AI and Math — A Guide for Parents

This is the fifth article in our “Guide for Parents” series about why and how K-12 students should learn AI. Previous articles covered the Reasons to Learn AI, the importance of Project Based Learning, the relationship between AI and Robotics, and the relationship between AI and Programming. In this article we cover an increasing question that parents have asked us, how much math do students need to learn to be productive with AI?

What is Artificial Intelligence?

Artificial Intelligence is about creating computer programs that can do things that human brains usually do. Examples are recognizing images, understanding text, finding patterns in examples, mapping solutions to problems, creating game strategies, etc. Artificial Intelligence programs usually start by Training (or Learning), and then apply the learning to solve new problems, or Predict what is going to happen next.

Examples of what you can do with Artificial Intelligence:

• You can build a personal digital assistant like Alexa who can answer questions and play music for you.
• You can detect objects in images. Self driving cars use this to help navigate.
• You can detect fraud. Financial companies use this to detect whether a credit card has been stolen.

How are AI and Math Related?

While there is a common perception that AI requires a PhD and a lot of math, that is not generally true. There is a lot that K-12 students can do with AI. It is true however that their appreciation of AI internals will grow when they learn certain types of math.

AI draws from many fields of Math, from Probability, Statistics, Calculus, Matrix Algebra, and more. However, there are three primary ways that AI and math intersect

• Some math is needed to understand whether or not an AI is performing well. For example, if you have an AI that is predicting whether an image is a Cat or a Dog, and it has been tested with 50 examples, getting 40 of them right is an Accuracy score of 80%, which is well above what would have happened if an AI had guessed randomly — which would have gotten 50%. Metrics like this can be understood by students with basic knowledge of Algebra, Averages and similar math. More advanced metrics typically require an entry level class in Algebra to appreciate.
• The datasets themselves have patterns that can be understood even without an AI. For example, if a dataset has prices of houses, basic statistics can be used to understand what the average, median house prices are. More statistics can show us what the distribution of house prices are, if some are outliers etc. These are important for AI because an understanding of data helps the human better appreciate the patterns in the data that they are asking the AI to learn from. The math required to appreciate these kinds of insights are Statistics and Data Representation.
• The algorithms (or techniques) that make up the AI learning itself are heavily math based. These include methods to digest the data and create models, find the most critical features (attributes) of the data to create Decision Trees, etc. For these functions, AI draws heavily from the math fields of Probability, Statistics, Calculus and Algebra.

What Math can my student learn to better prepare for AI?

The key things that parents of K12 students need to know about AI and math are:

(a) You do not need to know much math to get started with AI and learn and build AIs. To build an AI and understand whether it is working well, understanding of concepts like Averages is sufficient. Using websites like (http://aiclub.world), even students with no knowledge of algebra can build, use and improve an AI of their own. The next step is a Middle School class in Algebra which will introduce concepts like Square Roots, etc. which are used in other AI metrics.

(b) Any learning of Statistics is helpful not just to AI but even more broadly. In our information driven world, kids are frequently bombarded with data, from news reports, to polls and surveys, and are frequently told that the data supports some conclusion. A basic understanding of statistics will help them understand how to think about data, how to see patterns and distinguish them from outliers, and how to see whether a conclusion is well justified from the data. From an AI perspective, an understanding of Statistics will help students see whether the data that they give an AI is well structured, and be able to relate what the AI learns to the data itself. You can learn these concepts and apply them in an AI context in classes like this.

(c ) Any understanding of Matrix operations (how to multiply matrices, what it means to invert a matrix etc.) are helpful to give students more appreciation for how AI uses data to learn. Since most AIs operate on a table with each row being an example and each column being some attribute of the example (like the number of bathrooms in a house whose price you want to predict), most data sets are large matrices. Algebra of matrices, vectors and similar structures can help students start thinking about how patterns can be extracted from data sets. They can also use these math concepts to build their own AI algorithms from scratch in classes like this.

(d) While topics like Probability and Calculus are core to how AIs work internally, the level of Probability and Calculus needed to fully appreciate AI algorithms is usually taught in college classes. For example, a very common AI learning technique, Stochastic Gradient Descent, requires Partial Differential Equations (an advanced form of Calculus) to fully appreciate at a mathematical level. Even practicing professional Data Scientists and AI engineers sometimes do not understand this math. Given this, it is not required for K12 students try to acquire this level of math. There is a tremendous amount they can do with AI without it.

Level (a) is enough to learn and practice AI, understand AI’s strengths and limitations, and use AI to solve interesting problems. Level (b) brings an additional appreciation for the information hidden in data, and helps students create better data sets for training their AIs, and better AIs. Level ( c) can help students understand basic AI methods like Linear Regression, and even build such algorithms themselves directly from scratch.

AI, Math and Data — a Symbiotic Relationship

There is a strong symbiotic relationship between AI and math. In our experience, nearly half of students who learn AI report an increased interest in math after they build an AI. As students learn more about data, they start to appreciate the notion of data quality. Building custom AI projects shows students the characteristics of real life data gathering and reputable data. Custom projects also increase students’ interest in using math to understand their data and their AI.

Summary

AI can be a great way to increase interest in Math, and an interest in Math can lead to an interest in AI. By showing students how AI and math are related, they can see things they see every day (like Alexa, shopping recommendations, self driving cars etc.) and become curious about the math that powers it all!