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.

AI images are like funhouse mirrors.

Google's AI Blog introduced the puppy-slug in the summer of 2015.

Puppy-slug isn't a single image or character. "Puppy-slug" refers to Google's DeepDream's unsettling psychedelia. This tool uses convolutional neural networks to train models to recognize dataset entities. If researchers feed the model millions of dog pictures, the network will learn to recognize a dog.

DeepDream used neural networks to analyze and classify image data as well as generate its own images. DeepDream's early examples were created by training a convolutional network on dog images and asking it to add "dog-ness" to other images. The models analyzed images to find dog-like pixels and modified surrounding pixels to highlight them.

Puppy-slugs and other DeepDream images are ugly. Even when they don't trigger my trypophobia, they give me vertigo when my mind tries to reconcile familiar features and forms in unnatural, physically impossible arrangements. I feel like I've been poisoned by a forbidden mushroom or a noxious toad. I'm a Lovecraft character going mad from extradimensional exposure. They're gross!

Is this really how AIs see the world? This is possibly an even more unsettling topic that DeepDream raises than the blatant abjection of the images.

When these photographs originally circulated online, many friends were startled and scandalized. People imagined a computer's imagination would be literal, accurate, and boring. We didn't expect vivid hallucinations and organic-looking formations.

DeepDream's images didn't really show the machines' imaginations, at least not in the way that scared some people. DeepDream displays data visualizations. DeepDream reveals the "black box" of convolutional network training.

Some of these images look scary because the models don't "know" anything, at least not in the way we do.

These images are the result of advanced algorithms and calculators that compare pixel values. They can spot and reproduce trends from training data, but can't interpret it. If so, they'd know dogs have two eyes and one face per head. If machines can think creatively, they're keeping it quiet.

You could be forgiven for thinking otherwise, given OpenAI's Dall-impressive E's results. From a technological perspective, it's incredible.

Arthur C. Clarke once said, "Any sufficiently advanced technology is indistinguishable from magic." Dall-magic E's requires a lot of math, computer science, processing power, and research. OpenAI did a great job, and we should applaud them.

Dall-E and similar tools match words and phrases to image data to train generative models. Matching text to images requires sorting and defining the images. Untold millions of low-wage data entry workers, content creators optimizing images for SEO, and anyone who has used a Captcha to access a website make these decisions. These people could live and die without receiving credit for their work, even though the project wouldn't exist without them.

This technique produces images that are less like paintings and more like mirrors that reflect our own beliefs and ideals back at us, albeit via a very complex prism. Due to the limitations and biases that these models portray, we must exercise caution when viewing these images.

The issue was succinctly articulated by artist Mimi Onuoha in her piece "On Algorithmic Violence":

As we continue to see the rise of algorithms being used for civic, social, and cultural decision-making, it becomes that much more important that we name the reality that we are seeing. Not because it is exceptional, but because it is ubiquitous. Not because it creates new inequities, but because it has the power to cloak and amplify existing ones. Not because it is on the horizon, but because it is already here.

A completely operating application requires many processes and technical challenges. Implementing coding standards can make apps right, work, and faster.

With years of experience working in software houses. Many client apps are scarcely maintained.

Why are these programs "barely maintainable"? If we're used to coding concepts, we can probably tell if an app is awful or good from its codebase.

This is how I coded much of my app.

Make It Work

Before adopting any concept, make sure the apps are completely functional. Why have a fully maintained codebase if the app can't be used?

The user doesn't care if the app is created on a super server or uses the greatest coding practices. The user just cares if the program helps them.

After the application is working, we may implement coding principles.

You Aren’t Gonna Need It

As a junior software engineer, I kept unneeded code, components, comments, etc., thinking I'd need them later.

In reality, I never use that code for weeks or months.

First, we must remove useless code from our primary codebase. If you insist on keeping it because "you'll need it later," employ version control.

If we remove code from our codebase, we can quickly roll back or copy-paste the previous code without preserving it permanently.

The larger the codebase, the more maintenance required.

Keep It Simple Stupid

Indeed. Keep things simple.

Why complicate something if we can make it simpler?

Our code improvements should lessen the server load and be manageable by others.

If our code didn't pass those benchmarks, it's too convoluted and needs restructuring. Using an open-source code critic or code smell library, we can quickly rewrite the code.

Simpler codebases and processes utilize fewer server resources.

Don't Repeat Yourself

Have you ever needed an action or process before every action, such as ensuring the user is logged in before accessing user pages?

As you can see from the above code, I try to call is user login? in every controller action, and it should be optimized, because if we need to rename the method or change the logic, etc. We can improve this method's efficiency.

We can write a constructor/middleware/before action that calls is_user_login?

The code is more maintainable and readable after refactoring.

Each programming language or framework handles this issue differently, so be adaptable.

Clean Code

Clean code is a broad notion that you've probably heard of before.

When creating a function, method, module, or variable name, the first rule of clean code is to be precise and simple.

The name should express its value or logic as a whole, and follow code rules because every programming language is distinct.

If you want to learn more about this topic, I recommend reading https://www.amazon.com/Clean-Code-Handbook-Software-Craftsmanship/dp/0132350882.

Standing On The Shoulder of Giants

Use industry standards and mature technologies, not your own(s).

There are several resources that explain how to build boilerplate code with tools, how to code with best practices, etc.

I propose following current conventions, best practices, and standardization since we shouldn't innovate on top of them until it gives us a competitive edge.

Boy Scout Rule

What reduces programmers' productivity?

When we have to maintain or build a project with messy code, our productivity decreases.

Having to cope with sloppy code will slow us down (shame of us).

How to cope? Uncle Bob's book says, "Always leave the campground cleaner than you found it."

When developing new features or maintaining current ones, we must improve our codebase. We can fix minor issues too. Renaming variables, deleting whitespace, standardizing indentation, etc.

Make It Fast

After making our code more maintainable, efficient, and understandable, we can speed up our app.

Whether it's database indexing, architecture, caching, etc.

A smart craftsman understands that refactoring takes time and it's preferable to balance all the principles simultaneously. Don't YAGNI phase 1.

Using these ideas in each iteration/milestone, while giving the bottom items less time/care.

You can check one of my articles for further information. https://medium.com/life-at-mekari/why-does-my-website-run-very-slowly-and-how-do-i-optimize-it-for-free-b21f8a2f0162

https://medium.com/life-at-mekari/what-you-need-to-make-your-app-a-high-availability-system-tackling-the-technical-challenges-8896abec363f

Startup entrepreneurs assume what risks when pitching?

Last week I signed four NDAs.

Four!

NDA stands for non-disclosure agreement. A legal document given to someone receiving confidential information. By signing, the person pledges not to share the information for a certain time. If they do, they may be in breach of contract and face legal action.

Companies use NDAs to protect trade secrets and confidential internal information from employees and contractors. Appropriate. If you manage a huge, successful firm, you don't want your employees selling their information to your competitors. To be true, business NDAs don't always prevent corporate espionage, but they usually make employees and contractors think twice before sharing.

I understand employee and contractor NDAs, but I wasn't asked to sign one. I counsel entrepreneurs, thus the NDAs I signed last week were from startups that wanted my feedback on their concepts.

I’m not a startup investor. I give startup guidance online. Despite that, four entrepreneurs thought their company ideas were so important they wanted me to sign a generically written legal form they probably acquired from a shady, spam-filled legal templates website before we could chat.

False. One company tried to get me to sign their NDA a few days after our conversation. I gently rejected, but their tenacity encouraged me. I considered sending retroactive NDAs to everyone I've ever talked to about one of my startups in case they establish a successful company based on something I said.

Two of the other three NDAs were from nearly identical companies. Good thing I didn't sign an NDA for the first one, else they may have sued me for talking to the second one as though I control the firms people pitch me.

I wasn't talking to the fourth NDA company. Instead, I received an unsolicited email from someone who wanted comments on their fundraising pitch deck but required me to sign an NDA before sending it.

That's right, before I could read a random Internet stranger's unsolicited pitch deck, I had to sign his NDA, potentially limiting my ability to discuss what was in it.

You should understand. Advisors, mentors, investors, etc. talk to hundreds of businesses each year. They cannot manage all the companies they deal with, thus they cannot risk legal trouble by talking to someone. Well, if I signed NDAs for all the startups I spoke with, half of the 300+ articles I've written on Medium over the past several years could get me sued into the next century because I've undoubtedly addressed topics in my articles that I discussed with them.

The four NDAs I received last week are part of a recent trend of entrepreneurs sending out NDAs before meetings, despite the practical and legal issues. They act like asking someone to sign away their right to talk about all they see and hear in a day is as straightforward as asking for a glass of water.

Given this inflow of NDAs, I wanted to briefly remind entrepreneurs reading this blog about the merits and cons of requesting investors (or others in the startup ecosystem) to sign your NDA.

Benefits of having investors sign your NDA include:

None. Zero. Nothing.

Disadvantages of requesting investor NDAs:

• You'll come off as an amateur who has no idea what it takes to launch a successful firm.

• Investors won't trust you with their money since you appear to be a complete amateur.

• Printing NDAs will be a waste of paper because no genuine entrepreneur will ever sign one.

I apologize for missing any cons. Please leave your remarks.

Many developers do it, but I don't approve.

Aren't many programmers part-time? Many work full-time but also freelance. If the job agreement allows it, I see no problem.

Tech businesses' policies vary. I have a friend in Google, Germany. According to his contract, he couldn't do an outside job. Google owns any code he writes while employed.

I was shocked. Later, I found that different Google regions have different policies.

A corporation can normally establish any agreement before hiring you. They're negotiable. When there's no agreement, state law may apply. In court, law isn't so simple.

I won't delve into legal details. Instead, let’s talk about the incident.

How he was discovered

In one month, he missed two deadlines. His boss was frustrated because the assignment wasn't difficult to miss twice. When a team can't finish work on time, they all earn bad grades.

He annoyed the whole team. One team member (anonymous) told the project manager he worked on side projects during office hours. He may have missed deadlines because of this.

The project manager was furious. He needed evidence. The manager caught him within a week. The manager told higher-ups immediately.

The company wanted to set an example

Management could terminate him and settle the problem. But the company wanted to set an example for those developers who breached the regulation.

Because dismissal isn't enough. Every organization invests heavily in developer hiring. If developers depart or are fired after a few months, the company suffers.

The developer spent 10 months there. The employer sacked him and demanded ten months' pay. Or they'd sue him.

It was illegal and unethical. The youngster paid the fine and left the company quietly to protect his career.

Right or wrong?

Is the developer's behavior acceptable? Let's discuss developer malpractice.

During office hours, may developers work on other projects? If they're bored during office hours, they might not. Check the employment contract or state law.

If there's no employment clause, check country/state law. Because you can't justify breaking the law. Always. Most employers own their employees' work hours unless it's a contractual position.

If the company agrees, it's fine.

I also oppose companies that force developers to work overtime without pay.

Most states and countries have laws that help companies and workers. Law supports employers in this case. If any of the following are true, the company/employer owns the IP under California law.

• using the business's resources

• any equipment, including a laptop used for business.

• company's mobile device.

• offices of the company.

• business time as well. This is crucial. Because this occurred in the instance of my junior.

Company resources are dangerous. Because your company may own the product's IP.  If you have seen the TV show Silicon Valley, you have seen a similar situation there, right?

Conclusion

Simple rule. I avoid big side projects. I work on my laptop on weekends for side projects. I'm safe. But I also know that my company might not be happy with that.

As an employee, I suppose I can. I can make side money. I won't promote it, but I'll respect their time, resources, and task. I also sometimes work extra time to finish my company’s deadlines.

Skip this if you don't want to discover why your lively, no-brainer pitch isn't making $10k a month.

You don't want to be repulsive as an entrepreneur or anyone else. Making friends, influencing people, and converting strangers into customers will be difficult if your words evoke disgust, distrust, or disrespect. You may be one of many entrepreneurs who do this obliviously and involuntarily.

I've had to master selling my skills to recruiters (to land 6-figure jobs on Wall Street), selling companies to buyers in M&A transactions, and selling my own companies' products to strangers-turned-customers. I probably committed every cardinal sin of sales repulsion before realizing it was me or my poor salesmanship strategy.

If you're launching a new business, frustrated by low conversion rates, or just curious if you're repelling customers, read on to identify (and avoid) the 6 fatal errors that can kill any sales pitch.

1. The first indication

So many people fumble before they even speak because they assume their role is to convince the buyer. In other words, they expect to pressure, arm-twist, and combat objections until they convert the buyer. Actuality, the approach stinks of disgust, and emotionally-aware buyers would feel "gross" immediately.

Instead of trying to persuade a customer to buy, ask questions that will lead them to do so on their own. When a customer discovers your product or service on their own, they need less outside persuasion. Why not position your offer in a way that leads customers to sell themselves on it?

2. A flawless performance

Are you memorizing a sales script, tweaking video testimonials, and expunging historical blemishes before hitting "publish" on your new campaign? If so, you may be hurting your conversion rate.

Perfection may be a step too far and cause prospects to mistrust your sincerity. Become a great conversationalist to boost your sales. Seriously. Being charismatic is hard without being genuine and showing a little vulnerability.

People like vulnerability, even if it dents your perfect facade. Show the customer's stuttering testimonial. Open up about your or your company's past mistakes (and how you've since improved). Make your sales pitch a two-way conversation. Let the customer talk about themselves to build rapport. Real people sell, not canned scripts and movie-trailer testimonials.

If marketing or sales calls feel like a performance, you may be doing something wrong or leaving money on the table.

3. Your greatest phobia

Three minutes into prospect talks, I'd start sweating. I was talking 100 miles per hour, covering as many bases as possible to avoid the ones I feared. I knew my then-offering was inadequate and my firm had fears I hadn't addressed. So I word-vomited facts, features, and everything else to avoid the customer's concerns.

Do my prospects know I'm insecure? Maybe not, but it added an unnecessary and unhelpful layer of paranoia that kept me stressed, rushed, and on edge instead of connecting with the prospect. Skirting around a company, product, or service's flaws or objections is a poor, temporary, lazy (and cowardly) decision.

How can you project confidence and trust if you're afraid? Before you make another sales call, face your shortcomings, weak points, and objections. Your company won't be everyone's cup of tea, but you should have answers to every question or objection. You should be your business's top spokesperson and defender.

4. The unintentional apologies

Have you ever begged for a sale? I'm going to say no, however you may be unknowingly emitting sorry, inferior, insecure energy.

Young founders, first-time entrepreneurs, and those with severe imposter syndrome may elevate their target customer. This is common when trying to get first customers for obvious reasons.

• Since you're truly new at this, you naturally lack experience.

• You don't have the self-confidence boost of thousands or hundreds of closed deals or satisfied client results to remind you that your good or service is worthwhile.

• Getting those initial few clients seems like the most difficult task, as if doing so will decide the fate of your company as a whole (it probably won't, and you shouldn't actually place that much emphasis on any one transaction).

Customers can smell fear, insecurity, and anxiety just like they can smell B.S. If you believe your product or service improves clients' lives, selling it should feel like a benevolent act of service, not a sleazy money-grab. If you're a sincere entrepreneur, prospects will believe your proposition; if you're apprehensive, they'll notice.

Approach every sale as if you're fine with or without it. This has improved my salesmanship, marketing skills, and mental health. When you put pressure on yourself to close a sale or convince a difficult prospect "or else" (your company will fail, your rent will be late, your electricity will be cut), you emit desperation and lower the quality of your pitch. There's no point.

5. The endless promises

We've all read a million times how to answer or disprove prospects' arguments and add extra incentives to speed or secure the close. Some objections shouldn't be refuted. What if I told you not to offer certain incentives, bonuses, and promises? What if I told you to walk away from some prospects, even if it means losing your sales goal?

If you market to enough people, make enough sales calls, or grow enough companies, you'll encounter prospects who can't be satisfied. These prospects have endless questions, concerns, and requests for more, more, more that you'll never satisfy. These people are a distraction, a resource drain, and a test of your ability to cut losses before they erode your sanity and profit margin.

To appease or convert these insatiably needy, greedy Nellies into customers, you may agree with or acquiesce to every request and demand — even if you can't follow through. Once you overpromise and answer every hole they poke, their trust in you may wane quickly.

Telling a prospect what you can't do takes courage and integrity. If you're honest, upfront, and willing to admit when a product or service isn't right for the customer, you'll gain respect and positive customer experiences. Sometimes honesty is the most refreshing pitch and the deal-closer.

6. No matter what

Have you ever said, "I'll do anything to close this sale"? If so, you've probably already been disqualified. If a prospective customer haggles over a price, requests a discount, or continues to wear you down after you've made three concessions too many, you have a metal hook in your mouth, not them, and it may not end well. Why?

If you're so willing to cut a deal that you cut prices, comp services, extend payment plans, waive fees, etc., you betray your own confidence that your product or service was worth the stated price. They wonder if anyone is paying those prices, if you've ever had a customer (who wasn't a blood relative), and if you're legitimate or worth your rates.

Once a prospect senses that you'll do whatever it takes to get them to buy, their suspicions rise and they wonder why.

• Why are you cutting pricing if something is wrong with you or your service?

• Why are you so desperate for their sale?

• Why aren't more customers waiting in line to pay your pricing, and if they aren't, what on earth are they doing there?

That's what a prospect thinks when you reveal your lack of conviction, desperation, and willingness to give up control. Some prospects will exploit it to drain you dry, while others will be too frightened to buy from you even if you paid them.

Walking down a two-way street. Be casual.

If we track each act of repulsion to an uneasiness, fear, misperception, or impulse, it's evident that these sales and marketing disasters were forced communications. Stiff, imbalanced, divisive, combative, bravado-filled, and desperate. They were unnatural and accepted a power struggle between two sparring, suspicious, unequal warriors, rather than a harmonious oneness of two natural, but opposite parties shaking hands.

Sales should be natural, harmonious. Sales should feel good for both parties, not like one party is having their arm twisted.

You may be doing sales wrong if it feels repulsive, icky, or degrading. If you're thinking cringe-worthy thoughts about yourself, your product, service, or sales pitch, imagine what you're projecting to prospects. Don't make it unpleasant, repulsive, or cringeworthy.