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.

Ethereum is the second-largest cryptocurrency. The Merge, a mid-September event that will convert Ethereum's consensus process from proof-of-work to proof-of-stake if all goes according to plan, will be a game changer.

Why is Ethereum ditching proof-of-work? Because it can. We're talking about a fully functioning, open-source ecosystem with a capacity for evolution that other cryptocurrencies lack, a change that would allow it to scale up its performance from 15 transactions per second to 100,000 as its blockchain is used for more and more things. It would reduce its energy consumption by 99.95%. Vitalik Buterin, the system's founder, would play a less active role due to decentralization, and miners, who validated transactions through proof of work, would be far less important.

Why has this conversion taken so long and been so cautious? Because it involves modifying a core process while it's running to boost its performance. It requires running the new mechanism in test chains on an ever-increasing scale, assessing participant reactions, and checking for issues or restrictions. The last big test was in early June and was successful. All that's left is to converge the mechanism with the Ethereum blockchain to conclude the switch.

What's stopping Bitcoin, the leader in market capitalization and the cryptocurrency that began blockchain's appeal, from doing the same? Satoshi Nakamoto, whoever he or she is, departed from public life long ago, therefore there's no community leadership. Changing it takes a level of consensus that is impossible to achieve without strong leadership, which is why Bitcoin's evolution has been sluggish and conservative, with few modifications.

Secondly, The Merge will balance the consensus mechanism (proof-of-work or proof-of-stake) and the system decentralization or centralization. Proof-of-work prevents double-spending, thus validators must buy hardware. The system works, but it requires a lot of electricity and, as it scales up, tends to re-centralize as validators acquire more hardware and the entire network activity gets focused in a few nodes. Larger operations save more money, which increases profitability and market share. This evolution runs opposed to the concept of decentralization, and some anticipate that any system that uses proof of work as a consensus mechanism will evolve towards centralization, with fewer large firms able to invest in efficient network nodes.

Yet radical bitcoin enthusiasts share an opposite argument. In proof-of-stake, transaction validators put their funds at stake to attest that transactions are valid. The algorithm chooses who validates each transaction, giving more possibilities to nodes that put more coins at stake, which could open the door to centralization and government control.

In both cases, we're talking about long-term changes, but Bitcoin's proof-of-work has been evolving longer and seems to confirm those fears, while proof-of-stake is only employed in coins with a minuscule volume compared to Ethereum and has no predictive value.

As of mid-September, we will have two significant cryptocurrencies, each with a different consensus mechanisms and equally different characteristics: one is intrinsically conservative and used only for economic transactions, while the other has been evolving in open source mode, and can be used for other types of assets, smart contracts, or decentralized finance systems. Some even see it as the foundation of Web3.

Many things could change before September 15, but The Merge is likely to be a turning point. We'll have to follow this closely.

They depend heavily on open source..

Discord users send billions of messages daily. Users wish to search these messages. How do we index these to search by message keywords?

Let’s find out.

1. Discord utilizes Elasticsearch. Elasticsearch is a free, open search engine for textual, numerical, geographical, structured, and unstructured data. Apache Lucene powers Elasticsearch.
   

2. How does elastic search store data? It stores it as numerous key-value pairs in JSON documents.
   

3. How does elastic search index? Elastic search's index is inverted. An inverted index lists every unique word in every page and where it appears.

4. Elasticsearch indexes documents and generates an inverted index to make data searchable in near real-time. The index API adds or updates JSON documents in a given index.

1. Let's examine how discord uses Elastic Search. Elasticsearch prefers bulk indexing. Discord couldn't index real-time messages. You can't search posted messages. You want outdated messages.

6. Let's check what bulk indexing requires.
1. A temporary queue for incoming communications.
2. Indexer workers that index messages into elastic search.

1. Discord's queue is Celery. The queue is open-source. Elastic search won't run on a single server. It's clustered. Where should a message go? Where?

8. A shard allocator decides where to put the message. Nevertheless. Shattered? A shard combines elastic search and index on. So, these two form a shard which is used as a unit by discord. The elastic search itself has some shards. But this is different, so don’t get confused.

1. Now, the final part is service discovery — to discover the elastic search clusters and the hosts within that cluster. This, they do with the help of etcd another open source tool.
   

A great thing to notice here is that discord relies heavily on open source systems and their base implementations which is very different from a lot of other products.

“I think if I had time to do something else, I would be so excited to go after this company right now.”

Sam Altman, CEO of Open AI, recently discussed AI's present and future.

Open AI is important. They're creating the cyberpunk and sci-fi worlds.

They use the most advanced algorithms and data sets.

GPT-3...sound familiar? Open AI built most copyrighting software. Peppertype, Jasper AI, Rytr. If you've used any, you'll be shocked by the quality.

Open AI isn't only GPT-3. They created DallE-2 and Whisper (a speech recognition software released last week).

What will they do next? What's the next great chance?

Sam Altman, CEO of Open AI, recently gave a lecture about the next trillion-dollar AI opportunity.

Who is the organization behind Open AI?

Open AI first. If you know, skip it.

Open AI is one of the earliest private AI startups. Elon Musk, Greg Brockman, and Rebekah Mercer established OpenAI in December 2015.

OpenAI has helped its citizens and AI since its birth.

They have scary-good algorithms.

Their GPT-3 natural language processing program is excellent.

The algorithm's exponential growth is astounding. GPT-2 came out in November 2019. May 2020 brought GPT-3.

Massive computation and datasets improved the technique in just a year. New York Times said GPT-3 could write like a human.

Same for Dall-E. Dall-E 2 was announced in April 2022. Dall-E 2 won a Colorado art contest.

Open AI's algorithms challenge jobs we thought required human innovation.

So what does Sam Altman think?

The Present Situation and AI's Limitations

During the interview, Sam states that we are still at the tip of the iceberg.

So I think so far, we’ve been in the realm where you can do an incredible copywriting business or you can do an education service or whatever. But I don’t think we’ve yet seen the people go after the trillion dollar take on Google.

He's right that AI can't generate net new human knowledge. It can train and synthesize vast amounts of knowledge, but it simply reproduces human work.

“It’s not going to cure cancer. It’s not going to add to the sum total of human scientific knowledge.”

But the key word is yet.

And that is what I think will turn out to be wrong that most surprises the current experts in the field.

Reinforcing his point that massive innovations are yet to come.

But where?

The Next $1 Trillion AI Company

Sam predicts a bio or genomic breakthrough.

There’s been some promising work in genomics, but stuff on a bench top hasn’t really impacted it. I think that’s going to change. And I think this is one of these areas where there will be these new $100 billion to $1 trillion companies started, and those areas are rare.

Avoid human trials since they take time. Bio-materials or simulators are suitable beginning points.

AI may have a breakthrough. DeepMind, an OpenAI competitor, has developed AlphaFold to predict protein 3D structures.

It could change how we see proteins and their function. AlphaFold could provide fresh understanding into how proteins work and diseases originate by revealing their structure. This could lead to Alzheimer's and cancer treatments. AlphaFold could speed up medication development by revealing how proteins interact with medicines.

Deep Mind offered 200 million protein structures for scientists to download (including sustainability, food insecurity, and neglected diseases).

Being in AI for 4+ years, I'm amazed at the progress. We're past the hype cycle, as evidenced by the collapse of AI startups like C3 AI, and have entered a productive phase.

We'll see innovative enterprises that could replace Google and other trillion-dollar companies.

What happens after AI adoption is scary and unpredictable. How will AGI (Artificial General Intelligence) affect us? Highly autonomous systems that exceed humans at valuable work (Open AI)

My guess is that the things that we’ll have to figure out are how we think about fairly distributing wealth, access to AGI systems, which will be the commodity of the realm, and governance, how we collectively decide what they can do, what they don’t do, things like that. And I think figuring out the answer to those questions is going to just be huge. — Sam Altman CEO

SaaS spending is 40/40/20. 40% of operating expenses should be R&D, 40% sales and marketing, and 20% G&A. We wanted to see the statistics behind the rules of thumb. Since October 2017, 73 SaaS startups have gone public. Perhaps the rule of thumb should be 30/50/20. The data is below.

30/50/20. R&D accounts for 26% of opex, sales and marketing 48%, and G&A 22%. We think R&D/S&M/G&A should be 30/50/20.

There are outliers. There are exceptions to rules of thumb. Dropbox spent 45% on R&D whereas Zoom spent 13%. Zoom spent 73% on S&M, Dropbox 37%, and Bill.com 28%. Snowflake spent 130% of revenue on S&M, while their EBITDA margin is -192%.

G&A shouldn't stand out. Minimize G&A spending. Priorities should be product development and sales. Cloudflare, Sendgrid, Snowflake, and Palantir spend 36%, 34%, 37%, and 43% on G&A.

Another myth is that COGS is 20% of revenue. Median and averages are 29%.

Where is the profitability? Data-driven operating income calculations were simplified (Revenue COGS R&D S&M G&A). 20 of 73 IPO businesses reported operational income. Median and average operating income margins are -21% and -27%.

As long as you're growing fast, have outstanding retention, and marquee clients, you can burn cash since recurring income that doesn't churn is a valuable annuity.

The data was compelling overall. 30/50/20 is the new 40/40/20 for more established SaaS enterprises, unprofitability is alright as long as your business is expanding, and COGS can be somewhat more than 20% of revenue.

What they'll do is scarier.

My acquaintance recently joined a VC-funded startup. Money, equity, and upside possibilities were nice, but he had a nagging dread.

They just secured a $40M round and are hiring like crazy to prepare for their IPO in two years. All signals pointed to this startup's (a B2B IT business in a stable industry) success, and its equity-holding workers wouldn't pass that up.

Five months after starting the work, my friend struggled with leaving. We might overlook the awful culture and long hours at the proper price. This price plus the company's fate and survival abilities sent my friend departing in an unpleasant unplanned resignation before jumping on yet another sinking ship.

This affects founders. This affects VC-backed companies (and all businesses). This affects anyone starting, buying, or running a business.

Here's the under-the-table approach that's draining VC capital, leaving staff terrified (or jobless), founders rattled, and investors upset. How to recognize, solve, and avoid it

The unsettling reality behind door #1

You can't raise money off just your looks, right? If "looks" means your founding team's expertise, then maybe. In my friend's case, the founding team's strong qualifications and track records won over investors before talking figures.

They're hardly the only startup to raise money without a profitable customer acquisition strategy. Another firm raised money for an expensive sleep product because it's eco-friendly. They were off to the races with a few keywords and key players.

Both companies, along with numerous others, elected to invest on product development first. Company A employed all the tech, then courted half their market (they’re a tech marketplace that connects two parties). Company B spent millions on R&D to create a palatable product, then flooded the world with marketing.

My friend is on Company B's financial team, and he's seen where they've gone wrong. It's terrible.

Company A (tech market): Growing? Not quite. To achieve the ambitious expansion they (and their investors) demand, they've poured much of their little capital into salespeople: Cold-calling commission and salary salesmen. Is it working? Considering attrition and companies' dwindling capital, I don't think so.

Company B (green sleep) has been hiring, digital marketing, and opening new stores like crazy. Growing expenses should result in growing revenues and a favorable return on investment; if you grow too rapidly, you may neglect to check that ROI.

Once Company A cut headcount and Company B declared “going concerned”, my friend realized both startups had the same ailment and didn't recognize it.

I shouldn't have to ask a friend to verify a company's cash reserves and profitability to spot a financial problem. It happened anyhow.

The frightening part isn't that investors were willing to invest millions without product-market fit, CAC, or LTV estimates. That's alarming, but not as scary as the fact that startups aren't understanding the problem until VC rounds have dried up.

When they question consultants if their company will be around in 6 months. It’s a red flag. How will they stretch $20M through a 2-year recession with a $3M/month burn rate and no profitability? Alarms go off.

Who's in danger?

In a word, everyone who raised money without a profitable client acquisition strategy or enough resources to ride out dry spells.

Money mismanagement and poor priorities affect every industry (like sinking all your capital into your product, team, or tech, at the expense of probing what customer acquisition really takes and looks like).

This isn't about tech, real estate, or recession-proof luxury products. Fast, cheap, easy money flows into flashy-looking teams with buzzwords, trending industries, and attractive credentials.

If these companies can't show progress or get a profitable CAC, they can't raise more money. They die if they can't raise more money (or slash headcount and find shoestring budget solutions until they solve the real problem).

The kiss of death (and how to avoid it)

If you're running a startup and think raising VC is the answer, pause and evaluate. Do you need the money now?

I'm not saying VC is terrible or has no role. Founders have used it as a Band-Aid for larger, pervasive problems. Venture cash isn't a crutch for recruiting consumers profitably; it's rocket fuel to get you what and who you need.

Pay-to-play isn't a way to throw money at the wall and hope for a return. Pay-to-play works until you run out of money, and if you haven't mastered client acquisition, your cash will diminish quickly.

How can you avoid this bottomless pit? Tips:

• Understand your burn rate

• Keep an eye on your growth or profitability.

• Analyze each and every marketing channel and initiative.

• Make lucrative customer acquisition strategies and satisfied customers your top two priorities. not brand-new products. not stellar hires. avoid the fundraising rollercoaster to save time. If you succeed in these two tasks, investors will approach you with their thirsty offers rather than the other way around, and your cash reserves won't diminish as a result.

Not as much as your grandfather

My family friend always justified expensive, impractical expenditures by saying it was only monopoly money. In business, startups, and especially with money from investors expecting a return, that's not true.

More founders could understand that there isn't always another round if they viewed VC money as their own limited pool. When the well runs dry, you must refill it or save the day.

Venture financing isn't your grandpa's money. A discerning investor has entrusted you with dry powder in the hope that you'll use it wisely, strategically, and thoughtfully. Use it well.