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.

Starting a passive income stream with data science and programming

My website is fresh. But how do I monetize it?

Creating a passive-income website is difficult. Advertise first. But what useful are ads without traffic?

Let’s Generate Traffic And Put Our Programming Skills To Use

SEO boosts traffic (Search Engine Optimisation). Traffic generation is complex. Keywords matter more than text, URL, photos, etc.

My Python skills helped here. I wanted to find relevant, Google-trending keywords (tags) for my topic.

First The Code

I wrote the script below here.

import re
from string import punctuation

import nltk
from nltk import TreebankWordTokenizer, sent_tokenize
from nltk.corpus import stopwords


class KeywordsGenerator:
    def __init__(self, pytrends):
        self._pytrends = pytrends

    def generate_tags(self, file_path, top_words=30):
        file_text = self._get_file_contents(file_path)
        clean_text = self._remove_noise(file_text)
        top_words = self._get_top_words(clean_text, top_words)
        suggestions = []
        for top_word in top_words:
            suggestions.extend(self.get_suggestions(top_word))
        suggestions.extend(top_words)
        tags = self._clean_tokens(suggestions)
        return ",".join(list(set(tags)))

    def _remove_noise(self, text):
        #1. Convert Text To Lowercase and remove numbers
        lower_case_text = str.lower(text)
        just_text = re.sub(r'\d+', '', lower_case_text)
        #2. Tokenise Paragraphs To words
        list = sent_tokenize(just_text)
        tokenizer = TreebankWordTokenizer()
        tokens = tokenizer.tokenize(just_text)
        #3. Clean text
        clean = self._clean_tokens(tokens)
        return clean

    def _clean_tokens(self, tokens):
        clean_words = [w for w in tokens if w not in punctuation]
        stopwords_to_remove = stopwords.words('english')
        clean = [w for w in clean_words if w not in stopwords_to_remove and not w.isnumeric()]
        return clean

    def get_suggestions(self, keyword):
        print(f'Searching pytrends for {keyword}')
        result = []
        self._pytrends.build_payload([keyword], cat=0, timeframe='today 12-m')
        data = self._pytrends.related_queries()[keyword]['top']
        if data is None or data.values is None:
            return result
        result.extend([x[0] for x in data.values.tolist()][:2])
        return result

    def _get_file_contents(self, file_path):
        return open(file_path, "r", encoding='utf-8',errors='ignore').read()

    def _get_top_words(self, words, top):
        counts = dict()

        for word in words:
            if word in counts:
                counts[word] += 1
            else:
                counts[word] = 1

        return list({k: v for k, v in sorted(counts.items(), key=lambda item: item[1])}.keys())[:top]


if __name__ == "1__main__":
    from pytrends.request import TrendReq

    nltk.download('punkt')
    nltk.download('stopwords')
    pytrends = TrendReq(hl='en-GB', tz=360)
    tags = KeywordsGenerator(pytrends)\
              .generate_tags('text_file.txt')
    print(tags)

Then The Dependencies

This script requires:

nltk==3.7
pytrends==4.8.0

Analysis of the Script

I copy and paste my article into text file.txt, and the code returns the keywords as a comma-separated string.

To achieve this:

1. A class I made is called KeywordsGenerator.

2. This class has a function: generate_tags

3. The function generate_tags performs the following tasks:

• retrieves text file contents

• uses NLP to clean the text by tokenizing sentences into words, removing punctuation, and other elements.

• identifies the most frequent words that are relevant.

• The pytrends API is then used to retrieve related phrases that are trending for each word from Google.

• finally adds a comma to the end of the word list.

4. I then use the keywords and paste them into the SEO area of my website.

These terms are trending on Google and relevant to my topic. My site's rankings and traffic have improved since I added new keywords. This little script puts our knowledge to work. I shared the script in case anyone faces similar issues.

I hope it helps readers sell their work.

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.

Let's see this once-dominant IT corporation crumble.

What's the capital of Kazakhstan? If you don't know the answer, you can probably find it by Googling. Google Search returned results for Nur-Sultan in 0.66 seconds.

Google is the best search engine I've ever used. Did you know another search engine ruled the Internet? I'm sure you guessed Yahoo!

Google's friendly UI and wide selection of services make it my top choice. Let's explore Yahoo's decline.

Yahoo!

YAHOO stands for Yet Another Hierarchically Organized Oracle. Jerry Yang and David Filo established Yahoo.

Yahoo is primarily a search engine and email provider. It offers News and an advertising platform. It was a popular website in 1995 that let people search the Internet directly. Yahoo began offering free email in 1997 by acquiring RocketMail.

According to a study, Yahoo used Google Search Engine technology until 2000 and then developed its own in 2004.

Yahoo! rejected buying Google for $1 billion

Larry Page and Sergey Brin, Google's founders, approached Yahoo in 1998 to sell Google for $1 billion so they could focus on their studies. Yahoo denied the offer, thinking it was overvalued at the time.

Yahoo realized its error and offered Google $3 billion in 2002, but Google demanded $5 billion since it was more valuable. Yahoo thought $5 billion was overpriced for the existing market.

In 2022, Google is worth $1.56 Trillion.

What happened to Yahoo!

Yahoo refused to buy Google, and Google's valuation rose, making a purchase unfeasible.

Yahoo started losing users when Google launched Gmail. Google's UI was far cleaner than Yahoo's.

Yahoo offered $1 billion to buy Facebook in July 2006, but Zuckerberg and the board sought $1.1 billion. Yahoo rejected, and Facebook's valuation rose, making it difficult to buy.

Yahoo was losing users daily while Google and Facebook gained many. Google and Facebook's popularity soared. Yahoo lost value daily.

Microsoft offered $45 billion to buy Yahoo in February 2008, but Yahoo declined. Microsoft increased its bid to $47 billion after Yahoo said it was too low, but Yahoo rejected it. Then Microsoft rejected Yahoo’s 10% bid increase in May 2008.

In 2015, Verizon bought Yahoo for $4.5 billion, and Apollo Global Management bought 90% of Yahoo's shares for $5 billion in May 2021. Verizon kept 10%.

Yahoo's opportunity to acquire Google and Facebook could have been a turning moment. It declined Microsoft's $45 billion deal in 2008 and was sold to Verizon for $4.5 billion in 2015. Poor decisions and lack of vision caused its downfall. Yahoo's aim wasn't obvious and it didn't stick to a single domain.

Hence, a corporation needs a clear vision and a leader who can see its future.

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The American who bought a meme cryptocurrency.

Cryptocurrency is the financial underground.

I love it. But there’s one thing I hate: scams. Over the last few years the Dogecoin cryptocurrency saw massive gains.

Glauber Contessoto overreacted. He shared his rags-to-riches cryptocurrency with the media.

He's only wealthy on paper. No longer Dogecoin millionaire.

Here's what he's doing now. It'll make you rethink cryptocurrency investing.

Strange beginnings

Glauber once had a $36,000-a-year job.

He grew up poor and wanted to make his mother proud. Tesla was his first investment. He bought GameStop stock after Reddit boosted it.

He bought whatever was hot.

He was a young investor. Memes, not research, influenced his decisions.

Elon Musk (aka Papa Elon) began tweeting about Dogecoin.

Doge is a 2013 cryptocurrency. One founder is Australian. He insists it's funny.

He was shocked anyone bought it LOL.

Doge is a Shiba Inu-themed meme. Now whenever I see a Shiba Inu, I think of Doge.

Elon helped drive up the price of Doge by talking about it in 2020 and 2021 (don't take investment advice from Elon; he's joking and gaslighting you).

Glauber caved. He invested everything in Doge. He borrowed from family and friends. He maxed out his credit card to buy more Doge. Yuck.

Internet dubbed him a genius. Slumdog millionaire and The Dogefather were nicknames. Elon pumped Doge on social media.

Good times.

From $180,000 to $1,000,000+

TikTok skyrocketed Doge's price.

Reddit fueled up. Influencers recommended buying Doge because of its popularity. Glauber's motto:

Scared money doesn't earn.

Glauber was no broke ass anymore.

His $180,000 Dogecoin investment became $1M. He championed investing. He quit his dumb job like a rebellious millennial.

A puppy dog meme captivated the internet.

Rise and fall

Whenever I invest in anything I ask myself “what utility does this have?”

Dogecoin is useless.

You buy it for the cute puppy face and hope others will too, driving up the price. All cryptocurrencies fell in 2021's second half.

Central banks raised interest rates, and inflation became a pain.

Dogecoin fell more than others. 90% decline.

Glauber’s Dogecoin is now worth $323K. Still no sales. His dog god is unshakeable. Confidence rocks. Dogecoin millionaire recently said...

“I should have sold some.”

Yes, sir.

He now avoids speculative cryptocurrencies like Dogecoin and focuses on Bitcoin and Ethereum.

I've long said this. Starbucks is building on Ethereum.

It's useful. Useful. Developers use Ethereum daily. Investing makes you wiser over time, like the Dogecoin millionaire.

When risk b*tch slaps you, humility follows, as it did for me when I lost money.

You have to lose money to make money. Few understand.

Dogecoin's omissions

You might be thinking Dogecoin is crap.

I'll take a contrarian stance. Dogecoin does nothing, but it has a strong community. Dogecoin dominates internet memes.

It's silly.

Not quite. The message of crypto that many people forget is that it’s a change in business model.

Businesses create products and services, then advertise to find customers. Crypto Web3 works backwards. A company builds a fanbase but sells them nothing.

Once the community reaches MVC (minimum viable community), a business can be formed.

Community members are relational versus transactional. They're invested in a cause and care about it (typically ownership in the business via crypto).

In this new world, Dogecoin has the most important feature.

Summary

While Dogecoin does have a community I still dislike it.

It's all shady. Anything Elon Musk recommends is a bad investment (except SpaceX & Tesla are great companies).

Dogecoin Millionaire has wised up and isn't YOLOing into more dog memes.

Don't follow the crowd or the hype. Investing is a long-term sport based on fundamentals and research.

Since Ethereum's inception, I've spent 10,000 hours researching.

Dogecoin will be the foundation of something new, like Pets.com at the start of the dot-com revolution. But I doubt Doge will boom.

Be safe!