineering Fair, 2013. (Two separate projects, the first under Prof. Ilan Levine of IUSB and the second in collaboration with Notre Dame's QuarkNet lab.)

*Click to expand sections below. Also available on*LinkedIn.**Tech**## Algorithm Developer & Domain Expert

Third member of core team

Math Academy, May 2019 - present

Involved in all aspects of production of an intelligent tutoring system that seeks to become the ultimate online math learning platform. As the third member of the core team, my primary role involves developing algorithms and encoding domain-expert knowledge so that the system can behave like an experienced tutor.

Most notably, I created the Fractional Implicit Repetition (FIRe) model, which generalizes discrete spaced repetition on independent tasks to fractional implicit spaced repetition on highly connected knowledge graphs and is orders of magnitude more computationally efficient than conventional algorithms on knowledge spaces. Math Academy uses the FIRe model to estimate student knowledge profiles and select personalized tasks that optimize knowledge persistence over time, striking an optimal balance between learning new topics (maximizing knowledge gain) and reviewing already-seen topics (minimizing knowledge loss).

Additional noteworthy contributions include the following:

- conceptualized and created the initial version of the knowledge graph visualization
- developed tools for validating and editing the knowledge graph while students are simultaneously working on it
- developed algorithms that govern the amount of XP that a student is awarded or penalized for their performance on each task (to incentivize behavior that is optimal for learning)
- converted 1000+ preexisting textbook-style tutorials to interactive lessons, created hundreds of lessons from scratch, and put finishing touches on all lessons written by the content team

## Data Scientist - Analytics, R&D

Worked full time while simultaneously an undergraduate

Aunalytics, Jan 2016 - Feb 2018

Worked full time while simultaneously an undergraduate (transitioned to full-time after interning during sophomore year).

- Built predictive churn models & segmented user data to discover sales insights for clients.
- Developed prototypes of in-house data tools & migrated existing workflows onto Aunsight (custom data processing platform).
- Evaluated the potential of topological data analysis for practical use in the data science pipeline.

**Teaching**## Instructor - Computation & Modeling, Machine Learning, Intelligent Systems

Developed one of the most advanced high school applied math/CS sequences in the country

Math Academy (Non-Profit Division), May 2020 - present

Math Academy supports a highly accelerated math program (by the same name) within the Pasadena Unified School District. The program is the most advanced in the country; students take AP Calculus BC in 8th grade and study a full undergraduate math curriculum in high school.

In collaboration with Jason Roberts (founder of Math Academy), I developed and taught a special three-course math/CS sequence within the Math Academy program called Eurisko (eurisko.us). Eurisko is one of the most advanced high school math/CS sequences in the country.

- The first course in the sequence, Computation & Modeling, is inspired by MIT's Introduction to Computer Science, and goes far beyond it. Among other things, students write their own machine learning algorithms from scratch (including polynomial and logistic regression, k-nearest neighbors and k-means, and parameter fitting via gradient descent).
- The second course, Machine Learning, covers more advanced machine learning algorithms such as random forests and neural nets, and students also work together to implement Space Empires, an extremely complex board game that pushes their large-scale project skills (object-oriented design, version control, etc) to the limit. Again, students implement all algorithms from scratch before using any external libraries.
- The third course, Intelligent Systems, involves using evolutionary algorithms to develop agents that behave intelligently in complex environments. Students reproduce Blondie24 and continue implementing Space Empires with the goal of designing artificially intelligent agents to play it.

## Math Educator / Content Developer

Many organizations, Jan 2018 - May 2021

Tutored, taught, and developed math content both independently and for a variety of organizations.

- [May 2019 - May 2021] Independent tutoring
- [Jan 2018 - May 2020] Math Academy - developed 300+ tutorial videos, taught substitute/summer classes & TA sessions. (Tutorial videos were used in the early days but we've since moved away from them for efficiency reasons.)
- [Aug 2019 - May 2020] Pilgrim School - taught AP Calculus AB, physics, first-semester engineering
- [Aug-Sept 2019] IXL Learning - item writing
- [Jun-July 2019] Math Academy - taught Research and Presentation in Mathematics, Mathematical Problem Solving, Drawing Mathematics with Desmos
- [Apr 2019] Math Academy - substitute taught Linear Algebra / Multivariable Calculus
- [Mar 2018 - Mar 2019] FLEX College Prep - weekend SAT/ACT math classes
- [2018-19] Wrote 3 textbooks (for fun)
- [Feb 2018 - May 2019] LA Tutors 123 - tutored ~10 students
- [Jan 2018 - Mar 2020] HBar Tutoring - tutored ~20 students
- [Jan-Jun 2018] Study.com - item writing

## Math Instructor

Mathnasium, Mar 2013 - Jan 2018

Tutored ~250 students in grades K-12 over the course of 5 years, working primarily with middle/high school students taking algebra through calculus. (Evenings & weekends, 20h/week)

**Research Internships**## Theoretical Neuroscience

Vural Lab, iCeNSA, University of Notre Dame, Aug 2014 - May 2016

Simulated cyclic Hodgkin-Huxley neural networks with spike-timing dependent plasticity and later proved results under simplifying assumptions in the special case of tree networks. Project was a self-directed investigation advised by Prof. Dervis Can Vural of the Many-Body Physics group.

## Computational Neuroscience / Deep Learning

Synthetic Cognition Group (affiliated with LANL), New Mexico Consortium, May - Aug 2015

Implemented spiking neurons in a deep neural network in attempt to create an emergent phenomenon of brain oscillations during an image classification task. Worked in the synthetic cognition group, affiliated with Los Alamos National Lab.

## Experimental Particle Physics

Finalist, Intel International Science/Engineering Fair, 2013

QuarkNet (affiliated with CERN), University of Notre Dame, June 2013 - May 2014

Levine Lab (affiliated with Fermilab), IU South Bend, Sept 2012 - May 2013

Improved data transmission in Fermilab and CERN particle detectors by reducing signal loss at the detector surface. Finalist in Intel's International Science/Engineering Fair, 2013. (Two separate projects, the first under Prof. Ilan Levine of IUSB and the second in collaboration with Notre Dame's QuarkNet lab.)

Education

I earned a BS in Mathematics from Notre Dame on full-ride scholarship, and a MS in Computer Science (Machine Learning track) from Georgia Tech, while working full time.

Machine Learning track; simultaneously worked 60+ h/week

Glynn Honors Program; simultaneously worked 60h/week during junior/senior years

**MS, Computer Science**, Georgia Institute of Technology, 2020Machine Learning track; simultaneously worked 60+ h/week

**BS, Mathematics**, University of Notre Dame, 2018*Full-ride Lilly Scholarship (under 3% selection rate, applies to any university in Indiana)*Glynn Honors Program; simultaneously worked 60h/week during junior/senior years

Writing

**Books**

I write textbooks for fun as a way to consolidate and clarify my quantitative intuition. The goal is to provide deep intuition for the core concepts and connections, along with plenty of practice exercises, while remaining as concise as possible.

*Justin Math: Linear Algebra*(2019). print, pdf, digital*Justin Math: Calculus*(2019). print, pdf, digital*Justin Math: Algebra*(2018). print, pdf, digital

Several more books in preparation:

*Introductory Exercises in Computation*(expected summer 2022)*Classical Supervised Machine Learning*(with Sanjana Kulkarni; expected 2022)*Neural Networks*(expected 2024)

**Articles**

*The Ultimate High School Computer Science Sequence: 9 Months In*(2020). blog post*But WHERE do the Taylor Series and Lagrange Error Bound even come from?!*(2019). blog post