Using math to write efficient code in any language

Programmers design, build, test, and maintain software. Employ cases and personal preferences determine the programming languages we use throughout development. Mobile app developers use JavaScript or Dart. Some programmers design performance-first software in C/C++.

A generic source code includes language-specific grammar, pre-implemented function calls, mathematical operators, and control statements. Some mathematical principles assist us enhance our programming and problem-solving skills.

We all use basic mathematical concepts like formulas and relational operators (aka comparison operators) in programming in our daily lives. Beyond these mathematical syntaxes, we'll see discrete math topics. This narrative explains key math topics programmers must know. Master these ideas to produce clean and efficient software code.

Expressions in mathematics and built-in mathematical functions

A source code can only contain a mathematical algorithm or prebuilt API functions. We develop source code between these two ends. If you create code to fetch JSON data from a RESTful service, you'll invoke an HTTP client and won't conduct any math. If you write a function to compute the circle's area, you conduct the math there.

When your source code gets more mathematical, you'll need to use mathematical functions. Every programming language has a math module and syntactical operators. Good programmers always consider code readability, so we should learn to write readable mathematical expressions.

Linux utilizes clear math expressions.

Inbuilt max and min functions can minimize verbose if statements.

How can we compute the number of pages needed to display known data? In such instances, the ceil function is often utilized.

import math as m
results = 102
items_per_page = 10 
pages = m.ceil(results / items_per_page)
print(pages)

Learn to write clear, concise math expressions.

Combinatorics in Algorithm Design

Combinatorics theory counts, selects, and arranges numbers or objects. First, consider these programming-related questions. Four-digit PIN security? what options exist? What if the PIN has a prefix? How to locate all decimal number pairs?

Combinatorics questions. Software engineering jobs often require counting items. Combinatorics counts elements without counting them one by one or through other verbose approaches, therefore it enables us to offer minimum and efficient solutions to real-world situations. Combinatorics helps us make reliable decision tests without missing edge cases. Write a program to see if three inputs form a triangle. This is a question I commonly ask in software engineering interviews.

Graph theory is a subfield of combinatorics. Graph theory is used in computerized road maps and social media apps.

Logarithms and Geometry Understanding

Geometry studies shapes, angles, and sizes. Cartesian geometry involves representing geometric objects in multidimensional planes. Geometry is useful for programming. Cartesian geometry is useful for vector graphics, game development, and low-level computer graphics. We can simply work with 2D and 3D arrays as plane axes.

GetWindowRect is a Windows GUI SDK geometric object.

High-level GUI SDKs and libraries use geometric notions like coordinates, dimensions, and forms, therefore knowing geometry speeds up work with computer graphics APIs.

How does exponentiation's inverse function work? Logarithm is exponentiation's inverse function. Logarithm helps programmers find efficient algorithms and solve calculations. Writing efficient code involves finding algorithms with logarithmic temporal complexity. Programmers prefer binary search (O(log n)) over linear search (O(n)). Git source specifies O(log n):

Logarithms aid with programming math. Metas Watchman uses a logarithmic utility function to find the next power of two.

Employing Mathematical Data Structures

Programmers must know data structures to develop clean, efficient code. Stack, queue, and hashmap are computer science basics. Sets and graphs are discrete arithmetic data structures. Most computer languages include a set structure to hold distinct data entries. In most computer languages, graphs can be represented using neighboring lists or objects.

Using sets as deduped lists is powerful because set implementations allow iterators. Instead of a list (or array), store WebSocket connections in a set.

Most interviewers ask graph theory questions, yet current software engineers don't practice algorithms. Graph theory challenges become obligatory in IT firm interviews.

Recognizing Applications of Recursion

A function in programming isolates input(s) and output(s) (s). Programming functions may have originated from mathematical function theories. Programming and math functions are different but similar. Both function types accept input and return value.

Recursion involves calling the same function inside another function. In its implementation, you'll call the Fibonacci sequence. Recursion solves divide-and-conquer software engineering difficulties and avoids code repetition. I recently built the following recursive Dart code to render a Flutter multi-depth expanding list UI:

Recursion is not the natural linear way to solve problems, hence thinking recursively is difficult. Everything becomes clear when a mathematical function definition includes a base case and recursive call.

Conclusion

Every codebase uses arithmetic operators, relational operators, and expressions. To build mathematical expressions, we typically employ log, ceil, floor, min, max, etc. Combinatorics, geometry, data structures, and recursion help implement algorithms. Unless you operate in a pure mathematical domain, you may not use calculus, limits, and other complex math in daily programming (i.e., a game engine). These principles are fundamental for daily programming activities.

Master the above math fundamentals to build clean, efficient code.

This is arguably the best three-minute demonstration I've ever seen of anything. Derek Sivers turns a shaky video of a lone dancing guy at a music festival into a leadership lesson.

A leader must have the courage to stand alone and appear silly. But what he's doing is so straightforward that it's almost instructive. This is critical. You must be simple to follow!

Now comes the first follower, who plays an important role: he publicly demonstrates how to follow. The leader embraces him as an equal, so it's no longer about the leader — it's about them, plural. He's inviting his friends to join him. It takes courage to be the first follower! You stand out and dare to be mocked. Being a first follower is a style of leadership that is underappreciated. The first follower elevates a lone nut to the position of leader. If the first follower is the spark that starts the fire, the leader is the flint.

This link was sent to me by @ottmark, who noted its resemblance to Kurt Vonnegut's three categories of specialists required for revolution.

The rarest of these specialists, he claims, is an actual genius – a person capable generating seemingly wonderful ideas that are not widely known. "A genius working alone is generally dismissed as a crazy," he claims.

The second type of specialist is much easier to find: a highly intellectual person in good standing in his or her community who understands and admires the genius's new ideas and can attest that the genius is not insane. "A person like him working alone can only crave loudly for changes, but fail to say what their shapes should be," Slazinger argues.

Jeff Veen reduced the three personalities to "the inventor, the investor, and the evangelist" on Twitter.

I relocated my notes database from Roam Research to Obsidian earlier this year expecting to stay there for a long. Obsidian is a terrific tool, and I explained my move in that post.

Moving everything to Tana faster than intended. Tana? Why?

Tana is just another note-taking app, but it does it differently. Three note-taking apps existed before Tana:

1. simple note-taking programs like Apple Notes and Google Keep.

2. Roam Research and Obsidian are two graph-style applications that assisted connect your notes.

3. You can create effective tables and charts with data-focused tools like Notion and Airtable.

Tana is the first great software I've encountered that combines graph and data notes. Google Keep will certainly remain my rapid notes app of preference. This Shu Omi video gives a good overview:

Tana handles everything I did in Obsidian with books, people, and blog entries, plus more. I can find book quotes, log my workouts, and connect my thoughts more easily. It should make writing blog entries notes easier, so we'll see.

Tana is now invite-only, but if you're interested, visit their site and sign up. As Shu noted in the video above, the product hasn't been published yet but seems quite polished.

Whether I stay with Tana or not, I'm excited to see where these apps are going and how they can benefit us all.