Linear Inequalities [Math Mondays]

This might seem a little trivial at first, but this is one of the most important concepts in Math for Coding .

Aug 30, 2022

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Happy Math Monday Day my love,

This is such a rare event, one that happens only once a week. To celebrate this super special occasion, I have a special gift for you- a post on Linear Inequalities. TADA!!!

The reaction I’m expecting out of you for this one. Image Source

This is a very interesting topic because most people studying algebra tend to brush it off. It’s not their fault, people don’t focus on the correct aspects of these. While the Algebra 2 version of Linear Inequalities might seem banal and boring, working with LIs is a crucial skill for any developer/system designer. I know I’m promising a lot, but there’s a good reason for it. You’ll see it in today’s post.

This is not a hard topic to figure out. Image Source

Key Highlights

The What- LIs are simply ways of writing your equations to codify certain bounds/conditions on your domain. For example- saying x*5+2<3 just tells me that I want values of x that will not cross 1/5 (try seeing how I got that number). This is straightforward.
The Why- LIs efficiently allow you to store all the rules/constraints and solve for them. Even if you don’t get an exact solution (you often will not), methodically solving through them will allow you to filter out terrible solutions and restrict your search space to a much smaller domain. This is a big fat W.
Where they show up a lot- Everywhere. But you’ll see these a lot in Linear Optimization (where setting up these inequalities is all you do). The skill of learning to identify the correct boundaries based on rules will also help a lot if you get into multi-variate calculus and/or AI.
How to get good with these- Practice. For the basics, Khan Academy has good problems. It shouldn’t take too long for you to master the concept. The tricky part is actually implementing these for IRL examples. Reading through paragraphs and formulating them as inequalities is hard. To master this skill, you’ll need to practice deliberately breaking down situations into equations. Think of your local grocery store. How would you break down their operations into a system of equations and Inequalities? Awkward at first, but super worth it.

If you’re looking for a great place to start with this concept, I’m linking a video by Wrath of Math. This will be a good intro to the conventions and the basic solving process.

To learn Math more effectively, check out my post- Math is a Language. This is how you should learn it. [Math Mondays]

To know what Math Topics are most important for Computer Science, read this

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