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.

The trick Notion could use is simply Facebook-ing the hell out of them.

*Time travel to fifteen years ago.* Future-Me: “Hey! What are you up to?” Old-Me: “I am proofreading an article. It’s taking a few hours, but I will be done soon.” Future-Me: “You know, in the future, you will be using a google chrome plugin called Grammarly that will help you easily proofread articles in half that time.” Old-Me: “What is… Google Chrome?” Future-Me: “Gosh…”

I love Grammarly. It’s one of those products that I personally feel the effects of. I mean, Space X is a great company. But I am not a rocket writing this article in space (or am I?)…

No, I’m not. So I don’t personally feel a connection to Space X. So, if a company collapse occurs in the morning, I might write about it. But I will have zero emotions regarding it.

Yet, if Grammarly fails tomorrow, I will feel 1% emotionally distressed. So looking at the title of this article, you’d realize that I am betting against them. This is how much I believe in the critical business model that’s taking over the world, the one of Notion.

Notion How frequently do you go through your notes?

Grammarly is everywhere, which helps its success. Grammarly is available when you update LinkedIn on Chrome. Grammarly prevents errors in Google Docs.

My internal concentration isn't apparent in the previous paragraph. Not Grammarly. I should have used Chrome to make a Google doc and LinkedIn update. Without this base, Grammarly will be useless.

So, welcome to this business essay.

• Grammarly provides a solution.

• Another issue is resolved by Jasper.

• Your entire existence is supposed to be contained within Notion.

New Google Chrome is offline. It's an all-purpose notepad (in the near future.)

• How should I start my blog? Enter it in Note.

• an update on LinkedIn? If you mention it, it might be automatically uploaded there (with little help from another app.)

• An advanced thesis? You can brainstorm it with your coworkers.

This ad sounds great! I won't cry if Notion dies tomorrow.

I'll reread the following passages to illustrate why I think Notion could kill Grammarly and Jasper.

Notion is a fantastic app that incubates your work.

Smartly, they began with note-taking.

Hopefully, your work will be on Notion. Grammarly and Jasper are still must-haves.

Grammarly will proofread your typing while Jasper helps with copywriting and AI picture development.

They're the best, therefore you'll need them. Correct? Nah.

Notion might bombard them with Facebook posts.

Notion: “Hi Grammarly, do you want to sell your product to us?” Grammarly: “Dude, we are more valuable than you are. We’ve even raised $400m, while you raised $342m. Our last valuation round put us at $13 billion, while yours put you at $10 billion. Go to hell.” Notion: “Okay, we’ll speak again in five years.”

Notion: “Jasper, wanna sell?” Jasper: “Nah, we’re deep into AI and the field. You can’t compete with our people.” Notion: “How about you either sell or you turn into a Snapchat case?” Jasper: “…”

Notion is your home. Grammarly is your neighbor. Your track is Jasper.

What if you grew enough vegetables in your backyard to avoid the supermarket? No more visits.

What if your home had a beautiful treadmill? You won't rush outside as much (I disagree with my own metaphor). (You get it.)

It's Facebooking. Instagram Stories reduced your Snapchat usage. Notion will reduce your need to use Grammarly.

The Final Piece of the AI Puzzle

Let's talk about Notion first, since you've probably read about it everywhere.

• They raised $343 million, as I previously reported, and bought four businesses

• According to Forbes, Notion will have more than 20 million users by 2022. The number of users is up from 4 million in 2020.

If raising $1.8 billion was impressive, FTX wouldn't have fallen.

This article compares the basic product to two others. Notion is a day-long app.

Notion has released Notion AI to support writers. It's early, so it's not as good as Jasper. Then-Jasper isn't now-Jasper. In five years, Notion AI will be different.

With hard work, they may construct a Jasper-like writing assistant. They have resources and users.

At this point, it's all speculation. Jasper's copywriting is top-notch. Grammarly's proofreading is top-notch. Businesses are constrained by user activities.

If Notion's future business movements are strategic, they might become a blue ocean shark (or get acquired by an unbelievable amount.)

I love business mental teasers, so tell me:

• How do you feel? Are you a frequent Notion user?

• Do you dispute my position? I enjoy hearing opposing viewpoints.

Ironically, I proofread this with Grammarly.

As part of Meta's endeavor to establish an interactive live-streaming platform, the company is testing with influencers.

The NPE (new product experimentation team) has been testing Super since late 2020.

Bloomberg defined Super as a Cameo-inspired FaceTime-like gadget in 2020. The tool has evolved into a Twitch-like live streaming application.

Less than 100 creators have utilized Super: Creators can request access on Meta's website. Super isn't an Instagram, Facebook, or Meta extension.

“It’s a standalone project,” the spokesperson said about Super. “Right now, it’s web only. They have been testing it very quietly for about two years. The end goal [of NPE projects] is ultimately creating the next standalone project that could be part of the Meta family of products.” The spokesperson said the outreach this week was part of a drive to get more creators to test Super.

A 2021 pitch deck from Super reveals the inner workings of Meta.

The deck gathered feedback on possible sponsorship models, with mockups of brand deals & features. Meta reportedly paid creators $200 to $3,000 to test Super for 30 minutes.

Meta's pitch deck for Super live streaming was leaked.

What were the slides in the pitch deck for Metas Super?

Embed not supported: see full deck & article here →

View examples of Meta's pitch deck for Super:

Product Slides, first

The pitch deck begins with Super's mission:

Super is a Facebook-incubated platform which helps content creators connect with their fans digitally, and for super fans to meet and support their favorite creators. In the spirit of Late Night talk shows, we feature creators (“Superstars”), who are guests at a live, hosted conversation moderated by a Host.

This slide (and most of the deck) is text-heavy, with few icons, bullets, and illustrations to break up the content. Super's online app status (which requires no download or installation) might be used as a callout (rather than paragraph-form).

Meta's Super platform focuses on brand sponsorships and native placements, as shown in the slide above.

One of our theses is the idea that creators should benefit monetarily from their Super experiences, and we believe that offering a menu of different monetization strategies will enable the right experience for each creator. Our current focus is exploring sponsorship opportunities for creators, to better understand what types of sponsor placements will facilitate the best experience for all Super customers (viewers, creators, and advertisers).

Colorful mockups help bring Metas vision for Super to life.

2. Slide Features

Super's pitch deck focuses on the platform's features. The deck covers pre-show, pre-roll, and post-event for a Sponsored Experience.

• Pre-show: active 30 minutes before the show's start

• Pre-roll: Play a 15-minute commercial for the sponsor before the event (auto-plays once)

• Meet and Greet: This event can have a branding, such as Meet & Greet presented by [Snickers]

• Super Selfies: Makers and followers get a digital souvenir to post on social media.

• Post-Event: Possibility to draw viewers' attention to sponsored content/links during the after-show

Almost every screen displays the Sponsor logo, link, and/or branded background. Viewers can watch sponsor video while waiting for the event to start.

Slide 3: Business Model

Meta's presentation for Super is incomplete without numbers. Super's first slide outlines the creator, sponsor, and Super's obligations. Super does not charge creators any fees or commissions on sponsorship earnings.

How to make a great pitch deck

We hope you can use the Super pitch deck to improve your business. Bestpitchdeck.com/super-meta is a bookmarkable link.

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Managers spend much time in 1:1s. Most team members meet with supervisors regularly. 1:1s can help create relationships and tackle tough topics. Few appreciate the 1:1 format's potential. Most of the time, that potential is spent on small talk, surface-level updates, and ranting (Ugh, the marketing team isn’t stepping up the way I want them to).

What if you used that time to have deeper conversations and important insights? What if change was easy?

This post introduces a new 1:1 format to help you dive deeper, faster, and develop genuine relationships without losing impact.

A 1:1 is a chat, you would assume. Why use structure to talk to a coworker? Go! I know how to talk to people. I can write. I've always written. Also, This article was edited by Zoe.

Before you discard something, ask yourself if there's a good reason not to try anything new. Is the 1:1 only a talk, or do you want extra benefits? Try the steps below to discover more.

I. Reflection (5 minutes)

Context-free, broad comments waste time and are useless. Instead, give team members 5 minutes to write these 3 prompts.

1. What's effective?

2. What is decent but could be improved?

3. What is broken or missing?

Why these? They encourage people to be honest about all their experiences. Answering these questions helps people realize something isn't working. These prompts let people consider what's working.

Why take notes? Because you get more in less time. Will you feel awkward sitting quietly while your coworker writes? Probably. Persevere. Multi-task. Take a break from your afternoon meeting marathon. Any awkwardness will pay off.

What happens? After a few minutes of light conversation, create a template like the one given here and have team members fill in their replies. You can pre-share the template (with the caveat that this isn’t meant to take much prep time). Do this with your coworker: Answer the prompts. Everyone can benefit from pondering and obtaining guidance.

This step's output.

Part II: Talk (10-20 minutes)

Most individuals can explain what they see but not what's behind an answer. You don't like a meeting. Why not? Marketing partnership is difficult. What makes working with them difficult? I don't recommend slandering coworkers. Consider how your meetings, decisions, and priorities make work harder. The excellent stuff too. You want to know what's humming so you can reproduce the magic.

First, recognize some facts.

• Real power dynamics exist. To encourage individuals to be honest, you must provide a safe environment and extend clear invites. Even then, it may take a few 1:1s for someone to feel secure enough to go there in person. It is part of your responsibility to admit that it is normal.

• Curiosity and self-disclosure are crucial. Most leaders have received training to present themselves as the authorities. However, you will both benefit more from the dialogue if you can be open and honest about your personal experience, ask questions out of real curiosity, and acknowledge the pertinent sacrifices you're making as a leader.

• Honesty without bias is difficult and important. Due to concern for the feelings of others, people frequently hold back. Or if they do point anything out, they do so in a critical manner. The key is to be open and unapologetic about what you observe while not presuming that your viewpoint is correct and that of the other person is incorrect.

Let's go into some prompts (based on genuine conversations):

• “What do you notice across your answers?”

• “What about the way you/we/they do X, Y, or Z is working well?”

• “ Will you say more about item X in ‘What’s not working?’”

• “I’m surprised there isn’t anything about Z. Why is that?”

• “All of us tend to play some role in maintaining certain patterns. How might you/we be playing a role in this pattern persisting?”

• “How might the way we meet, make decisions, or collaborate play a role in what’s currently happening?”

Consider the preceding example. What about the Monday meeting isn't working? Why? or What about the way we work with marketing makes collaboration harder? Remember to share your honest observations!

Third section: observe patterns (10-15 minutes)

Leaders desire to empower their people but don't know how. We also have many preconceptions about what empowerment means to us and how it works. The next phase in this 1:1 format will assist you and your team member comprehend team power and empowerment. This understanding can help you support and shift your team member's behavior, especially where you disagree.

How to? After discussing the stated responses, ask each team member what they can control, influence, and not control. Mark their replies. You can do the same, adding colors where you disagree.

This step's output.

Next, consider the color constellation. Discuss these questions:

• Is one color much more prevalent than the other? Why, if so?

• Are the colors for the "what's working," "what's fine," and "what's not working" categories clearly distinct? Why, if so?

• Do you have any disagreements? If yes, specifically where does your viewpoint differ? What activities do you object to? (Remember, there is no right or wrong in this. Give explicit details and ask questions with curiosity.)

Example: Based on the colors, you can ask, Is the marketing meeting's quality beyond your control? Were our marketing partners consulted? Are there any parts of team decisions we can control? We can't control people, but have we explored another decision-making method? How can we collaborate and generate governance-related information to reduce work, even if the requirement for prep can't be eliminated?

Consider the top one or two topics for this conversation. No 1:1 can cover everything, and that's OK. Focus on the present.

Part IV: Determine the next step (5 minutes)

Last, examine what this conversation means for you and your team member. It's easy to think we know the next moves when we don't.

Like what? You and your teammate answer these questions.

1. What does this signify moving ahead for me? What can I do to change this? Make requests, for instance, and see how people respond before thinking they won't be responsive.

2. What demands do I have on other people or my partners? What should I do first? E.g. Make a suggestion to marketing that we hold a monthly retrospective so we can address problems and exchange input more frequently. Include it on the meeting's agenda for next Monday.

Close the 1:1 by sharing what you noticed about the chat. Observations? Learn anything?

Yourself, you, and the 1:1

As a leader, you either reinforce or disrupt habits. Try this template if you desire greater ownership, empowerment, or creativity. Consider how you affect surrounding dynamics. How can you expect others to try something new in high-stakes scenarios, like meetings with cross-functional partners or senior stakeholders, if you won't? How can you expect deep thought and relationship if you don't encourage it in 1:1s? What pattern could this new format disrupt or reinforce?

Fight reluctance. First attempts won't be ideal, and that's OK. You'll only learn by trying.

Orion's red supergiant Betelgeuse erupted. This is astronomers' most magnificent occurrence.

Betelgeuse, a supergiant star in Orion, garnered attention in 2019 for its peculiar appearance. It continued to dim in 2020.

The star was previously thought to explode as a supernova. Studying the event has revealed what happened to Betelgeuse since it happened.

Astronomers saw that the star released a large amount of material, causing it to lose a section of its surface.

They have never seen anything like this and are unsure what caused the star to release so much material.

According to Harvard-Smithsonian Center for Astrophysics astrophysicist Andrea Dupre, astronomers' data reveals an unexplained mystery.

They say it's a new technique to examine star evolution. The James Webb telescope revealed the star's surface features.

Corona flares are stellar mass ejections. These eruptions change the Sun's outer atmosphere.

This could affect power grids and satellite communications if it hits Earth.

Betelgeuse's flare ejected four times more material than the Sun's corona flare.

Astronomers have monitored star rhythms for 50 years. They've seen its dimming and brightening cycle start, stop, and repeat.

Monitoring Betelgeuse's pulse revealed the eruption's power.

Dupre believes the star's convection cells are still amplifying the blast's effects, comparing it to an imbalanced washing machine tub.

The star's outer layer has returned to normal, Hubble data shows. The photosphere slowly rebuilds its springy surface.

Dupre noted the star's unusual behavior. For instance, it’s causing its interior to bounce.

This suggests that the mass ejections that caused the star's surface to lose mass were two separate processes.

Researchers hope to better understand star mass ejection with the James Webb Space Telescope.