Education

ENSOFT Math

Video lessons from ENSOFT on mathematical thinking: how vague, intuitive ideas become precise, actionable concepts.

Episode 1 · Quantifying Connectedness

Which node in a graph is more connected, and by how much? Putting a number on that intuition leads to the idea behind Google’s PageRank.

Next Episode 2 · Matrix Algebra

Where the Series Is Going

Linear Algebra

Linear algebra made simple enough for a high school student to understand and apply. It turns amorphous ideas into clear, precise quantities, and gives the computational methods for working with them.

Newton’s Calculus

From episode 1: a curve labeled Newton, and a timeline that reaches limits about 300 years later.

Calculus the way Newton did it: high school algebra powered by infinity, the idea John Wallis brought into algebra. Newton’s calculus was about computing, and modern computing methods such as neural networks are variations of it.

Algebra for Graph Problems

From episode 1: Dijkstra’s algorithm settles node D at 3 and misses the path through C, which costs −6.

Graph algorithms are usually taught by walking the graph. Algebra solves graph problems without walking it, which matters when an application graph has more paths than all the computing power on Earth could process one by one.

Claude Shannon’s Information Theory

From episode 1: the words Follow the white pass through embed, attention, mlp, and softmax blocks to scored next words, over a rain of bits.

Shannon made information a quantity you can measure, the hard science behind digital communication. The series uses it to look at large language models as information processing systems.

ENSOFT Research

Related Research

All Algebra & Graphs research →

19 November 2025

A High School Algebra Solution for the Shortest Path Problem

An algebraic framework for graph problems, demonstrated on the shortest-path problem as an alternative to traversal algorithms such as Dijkstra and Bellman–Ford. Path segments are modeled as algebraic expressions, and shortest paths—including in graphs with negative edge weights and negative cycles—are derived through equation solving and factorization rather than iterative state updates. The paper also examines “all-paths” problems where explicit graph traversal becomes intractable.

Suresh C. Kothari, Payas AwadhutkarRead the paper →

Figure 1 of the paper: a directed graph with vertices v0 through v7 and edges e1 through e9, beside its algebraic equations, one for each vertex. — Figure 1 · A graph as algebraic equations