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.

It's free now.

Most content writers—including me—write about side hustles because they do well.

I wrote several articles on a profitable programming side hustle.

Later, I learnt about AI content-generating platforms like Jasper.ai and Copy.ai, which I thought were terrible because they required subscriptions and had bad content. Even I dislike automatic online posting.

Since ChatGPT is becoming more popular, I tried it. It's free now.

Note: I wasn’t compensated to write this piece by this tool. In other words, I don’t receive any payment from their founders. There is no affiliate link, and right now it is free to use. Also, ChatGPT can do a lot more than what I ever did.

Begin.

OpenAI account registration requires visiting the website (if you don’t have one). Just write anything into the chatbot and get a response.

First, I wrote about the top 10 2023 side businesses.

This came in seconds.

2023 is shaping up to be a year of growth and opportunity for entrepreneurs and side hustlers. With the rise of remote work and the growing gig economy, there are many income streams to consider launching in the coming year. Here are the top 10 income streams to launch in 2023:

1. Virtual Assistant — The demand for virtual assistants is on the rise as more businesses move online. As a virtual assistant, you can offer administrative, technical, or creative services to clients remotely.

2. Online Tutoring — If you have expertise in a particular subject, consider becoming an online tutor. There are many platforms that connect tutors with students looking for help with their studies.

3. Freelance Writing — If you have a knack for writing, consider becoming a freelance writer. You can offer your services to businesses, bloggers, and individuals looking for content for their websites or social media platforms.

4. Graphic Design — If you have a talent for design, consider starting a graphic design side hustle. You can create logos, banners, and other visual content for businesses and individuals.

5. Social Media Management — Many businesses are looking for help with managing their social media accounts. As a social media manager, you can help businesses create and execute social media strategies to reach their target audience.

6. Dropshipping — Dropshipping is a business model where you sell products without actually holding any inventory. You can partner with suppliers and ship the products directly to the customer on behalf of the business.

7. Pet Sitting — If you love animals, consider starting a pet-sitting side hustle. You can offer your services to pet owners who need someone to take care of their pets while they are away.

8. Home Cleaning — With busy schedules, many people are looking for help with cleaning their homes. As a home cleaning service provider, you can offer your services to help keep homes tidy and organized.

9. Event Planning — If you have a talent for organization and planning, consider starting an event planning side hustle. You can offer your services to help plan and execute events for businesses and individuals.

10. Online Teaching — With the rise of online education, there is a growing demand for online teachers. If you have expertise in a particular subject, consider becoming an online teacher and offer your services to students looking for personalized instruction.

In conclusion, 2023 is shaping up to be a great year for launching new income streams. Whether you are looking to start a virtual assistant business, become an online tutor, or offer home cleaning services, there are many opportunities to turn your skills and expertise into a profitable side hustle.

Better than most online side hustle posts, right?

Write about the top 10 programming side hustles to start in 2023.

I got this.

If you are a programmer looking to start a side hustle, 2023 is the perfect time to launch your own business. With the growing demand for software and app development, there are many opportunities for programmers to turn their skills into a profitable side hustle. Here are the top 10 programming side hustles to start in 2023:

1. App Development — With the rise of smartphones and tablets, there is a growing demand for app development. You can offer your services to businesses and individuals looking to create custom apps for their needs.

2. Website Development — Many businesses and individuals are looking for help with creating and maintaining their websites. As a website developer, you can offer your services to help design, build, and manage websites for your clients.

3. Software Development — If you have expertise in a particular programming language, consider starting a software development side hustle. You can offer your services to businesses and individuals looking to create custom software solutions for their needs.

4. Game Development — The gaming industry is thriving, and there is a growing demand for game development. If you have experience in game development, you can offer your services to businesses and individuals looking to create custom games.

5. Data Analysis — With the rise of big data, there is a growing demand for data analysts. As a data analyst, you can offer your services to businesses and individuals looking to make sense of their data and gain insights from it.

6. Machine Learning — Machine learning is a rapidly growing field, and there is a growing demand for machine learning experts. If you have experience in machine learning, you can offer your services to businesses and individuals looking to develop custom machine learning solutions.

7. Cloud Computing — With the rise of cloud computing, there is a growing demand for cloud experts. If you have experience in cloud computing, you can offer your services to businesses and individuals looking to migrate their applications and data to the cloud.

8. Blockchain Development — Blockchain technology is gaining popularity, and there is a growing demand for blockchain developers. If you have experience in blockchain development, you can offer your services to businesses and individuals looking to develop custom blockchain solutions.

9. Artificial Intelligence — Artificial intelligence is a rapidly growing field, and there is a growing demand for AI experts. If you have experience in artificial intelligence, you can offer your services to businesses and individuals looking to develop custom AI solutions.

10. Virtual Reality — Virtual reality is an exciting and emerging technology, and there is a growing demand for VR developers. If you have experience in VR development, you can offer your services to businesses and individuals looking to create custom VR experiences.

In conclusion, 2023 is a great time to start a programming side hustle. Whether you are interested in app development, website development, or machine learning, there are many opportunities for programmers to turn their skills into a profitable business.

These two blogs show that AI can simplify blog authoring.

I asked some tough programming questions, and most were suitable.

The content may occasionally not be what we want, but it will almost always be very helpful to you.

Enjoy.

Las Vegas hosted CES 2023. This third and last look at CES 2023 previews upcoming consumer electronics trends that will be crucial for market share.

Definitely start with ICT. Qualcomm CEO Cristiano Amon spoke to CNBC from Las Vegas on China's crackdown and the company's automated driving systems for electric vehicles (EV). The business showed a concept car and its latest Snapdragon processor designs, which offer expanded digital interactions through SalesForce-partnered CRM platforms.

Qualcomm CEO Meets SK Hynix Vice Chairman at CES 2023 On Jan. 6, SK hynix Inc.'s vice chairman and co-CEO Park Jung-ho discussed strengthening www.businesskorea.co.kr.

Electrification is reviving Michigan's automobile industry. Michigan Local News reports that $14 billion in EV and battery manufacturing investments will benefit the state. The report also revealed that the Strategic Outreach and Attraction Reserve (SOAR) fund had generated roughly $1 billion for the state's automotive sector.

Michigan to "dominate" EV battery manufacturing after $2B investment. Michigan spent $2 billion to safeguard www.mlive.com.

Ars Technica is great for technology, society, and the future. After CES 2023, Jonathan M. Gitlin published How many electric car chargers are enough? Read about EV charging network issues and infrastructure spending. Politics aside, rapid technological advances enable EV charging network expansion in American cities and abroad.

New research says US needs 8x more EV chargers by 2030. Electric vehicle skepticism—which is widespread—is fundamentally about infrastructure. arstechnica.com

Finally, the UNEP's The Future of Electric Vehicles and Material Resources: A Foresight Brief. Understanding how lithium-ion batteries will affect EV sales is crucial. Climate change affects EVs in various ways, but electrification and mining trends stand out because more EVs demand more energy-intensive metals and rare earths. Areas & Producers has been publishing my electrification and mining trends articles. Follow me if you wish to write for the publication.

Producers This magazine analyzes medium.com-related corporate, legal, and international news to examine a paradigm shift.

The Weekend Brief (TWB) will routinely cover tech, industrials, and global commodities in global markets, including stock markets. Read more about the future of key areas and critical producers of the global economy in Areas & Producers.

TotalEnergies, Stellantis Form Automotive Cells Company (ACC) A joint-venture to design and build electric vehicles (EVs) was formed in 2020.

Product game mindsets? How do these vary from Project mindset?

1950s spawned the Iron Triangle. Project people everywhere know and live by it. In stakeholder meetings, it is used to stretch the timeframe, request additional money, or reduce scope.

Quality was added to this triangle as things matured.

Quality was intended to be transformative, but none of these principles addressed why we conduct projects.

Value and benefits are key.

Product value is quantified by ROI, revenue, profit, savings, or other metrics. For me, every project or product delivery is about value.

Most project managers, especially those schooled 5-10 years or more ago (thousands working in huge corporations worldwide), understand the world in terms of the iron triangle. What does that imply? They worry about:

a) enough time to get the thing done.

b) have enough resources (budget) to get the thing done.

c) have enough scope to fit within (a) and (b) >> note, they never have too little scope, not that I have ever seen! although, theoretically, this could happen.

Boom—iron triangle.

To make the triangle function, project managers will utilize formal governance (Steering) to move those things. Increase money, scope, or both if time is short. Lacking funds? Increase time, scope, or both.

In current product development, shifting each item considerably may not yield value/benefit.

Even terrible. This approach will fail because it deprioritizes Value/Benefit by focusing the major stakeholders (Steering participants) and delivery team(s) on Time, Scope, and Budget restrictions.

Pre-agile, this problem was terrible. IT projects failed wildly. History is here.

Value, or benefit, is central to the product method. Product managers spend most of their time planning value-delivery paths.

Product people consider risk, schedules, scope, and budget, but value comes first. Let me illustrate.

Imagine managing internal products in an enterprise. Your core customer team needs a rapid text record of a chat to fix a problem. The consumer wants a feature/features added to a product you're producing because they think it's the greatest spot.

Project-minded, I may say;

Ok, I have budget as this is an existing project, due to run for a year. This is a new requirement to add to the features we’re already building. I think I can keep the deadline, and include this scope, as it sounds related to the feature set we’re building to give the desired result”.

This attitude repeats Scope, Time, and Budget.

Since it meets those standards, a project manager will likely approve it. If they have a backlog, they may add it and start specking it out assuming it will be built.

Instead, think like a product;

What problem does this feature idea solve? Is that problem relevant to the product I am building? Can that problem be solved quicker/better via another route ? Is it the most valuable problem to solve now? Is the problem space aligned to our current or future strategy? or do I need to alter/update the strategy?

A product mindset allows you to focus on timing, resource/cost, feasibility, feature detail, and so on after answering the aforementioned questions.

The above oversimplifies because

Leadership in discovery

Project managers are facilitators of ideas. This is as far as they normally go in the ‘idea’ space.

Business Requirements collection in classic project delivery requires extensive upfront documentation.

Agile project delivery analyzes requirements iteratively.

However, the project manager is a facilitator/planner first and foremost, therefore topic knowledge is not expected.

I mean business domain, not technical domain (to confuse matters, it is true that in some instances, it can be both technical and business domains that are important for a single individual to master).

Product managers are domain experts. They will become one if they are training/new.

They lead discovery.

Product Manager-led discovery is much more than requirements gathering.

Requirements gathering involves a Business Analyst interviewing people and documenting their requests.

The project manager calculates what fits and what doesn't using their Iron Triangle (presumably in their head) and reports back to Steering.

If this requirements-gathering exercise failed to identify requirements, what would a project manager do? or bewildered by project requirements and scope?

They would tell Steering they need a Business SME or Business Lead assigning or more of their time.

Product discovery requires the Product Manager's subject knowledge and a new mindset.

How should a Product Manager handle confusing requirements?

Product Managers handle these challenges with their talents and tools. They use their own knowledge to fill in ambiguity, but they have the discipline to validate those assumptions.

To define the problem, they may perform qualitative or quantitative primary research.

They might discuss with UX and Engineering on a whiteboard and test assumptions or hypotheses.

Do Product Managers escalate confusing requirements to Steering/Senior leaders? They would fix that themselves.

Product managers raise unclear strategy and outcomes to senior stakeholders. Open talks, soft skills, and data help them do this. They rarely raise requirements since they have their own means of handling them without top stakeholder participation.

Discovery is greenfield, exploratory, research-based, and needs higher-order stakeholder management, user research, and UX expertise.

Product Managers also aid discovery. They lead discovery. They will not leave customer/user engagement to a Business Analyst. Administratively, a business analyst could aid. In fact, many product organizations discourage business analysts (rely on PM, UX, and engineer involvement with end-users instead).

The Product Manager must drive user interaction, research, ideation, and problem analysis, therefore a Product professional must be skilled and confident.

Creating vs. receiving and having an entrepreneurial attitude

Product novices and project managers focus on details rather than the big picture. Project managers prefer spreadsheets to strategy whiteboards and vision statements.

These folks ask their manager or senior stakeholders, "What should we do?"

They then elaborate (in Jira, in XLS, in Confluence or whatever).

They want that plan populated fast because it reduces uncertainty about what's going on and who's supposed to do what.

Skilled Product Managers don't only ask folks Should we?

They're suggesting this, or worse, Senior stakeholders, here are some options. After asking and researching, they determine what value this product adds, what problems it solves, and what behavior it changes.

Therefore, to move into Product, you need to broaden your view and have courage in your ability to discover ideas, find insightful pieces of information, and collate them to form a valuable plan of action. You are constantly defining RoI and building Business Cases, so much so that you no longer create documents called Business Cases, it is simply ingrained in your work through metrics, intelligence, and insights.

Product Management is not a free lunch.

Plateless.

Plates and food must be prepared.

In conclusion, Product Managers must make at least three mentality shifts:

1. You put value first in all things. Time, money, and scope are not as important as knowing what is valuable.

2. You have faith in the field and have the ability to direct the search. YYou facilitate, but you don’t just facilitate. You wouldn't want to limit your domain expertise in that manner.

3. You develop concepts, strategies, and vision. You are not a waiter or an inbox where other people can post suggestions; you don't merely ask folks for opinion and record it. However, you excel at giving things that aren't clearly spoken or written down physical form.

Discover How We Used Facebook Ads to Grow a New Mobile App from $0 to $15K MRR in Just 6 Months and Our Strategy to Hit $100K a Month.

Our client introduced a mobile app for Poshmark resellers in December and wanted as many to experience it and subscribe to the monthly plan.

An Error We Committed

We initiated a Facebook ad campaign with a "awareness" goal, not "installs." This sent them to a landing page that linked to the iPhone App Store and Android Play Store. Smart, right?

We got some installs, but we couldn't tell how many came from the ad versus organic/other channels because the objective we chose only reported landing page clicks, not app installs.

We didn't know which interest groups/audiences had the best cost per install (CPI) to optimize and scale our budget.

After spending $700 without adequate data (installs and trials report), we stopped the campaign and worked with our client's app developer to set up app events tracking.

This allowed us to create an installs campaign and track installs, trials, and purchases (in some cases).

Finding a Successful Audience

Once we knew what ad sets brought in what installs at what cost, we began optimizing and testing other interest groups and audiences, growing the profitable low CPI ones and eliminating the high CPI ones.

We did all our audience testing using an ABO campaign (Ad Set Budget Optimization), spending $10 to $30 on each ad set for three days and optimizing afterward. All ad sets under $30 were moved to a CBO campaign (Campaign Budget Optimization).

We let Facebook's AI decide how much to spend on each ad set, usually the one most likely to convert at the lowest cost.

If the CBO campaign maintains a nice CPI, we keep increasing the budget by $50 every few days or duplicating it sometimes in order to double the budget. This is how we've scaled to $400/day profitably.

Finding Successful Creatives

Per campaign, we tested 2-6 images/videos. Same ad copy and CTA. There was no clear winner because some images did better with some interest groups.

The image above with mail packages, for example, got us a cheap CPI of $9.71 from our Goodwill Stores interest group but, a high $48 CPI from our lookalike audience. Once we had statistically significant data, we turned off the high-cost ad.

New marketers who are just discovering A/B testing may assume it's black and white — winner and loser. However, Facebook ads' machine learning and reporting has gotten so sophisticated that it's hard to call a creative a flat-out loser, but rather a 'bad fit' for some audiences, and perfect for others.

You can see how each creative performs across age groups and optimize.

How Many Installs Did It Take Us to Earn $15K Per Month?

Six months after paying $25K, we got 1,940 app installs, 681 free trials, and 522 $30 monthly subscriptions. 522 * $30 gives us $15,660 in monthly recurring revenue (MRR).

Next, what? $100K per month

The conversation above is with the app's owner. We got on a 30-minute call where I shared how I plan to get the app to be making $100K a month like I’ve done for other businesses.

Reverse Engineering $100K

Formula:

For $100K/month, we need 3,334 people to pay $30/month. 522 people pay that. We need 2,812 more paid users.

522 paid users from 1,940 installs is a 27% conversion rate. To hit $100K/month, we need 10,415 more installs. Assuming...

With a $400 daily ad spend, we average 40 installs per day. This means that if everything stays the same, it would take us 260 days (around 9 months) to get to $100K a month (MRR).

Conclusion

You must market your goods to reach your income objective (without waiting forever). Paid ads is the way to go if you hate knocking on doors or irritating friends and family (who aren’t scalable anyways).

You must also test and optimize different angles, audiences, interest groups, and creatives.